0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.12/0.38 % Computer : n004.cluster.edu 0.12/0.38 % Model : x86_64 x86_64 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.38 % Memory : 8046.5625MB 0.12/0.38 % OS : Linux 6.8.0-71-generic 0.12/0.38 % CPULimit : 1440 0.12/0.38 % WCLimit : 180 0.12/0.38 % DateTime : Mon Jul 27 15:03:24 UTC 2026 0.12/0.38 % CPUTime : 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.12/0.41 Running higher-order theorem proving 0.12/0.46 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox/benchmark/theBenchmark.p 1.08/0.64 % (3200883)Detected a higher-order problem, will run a greedy HOL sequence. 1.08/0.64 % (3200895)lrs+10_16_si=on:nwc=1.5:random_seed=1639406884:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi) 1.08/0.64 % (3200895)Instruction limit reached! 1.08/0.64 % (3200895)------------------------------ 1.08/0.64 % (3200895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.08/0.64 % (3200895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.08/0.64 % (3200895)CaDiCaL version: 2.1.3 1.08/0.64 % (3200895)Termination reason: Instruction limit 1.08/0.64 % (3200895)Termination phase: shuffling 1.08/0.64 % (3200895)Time elapsed: 0.006 s 1.08/0.64 % (3200895)Peak memory usage: 10 MB 1.08/0.64 % (3200895)Instructions burned: 20 (million) 1.08/0.64 % (3200900)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 1.08/0.64 % (3200900)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 1.08/0.64 % (3200894)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2524098945:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi) 1.08/0.64 % (3200898)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=605241615:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi) 1.08/0.64 % (3200897)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1577664460:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1799 on theBenchmark for (1799ds/634Mi) 1.08/0.64 % (3200899)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=614732147:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi) 1.08/0.64 % (3200900)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1022931498:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi) 1.08/0.64 % (3200896)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3160729874:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi) 1.08/0.64 % (3200896)Instruction limit reached! 1.08/0.64 % (3200896)------------------------------ 1.08/0.64 % (3200896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.08/0.64 % (3200896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.08/0.64 % (3200896)CaDiCaL version: 2.1.3 1.08/0.64 % (3200896)Termination reason: Instruction limit 1.08/0.64 % (3200896)Termination phase: shuffling 1.08/0.64 % (3200896)Time elapsed: 0.002 s 1.08/0.64 % (3200896)Peak memory usage: 9 MB 1.08/0.64 % (3200896)Instructions burned: 3 (million) 1.08/0.64 % (3200905)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1429197094:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 1.08/0.64 % (3200905)Instruction limit reached! 1.08/0.64 % (3200905)------------------------------ 1.08/0.64 % (3200905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.08/0.64 % (3200905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.08/0.64 % (3200905)CaDiCaL version: 2.1.3 1.08/0.64 % (3200905)Termination reason: Instruction limit 1.08/0.64 % (3200905)Termination phase: shuffling 1.08/0.64 % (3200905)Time elapsed: 0.001 s 1.08/0.64 % (3200905)Peak memory usage: 10 MB 1.08/0.64 % (3200905)Instructions burned: 2 (million) 1.08/0.64 % (3200898)Instruction limit reached! 1.08/0.64 % (3200898)------------------------------ 1.08/0.64 % (3200898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.08/0.64 % (3200898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.08/0.64 % (3200898)CaDiCaL version: 2.1.3 1.08/0.64 % (3200898)Termination reason: Instruction limit 1.08/0.64 % (3200898)Termination phase: shuffling 1.08/0.64 % (3200898)Time elapsed: 0.015 s 1.08/0.64 % (3200898)Peak memory usage: 10 MB 1.08/0.64 % (3200898)Instructions burned: 24 (million) 1.08/0.64 % (3200916)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 1.08/0.69 % (3200916)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2992209908:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1799 on theBenchmark for (1799ds/7Mi) 1.08/0.69 % (3200916)Instruction limit reached! 1.08/0.69 % (3200916)------------------------------ 1.08/0.69 % (3200916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.08/0.69 % (3200916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.08/0.69 % (3200916)CaDiCaL version: 2.1.3 1.08/0.69 % (3200916)Termination reason: Instruction limit 1.08/0.69 % (3200916)Termination phase: shuffling 1.08/0.69 % (3200916)Time elapsed: 0.003 s 1.08/0.69 % (3200916)Peak memory usage: 10 MB 1.08/0.69 % (3200916)Instructions burned: 7 (million) 1.08/0.69 % (3200913)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1402549781:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1799 on theBenchmark for (1799ds/5Mi) 1.08/0.69 % (3200913)Instruction limit reached! 1.08/0.69 % (3200913)------------------------------ 1.08/0.69 % (3200913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.08/0.69 % (3200913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.08/0.69 % (3200913)CaDiCaL version: 2.1.3 1.08/0.69 % (3200913)Termination reason: Instruction limit 1.08/0.69 % (3200913)Termination phase: shuffling 1.08/0.69 % (3200913)Time elapsed: 0.005 s 1.08/0.69 % (3200913)Peak memory usage: 10 MB 1.08/0.69 % (3200913)Instructions burned: 6 (million) 1.08/0.69 % (3200917)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1376626443:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_1799 on theBenchmark for (1799ds/12Mi) 1.08/0.69 % (3200899)Instruction limit reached! 1.08/0.69 % (3200899)------------------------------ 1.08/0.69 % (3200899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.08/0.69 % (3200899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.08/0.69 % (3200899)CaDiCaL version: 2.1.3 1.08/0.69 % (3200899)Termination reason: Instruction limit 1.08/0.69 % (3200899)Termination phase: SInE selection 1.08/0.69 % (3200899)Time elapsed: 0.047 s 1.08/0.69 % (3200899)Peak memory usage: 10 MB 1.08/0.69 % (3200899)Instructions burned: 75 (million) 1.08/0.69 % (3200921)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 1.08/0.69 % (3200921)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 1.08/0.69 % (3200921)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=889763524:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1799 on theBenchmark for (1799ds/28Mi) 1.08/0.69 % (3200894)Instruction limit reached! 1.08/0.69 % (3200894)------------------------------ 1.08/0.69 % (3200894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.08/0.69 % (3200894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.08/0.69 % (3200894)CaDiCaL version: 2.1.3 1.08/0.69 % (3200894)Termination reason: Instruction limit 1.08/0.69 % (3200894)Termination phase: Property scanning 1.08/0.69 % (3200894)Time elapsed: 0.056 s 1.08/0.69 % (3200894)Peak memory usage: 10 MB 1.08/0.69 % (3200894)Instructions burned: 88 (million) 1.08/0.69 % (3200917)Instruction limit reached! 1.08/0.69 % (3200917)------------------------------ 1.08/0.69 % (3200917)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.08/0.69 % (3200917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.08/0.69 % (3200917)CaDiCaL version: 2.1.3 1.08/0.69 % (3200917)Termination reason: Instruction limit 1.08/0.69 % (3200917)Termination phase: shuffling 1.08/0.69 % (3200917)Time elapsed: 0.012 s 1.08/0.69 % (3200917)Peak memory usage: 10 MB 1.08/0.69 % (3200917)Instructions burned: 20 (million) 1.08/0.69 % (3200921)Instruction limit reached! 1.08/0.69 % (3200921)------------------------------ 1.08/0.69 % (3200921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.08/0.69 % (3200921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.08/0.69 % (3200921)CaDiCaL version: 2.1.3 1.08/0.69 % (3200921)Termination reason: Instruction limit 1.47/0.72 % (3200921)Termination phase: Property scanning 1.47/0.72 % (3200921)Time elapsed: 0.011 s 1.47/0.72 % (3200921)Peak memory usage: 10 MB 1.47/0.72 % (3200921)Instructions burned: 28 (million) 1.47/0.72 % (3200923)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3933096921:i=86:piset=equals:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/86Mi) 1.47/0.72 % (3200927)lrs+10_1_si=on:cs=on:random_seed=1735792520:i=8:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/8Mi) 1.47/0.72 % (3200927)Instruction limit reached! 1.47/0.72 % (3200927)------------------------------ 1.47/0.72 % (3200927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.72 % (3200927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.72 % (3200927)CaDiCaL version: 2.1.3 1.47/0.72 % (3200927)Termination reason: Instruction limit 1.47/0.72 % (3200927)Termination phase: shuffling 1.47/0.72 % (3200927)Time elapsed: 0.003 s 1.47/0.72 % (3200927)Peak memory usage: 9 MB 1.47/0.72 % (3200927)Instructions burned: 9 (million) 1.47/0.72 % (3200930)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on 1.47/0.72 % (3200932)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1093896186:st=2:i=249:sd=1:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/249Mi) 1.47/0.72 % (3200930)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=801207901:i=2:add=on:rtra=on_1798 on theBenchmark for (1798ds/2Mi) 1.47/0.72 % (3200930)Instruction limit reached! 1.47/0.72 % (3200930)------------------------------ 1.47/0.72 % (3200930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.72 % (3200930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.72 % (3200930)CaDiCaL version: 2.1.3 1.47/0.72 % (3200930)Termination reason: Instruction limit 1.47/0.72 % (3200930)Termination phase: shuffling 1.47/0.72 % (3200930)Time elapsed: 0.002 s 1.47/0.72 % (3200930)Peak memory usage: 10 MB 1.47/0.72 % (3200930)Instructions burned: 3 (million) 1.47/0.72 % (3200931)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3459538027:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_1798 on theBenchmark for (1798ds/38Mi) 1.47/0.72 % (3200935)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=716830172:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1798 on theBenchmark for (1798ds/25Mi) 1.47/0.72 % (3200935)Instruction limit reached! 1.47/0.72 % (3200935)------------------------------ 1.47/0.72 % (3200935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.72 % (3200935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.72 % (3200935)CaDiCaL version: 2.1.3 1.47/0.72 % (3200935)Termination reason: Instruction limit 1.47/0.72 % (3200935)Termination phase: shuffling 1.47/0.72 % (3200935)Time elapsed: 0.008 s 1.47/0.72 % (3200935)Peak memory usage: 10 MB 1.47/0.72 % (3200935)Instructions burned: 25 (million) 1.47/0.72 % (3200900)Instruction limit reached! 1.47/0.72 % (3200900)------------------------------ 1.47/0.72 % (3200900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.72 % (3200900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.72 % (3200900)CaDiCaL version: 2.1.3 1.47/0.72 % (3200900)Termination reason: Instruction limit 1.47/0.72 % (3200900)Termination phase: Saturation 1.47/0.72 % (3200900)Time elapsed: 0.109 s 1.47/0.72 % (3200900)Peak memory usage: 12 MB 1.47/0.72 % (3200900)Instructions burned: 158 (million) 1.47/0.72 % (3200931)Instruction limit reached! 1.47/0.72 % (3200931)------------------------------ 1.47/0.72 % (3200931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.72 % (3200931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.72 % (3200931)CaDiCaL version: 2.1.3 1.47/0.72 % (3200931)Termination reason: Instruction limit 1.47/0.72 % (3200931)Termination phase: shuffling 1.47/0.72 % (3200931)Time elapsed: 0.022 s 1.47/0.72 % (3200931)Peak memory usage: 9 MB 1.47/0.72 % (3200931)Instructions burned: 38 (million) 1.47/0.72 % (3200943)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=276783717:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/327Mi) 1.47/0.77 % (3200939)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2983320693:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_1798 on theBenchmark for (1798ds/14Mi) 1.47/0.77 % (3200939)Instruction limit reached! 1.47/0.77 % (3200939)------------------------------ 1.47/0.77 % (3200939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.77 % (3200939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.77 % (3200939)CaDiCaL version: 2.1.3 1.47/0.77 % (3200939)Termination reason: Instruction limit 1.47/0.77 % (3200939)Termination phase: shuffling 1.47/0.77 % (3200939)Time elapsed: 0.009 s 1.47/0.77 % (3200939)Peak memory usage: 10 MB 1.47/0.77 % (3200939)Instructions burned: 14 (million) 1.47/0.77 % (3200923)Instruction limit reached! 1.47/0.77 % (3200923)------------------------------ 1.47/0.77 % (3200923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.77 % (3200923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.77 % (3200923)CaDiCaL version: 2.1.3 1.47/0.77 % (3200923)Termination reason: Instruction limit 1.47/0.77 % (3200923)Termination phase: Property scanning 1.47/0.77 % (3200923)Time elapsed: 0.064 s 1.47/0.77 % (3200923)Peak memory usage: 10 MB 1.47/0.77 % (3200923)Instructions burned: 87 (million) 1.47/0.77 % (3200932)Refutation not found, incomplete strategy 1.47/0.77 % (3200932)------------------------------ 1.47/0.77 % (3200932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.77 % (3200932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.77 % (3200932)CaDiCaL version: 2.1.3 1.47/0.77 % (3200932)Termination reason: Refutation not found, incomplete strategy 1.47/0.77 % (3200932)Time elapsed: 0.053 s 1.47/0.77 % (3200932)Peak memory usage: 15 MB 1.47/0.77 % (3200932)Instructions burned: 145 (million) 1.47/0.77 % (3200932)------------------------------ 1.47/0.77 % (3200932)------------------------------ 1.47/0.77 % (3200944)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1006945371:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_1798 on theBenchmark for (1798ds/14Mi) 1.47/0.77 % (3200946)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1464563526:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_1798 on theBenchmark for (1798ds/2Mi) 1.47/0.77 % (3200946)Instruction limit reached! 1.47/0.77 % (3200946)------------------------------ 1.47/0.77 % (3200946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.77 % (3200946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.77 % (3200946)CaDiCaL version: 2.1.3 1.47/0.77 % (3200946)Termination reason: Instruction limit 1.47/0.77 % (3200946)Termination phase: shuffling 1.47/0.77 % (3200946)Time elapsed: 0.002 s 1.47/0.77 % (3200946)Peak memory usage: 10 MB 1.47/0.77 % (3200946)Instructions burned: 3 (million) 1.47/0.77 % (3200944)Instruction limit reached! 1.47/0.77 % (3200944)------------------------------ 1.47/0.77 % (3200944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.77 % (3200944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.77 % (3200944)CaDiCaL version: 2.1.3 1.47/0.77 % (3200944)Termination reason: Instruction limit 1.47/0.77 % (3200944)Termination phase: shuffling 1.47/0.77 % (3200944)Time elapsed: 0.009 s 1.47/0.77 % (3200944)Peak memory usage: 10 MB 1.47/0.77 % (3200944)Instructions burned: 15 (million) 1.47/0.77 % (3200952)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=4195673903:cond=on:i=60:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/60Mi) 1.47/0.77 % (3200950)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=423558077:i=26:ep=R:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/26Mi) 1.47/0.77 % (3200951)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1309576120:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_1798 on theBenchmark for (1798ds/23Mi) 1.47/0.77 % (3200952)Instruction limit reached! 1.47/0.77 % (3200952)------------------------------ 1.47/0.77 % (3200952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.77 % (3200952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.15/0.86 % (3200952)CaDiCaL version: 2.1.3 2.15/0.86 % (3200952)Termination reason: Instruction limit 2.15/0.86 % (3200952)Termination phase: Property scanning 2.15/0.86 % (3200952)Time elapsed: 0.019 s 2.15/0.86 % (3200952)Peak memory usage: 10 MB 2.15/0.86 % (3200952)Instructions burned: 62 (million) 2.15/0.86 % (3200955)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 2.15/0.86 % (3200955)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs 2.15/0.86 % (3200956)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off 2.15/0.86 % (3200951)Instruction limit reached! 2.15/0.86 % (3200951)------------------------------ 2.15/0.86 % (3200951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.15/0.86 % (3200951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.15/0.86 % (3200951)CaDiCaL version: 2.1.3 2.15/0.86 % (3200951)Termination reason: Instruction limit 2.15/0.86 % (3200951)Termination phase: shuffling 2.15/0.86 % (3200951)Time elapsed: 0.014 s 2.15/0.86 % (3200951)Peak memory usage: 10 MB 2.15/0.86 % (3200951)Instructions burned: 24 (million) 2.15/0.86 % (3200955)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=1643452907:i=14:add=off:nm=40:rtra=on:rawr=on_1797 on theBenchmark for (1797ds/14Mi) 2.15/0.86 % (3200956)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=1378685416:i=8:nm=2:rtra=on:fe=abstraction:inj=on_1797 on theBenchmark for (1797ds/8Mi) 2.15/0.86 % (3200950)Instruction limit reached! 2.15/0.86 % (3200950)------------------------------ 2.15/0.86 % (3200950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.15/0.86 % (3200950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.15/0.86 % (3200950)CaDiCaL version: 2.1.3 2.15/0.86 % (3200950)Termination reason: Instruction limit 2.15/0.86 % (3200950)Termination phase: Property scanning 2.15/0.86 % (3200950)Time elapsed: 0.021 s 2.15/0.86 % (3200950)Peak memory usage: 10 MB 2.15/0.86 % (3200950)Instructions burned: 28 (million) 2.15/0.86 % (3200956)Instruction limit reached! 2.15/0.86 % (3200956)------------------------------ 2.15/0.86 % (3200956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.15/0.86 % (3200956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.15/0.86 % (3200956)CaDiCaL version: 2.1.3 2.15/0.86 % (3200956)Termination reason: Instruction limit 2.15/0.86 % (3200956)Termination phase: shuffling 2.15/0.86 % (3200956)Time elapsed: 0.005 s 2.15/0.86 % (3200956)Peak memory usage: 10 MB 2.15/0.86 % (3200956)Instructions burned: 9 (million) 2.15/0.86 % (3200955)Instruction limit reached! 2.15/0.86 % (3200955)------------------------------ 2.15/0.86 % (3200955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.15/0.86 % (3200955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.15/0.86 % (3200955)CaDiCaL version: 2.1.3 2.15/0.86 % (3200955)Termination reason: Instruction limit 2.15/0.86 % (3200955)Termination phase: Property scanning 2.15/0.86 % (3200955)Time elapsed: 0.011 s 2.15/0.86 % (3200955)Peak memory usage: 10 MB 2.15/0.86 % (3200955)Instructions burned: 15 (million) 2.15/0.86 % (3200943)Refutation not found, incomplete strategy 2.15/0.86 % (3200943)------------------------------ 2.15/0.86 % (3200943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.15/0.86 % (3200943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.15/0.86 % (3200943)CaDiCaL version: 2.1.3 2.15/0.86 % (3200943)Termination reason: Refutation not found, incomplete strategy 2.15/0.86 % (3200943)Time elapsed: 0.074 s 2.15/0.86 % (3200943)Peak memory usage: 14 MB 2.15/0.86 % (3200943)Instructions burned: 181 (million) 2.15/0.86 % (3200961)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=2255763039:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_1797 on theBenchmark for (1797ds/31Mi) 2.15/0.86 % (3200943)------------------------------ 2.46/0.98 % (3200943)------------------------------ 2.46/0.98 % (3200965)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3947998055:i=23:rtra=on:ntd=on_1797 on theBenchmark for (1797ds/23Mi) 2.46/0.98 % (3200963)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1827902290:i=7:hud=5:bd=preordered:rtra=on:bet=on_1797 on theBenchmark for (1797ds/7Mi) 2.46/0.98 % (3200965)Instruction limit reached! 2.46/0.98 % (3200965)------------------------------ 2.46/0.98 % (3200965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.46/0.98 % (3200965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.46/0.98 % (3200965)CaDiCaL version: 2.1.3 2.46/0.98 % (3200965)Termination reason: Instruction limit 2.46/0.98 % (3200965)Termination phase: Property scanning 2.46/0.98 % (3200965)Time elapsed: 0.009 s 2.46/0.98 % (3200965)Peak memory usage: 10 MB 2.46/0.98 % (3200965)Instructions burned: 24 (million) 2.46/0.98 % (3200969)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3013590746:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_1797 on theBenchmark for (1797ds/143Mi) 2.46/0.98 % (3200961)Instruction limit reached! 2.46/0.98 % (3200961)------------------------------ 2.46/0.98 % (3200961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.46/0.98 % (3200961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.46/0.98 % (3200961)CaDiCaL version: 2.1.3 2.46/0.98 % (3200961)Termination reason: Instruction limit 2.46/0.98 % (3200961)Termination phase: Property scanning 2.46/0.98 % (3200961)Time elapsed: 0.024 s 2.46/0.98 % (3200961)Peak memory usage: 10 MB 2.46/0.98 % (3200961)Instructions burned: 31 (million) 2.46/0.98 % (3200963)Instruction limit reached! 2.46/0.98 % (3200963)------------------------------ 2.46/0.98 % (3200963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.46/0.98 % (3200963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.46/0.98 % (3200963)CaDiCaL version: 2.1.3 2.46/0.98 % (3200963)Termination reason: Instruction limit 2.46/0.98 % (3200963)Termination phase: shuffling 2.46/0.98 % (3200963)Time elapsed: 0.005 s 2.46/0.98 % (3200963)Peak memory usage: 10 MB 2.46/0.98 % (3200963)Instructions burned: 7 (million) 2.46/0.98 % (3200966)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=133245515:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_1797 on theBenchmark for (1797ds/20Mi) 2.46/0.98 % (3200968)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=16921955:i=1240:rtra=on:ixr=off_1797 on theBenchmark for (1797ds/1240Mi) 2.46/0.98 % (3200966)Instruction limit reached! 2.46/0.98 % (3200966)------------------------------ 2.46/0.98 % (3200966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.46/0.98 % (3200966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.46/0.98 % (3200966)CaDiCaL version: 2.1.3 2.46/0.98 % (3200966)Termination reason: Instruction limit 2.46/0.98 % (3200966)Termination phase: shuffling 2.46/0.98 % (3200966)Time elapsed: 0.012 s 2.46/0.98 % (3200966)Peak memory usage: 10 MB 2.46/0.98 % (3200966)Instructions burned: 20 (million) 2.46/0.98 % (3200974)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4143779474:i=42:hud=10:rtra=on_1797 on theBenchmark for (1797ds/42Mi) 2.46/0.98 % (3200976)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 2.46/0.98 % (3200973)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3092232773:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_1797 on theBenchmark for (1797ds/193Mi) 2.46/0.98 % (3200976)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3770674181:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1797 on theBenchmark for (1797ds/7Mi) 2.46/0.98 % (3200974)Instruction limit reached! 2.46/0.98 % (3200974)------------------------------ 2.46/0.98 % (3200974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.46/0.98 % (3200974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.46/0.98 % (3200974)CaDiCaL version: 2.1.3 2.46/0.98 % (3200974)Termination reason: Instruction limit 2.46/0.98 % (3200974)Termination phase: shuffling 2.46/0.98 % (3200974)Time elapsed: 0.014 s 3.90/1.08 % (3200974)Peak memory usage: 10 MB 3.90/1.08 % (3200974)Instructions burned: 42 (million) 3.90/1.08 % (3200976)Instruction limit reached! 3.90/1.08 % (3200976)------------------------------ 3.90/1.08 % (3200976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.90/1.08 % (3200976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.90/1.08 % (3200976)CaDiCaL version: 2.1.3 3.90/1.08 % (3200976)Termination reason: Instruction limit 3.90/1.08 % (3200976)Termination phase: shuffling 3.90/1.08 % (3200976)Time elapsed: 0.006 s 3.90/1.08 % (3200976)Peak memory usage: 10 MB 3.90/1.08 % (3200976)Instructions burned: 8 (million) 3.90/1.08 % (3200978)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2430670002:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_1797 on theBenchmark for (1797ds/181Mi) 3.90/1.08 % (3200969)Instruction limit reached! 3.90/1.08 % (3200969)------------------------------ 3.90/1.08 % (3200969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.90/1.08 % (3200969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.90/1.08 % (3200969)CaDiCaL version: 2.1.3 3.90/1.08 % (3200969)Termination reason: Instruction limit 3.90/1.08 % (3200969)Termination phase: Saturation 3.90/1.08 % (3200969)Time elapsed: 0.051 s 3.90/1.08 % (3200969)Peak memory usage: 11 MB 3.90/1.08 % (3200969)Instructions burned: 144 (million) 3.90/1.08 % (3200983)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=1446650739:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1796 on theBenchmark for (1796ds/169Mi) 3.90/1.08 % (3200984)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on 3.90/1.08 % (3200984)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3143250573:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_1796 on theBenchmark for (1796ds/6Mi) 3.90/1.08 % (3200984)Instruction limit reached! 3.90/1.08 % (3200984)------------------------------ 3.90/1.08 % (3200984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.90/1.08 % (3200984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.90/1.08 % (3200984)CaDiCaL version: 2.1.3 3.90/1.08 % (3200984)Termination reason: Instruction limit 3.90/1.08 % (3200984)Termination phase: shuffling 3.90/1.08 % (3200984)Time elapsed: 0.005 s 3.90/1.08 % (3200984)Peak memory usage: 10 MB 3.90/1.08 % (3200984)Instructions burned: 7 (million) 3.90/1.08 % (3200988)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=432617938:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1796 on theBenchmark for (1796ds/22Mi) 3.90/1.08 % (3200993)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2463355954:i=19:add=on:rtra=on_1796 on theBenchmark for (1796ds/19Mi) 3.90/1.08 % (3200988)Instruction limit reached! 3.90/1.08 % (3200988)------------------------------ 3.90/1.08 % (3200988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.90/1.08 % (3200988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.90/1.08 % (3200988)CaDiCaL version: 2.1.3 3.90/1.08 % (3200988)Termination reason: Instruction limit 3.90/1.08 % (3200988)Termination phase: shuffling 3.90/1.08 % (3200988)Time elapsed: 0.015 s 3.90/1.08 % (3200988)Peak memory usage: 10 MB 3.90/1.08 % (3200988)Instructions burned: 23 (million) 3.90/1.08 % (3200993)Instruction limit reached! 3.90/1.08 % (3200993)------------------------------ 3.90/1.08 % (3200993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.90/1.08 % (3200993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.90/1.08 % (3200993)CaDiCaL version: 2.1.3 3.90/1.08 % (3200993)Termination reason: Instruction limit 3.90/1.08 % (3200993)Termination phase: Property scanning 3.90/1.08 % (3200993)Time elapsed: 0.014 s 3.90/1.08 % (3200993)Peak memory usage: 10 MB 3.90/1.08 % (3200993)Instructions burned: 19 (million) 3.90/1.08 % (3200978)Instruction limit reached! 3.90/1.08 % (3200978)------------------------------ 3.90/1.08 % (3200978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.90/1.08 % (3200978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.90/1.15 % (3200978)CaDiCaL version: 2.1.3 3.90/1.15 % (3200978)Termination reason: Instruction limit 3.90/1.15 % (3200978)Termination phase: Saturation 3.90/1.15 % (3200978)Time elapsed: 0.071 s 3.90/1.15 % (3200978)Peak memory usage: 15 MB 3.90/1.15 % (3200978)Instructions burned: 182 (million) 3.90/1.15 % (3200997)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1859571980:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_1796 on theBenchmark for (1796ds/316Mi) 3.90/1.15 % (3200998)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=423046228:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_1796 on theBenchmark for (1796ds/853Mi) 3.90/1.15 % (3200999)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=1420701647:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_1796 on theBenchmark for (1796ds/45Mi) 3.90/1.15 % (3200973)Instruction limit reached! 3.90/1.15 % (3200973)------------------------------ 3.90/1.15 % (3200973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.90/1.15 % (3200973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.90/1.15 % (3200973)CaDiCaL version: 2.1.3 3.90/1.15 % (3200973)Termination reason: Instruction limit 3.90/1.15 % (3200973)Termination phase: Saturation 3.90/1.15 % (3200973)Time elapsed: 0.139 s 3.90/1.15 % (3200973)Peak memory usage: 15 MB 3.90/1.15 % (3200973)Instructions burned: 193 (million) 3.90/1.15 % (3200999)Instruction limit reached! 3.90/1.15 % (3200999)------------------------------ 3.90/1.15 % (3200999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.90/1.15 % (3200999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.90/1.15 % (3200999)CaDiCaL version: 2.1.3 3.90/1.15 % (3200999)Termination reason: Instruction limit 3.90/1.15 % (3200999)Termination phase: shuffling 3.90/1.15 % (3200999)Time elapsed: 0.030 s 3.90/1.15 % (3200999)Peak memory usage: 10 MB 3.90/1.15 % (3200999)Instructions burned: 45 (million) 3.90/1.15 % (3200983)Instruction limit reached! 3.90/1.15 % (3200983)------------------------------ 3.90/1.15 % (3200983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.90/1.15 % (3200983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.90/1.15 % (3200983)CaDiCaL version: 2.1.3 3.90/1.15 % (3200983)Termination reason: Instruction limit 3.90/1.15 % (3200983)Termination phase: Saturation 3.90/1.15 % (3200983)Time elapsed: 0.120 s 3.90/1.15 % (3200983)Peak memory usage: 16 MB 3.90/1.15 % (3200983)Instructions burned: 169 (million) 3.90/1.15 % (3201008)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=4091062090:i=480:rtra=on_1795 on theBenchmark for (1795ds/480Mi) 3.90/1.15 % (3201009)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3882587660:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_1795 on theBenchmark for (1795ds/21Mi) 3.90/1.15 % (3201010)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on 3.90/1.15 % (3201009)Instruction limit reached! 3.90/1.15 % (3201009)------------------------------ 3.90/1.15 % (3201009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.90/1.15 % (3201009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.90/1.15 % (3201009)CaDiCaL version: 2.1.3 3.90/1.15 % (3201009)Termination reason: Instruction limit 3.90/1.15 % (3201009)Termination phase: shuffling 3.90/1.15 % (3201009)Time elapsed: 0.008 s 3.90/1.15 % (3201009)Peak memory usage: 9 MB 3.90/1.15 % (3201009)Instructions burned: 25 (million) 3.90/1.15 % (3201010)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=370212471:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_1795 on theBenchmark for (1795ds/200Mi) 3.90/1.15 % (3201014)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1895488561:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_1795 on theBenchmark for (1795ds/13Mi) 3.90/1.15 % (3201014)Instruction limit reached! 3.90/1.15 % (3201014)------------------------------ 5.66/1.31 % (3201014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.66/1.31 % (3201014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.66/1.31 % (3201014)CaDiCaL version: 2.1.3 5.66/1.31 % (3201014)Termination reason: Instruction limit 5.66/1.31 % (3201014)Termination phase: shuffling 5.66/1.31 % (3201014)Time elapsed: 0.006 s 5.66/1.31 % (3201014)Peak memory usage: 10 MB 5.66/1.31 % (3201014)Instructions burned: 16 (million) 5.66/1.31 % (3201008)Refutation not found, incomplete strategy 5.66/1.31 % (3201008)------------------------------ 5.66/1.31 % (3201008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.66/1.31 % (3201008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.66/1.31 % (3201008)CaDiCaL version: 2.1.3 5.66/1.31 % (3201008)Termination reason: Refutation not found, incomplete strategy 5.66/1.31 % (3201008)Time elapsed: 0.060 s 5.66/1.31 % (3201008)Peak memory usage: 15 MB 5.66/1.31 % (3201008)Instructions burned: 162 (million) 5.66/1.31 % (3201008)------------------------------ 5.66/1.31 % (3201008)------------------------------ 5.66/1.31 % (3201019)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3348935760:i=66:s2at=3:nm=2:rtra=on:rawr=on_1794 on theBenchmark for (1794ds/66Mi) 5.66/1.31 % (3200897)Instruction limit reached! 5.66/1.31 % (3200897)------------------------------ 5.66/1.31 % (3200897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.66/1.31 % (3200897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.66/1.31 % (3200897)CaDiCaL version: 2.1.3 5.66/1.31 % (3200897)Termination reason: Instruction limit 5.66/1.31 % (3200897)Termination phase: Saturation 5.66/1.31 % (3200897)Time elapsed: 0.502 s 5.66/1.31 % (3200897)Peak memory usage: 18 MB 5.66/1.31 % (3200897)Instructions burned: 634 (million) 5.66/1.31 % (3201020)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=4282226175:i=51:fsr=off:rtra=on_1794 on theBenchmark for (1794ds/51Mi) 5.66/1.31 % (3201019)Instruction limit reached! 5.66/1.31 % (3201019)------------------------------ 5.66/1.31 % (3201019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.66/1.31 % (3201019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.66/1.31 % (3201019)CaDiCaL version: 2.1.3 5.66/1.31 % (3201019)Termination reason: Instruction limit 5.66/1.31 % (3201019)Termination phase: Property scanning 5.66/1.31 % (3201019)Time elapsed: 0.039 s 5.66/1.31 % (3201019)Peak memory usage: 11 MB 5.66/1.31 % (3201019)Instructions burned: 66 (million) 5.66/1.31 % (3201026)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=1063528194:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_1794 on theBenchmark for (1794ds/137Mi) 5.66/1.31 % (3201020)Instruction limit reached! 5.66/1.31 % (3201020)------------------------------ 5.66/1.31 % (3201020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.66/1.31 % (3201020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.66/1.31 % (3201020)CaDiCaL version: 2.1.3 5.66/1.31 % (3201020)Termination reason: Instruction limit 5.66/1.31 % (3201020)Termination phase: shuffling 5.66/1.31 % (3201020)Time elapsed: 0.032 s 5.66/1.31 % (3201020)Peak memory usage: 10 MB 5.66/1.31 % (3201020)Instructions burned: 51 (million) 5.66/1.31 % (3201024)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3385507109:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_1794 on theBenchmark for (1794ds/31Mi) 5.66/1.31 % (3200997)Instruction limit reached! 5.66/1.31 % (3200997)------------------------------ 5.66/1.31 % (3200997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.66/1.31 % (3200997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.66/1.31 % (3200997)CaDiCaL version: 2.1.3 5.66/1.31 % (3200997)Termination reason: Instruction limit 5.66/1.31 % (3200997)Termination phase: Saturation 5.66/1.31 % (3200997)Time elapsed: 0.200 s 5.66/1.31 % (3200997)Peak memory usage: 15 MB 5.66/1.31 % (3200997)Instructions burned: 316 (million) 5.66/1.31 % (3201024)Instruction limit reached! 5.66/1.31 % (3201024)------------------------------ 5.66/1.31 % (3201024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.66/1.31 % (3201024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.21/1.41 % (3201024)CaDiCaL version: 2.1.3 6.21/1.41 % (3201024)Termination reason: Instruction limit 6.21/1.41 % (3201024)Termination phase: Property scanning 6.21/1.41 % (3201024)Time elapsed: 0.024 s 6.21/1.41 % (3201024)Peak memory usage: 10 MB 6.21/1.41 % (3201024)Instructions burned: 31 (million) 6.21/1.41 % (3201030)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=788774519:cond=on:i=34:hud=10:nm=10:rtra=on_1794 on theBenchmark for (1794ds/34Mi) 6.21/1.41 % (3201010)Instruction limit reached! 6.21/1.41 % (3201010)------------------------------ 6.21/1.41 % (3201010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.21/1.41 % (3201010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.21/1.41 % (3201010)CaDiCaL version: 2.1.3 6.21/1.41 % (3201010)Termination reason: Instruction limit 6.21/1.41 % (3201010)Termination phase: Saturation 6.21/1.41 % (3201010)Time elapsed: 0.136 s 6.21/1.41 % (3201010)Peak memory usage: 12 MB 6.21/1.41 % (3201010)Instructions burned: 201 (million) 6.21/1.41 % (3201031)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=319148149:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_1794 on theBenchmark for (1794ds/67Mi) 6.21/1.41 % (3201026)Instruction limit reached! 6.21/1.41 % (3201026)------------------------------ 6.21/1.41 % (3201026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.21/1.41 % (3201026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.21/1.41 % (3201026)CaDiCaL version: 2.1.3 6.21/1.41 % (3201026)Termination reason: Instruction limit 6.21/1.41 % (3201026)Termination phase: Saturation 6.21/1.41 % (3201026)Time elapsed: 0.043 s 6.21/1.41 % (3201026)Peak memory usage: 12 MB 6.21/1.41 % (3201026)Instructions burned: 140 (million) 6.21/1.41 % (3201038)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=1200715708:cond=on:i=96:bd=all:rtra=on_1793 on theBenchmark for (1793ds/96Mi) 6.21/1.41 % (3201034)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off 6.21/1.41 % (3201034)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=1583737416:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_1793 on theBenchmark for (1793ds/180Mi) 6.21/1.41 % (3201030)Instruction limit reached! 6.21/1.41 % (3201030)------------------------------ 6.21/1.41 % (3201030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.21/1.41 % (3201030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.21/1.41 % (3201030)CaDiCaL version: 2.1.3 6.21/1.41 % (3201030)Termination reason: Instruction limit 6.21/1.41 % (3201030)Termination phase: Property scanning 6.21/1.41 % (3201030)Time elapsed: 0.026 s 6.21/1.41 % (3201030)Peak memory usage: 10 MB 6.21/1.41 % (3201030)Instructions burned: 34 (million) 6.21/1.41 % (3201036)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=4058028567:st=2:i=246:sd=3:rtra=on:ss=axioms_1793 on theBenchmark for (1793ds/246Mi) 6.21/1.41 % (3201038)Instruction limit reached! 6.21/1.41 % (3201038)------------------------------ 6.21/1.41 % (3201038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.21/1.41 % (3201038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.21/1.41 % (3201038)CaDiCaL version: 2.1.3 6.21/1.41 % (3201038)Termination reason: Instruction limit 6.21/1.41 % (3201038)Termination phase: Property scanning 6.21/1.41 % (3201038)Time elapsed: 0.018 s 6.21/1.41 % (3201038)Peak memory usage: 11 MB 6.21/1.41 % (3201038)Instructions burned: 101 (million) 6.21/1.41 % (3201031)Instruction limit reached! 6.21/1.41 % (3201031)------------------------------ 6.21/1.41 % (3201031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.21/1.41 % (3201031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.21/1.41 % (3201031)CaDiCaL version: 2.1.3 6.21/1.41 % (3201031)Termination reason: Instruction limit 6.21/1.41 % (3201031)Termination phase: Property scanning 6.21/1.41 % (3201031)Time elapsed: 0.042 s 6.21/1.41 % (3201031)Peak memory usage: 10 MB 6.21/1.41 % (3201031)Instructions burned: 68 (million) 6.21/1.41 % (3201045)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=2640202726:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_1793 on theBenchmark for (1793ds/515Mi) 6.62/1.58 % (3201042)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=3149058912:i=427:sd=1:rtra=on:ss=axioms_1793 on theBenchmark for (1793ds/427Mi) 6.62/1.58 % (3201044)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3961540536:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_1793 on theBenchmark for (1793ds/874Mi) 6.62/1.58 % (3201042)Refutation not found, incomplete strategy 6.62/1.58 % (3201042)------------------------------ 6.62/1.58 % (3201042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.62/1.58 % (3201042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.62/1.58 % (3201042)CaDiCaL version: 2.1.3 6.62/1.58 % (3201042)Termination reason: Refutation not found, incomplete strategy 6.62/1.58 % (3201042)Time elapsed: 0.092 s 6.62/1.58 % (3201042)Peak memory usage: 14 MB 6.62/1.58 % (3201042)Instructions burned: 132 (million) 6.62/1.58 % (3201042)------------------------------ 6.62/1.58 % (3201042)------------------------------ 6.62/1.58 % (3201034)Instruction limit reached! 6.62/1.58 % (3201034)------------------------------ 6.62/1.58 % (3201034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.62/1.58 % (3201034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.62/1.58 % (3201034)CaDiCaL version: 2.1.3 6.62/1.58 % (3201034)Termination reason: Instruction limit 6.62/1.58 % (3201034)Termination phase: Saturation 6.62/1.58 % (3201034)Time elapsed: 0.128 s 6.62/1.58 % (3201034)Peak memory usage: 12 MB 6.62/1.58 % (3201034)Instructions burned: 180 (million) 6.62/1.58 % (3201036)Refutation not found, incomplete strategy 6.62/1.58 % (3201036)------------------------------ 6.62/1.58 % (3201036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.62/1.58 % (3201036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.62/1.58 % (3201036)CaDiCaL version: 2.1.3 6.62/1.58 % (3201036)Termination reason: Refutation not found, incomplete strategy 6.62/1.58 % (3201036)Time elapsed: 0.130 s 6.62/1.58 % (3201036)Peak memory usage: 15 MB 6.62/1.58 % (3201036)Instructions burned: 177 (million) 6.62/1.58 % (3201036)------------------------------ 6.62/1.58 % (3201036)------------------------------ 6.62/1.58 % (3201044)Refutation not found, incomplete strategy 6.62/1.58 % (3201044)------------------------------ 6.62/1.58 % (3201044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.62/1.58 % (3201044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.62/1.58 % (3201044)CaDiCaL version: 2.1.3 6.62/1.58 % (3201044)Termination reason: Refutation not found, incomplete strategy 6.62/1.58 % (3201044)Time elapsed: 0.100 s 6.62/1.58 % (3201044)Peak memory usage: 14 MB 6.62/1.58 % (3201044)Instructions burned: 181 (million) 6.62/1.58 % (3201044)------------------------------ 6.62/1.58 % (3201044)------------------------------ 6.62/1.58 % (3201051)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=724353045:st=1.5:i=130:rtra=on:ss=axioms_1792 on theBenchmark for (1792ds/130Mi) 6.62/1.58 % (3201052)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3427263260:i=44:ep=R:rtra=on:ntd=on_1792 on theBenchmark for (1792ds/44Mi) 6.62/1.58 % (3201045)Instruction limit reached! 6.62/1.58 % (3201045)------------------------------ 6.62/1.58 % (3201045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.62/1.58 % (3201045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.62/1.58 % (3201045)CaDiCaL version: 2.1.3 6.62/1.58 % (3201045)Termination reason: Instruction limit 6.62/1.58 % (3201045)Termination phase: Saturation 6.62/1.58 % (3201045)Time elapsed: 0.130 s 6.62/1.58 % (3201045)Peak memory usage: 15 MB 6.62/1.58 % (3201045)Instructions burned: 515 (million) 6.62/1.58 % (3201054)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=4092836236:s2a=on:i=571:nm=16:rtra=on_1792 on theBenchmark for (1792ds/571Mi) 6.62/1.58 % (3201055)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=2203437480:i=450:rtra=on:ixr=off:ntd=on_1792 on theBenchmark for (1792ds/450Mi) 6.62/1.58 % (3201060)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=281125664:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_1791 on theBenchmark for (1791ds/95Mi) 6.62/1.58 % (3201052)Instruction limit reached! 7.12/1.67 % (3201052)------------------------------ 7.12/1.67 % (3201052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.12/1.67 % (3201052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.12/1.67 % (3201052)CaDiCaL version: 2.1.3 7.12/1.67 % (3201052)Termination reason: Instruction limit 7.12/1.67 % (3201052)Termination phase: Function definition elimination 7.12/1.67 % (3201052)Time elapsed: 0.033 s 7.12/1.67 % (3201052)Peak memory usage: 10 MB 7.12/1.67 % (3201052)Instructions burned: 44 (million) 7.12/1.67 % (3201060)Instruction limit reached! 7.12/1.67 % (3201060)------------------------------ 7.12/1.67 % (3201060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.12/1.67 % (3201060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.12/1.67 % (3201060)CaDiCaL version: 2.1.3 7.12/1.67 % (3201060)Termination reason: Instruction limit 7.12/1.67 % (3201060)Termination phase: Function definition elimination 7.12/1.67 % (3201060)Time elapsed: 0.017 s 7.12/1.67 % (3201060)Peak memory usage: 10 MB 7.12/1.67 % (3201060)Instructions burned: 95 (million) 7.12/1.67 % (3201069)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=2890537099:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_1791 on theBenchmark for (1791ds/105Mi) 7.12/1.67 % (3201067)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=854558514:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_1791 on theBenchmark for (1791ds/65Mi) 7.12/1.67 % (3201069)Instruction limit reached! 7.12/1.67 % (3201069)------------------------------ 7.12/1.67 % (3201069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.12/1.67 % (3201069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.12/1.67 % (3201069)CaDiCaL version: 2.1.3 7.12/1.67 % (3201069)Termination reason: Instruction limit 7.12/1.67 % (3201069)Termination phase: Saturation 7.12/1.67 % (3201069)Time elapsed: 0.022 s 7.12/1.67 % (3201069)Peak memory usage: 11 MB 7.12/1.67 % (3201069)Instructions burned: 107 (million) 7.12/1.67 % (3201073)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=4048203743:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_1791 on theBenchmark for (1791ds/5755Mi) 7.12/1.67 % (3201051)Instruction limit reached! 7.12/1.67 % (3201051)------------------------------ 7.12/1.67 % (3201051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.12/1.67 % (3201051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.12/1.67 % (3201051)CaDiCaL version: 2.1.3 7.12/1.67 % (3201051)Termination reason: Instruction limit 7.12/1.67 % (3201051)Termination phase: Saturation 7.12/1.67 % (3201051)Time elapsed: 0.099 s 7.12/1.67 % (3201051)Peak memory usage: 14 MB 7.12/1.67 % (3201051)Instructions burned: 130 (million) 7.12/1.67 % (3201076)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=1673967848:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_1790 on theBenchmark for (1790ds/375Mi) 7.12/1.67 % (3201067)Instruction limit reached! 7.12/1.67 % (3201067)------------------------------ 7.12/1.67 % (3201067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.12/1.67 % (3201067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.12/1.67 % (3201067)CaDiCaL version: 2.1.3 7.12/1.67 % (3201067)Termination reason: Instruction limit 7.12/1.67 % (3201067)Termination phase: Property scanning 7.12/1.67 % (3201067)Time elapsed: 0.047 s 7.12/1.67 % (3201067)Peak memory usage: 11 MB 7.12/1.67 % (3201067)Instructions burned: 66 (million) 7.12/1.67 % (3201078)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1645918268:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1790 on theBenchmark for (1790ds/495Mi) 7.12/1.67 % (3201054)Refutation not found, incomplete strategy 7.12/1.67 % (3201054)------------------------------ 7.12/1.67 % (3201054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.12/1.67 % (3201054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.21/1.85 % (3201054)CaDiCaL version: 2.1.3 8.21/1.85 % (3201054)Termination reason: Refutation not found, incomplete strategy 8.21/1.85 % (3201054)Time elapsed: 0.120 s 8.21/1.85 % (3201054)Peak memory usage: 14 MB 8.21/1.85 % (3201054)Instructions burned: 165 (million) 8.21/1.85 % (3201054)------------------------------ 8.21/1.85 % (3201054)------------------------------ 8.21/1.85 % (3201080)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=3278074617:cond=on:i=34:hud=10:nm=10:rtra=on_1790 on theBenchmark for (1790ds/34Mi) 8.21/1.85 % (3201080)Instruction limit reached! 8.21/1.85 % (3201080)------------------------------ 8.21/1.85 % (3201080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.21/1.85 % (3201080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.21/1.85 % (3201080)CaDiCaL version: 2.1.3 8.21/1.85 % (3201080)Termination reason: Instruction limit 8.21/1.85 % (3201080)Termination phase: Property scanning 8.21/1.85 % (3201080)Time elapsed: 0.027 s 8.21/1.85 % (3201080)Peak memory usage: 10 MB 8.21/1.85 % (3201080)Instructions burned: 35 (million) 8.21/1.85 % (3201086)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=4152526378:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_1790 on theBenchmark for (1790ds/91Mi) 8.21/1.85 % (3200998)Instruction limit reached! 8.21/1.85 % (3200998)------------------------------ 8.21/1.85 % (3200998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.21/1.85 % (3200998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.21/1.85 % (3200998)CaDiCaL version: 2.1.3 8.21/1.85 % (3200998)Termination reason: Instruction limit 8.21/1.85 % (3200998)Termination phase: Saturation 8.21/1.85 % (3200998)Time elapsed: 0.639 s 8.21/1.85 % (3200998)Peak memory usage: 19 MB 8.21/1.85 % (3200998)Instructions burned: 853 (million) 8.21/1.85 % (3201090)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=177248440:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_1789 on theBenchmark for (1789ds/66Mi) 8.21/1.85 % (3201078)Instruction limit reached! 8.21/1.85 % (3201078)------------------------------ 8.21/1.85 % (3201078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.21/1.85 % (3201078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.21/1.85 % (3201078)CaDiCaL version: 2.1.3 8.21/1.85 % (3201078)Termination reason: Instruction limit 8.21/1.85 % (3201078)Termination phase: Saturation 8.21/1.85 % (3201078)Time elapsed: 0.151 s 8.21/1.85 % (3201078)Peak memory usage: 15 MB 8.21/1.85 % (3201078)Instructions burned: 496 (million) 8.21/1.85 % (3201086)Instruction limit reached! 8.21/1.85 % (3201086)------------------------------ 8.21/1.85 % (3201086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.21/1.85 % (3201086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.21/1.85 % (3201086)CaDiCaL version: 2.1.3 8.21/1.85 % (3201086)Termination reason: Instruction limit 8.21/1.85 % (3201086)Termination phase: Property scanning 8.21/1.85 % (3201086)Time elapsed: 0.059 s 8.21/1.85 % (3201086)Peak memory usage: 10 MB 8.21/1.85 % (3201086)Instructions burned: 91 (million) 8.21/1.85 % (3201093)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2912427015:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1789 on theBenchmark for (1789ds/22Mi) 8.21/1.85 % (3201093)Instruction limit reached! 8.21/1.85 % (3201093)------------------------------ 8.21/1.85 % (3201093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.21/1.85 % (3201093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.21/1.85 % (3201093)CaDiCaL version: 2.1.3 8.21/1.85 % (3201093)Termination reason: Instruction limit 8.21/1.85 % (3201093)Termination phase: shuffling 8.21/1.85 % (3201093)Time elapsed: 0.004 s 8.21/1.85 % (3201093)Peak memory usage: 10 MB 8.21/1.85 % (3201093)Instructions burned: 24 (million) 8.21/1.85 % (3201096)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2453581208:i=28:sd=1:rtra=on:ss=axioms:sgt=64_1789 on theBenchmark for (1789ds/28Mi) 8.21/1.85 % (3201090)Instruction limit reached! 8.21/1.85 % (3201090)------------------------------ 8.21/1.85 % (3201090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.21/1.85 % (3201090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.84/1.95 % (3201090)CaDiCaL version: 2.1.3 8.84/1.95 % (3201090)Termination reason: Instruction limit 8.84/1.95 % (3201090)Termination phase: Property scanning 8.84/1.95 % (3201090)Time elapsed: 0.040 s 8.84/1.95 % (3201090)Peak memory usage: 10 MB 8.84/1.95 % (3201090)Instructions burned: 66 (million) 8.84/1.95 % (3201096)Instruction limit reached! 8.84/1.95 % (3201096)------------------------------ 8.84/1.95 % (3201096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.84/1.95 % (3201096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.84/1.95 % (3201096)CaDiCaL version: 2.1.3 8.84/1.95 % (3201096)Termination reason: Instruction limit 8.84/1.95 % (3201096)Termination phase: shuffling 8.84/1.95 % (3201096)Time elapsed: 0.005 s 8.84/1.95 % (3201096)Peak memory usage: 10 MB 8.84/1.95 % (3201096)Instructions burned: 31 (million) 8.84/1.95 % (3201099)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on 8.84/1.95 % (3201099)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=2894627017:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_1788 on theBenchmark for (1788ds/137Mi) 8.84/1.95 % (3201094)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=1564003898:i=338:bd=all:ins=4:rtra=on_1789 on theBenchmark for (1789ds/338Mi) 8.84/1.95 % (3201100)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=821966424:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_1788 on theBenchmark for (1788ds/340Mi) 8.84/1.95 % (3201076)Instruction limit reached! 8.84/1.95 % (3201076)------------------------------ 8.84/1.95 % (3201076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.84/1.95 % (3201076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.84/1.95 % (3201076)CaDiCaL version: 2.1.3 8.84/1.95 % (3201076)Termination reason: Instruction limit 8.84/1.95 % (3201076)Termination phase: Saturation 8.84/1.95 % (3201076)Time elapsed: 0.232 s 8.84/1.95 % (3201076)Peak memory usage: 14 MB 8.84/1.95 % (3201076)Instructions burned: 375 (million) 8.84/1.95 % (3201055)Instruction limit reached! 8.84/1.95 % (3201055)------------------------------ 8.84/1.95 % (3201055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.84/1.95 % (3201055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.84/1.95 % (3201055)CaDiCaL version: 2.1.3 8.84/1.95 % (3201055)Termination reason: Instruction limit 8.84/1.95 % (3201055)Termination phase: Saturation 8.84/1.95 % (3201055)Time elapsed: 0.331 s 8.84/1.95 % (3201055)Peak memory usage: 14 MB 8.84/1.95 % (3201055)Instructions burned: 453 (million) 8.84/1.95 % (3201099)Instruction limit reached! 8.84/1.95 % (3201099)------------------------------ 8.84/1.95 % (3201099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.84/1.95 % (3201099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.84/1.95 % (3201099)CaDiCaL version: 2.1.3 8.84/1.95 % (3201099)Termination reason: Instruction limit 8.84/1.95 % (3201099)Termination phase: Saturation 8.84/1.95 % (3201099)Time elapsed: 0.028 s 8.84/1.95 % (3201099)Peak memory usage: 12 MB 8.84/1.95 % (3201099)Instructions burned: 140 (million) 8.84/1.95 % (3201105)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on 8.84/1.95 % (3201105)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=2499070249:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_1788 on theBenchmark for (1788ds/373Mi) 8.84/1.95 % (3201104)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=4034185511:i=227:sd=1:bd=all:rtra=on:ss=axioms_1788 on theBenchmark for (1788ds/227Mi) 8.84/1.95 % (3201106)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=428493843:i=116:ep=RSTC:rtra=on:ntd=on_1788 on theBenchmark for (1788ds/116Mi) 8.84/1.95 % (3200968)Instruction limit reached! 8.84/1.95 % (3200968)------------------------------ 8.84/1.95 % (3200968)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.84/1.95 % (3200968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.81/2.20 % (3200968)CaDiCaL version: 2.1.3 11.81/2.20 % (3200968)Termination reason: Instruction limit 11.81/2.20 % (3200968)Termination phase: Saturation 11.81/2.20 % (3200968)Time elapsed: 0.922 s 11.81/2.20 % (3200968)Peak memory usage: 16 MB 11.81/2.20 % (3200968)Instructions burned: 1240 (million) 11.81/2.20 % (3201114)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=457142340:i=575:rtra=on_1787 on theBenchmark for (1787ds/575Mi) 11.81/2.20 % (3201106)Instruction limit reached! 11.81/2.20 % (3201106)------------------------------ 11.81/2.20 % (3201106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.81/2.20 % (3201106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.81/2.20 % (3201106)CaDiCaL version: 2.1.3 11.81/2.20 % (3201106)Termination reason: Instruction limit 11.81/2.20 % (3201106)Termination phase: Property scanning 11.81/2.20 % (3201106)Time elapsed: 0.063 s 11.81/2.20 % (3201106)Peak memory usage: 10 MB 11.81/2.20 % (3201106)Instructions burned: 116 (million) 11.81/2.20 % (3201105)Instruction limit reached! 11.81/2.20 % (3201105)------------------------------ 11.81/2.20 % (3201105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.81/2.20 % (3201105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.81/2.20 % (3201105)CaDiCaL version: 2.1.3 11.81/2.20 % (3201105)Termination reason: Instruction limit 11.81/2.20 % (3201105)Termination phase: Saturation 11.81/2.20 % (3201105)Time elapsed: 0.096 s 11.81/2.20 % (3201105)Peak memory usage: 13 MB 11.81/2.20 % (3201105)Instructions burned: 377 (million) 11.81/2.20 % (3201118)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2406810389:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_1787 on theBenchmark for (1787ds/270Mi) 11.81/2.20 % (3201119)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=489493465:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1787 on theBenchmark for (1787ds/9840Mi) 11.81/2.20 % (3201104)Refutation not found, incomplete strategy 11.81/2.20 % (3201104)------------------------------ 11.81/2.20 % (3201104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.81/2.20 % (3201104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.81/2.20 % (3201104)CaDiCaL version: 2.1.3 11.81/2.20 % (3201104)Termination reason: Refutation not found, incomplete strategy 11.81/2.20 % (3201104)Time elapsed: 0.121 s 11.81/2.20 % (3201104)Peak memory usage: 16 MB 11.81/2.20 % (3201104)Instructions burned: 171 (million) 11.81/2.20 % (3201104)------------------------------ 11.81/2.20 % (3201104)------------------------------ 11.81/2.20 % (3201100)Instruction limit reached! 11.81/2.20 % (3201100)------------------------------ 11.81/2.20 % (3201100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.81/2.20 % (3201100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.81/2.20 % (3201100)CaDiCaL version: 2.1.3 11.81/2.20 % (3201100)Termination reason: Instruction limit 11.81/2.20 % (3201100)Termination phase: Saturation 11.81/2.20 % (3201100)Time elapsed: 0.186 s 11.81/2.20 % (3201100)Peak memory usage: 13 MB 11.81/2.20 % (3201100)Instructions burned: 341 (million) 11.81/2.20 % (3201123)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=3130604260:i=421:rtra=on:ss=axioms_1786 on theBenchmark for (1786ds/421Mi) 11.81/2.20 % (3201124)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 11.81/2.20 % (3201124)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=1617664058:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_1786 on theBenchmark for (1786ds/270Mi) 11.81/2.20 % (3201094)Instruction limit reached! 11.81/2.20 % (3201094)------------------------------ 11.81/2.20 % (3201094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.81/2.20 % (3201094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.81/2.20 % (3201094)CaDiCaL version: 2.1.3 11.81/2.20 % (3201094)Termination reason: Instruction limit 13.84/2.65 % (3201094)Termination phase: Saturation 13.84/2.65 % (3201094)Time elapsed: 0.254 s 13.84/2.65 % (3201094)Peak memory usage: 17 MB 13.84/2.65 % (3201094)Instructions burned: 338 (million) 13.84/2.65 % (3201123)Refutation not found, incomplete strategy 13.84/2.65 % (3201123)------------------------------ 13.84/2.65 % (3201123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.84/2.65 % (3201123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.84/2.65 % (3201123)CaDiCaL version: 2.1.3 13.84/2.65 % (3201123)Termination reason: Refutation not found, incomplete strategy 13.84/2.65 % (3201123)Time elapsed: 0.078 s 13.84/2.65 % (3201123)Peak memory usage: 14 MB 13.84/2.65 % (3201123)Instructions burned: 141 (million) 13.84/2.65 % (3201123)------------------------------ 13.84/2.65 % (3201123)------------------------------ 13.84/2.65 % (3201129)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3047195161:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_1786 on theBenchmark for (1786ds/31Mi) 13.84/2.65 % (3201118)Instruction limit reached! 13.84/2.65 % (3201118)------------------------------ 13.84/2.65 % (3201118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.84/2.65 % (3201118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.84/2.65 % (3201118)CaDiCaL version: 2.1.3 13.84/2.65 % (3201118)Termination reason: Instruction limit 13.84/2.65 % (3201118)Termination phase: Saturation 13.84/2.65 % (3201118)Time elapsed: 0.164 s 13.84/2.65 % (3201118)Peak memory usage: 13 MB 13.84/2.65 % (3201118)Instructions burned: 270 (million) 13.84/2.65 % (3201129)Instruction limit reached! 13.84/2.65 % (3201129)------------------------------ 13.84/2.65 % (3201129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.84/2.65 % (3201129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.84/2.65 % (3201129)CaDiCaL version: 2.1.3 13.84/2.65 % (3201129)Termination reason: Instruction limit 13.84/2.65 % (3201129)Termination phase: Property scanning 13.84/2.65 % (3201129)Time elapsed: 0.025 s 13.84/2.65 % (3201129)Peak memory usage: 10 MB 13.84/2.65 % (3201129)Instructions burned: 31 (million) 13.84/2.65 % (3201124)Instruction limit reached! 13.84/2.65 % (3201124)------------------------------ 13.84/2.65 % (3201124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.84/2.65 % (3201124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.84/2.65 % (3201124)CaDiCaL version: 2.1.3 13.84/2.65 % (3201124)Termination reason: Instruction limit 13.84/2.65 % (3201124)Termination phase: Saturation 13.84/2.65 % (3201124)Time elapsed: 0.096 s 13.84/2.65 % (3201124)Peak memory usage: 12 MB 13.84/2.65 % (3201124)Instructions burned: 274 (million) 13.84/2.65 % (3201132)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 13.84/2.65 % (3201132)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 13.84/2.65 % (3201132)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=895639511:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_1785 on theBenchmark for (1785ds/1440Mi) 13.84/2.65 % (3201136)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=2838694968:i=111:add=on:fgj=on:rtra=on:fdi=1024_1785 on theBenchmark for (1785ds/111Mi) 13.84/2.65 % (3201134)dis+10_2_sil=128000:si=on:random_seed=2738544217:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_1785 on theBenchmark for (1785ds/339Mi) 13.84/2.65 % (3201136)Instruction limit reached! 13.84/2.65 % (3201136)------------------------------ 13.84/2.65 % (3201136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.84/2.65 % (3201136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.84/2.65 % (3201136)CaDiCaL version: 2.1.3 13.84/2.65 % (3201136)Termination reason: Instruction limit 13.84/2.65 % (3201136)Termination phase: Property scanning 13.84/2.65 % (3201136)Time elapsed: 0.021 s 13.84/2.65 % (3201136)Peak memory usage: 10 MB 13.84/2.65 % (3201136)Instructions burned: 114 (million) 13.84/2.65 % (3201137)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=4215105307:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1785 on theBenchmark for (1785ds/122Mi) 16.82/2.93 % (3201143)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=2417211929:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_1785 on theBenchmark for (1785ds/136Mi) 16.82/2.93 % (3201143)Instruction limit reached! 16.82/2.93 % (3201143)------------------------------ 16.82/2.93 % (3201143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 16.82/2.93 % (3201143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 16.82/2.93 % (3201143)CaDiCaL version: 2.1.3 16.82/2.93 % (3201143)Termination reason: Instruction limit 16.82/2.93 % (3201143)Termination phase: Property scanning 16.82/2.93 % (3201143)Time elapsed: 0.025 s 16.82/2.93 % (3201143)Peak memory usage: 10 MB 16.82/2.93 % (3201143)Instructions burned: 136 (million) 16.82/2.93 % (3201146)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1130455011:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1784 on theBenchmark for (1784ds/232Mi) 16.82/2.93 % (3201137)Instruction limit reached! 16.82/2.93 % (3201137)------------------------------ 16.82/2.93 % (3201137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 16.82/2.93 % (3201137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 16.82/2.93 % (3201137)CaDiCaL version: 2.1.3 16.82/2.93 % (3201137)Termination reason: Instruction limit 16.82/2.93 % (3201137)Termination phase: Saturation 16.82/2.93 % (3201137)Time elapsed: 0.084 s 16.82/2.93 % (3201137)Peak memory usage: 13 MB 16.82/2.93 % (3201137)Instructions burned: 123 (million) 16.82/2.93 % (3201146)Refutation not found, incomplete strategy 16.82/2.93 % (3201146)------------------------------ 16.82/2.93 % (3201146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 16.82/2.93 % (3201146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 16.82/2.93 % (3201146)CaDiCaL version: 2.1.3 16.82/2.93 % (3201146)Termination reason: Refutation not found, incomplete strategy 16.82/2.93 % (3201146)Time elapsed: 0.061 s 16.82/2.93 % (3201146)Peak memory usage: 14 MB 16.82/2.93 % (3201146)Instructions burned: 203 (million) 16.82/2.93 % (3201146)------------------------------ 16.82/2.93 % (3201146)------------------------------ 16.82/2.93 % (3201150)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=1100266128:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_1784 on theBenchmark for (1784ds/1254Mi) 16.82/2.93 % (3201151)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs 16.82/2.93 % (3201151)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=891343565:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_1784 on theBenchmark for (1784ds/281Mi) 16.82/2.93 % (3201114)Instruction limit reached! 16.82/2.93 % (3201114)------------------------------ 16.82/2.93 % (3201114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 16.82/2.93 % (3201114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 16.82/2.93 % (3201114)CaDiCaL version: 2.1.3 16.82/2.93 % (3201114)Termination reason: Instruction limit 16.82/2.93 % (3201114)Termination phase: Saturation 16.82/2.93 % (3201114)Time elapsed: 0.405 s 16.82/2.93 % (3201114)Peak memory usage: 17 MB 16.82/2.93 % (3201114)Instructions burned: 577 (million) 16.82/2.93 % (3201158)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=489174669:i=619:add=on:rtra=on_1783 on theBenchmark for (1783ds/619Mi) 16.82/2.93 % (3201134)Instruction limit reached! 16.82/2.93 % (3201134)------------------------------ 16.82/2.93 % (3201134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 16.82/2.93 % (3201134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 16.82/2.93 % (3201134)CaDiCaL version: 2.1.3 16.82/2.93 % (3201134)Termination reason: Instruction limit 16.82/2.93 % (3201134)Termination phase: Saturation 16.82/2.93 % (3201134)Time elapsed: 0.233 s 16.82/2.93 % (3201134)Peak memory usage: 15 MB 16.82/2.93 % (3201134)Instructions burned: 340 (million) 16.82/2.93 % (3201161)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2845308349:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_1782 on theBenchmark for (1782ds/865Mi) 17.93/3.14 % (3201151)Instruction limit reached! 17.93/3.14 % (3201151)------------------------------ 17.93/3.14 % (3201151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 17.93/3.14 % (3201151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 17.93/3.14 % (3201151)CaDiCaL version: 2.1.3 17.93/3.14 % (3201151)Termination reason: Instruction limit 17.93/3.14 % (3201151)Termination phase: Saturation 17.93/3.14 % (3201151)Time elapsed: 0.143 s 17.93/3.14 % (3201151)Peak memory usage: 13 MB 17.93/3.14 % (3201151)Instructions burned: 281 (million) 17.93/3.14 % (3201165)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2072111949:i=212:sd=1:rtra=on:ss=axioms:sgt=64_1782 on theBenchmark for (1782ds/212Mi) 17.93/3.14 % (3201165)Instruction limit reached! 17.93/3.14 % (3201165)------------------------------ 17.93/3.14 % (3201165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 17.93/3.14 % (3201165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 17.93/3.14 % (3201165)CaDiCaL version: 2.1.3 17.93/3.14 % (3201165)Termination reason: Instruction limit 17.93/3.14 % (3201165)Termination phase: Saturation 17.93/3.14 % (3201165)Time elapsed: 0.149 s 17.93/3.14 % (3201165)Peak memory usage: 12 MB 17.93/3.14 % (3201165)Instructions burned: 212 (million) 17.93/3.14 % (3201171)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=918414460:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_1780 on theBenchmark for (1780ds/130Mi) 17.93/3.14 % (3201158)Refutation not found, incomplete strategy 17.93/3.14 % (3201158)------------------------------ 17.93/3.14 % (3201158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 17.93/3.14 % (3201158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 17.93/3.14 % (3201158)CaDiCaL version: 2.1.3 17.93/3.14 % (3201158)Termination reason: Refutation not found, incomplete strategy 17.93/3.14 % (3201158)Time elapsed: 0.316 s 17.93/3.14 % (3201158)Peak memory usage: 16 MB 17.93/3.14 % (3201158)Instructions burned: 433 (million) 17.93/3.14 % (3201158)------------------------------ 17.93/3.14 % (3201158)------------------------------ 17.93/3.14 % (3201174)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=87038482:st=1.5:i=346:rtra=on:ss=axioms_1780 on theBenchmark for (1780ds/346Mi) 17.93/3.14 % (3201171)Instruction limit reached! 17.93/3.14 % (3201171)------------------------------ 17.93/3.14 % (3201171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 17.93/3.14 % (3201171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 17.93/3.14 % (3201171)CaDiCaL version: 2.1.3 17.93/3.14 % (3201171)Termination reason: Instruction limit 17.93/3.14 % (3201171)Termination phase: Saturation 17.93/3.14 % (3201171)Time elapsed: 0.094 s 17.93/3.14 % (3201171)Peak memory usage: 13 MB 17.93/3.14 % (3201171)Instructions burned: 130 (million) 17.93/3.14 % (3201179)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=1853023542:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_1779 on theBenchmark for (1779ds/152Mi) 17.93/3.14 % (3201174)Refutation not found, incomplete strategy 17.93/3.14 % (3201174)------------------------------ 17.93/3.14 % (3201174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 17.93/3.14 % (3201174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 17.93/3.14 % (3201174)CaDiCaL version: 2.1.3 17.93/3.14 % (3201174)Termination reason: Refutation not found, incomplete strategy 17.93/3.14 % (3201174)Time elapsed: 0.107 s 17.93/3.14 % (3201174)Peak memory usage: 14 MB 17.93/3.14 % (3201174)Instructions burned: 137 (million) 17.93/3.14 % (3201174)------------------------------ 17.93/3.14 % (3201174)------------------------------ 17.93/3.14 % (3201182)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2061924944:i=75:ep=R:rtra=on:ntd=on_1778 on theBenchmark for (1778ds/75Mi) 17.93/3.14 % (3201179)Instruction limit reached! 17.93/3.14 % (3201179)------------------------------ 17.93/3.14 % (3201179)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 17.93/3.14 % (3201179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 17.93/3.14 % (3201179)CaDiCaL version: 2.1.3 17.93/3.14 % (3201179)Termination reason: Instruction limit 20.35/3.50 % (3201179)Termination phase: Saturation 20.35/3.50 % (3201179)Time elapsed: 0.088 s 20.35/3.50 % (3201179)Peak memory usage: 12 MB 20.35/3.50 % (3201179)Instructions burned: 152 (million) 20.35/3.50 % (3201186)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=3855897206:st=2.5:i=387:sd=2:rtra=on:ss=axioms_1778 on theBenchmark for (1778ds/387Mi) 20.35/3.50 % (3201182)Instruction limit reached! 20.35/3.50 % (3201182)------------------------------ 20.35/3.50 % (3201182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.35/3.50 % (3201182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.35/3.50 % (3201182)CaDiCaL version: 2.1.3 20.35/3.50 % (3201182)Termination reason: Instruction limit 20.35/3.50 % (3201182)Termination phase: Property scanning 20.35/3.50 % (3201182)Time elapsed: 0.060 s 20.35/3.50 % (3201182)Peak memory usage: 10 MB 20.35/3.50 % (3201182)Instructions burned: 75 (million) 20.35/3.50 % (3201188)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=259293567:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_1777 on theBenchmark for (1777ds/148Mi) 20.35/3.50 % (3201188)Instruction limit reached! 20.35/3.50 % (3201188)------------------------------ 20.35/3.50 % (3201188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.35/3.50 % (3201188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.35/3.50 % (3201188)CaDiCaL version: 2.1.3 20.35/3.50 % (3201188)Termination reason: Instruction limit 20.35/3.50 % (3201188)Termination phase: Saturation 20.35/3.50 % (3201188)Time elapsed: 0.065 s 20.35/3.50 % (3201188)Peak memory usage: 12 MB 20.35/3.50 % (3201188)Instructions burned: 148 (million) 20.35/3.50 % (3201186)Refutation not found, incomplete strategy 20.35/3.50 % (3201186)------------------------------ 20.35/3.50 % (3201186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.35/3.50 % (3201186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.35/3.50 % (3201186)CaDiCaL version: 2.1.3 20.35/3.50 % (3201186)Termination reason: Refutation not found, incomplete strategy 20.35/3.50 % (3201186)Time elapsed: 0.110 s 20.35/3.50 % (3201186)Peak memory usage: 15 MB 20.35/3.50 % (3201186)Instructions burned: 144 (million) 20.35/3.50 % (3201186)------------------------------ 20.35/3.50 % (3201186)------------------------------ 20.35/3.50 % (3201190)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=3466155167:i=161:piset=and:rtra=on:ntd=on_1776 on theBenchmark for (1776ds/161Mi) 20.35/3.50 % (3201191)lrs+10_1_sil=128000:si=on:random_seed=1723816455:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_1776 on theBenchmark for (1776ds/888Mi) 20.35/3.50 % (3201161)Instruction limit reached! 20.35/3.50 % (3201161)------------------------------ 20.35/3.50 % (3201161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.35/3.50 % (3201161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.35/3.50 % (3201161)CaDiCaL version: 2.1.3 20.35/3.50 % (3201161)Termination reason: Instruction limit 20.35/3.50 % (3201161)Termination phase: Saturation 20.35/3.50 % (3201161)Time elapsed: 0.652 s 20.35/3.50 % (3201161)Peak memory usage: 20 MB 20.35/3.50 % (3201161)Instructions burned: 865 (million) 20.35/3.50 % (3201197)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=3509970443:i=136:add=on:ins=4:rtra=on:sup=off_1776 on theBenchmark for (1776ds/136Mi) 20.35/3.50 % (3201150)Instruction limit reached! 20.35/3.50 % (3201150)------------------------------ 20.35/3.50 % (3201150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.35/3.50 % (3201150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.35/3.50 % (3201150)CaDiCaL version: 2.1.3 20.35/3.50 % (3201150)Termination reason: Instruction limit 20.35/3.50 % (3201150)Termination phase: Saturation 20.35/3.50 % (3201150)Time elapsed: 0.821 s 20.35/3.50 % (3201150)Peak memory usage: 21 MB 20.35/3.50 % (3201150)Instructions burned: 1255 (million) 20.35/3.50 % (3201199)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=461727979:i=88:s2at=3:nm=2:rtra=on:rawr=on_1775 on theBenchmark for (1775ds/88Mi) 20.35/3.50 % (3201197)Instruction limit reached! 20.35/3.50 % (3201197)------------------------------ 22.02/3.76 % (3201197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.02/3.76 % (3201197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.02/3.76 % (3201197)CaDiCaL version: 2.1.3 22.02/3.76 % (3201197)Termination reason: Instruction limit 22.02/3.76 % (3201197)Termination phase: Property scanning 22.02/3.76 % (3201197)Time elapsed: 0.050 s 22.02/3.76 % (3201197)Peak memory usage: 11 MB 22.02/3.76 % (3201197)Instructions burned: 137 (million) 22.02/3.76 % (3201190)Instruction limit reached! 22.02/3.76 % (3201190)------------------------------ 22.02/3.76 % (3201190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.02/3.76 % (3201190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.02/3.76 % (3201190)CaDiCaL version: 2.1.3 22.02/3.76 % (3201190)Termination reason: Instruction limit 22.02/3.76 % (3201190)Termination phase: Saturation 22.02/3.76 % (3201190)Time elapsed: 0.111 s 22.02/3.76 % (3201190)Peak memory usage: 11 MB 22.02/3.76 % (3201190)Instructions burned: 163 (million) 22.02/3.76 % (3201203)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1734356297:i=2186:rtra=on:ixr=off_1775 on theBenchmark for (1775ds/2186Mi) 22.02/3.76 % (3201201)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=480250641:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_1775 on theBenchmark for (1775ds/93Mi) 22.02/3.76 % (3201199)Instruction limit reached! 22.02/3.76 % (3201199)------------------------------ 22.02/3.76 % (3201199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.02/3.76 % (3201199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.02/3.76 % (3201199)CaDiCaL version: 2.1.3 22.02/3.76 % (3201199)Termination reason: Instruction limit 22.02/3.76 % (3201199)Termination phase: Property scanning 22.02/3.76 % (3201199)Time elapsed: 0.068 s 22.02/3.76 % (3201199)Peak memory usage: 11 MB 22.02/3.76 % (3201199)Instructions burned: 88 (million) 22.02/3.76 % (3201132)Instruction limit reached! 22.02/3.76 % (3201132)------------------------------ 22.02/3.76 % (3201132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.02/3.76 % (3201132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.02/3.76 % (3201132)CaDiCaL version: 2.1.3 22.02/3.76 % (3201132)Termination reason: Instruction limit 22.02/3.76 % (3201132)Termination phase: Saturation 22.02/3.76 % (3201132)Time elapsed: 1.085 s 22.02/3.76 % (3201132)Peak memory usage: 22 MB 22.02/3.76 % (3201132)Instructions burned: 1440 (million) 22.02/3.76 % (3201209)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4220315554:s2a=on:i=240:rtra=on:ntd=on_1774 on theBenchmark for (1774ds/240Mi) 22.02/3.76 % (3201201)Instruction limit reached! 22.02/3.76 % (3201201)------------------------------ 22.02/3.76 % (3201201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.02/3.76 % (3201201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.02/3.76 % (3201201)CaDiCaL version: 2.1.3 22.02/3.76 % (3201201)Termination reason: Instruction limit 22.02/3.76 % (3201201)Termination phase: Property scanning 22.02/3.76 % (3201201)Time elapsed: 0.070 s 22.02/3.76 % (3201201)Peak memory usage: 11 MB 22.02/3.76 % (3201201)Instructions burned: 93 (million) 22.02/3.76 % (3201210)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=1302051515:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_1774 on theBenchmark for (1774ds/805Mi) 22.02/3.76 % (3201213)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on 22.02/3.76 % (3201213)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=2290894093:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_1774 on theBenchmark for (1774ds/391Mi) 22.02/3.76 % (3201191)Instruction limit reached! 22.02/3.76 % (3201191)------------------------------ 22.02/3.76 % (3201191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.02/3.76 % (3201191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.02/3.76 % (3201191)CaDiCaL version: 2.1.3 22.02/3.76 % (3201191)Termination reason: Instruction limit 22.02/3.76 % (3201191)Termination phase: Saturation 23.17/3.98 % (3201191)Time elapsed: 0.310 s 23.17/3.98 % (3201191)Peak memory usage: 15 MB 23.17/3.98 % (3201191)Instructions burned: 890 (million) 23.17/3.98 % (3201217)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=1823204911:i=355:av=off:fsr=off:rtra=on:ixr=off_1773 on theBenchmark for (1773ds/355Mi) 23.17/3.98 % (3201209)Instruction limit reached! 23.17/3.98 % (3201209)------------------------------ 23.17/3.98 % (3201209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 23.17/3.98 % (3201209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 23.17/3.98 % (3201209)CaDiCaL version: 2.1.3 23.17/3.98 % (3201209)Termination reason: Instruction limit 23.17/3.98 % (3201209)Termination phase: Saturation 23.17/3.98 % (3201209)Time elapsed: 0.169 s 23.17/3.98 % (3201209)Peak memory usage: 13 MB 23.17/3.98 % (3201209)Instructions burned: 241 (million) 23.17/3.98 % (3201219)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=1543945176:lrd=on:i=314:sd=1:rtra=on:ss=axioms_1772 on theBenchmark for (1772ds/314Mi) 23.17/3.98 % (3201213)Refutation not found, incomplete strategy 23.17/3.98 % (3201213)------------------------------ 23.17/3.98 % (3201213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 23.17/3.98 % (3201213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 23.17/3.98 % (3201213)CaDiCaL version: 2.1.3 23.17/3.98 % (3201213)Termination reason: Refutation not found, incomplete strategy 23.17/3.98 % (3201213)Time elapsed: 0.183 s 23.17/3.98 % (3201213)Peak memory usage: 14 MB 23.17/3.98 % (3201213)Instructions burned: 253 (million) 23.17/3.98 % (3201213)------------------------------ 23.17/3.98 % (3201213)------------------------------ 23.17/3.98 % (3201219)Refutation not found, incomplete strategy 23.17/3.98 % (3201219)------------------------------ 23.17/3.98 % (3201219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 23.17/3.98 % (3201219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 23.17/3.98 % (3201219)CaDiCaL version: 2.1.3 23.17/3.98 % (3201219)Termination reason: Refutation not found, incomplete strategy 23.17/3.98 % (3201219)Time elapsed: 0.055 s 23.17/3.98 % (3201219)Peak memory usage: 14 MB 23.17/3.98 % (3201219)Instructions burned: 152 (million) 23.17/3.98 % (3201219)------------------------------ 23.17/3.98 % (3201219)------------------------------ 23.17/3.98 % (3201223)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=1090177324:s2a=on:i=251:fsr=off:rtra=on_1772 on theBenchmark for (1772ds/251Mi) 23.17/3.98 % (3201225)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=4159086434:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2470:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_1771 on theBenchmark for (1771ds/2470Mi) 23.17/3.98 % (3201217)Instruction limit reached! 23.17/3.98 % (3201217)------------------------------ 23.17/3.98 % (3201217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 23.17/3.98 % (3201217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 23.17/3.98 % (3201217)CaDiCaL version: 2.1.3 23.17/3.98 % (3201217)Termination reason: Instruction limit 23.17/3.98 % (3201217)Termination phase: Saturation 23.17/3.98 % (3201217)Time elapsed: 0.193 s 23.17/3.98 % (3201217)Peak memory usage: 14 MB 23.17/3.98 % (3201217)Instructions burned: 355 (million) 23.17/3.98 % (3201229)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=3751399113:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_1771 on theBenchmark for (1771ds/673Mi) 23.17/3.98 % (3201223)Instruction limit reached! 23.17/3.98 % (3201223)------------------------------ 23.17/3.98 % (3201223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 23.17/3.98 % (3201223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 23.17/3.98 % (3201223)CaDiCaL version: 2.1.3 23.17/3.98 % (3201223)Termination reason: Instruction limit 23.17/3.98 % (3201223)Termination phase: Saturation 23.17/3.98 % (3201223)Time elapsed: 0.179 s 23.17/3.98 % (3201223)Peak memory usage: 12 MB 23.17/3.98 % (3201223)Instructions burned: 252 (million) 23.17/3.98 % (3201231)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=2277724517:i=116:ep=RSTC:rtra=on:ntd=on_1770 on theBenchmark for (1770ds/116Mi) 27.10/4.43 % (3201231)Instruction limit reached! 27.10/4.43 % (3201231)------------------------------ 27.10/4.43 % (3201231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.10/4.43 % (3201231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.10/4.43 % (3201231)CaDiCaL version: 2.1.3 27.10/4.43 % (3201231)Termination reason: Instruction limit 27.10/4.43 % (3201231)Termination phase: Property scanning 27.10/4.43 % (3201231)Time elapsed: 0.078 s 27.10/4.43 % (3201231)Peak memory usage: 10 MB 27.10/4.43 % (3201231)Instructions burned: 117 (million) 27.10/4.43 % (3201210)Instruction limit reached! 27.10/4.43 % (3201210)------------------------------ 27.10/4.43 % (3201210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.10/4.43 % (3201210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.10/4.43 % (3201210)CaDiCaL version: 2.1.3 27.10/4.43 % (3201210)Termination reason: Instruction limit 27.10/4.43 % (3201210)Termination phase: Saturation 27.10/4.43 % (3201210)Time elapsed: 0.554 s 27.10/4.43 % (3201210)Peak memory usage: 17 MB 27.10/4.43 % (3201210)Instructions burned: 806 (million) 27.10/4.43 % (3201236)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2244476680:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_1768 on theBenchmark for (1768ds/270Mi) 27.10/4.43 % (3201237)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2350589448:hsq=on:hsqr=16,1:s2a=on:i=30:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1768 on theBenchmark for (1768ds/30Mi) 27.10/4.43 % (3201229)Instruction limit reached! 27.10/4.43 % (3201229)------------------------------ 27.10/4.43 % (3201229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.10/4.43 % (3201229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.10/4.43 % (3201229)CaDiCaL version: 2.1.3 27.10/4.43 % (3201229)Termination reason: Instruction limit 27.10/4.43 % (3201229)Termination phase: Saturation 27.10/4.43 % (3201229)Time elapsed: 0.264 s 27.10/4.43 % (3201229)Peak memory usage: 15 MB 27.10/4.43 % (3201229)Instructions burned: 673 (million) 27.10/4.43 % (3201237)Instruction limit reached! 27.10/4.43 % (3201237)------------------------------ 27.10/4.43 % (3201237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.10/4.43 % (3201237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.10/4.43 % (3201237)CaDiCaL version: 2.1.3 27.10/4.43 % (3201237)Termination reason: Instruction limit 27.10/4.43 % (3201237)Termination phase: shuffling 27.10/4.43 % (3201237)Time elapsed: 0.021 s 27.10/4.43 % (3201237)Peak memory usage: 10 MB 27.10/4.43 % (3201237)Instructions burned: 32 (million) 27.10/4.43 % (3201240)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off 27.10/4.43 % (3201240)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=3786343420:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_1768 on theBenchmark for (1768ds/39Mi) 27.10/4.43 % (3201241)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=4170013626:i=365:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_1768 on theBenchmark for (1768ds/365Mi) 27.10/4.43 % (3201240)Instruction limit reached! 27.10/4.43 % (3201240)------------------------------ 27.10/4.43 % (3201240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.10/4.43 % (3201240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.10/4.43 % (3201240)CaDiCaL version: 2.1.3 27.10/4.43 % (3201240)Termination reason: Instruction limit 27.10/4.43 % (3201240)Termination phase: Function definition elimination 27.10/4.43 % (3201240)Time elapsed: 0.016 s 27.10/4.43 % (3201240)Peak memory usage: 10 MB 27.10/4.43 % (3201240)Instructions burned: 41 (million) 27.10/4.43 % (3201245)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2911518653:i=158:av=off:rtra=on_1767 on theBenchmark for (1767ds/158Mi) 27.10/4.43 % (3201245)Instruction limit reached! 27.10/4.43 % (3201245)------------------------------ 27.10/4.43 % (3201245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.10/4.43 % (3201245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 28.89/4.74 % (3201245)CaDiCaL version: 2.1.3 28.89/4.74 % (3201245)Termination reason: Instruction limit 28.89/4.74 % (3201245)Termination phase: Saturation 28.89/4.74 % (3201245)Time elapsed: 0.060 s 28.89/4.74 % (3201245)Peak memory usage: 12 MB 28.89/4.74 % (3201245)Instructions burned: 159 (million) 28.89/4.74 % (3201248)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 28.89/4.74 % (3201248)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=4063864893:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_1767 on theBenchmark for (1767ds/252Mi) 28.89/4.74 % (3201236)Instruction limit reached! 28.89/4.74 % (3201236)------------------------------ 28.89/4.74 % (3201236)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 28.89/4.74 % (3201236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 28.89/4.74 % (3201236)CaDiCaL version: 2.1.3 28.89/4.74 % (3201236)Termination reason: Instruction limit 28.89/4.74 % (3201236)Termination phase: Saturation 28.89/4.74 % (3201236)Time elapsed: 0.191 s 28.89/4.74 % (3201236)Peak memory usage: 12 MB 28.89/4.74 % (3201236)Instructions burned: 271 (million) 28.89/4.74 % (3201250)lrs+10_1_cnfonf=off:si=on:sos=on:uwa=off:random_seed=2808065654:i=213:rtra=on:ss=axioms_1766 on theBenchmark for (1766ds/213Mi) 28.89/4.74 % (3201241)Instruction limit reached! 28.89/4.74 % (3201241)------------------------------ 28.89/4.74 % (3201241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 28.89/4.74 % (3201241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 28.89/4.74 % (3201241)CaDiCaL version: 2.1.3 28.89/4.74 % (3201241)Termination reason: Instruction limit 28.89/4.74 % (3201241)Termination phase: Saturation 28.89/4.74 % (3201241)Time elapsed: 0.199 s 28.89/4.74 % (3201241)Peak memory usage: 14 MB 28.89/4.74 % (3201241)Instructions burned: 366 (million) 28.89/4.74 % (3201253)dis+1010_28_sil=128000:tgt=full:plsq=on:plsqc=1:cnfonf=off:si=on:plsqr=128,1:uwa=off:slsqc=2:sac=on:slsq=on:random_seed=4001820150:st=3:i=160:s2at=3:bd=preordered:nm=16:rtra=on:ss=axioms:ntd=on_1765 on theBenchmark for (1765ds/160Mi) 28.89/4.74 % (3201250)Refutation not found, incomplete strategy 28.89/4.74 % (3201250)------------------------------ 28.89/4.74 % (3201250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 28.89/4.74 % (3201250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 28.89/4.74 % (3201250)CaDiCaL version: 2.1.3 28.89/4.74 % (3201250)Termination reason: Refutation not found, incomplete strategy 28.89/4.74 % (3201250)Time elapsed: 0.102 s 28.89/4.74 % (3201250)Peak memory usage: 14 MB 28.89/4.74 % (3201250)Instructions burned: 139 (million) 28.89/4.74 % (3201250)------------------------------ 28.89/4.74 % (3201250)------------------------------ 28.89/4.74 % (3201253)Instruction limit reached! 28.89/4.74 % (3201253)------------------------------ 28.89/4.74 % (3201253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 28.89/4.74 % (3201253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 28.89/4.74 % (3201253)CaDiCaL version: 2.1.3 28.89/4.74 % (3201253)Termination reason: Instruction limit 28.89/4.74 % (3201253)Termination phase: Saturation 28.89/4.74 % (3201253)Time elapsed: 0.060 s 28.89/4.74 % (3201253)Peak memory usage: 13 MB 28.89/4.74 % (3201253)Instructions burned: 162 (million) 28.89/4.74 % (3201248)Instruction limit reached! 28.89/4.74 % (3201248)------------------------------ 28.89/4.74 % (3201248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 28.89/4.74 % (3201248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 28.89/4.74 % (3201248)CaDiCaL version: 2.1.3 28.89/4.74 % (3201248)Termination reason: Instruction limit 28.89/4.74 % (3201248)Termination phase: Saturation 28.89/4.74 % (3201248)Time elapsed: 0.172 s 28.89/4.74 % (3201248)Peak memory usage: 12 MB 28.89/4.74 % (3201248)Instructions burned: 252 (million) 28.89/4.74 % (3201256)WARNING Broken Constraint: if ho_split_queue_layered_arrangement(off) has been set then ho_split_queue(off) is equal to on 28.89/4.74 % (3201256)ott+1010_40_sil=128000:tgt=full:plsq=on:plsqc=5:si=on:sos=all:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=188586123:i=237:hsql=off:fgj=on:piset=all_but_not_eq:bd=preordered:av=off:rtra=on:ss=axioms:sgt=4:rawr=on_1765 on theBenchmark for (1765ds/237Mi) 29.99/4.88 % (3201255)lrs+1010_2:3_sil=128000:cnfonf=off:e2e=on:si=on:sp=unary_first:uwa=off:br=off:lftc=80:random_seed=3333035879:hsq=on:hsqr=16,1:i=763:kws=inv_frequency:piset=and:bd=all:rtra=on:ntd=on_1765 on theBenchmark for (1765ds/763Mi) 29.99/4.88 % (3201257)dis+1002_1_drc=ordering:cnfonf=lazy_not_gen_be_off:si=on:lma=off:cbe=off:uwa=off:random_seed=1217135788:s2a=on:i=386:rtra=on:ntd=on_1765 on theBenchmark for (1765ds/386Mi) 29.99/4.88 % (3201256)Refutation not found, incomplete strategy 29.99/4.88 % (3201256)------------------------------ 29.99/4.88 % (3201256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 29.99/4.88 % (3201256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 29.99/4.88 % (3201256)CaDiCaL version: 2.1.3 29.99/4.88 % (3201256)Termination reason: Refutation not found, incomplete strategy 29.99/4.88 % (3201256)Time elapsed: 0.081 s 29.99/4.88 % (3201256)Peak memory usage: 16 MB 29.99/4.88 % (3201256)Instructions burned: 212 (million) 29.99/4.88 % (3201256)------------------------------ 29.99/4.88 % (3201256)------------------------------ 29.99/4.88 % (3201261)dis+10_128_to=lpo:sil=128000:si=on:spb=intro:uwa=off:random_seed=3338298163:i=300:piset=and:nm=32:rtra=on_1764 on theBenchmark for (1764ds/300Mi) 29.99/4.88 % (3201261)Instruction limit reached! 29.99/4.88 % (3201261)------------------------------ 29.99/4.88 % (3201261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 29.99/4.88 % (3201261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 29.99/4.88 % (3201261)CaDiCaL version: 2.1.3 29.99/4.88 % (3201261)Termination reason: Instruction limit 29.99/4.88 % (3201261)Termination phase: Saturation 29.99/4.88 % (3201261)Time elapsed: 0.122 s 29.99/4.88 % (3201261)Peak memory usage: 13 MB 29.99/4.88 % (3201261)Instructions burned: 302 (million) 29.99/4.88 % (3201265)dis+1010_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:urr=on:random_seed=4273268283:st=5:s2a=on:i=567:sd=2:rtra=on:ss=axioms_1762 on theBenchmark for (1762ds/567Mi) 29.99/4.88 % (3201257)Instruction limit reached! 29.99/4.88 % (3201257)------------------------------ 29.99/4.88 % (3201257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 29.99/4.88 % (3201257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 29.99/4.88 % (3201257)CaDiCaL version: 2.1.3 29.99/4.88 % (3201257)Termination reason: Instruction limit 29.99/4.88 % (3201257)Termination phase: Saturation 29.99/4.88 % (3201257)Time elapsed: 0.277 s 29.99/4.88 % (3201257)Peak memory usage: 13 MB 29.99/4.88 % (3201257)Instructions burned: 386 (million) 29.99/4.88 % (3201268)lrs+1010_1_si=on:uwa=one_side_interpreted:random_seed=3891466536:s2a=on:i=379:sd=1:rtra=on:ss=axioms:sgt=128_1761 on theBenchmark for (1761ds/379Mi) 29.99/4.88 % (3201255)Refutation not found, incomplete strategy 29.99/4.88 % (3201255)------------------------------ 29.99/4.88 % (3201255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 29.99/4.88 % (3201255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 29.99/4.88 % (3201255)CaDiCaL version: 2.1.3 29.99/4.88 % (3201255)Termination reason: Refutation not found, incomplete strategy 29.99/4.88 % (3201255)Time elapsed: 0.320 s 29.99/4.88 % (3201255)Peak memory usage: 17 MB 29.99/4.88 % (3201255)Instructions burned: 449 (million) 29.99/4.88 % (3201255)------------------------------ 29.99/4.88 % (3201255)------------------------------ 29.99/4.88 % (3201270)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=2733995348:s2a=on:i=429:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_1761 on theBenchmark for (1761ds/429Mi) 29.99/4.88 % (3201203)Instruction limit reached! 29.99/4.88 % (3201203)------------------------------ 29.99/4.88 % (3201203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 29.99/4.88 % (3201203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 29.99/4.88 % (3201203)CaDiCaL version: 2.1.3 29.99/4.88 % (3201203)Termination reason: Instruction limit 29.99/4.88 % (3201203)Termination phase: Saturation 29.99/4.88 % (3201203)Time elapsed: 1.433 s 29.99/4.88 % (3201203)Peak memory usage: 18 MB 29.99/4.88 % (3201203)Instructions burned: 2187 (million) 29.99/4.88 % (3201273)ott+10_1_to=lpo:sil=128000:e2e=on:si=on:sos=on:uwa=off:sac=on:random_seed=1727050637:i=478:bd=all:rtra=on_1760 on theBenchmark for (1760ds/478Mi) 32.65/5.21 % (3201265)Refutation not found, incomplete strategy 32.65/5.21 % (3201265)------------------------------ 32.65/5.21 % (3201265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 32.65/5.21 % (3201265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 32.65/5.21 % (3201265)CaDiCaL version: 2.1.3 32.65/5.21 % (3201265)Termination reason: Refutation not found, incomplete strategy 32.65/5.21 % (3201265)Time elapsed: 0.226 s 32.65/5.21 % (3201265)Peak memory usage: 15 MB 32.65/5.21 % (3201265)Instructions burned: 358 (million) 32.65/5.21 % (3201265)------------------------------ 32.65/5.21 % (3201265)------------------------------ 32.65/5.21 % (3201275)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3007686189:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1760 on theBenchmark for (1760ds/445Mi) 32.65/5.21 % (3201268)Instruction limit reached! 32.65/5.21 % (3201268)------------------------------ 32.65/5.21 % (3201268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 32.65/5.21 % (3201268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 32.65/5.21 % (3201268)CaDiCaL version: 2.1.3 32.65/5.21 % (3201268)Termination reason: Instruction limit 32.65/5.21 % (3201268)Termination phase: Saturation 32.65/5.21 % (3201268)Time elapsed: 0.257 s 32.65/5.21 % (3201268)Peak memory usage: 14 MB 32.65/5.21 % (3201268)Instructions burned: 380 (million) 32.65/5.21 % (3201270)Instruction limit reached! 32.65/5.21 % (3201270)------------------------------ 32.65/5.21 % (3201270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 32.65/5.21 % (3201270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 32.65/5.21 % (3201270)CaDiCaL version: 2.1.3 32.65/5.21 % (3201270)Termination reason: Instruction limit 32.65/5.21 % (3201270)Termination phase: Saturation 32.65/5.21 % (3201270)Time elapsed: 0.230 s 32.65/5.21 % (3201270)Peak memory usage: 15 MB 32.65/5.21 % (3201270)Instructions burned: 430 (million) 32.65/5.21 % (3201281)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=831663241:i=302:sd=2:bd=preordered:rtra=on:ss=axioms_1759 on theBenchmark for (1759ds/302Mi) 32.65/5.21 % (3201280)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=1716494670:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_1759 on theBenchmark for (1759ds/71Mi) 32.65/5.21 % (3201280)Instruction limit reached! 32.65/5.21 % (3201280)------------------------------ 32.65/5.21 % (3201280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 32.65/5.21 % (3201280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 32.65/5.21 % (3201280)CaDiCaL version: 2.1.3 32.65/5.21 % (3201280)Termination reason: Instruction limit 32.65/5.21 % (3201280)Termination phase: Property scanning 32.65/5.21 % (3201280)Time elapsed: 0.053 s 32.65/5.21 % (3201280)Peak memory usage: 10 MB 32.65/5.21 % (3201280)Instructions burned: 72 (million) 32.65/5.21 % (3201285)lrs+10_1_sil=128000:fde=none:cnfonf=off:si=on:uwa=off:random_seed=3122118764:s2a=on:i=4980:sd=2:bd=all:rtra=on:ss=axioms:ntd=on_1758 on theBenchmark for (1758ds/4980Mi) 32.65/5.21 % (3201275)Instruction limit reached! 32.65/5.21 % (3201275)------------------------------ 32.65/5.21 % (3201275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 32.65/5.22 % (3201275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 32.65/5.22 % (3201275)CaDiCaL version: 2.1.3 32.65/5.22 % (3201275)Termination reason: Instruction limit 32.65/5.22 % (3201275)Termination phase: Saturation 32.65/5.22 % (3201275)Time elapsed: 0.239 s 32.65/5.22 % (3201275)Peak memory usage: 15 MB 32.65/5.22 % (3201275)Instructions burned: 445 (million) 32.65/5.22 % (3201281)Refutation not found, incomplete strategy 32.65/5.22 % (3201281)------------------------------ 32.65/5.22 % (3201281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 32.65/5.22 % (3201281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 32.65/5.22 % (3201281)CaDiCaL version: 2.1.3 32.65/5.22 % (3201281)Termination reason: Refutation not found, incomplete strategy 32.65/5.22 % (3201281)Time elapsed: 0.136 s 32.65/5.22 % (3201281)Peak memory usage: 16 MB 32.65/5.22 % (3201281)Instructions burned: 204 (million) 32.65/5.22 % (3201281)------------------------------ 32.65/5.22 % (3201281)------------------------------ 32.65/5.22 % (3201289)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 33.78/5.42 % (3201289)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 33.78/5.42 % (3201289)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4139138219:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1757 on theBenchmark for (1757ds/100Mi) 33.78/5.42 % (3201290)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2268871717:i=76:piset=equals:rtra=on:ntd=on_1757 on theBenchmark for (1757ds/76Mi) 33.78/5.42 % (3201273)Instruction limit reached! 33.78/5.42 % (3201273)------------------------------ 33.78/5.42 % (3201273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 33.78/5.42 % (3201273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 33.78/5.42 % (3201273)CaDiCaL version: 2.1.3 33.78/5.42 % (3201273)Termination reason: Instruction limit 33.78/5.42 % (3201273)Termination phase: Saturation 33.78/5.42 % (3201273)Time elapsed: 0.348 s 33.78/5.42 % (3201273)Peak memory usage: 18 MB 33.78/5.42 % (3201273)Instructions burned: 479 (million) 33.78/5.42 % (3201294)lrs+10_1_to=lpo:sil=128000:cnfonf=off:si=on:sp=unary_first:sos=all:spb=goal:uwa=off:random_seed=442012228:i=289:rtra=on_1756 on theBenchmark for (1756ds/289Mi) 33.78/5.42 % (3201290)Instruction limit reached! 33.78/5.42 % (3201290)------------------------------ 33.78/5.42 % (3201290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 33.78/5.42 % (3201290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 33.78/5.42 % (3201290)CaDiCaL version: 2.1.3 33.78/5.42 % (3201290)Termination reason: Instruction limit 33.78/5.42 % (3201290)Termination phase: Property scanning 33.78/5.42 % (3201290)Time elapsed: 0.056 s 33.78/5.42 % (3201290)Peak memory usage: 10 MB 33.78/5.42 % (3201290)Instructions burned: 77 (million) 33.78/5.42 % (3201289)Instruction limit reached! 33.78/5.42 % (3201289)------------------------------ 33.78/5.42 % (3201289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 33.78/5.42 % (3201289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 33.78/5.42 % (3201289)CaDiCaL version: 2.1.3 33.78/5.42 % (3201289)Termination reason: Instruction limit 33.78/5.42 % (3201289)Termination phase: Saturation 33.78/5.42 % (3201289)Time elapsed: 0.074 s 33.78/5.42 % (3201289)Peak memory usage: 11 MB 33.78/5.42 % (3201289)Instructions burned: 100 (million) 33.78/5.42 % (3201285)Refutation not found, incomplete strategy 33.78/5.42 % (3201285)------------------------------ 33.78/5.42 % (3201285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 33.78/5.42 % (3201285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 33.78/5.42 % (3201285)CaDiCaL version: 2.1.3 33.78/5.42 % (3201285)Termination reason: Refutation not found, incomplete strategy 33.78/5.42 % (3201285)Time elapsed: 0.163 s 33.78/5.42 % (3201285)Peak memory usage: 16 MB 33.78/5.42 % (3201285)Instructions burned: 225 (million) 33.78/5.42 % (3201285)------------------------------ 33.78/5.42 % (3201285)------------------------------ 33.78/5.42 % (3201297)lrs+2_64_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_first:bsr=unit_only:cbe=off:uwa=interpreted_only:nwc=0.5:slsqc=5:sac=on:slsq=on:random_seed=3147388568:i=493:s2at=5:kws=frequency:doe=on:rtra=on:er=known_1756 on theBenchmark for (1756ds/493Mi) 33.78/5.42 % (3201299)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs 33.78/5.42 % (3201298)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=2091346157:cond=on:i=34:hud=10:nm=10:rtra=on_1756 on theBenchmark for (1756ds/34Mi) 33.78/5.42 % (3201299)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=1702281298:i=372:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_1756 on theBenchmark for (1756ds/372Mi) 33.78/5.42 % (3201298)Instruction limit reached! 33.78/5.42 % (3201298)------------------------------ 33.78/5.42 % (3201298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 34.61/5.70 % (3201298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 34.61/5.70 % (3201298)CaDiCaL version: 2.1.3 34.61/5.70 % (3201298)Termination reason: Instruction limit 34.61/5.70 % (3201298)Termination phase: Property scanning 34.61/5.70 % (3201298)Time elapsed: 0.026 s 34.61/5.70 % (3201298)Peak memory usage: 10 MB 34.61/5.70 % (3201298)Instructions burned: 34 (million) 34.61/5.70 % (3201303)lrs+1002_1024_sil=128000:tgt=ground:e2e=on:si=on:uwa=interpreted_only:fd=off:nwc=1:random_seed=3846689815:cts=off:avsq=on:i=670:avsqr=1,16:nm=16:rtra=on_1755 on theBenchmark for (1755ds/670Mi) 34.61/5.70 % (3201294)Instruction limit reached! 34.61/5.70 % (3201294)------------------------------ 34.61/5.70 % (3201294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 34.61/5.70 % (3201294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 34.61/5.70 % (3201294)CaDiCaL version: 2.1.3 34.61/5.70 % (3201294)Termination reason: Instruction limit 34.61/5.70 % (3201294)Termination phase: Saturation 34.61/5.70 % (3201294)Time elapsed: 0.199 s 34.61/5.70 % (3201294)Peak memory usage: 14 MB 34.61/5.70 % (3201294)Instructions burned: 292 (million) 34.61/5.70 % (3201225)Instruction limit reached! 34.61/5.70 % (3201225)------------------------------ 34.61/5.70 % (3201225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 34.61/5.70 % (3201225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 34.61/5.70 % (3201225)CaDiCaL version: 2.1.3 34.61/5.70 % (3201225)Termination reason: Instruction limit 34.61/5.70 % (3201225)Termination phase: Saturation 34.61/5.70 % (3201225)Time elapsed: 1.714 s 34.61/5.70 % (3201225)Peak memory usage: 19 MB 34.61/5.70 % (3201225)Instructions burned: 2472 (million) 34.61/5.70 % (3201308)dis+10_128_sil=128000:tgt=full:plsq=on:plsqc=3:cnfonf=off:si=on:sp=arity:spb=goal_then_units:uwa=one_side_interpreted:nwc=1.5:random_seed=3593920577:i=857:add=off:kws=frequency:rtra=on:ntd=on_1754 on theBenchmark for (1754ds/857Mi) 34.61/5.70 % (3201307)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=615318912:hsq=on:st=2:i=647:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1754 on theBenchmark for (1754ds/647Mi) 34.61/5.70 % (3201299)Instruction limit reached! 34.61/5.70 % (3201299)------------------------------ 34.61/5.70 % (3201299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 34.61/5.70 % (3201299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 34.61/5.70 % (3201299)CaDiCaL version: 2.1.3 34.61/5.70 % (3201299)Termination reason: Instruction limit 34.61/5.70 % (3201299)Termination phase: Saturation 34.61/5.70 % (3201299)Time elapsed: 0.244 s 34.61/5.70 % (3201299)Peak memory usage: 15 MB 34.61/5.70 % (3201299)Instructions burned: 372 (million) 34.61/5.70 % (3201313)dis+1010_4_anc=all_dependent:to=lpo:sil=128000:fde=unused:cnfonf=conj_eager:si=on:sp=reverse_frequency:lma=off:spb=intro:cbe=off:uwa=off:random_seed=1009935276:i=693:add=off:fsr=off:rtra=on:fe=abstraction:ntd=on_1753 on theBenchmark for (1753ds/693Mi) 34.61/5.70 % (3201307)Refutation not found, incomplete strategy 34.61/5.70 % (3201307)------------------------------ 34.61/5.70 % (3201307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 34.61/5.70 % (3201307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 34.61/5.70 % (3201307)CaDiCaL version: 2.1.3 34.61/5.70 % (3201307)Termination reason: Refutation not found, incomplete strategy 34.61/5.70 % (3201307)Time elapsed: 0.148 s 34.61/5.70 % (3201307)Peak memory usage: 14 MB 34.61/5.70 % (3201307)Instructions burned: 203 (million) 34.61/5.70 % (3201307)------------------------------ 34.61/5.70 % (3201307)------------------------------ 34.61/5.70 % (3201297)Instruction limit reached! 34.61/5.70 % (3201297)------------------------------ 34.61/5.70 % (3201297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 34.61/5.70 % (3201297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 34.61/5.70 % (3201297)CaDiCaL version: 2.1.3 34.61/5.70 % (3201297)Termination reason: Instruction limit 34.61/5.70 % (3201297)Termination phase: Saturation 34.61/5.70 % (3201297)Time elapsed: 0.359 s 34.61/5.70 % (3201297)Peak memory usage: 14 MB 34.61/5.70 % (3201297)Instructions burned: 493 (million) 34.61/5.70 % (3201315)dis+10_7_sil=128000:cnfonf=lazy_gen:si=on:sos=on:random_seed=2864477013:i=285:hud=10:bd=all:rtra=on:ss=axioms_1752 on theBenchmark for (1752ds/285Mi) 38.98/6.16 % (3201316)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on 38.98/6.16 % (3201316)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=1383598206:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_1752 on theBenchmark for (1752ds/52Mi) 38.98/6.16 % (3201316)Instruction limit reached! 38.98/6.16 % (3201316)------------------------------ 38.98/6.16 % (3201316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 38.98/6.16 % (3201316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 38.98/6.16 % (3201316)CaDiCaL version: 2.1.3 38.98/6.16 % (3201316)Termination reason: Instruction limit 38.98/6.16 % (3201316)Termination phase: shuffling 38.98/6.16 % (3201316)Time elapsed: 0.030 s 38.98/6.16 % (3201316)Peak memory usage: 10 MB 38.98/6.16 % (3201316)Instructions burned: 52 (million) 38.98/6.16 % (3201320)dis+10_1_si=on:random_seed=2889364250:i=407:sd=4:rtra=on:ss=axioms:sgt=20_1752 on theBenchmark for (1752ds/407Mi) 38.98/6.16 % (3201308)Refutation not found, incomplete strategy 38.98/6.16 % (3201308)------------------------------ 38.98/6.16 % (3201308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 38.98/6.16 % (3201308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 38.98/6.16 % (3201308)CaDiCaL version: 2.1.3 38.98/6.16 % (3201308)Termination reason: Refutation not found, incomplete strategy 38.98/6.16 % (3201308)Time elapsed: 0.264 s 38.98/6.16 % (3201308)Peak memory usage: 16 MB 38.98/6.16 % (3201308)Instructions burned: 432 (million) 38.98/6.16 % (3201308)------------------------------ 38.98/6.16 % (3201308)------------------------------ 38.98/6.16 % (3201322)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=878669173:i=2240:bs=unit_only:ins=25:rtra=on:ntd=on_1751 on theBenchmark for (1751ds/2240Mi) 38.98/6.16 % (3201315)Refutation not found, incomplete strategy 38.98/6.16 % (3201315)------------------------------ 38.98/6.16 % (3201315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 38.98/6.16 % (3201315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 38.98/6.16 % (3201315)CaDiCaL version: 2.1.3 38.98/6.16 % (3201315)Termination reason: Refutation not found, incomplete strategy 38.98/6.16 % (3201315)Time elapsed: 0.116 s 38.98/6.16 % (3201315)Peak memory usage: 16 MB 38.98/6.16 % (3201315)Instructions burned: 154 (million) 38.98/6.16 % (3201315)------------------------------ 38.98/6.16 % (3201315)------------------------------ 38.98/6.16 % (3201325)lrs+10_1_sil=128000:e2e=on:si=on:uwa=interpreted_only:random_seed=3573032893:st=2:i=336:sd=1:rtra=on:ss=axioms:ntd=on_1751 on theBenchmark for (1751ds/336Mi) 38.98/6.16 % (3201303)Instruction limit reached! 38.98/6.16 % (3201303)------------------------------ 38.98/6.16 % (3201303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 38.98/6.16 % (3201303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 38.98/6.16 % (3201303)CaDiCaL version: 2.1.3 38.98/6.16 % (3201303)Termination reason: Instruction limit 38.98/6.16 % (3201303)Termination phase: Saturation 38.98/6.16 % (3201303)Time elapsed: 0.453 s 38.98/6.16 % (3201303)Peak memory usage: 16 MB 38.98/6.16 % (3201303)Instructions burned: 671 (million) 38.98/6.16 % (3201325)Refutation not found, incomplete strategy 38.98/6.16 % (3201325)------------------------------ 38.98/6.16 % (3201325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 38.98/6.16 % (3201325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 38.98/6.16 % (3201325)CaDiCaL version: 2.1.3 38.98/6.16 % (3201325)Termination reason: Refutation not found, incomplete strategy 38.98/6.16 % (3201325)Time elapsed: 0.039 s 38.98/6.16 % (3201325)Peak memory usage: 14 MB 38.98/6.16 % (3201325)Instructions burned: 190 (million) 38.98/6.16 % (3201325)------------------------------ 38.98/6.16 % (3201325)------------------------------ 38.98/6.16 % (3201327)lrs+10_1_to=lpo:sil=128000:fde=none:cnfonf=off:si=on:sp=unary_first:urr=on:uwa=one_side_constant:random_seed=380041708:s2a=on:i=1142:s2at=3:bd=all:rtra=on_1751 on theBenchmark for (1751ds/1142Mi) 38.98/6.16 % (3201328)dis+1002_1_sil=128000:si=on:uwa=off:random_seed=1430609151:st=3:i=376:sd=4:rtra=on:ss=axioms:ntd=on_1750 on theBenchmark for (1750ds/376Mi) 40.23/6.37 % (3201073)Instruction limit reached! 40.23/6.37 % (3201073)------------------------------ 40.23/6.37 % (3201073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 40.23/6.37 % (3201073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 40.23/6.37 % (3201073)CaDiCaL version: 2.1.3 40.23/6.37 % (3201073)Termination reason: Instruction limit 40.23/6.37 % (3201073)Termination phase: Saturation 40.23/6.37 % (3201073)Time elapsed: 4.185 s 40.23/6.37 % (3201073)Peak memory usage: 30 MB 40.23/6.37 % (3201073)Instructions burned: 5756 (million) 40.23/6.37 % (3201328)Refutation not found, incomplete strategy 40.23/6.37 % (3201328)------------------------------ 40.23/6.37 % (3201328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 40.23/6.37 % (3201328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 40.23/6.37 % (3201328)CaDiCaL version: 2.1.3 40.23/6.37 % (3201328)Termination reason: Refutation not found, incomplete strategy 40.23/6.37 % (3201328)Time elapsed: 0.146 s 40.23/6.37 % (3201328)Peak memory usage: 15 MB 40.23/6.37 % (3201328)Instructions burned: 202 (million) 40.23/6.37 % (3201328)------------------------------ 40.23/6.37 % (3201328)------------------------------ 40.23/6.37 % (3201320)Instruction limit reached! 40.23/6.37 % (3201320)------------------------------ 40.23/6.37 % (3201320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 40.23/6.37 % (3201320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 40.23/6.37 % (3201320)CaDiCaL version: 2.1.3 40.23/6.37 % (3201320)Termination reason: Instruction limit 40.23/6.37 % (3201320)Termination phase: Saturation 40.23/6.37 % (3201320)Time elapsed: 0.283 s 40.23/6.37 % (3201320)Peak memory usage: 15 MB 40.23/6.37 % (3201320)Instructions burned: 408 (million) 40.23/6.37 % (3201334)dis+1002_4:1_anc=none:sil=128000:sas=cadical:si=on:sp=weighted_frequency:sos=on:uwa=one_side_interpreted:random_seed=3491133144:i=766:bd=all:rtra=on_1749 on theBenchmark for (1749ds/766Mi) 40.23/6.37 % (3201335)WARNING Broken Constraint: if avatar_split_queue_cutoffs(4) has been set then avatar_split_queue(off) is equal to on 40.23/6.37 % (3201336)dis+1010_1024_sil=128000:plsq=on:plsqc=1:e2e=on:si=on:lma=off:plsqr=64,1:uwa=interpreted_only:fd=off:random_seed=1151608653:i=6359:add=on:kws=inv_frequency:aac=none:rtra=on:c=on:er=filter:ntd=on_1749 on theBenchmark for (1749ds/6359Mi) 40.23/6.37 % (3201335)lrs+10_1_to=kbo:si=on:sp=const_frequency:sos=on:spb=non_intro:uwa=hol:avsqc=4:random_seed=339385222:st=3:uwa_fpi=on:i=959:fgj=on:piset=pi_sigma:hud=5:nm=16:rtra=on:fe=abstraction:ss=axioms:ixr=off:ntd=on_1749 on theBenchmark for (1749ds/959Mi) 40.23/6.37 % (3201313)Instruction limit reached! 40.23/6.37 % (3201313)------------------------------ 40.23/6.37 % (3201313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 40.23/6.37 % (3201313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 40.23/6.37 % (3201313)CaDiCaL version: 2.1.3 40.23/6.37 % (3201313)Termination reason: Instruction limit 40.23/6.37 % (3201313)Termination phase: Saturation 40.23/6.37 % (3201313)Time elapsed: 0.527 s 40.23/6.37 % (3201313)Peak memory usage: 15 MB 40.23/6.37 % (3201313)Instructions burned: 693 (million) 40.23/6.37 % (3201341)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2007345113:st=4:i=35:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_1748 on theBenchmark for (1748ds/35Mi) 40.23/6.37 % (3201341)Instruction limit reached! 40.23/6.37 % (3201341)------------------------------ 40.23/6.37 % (3201341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 40.23/6.37 % (3201341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 40.23/6.37 % (3201341)CaDiCaL version: 2.1.3 40.23/6.37 % (3201341)Termination reason: Instruction limit 40.23/6.37 % (3201341)Termination phase: shuffling 40.23/6.37 % (3201341)Time elapsed: 0.007 s 40.23/6.37 % (3201341)Peak memory usage: 10 MB 40.23/6.37 % (3201341)Instructions burned: 41 (million) 40.23/6.37 % (3201343)dis+10_1_sfv=off:sil=128000:cnfonf=lazy_gen:si=on:uwa=off:nwc=1:chr=on:random_seed=494273364:hsq=on:hsqr=1,8:i=53:hsql=off:bd=all:rtra=on:ixr=off_1747 on theBenchmark for (1747ds/53Mi) 40.23/6.37 % (3201343)Instruction limit reached! 40.23/6.37 % (3201343)------------------------------ 40.23/6.37 % (3201343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 41.77/6.56 % (3201343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 41.77/6.56 % (3201343)CaDiCaL version: 2.1.3 41.77/6.56 % (3201343)Termination reason: Instruction limit 41.77/6.56 % (3201343)Termination phase: Property scanning 41.77/6.56 % (3201343)Time elapsed: 0.011 s 41.77/6.56 % (3201343)Peak memory usage: 10 MB 41.77/6.56 % (3201343)Instructions burned: 54 (million) 41.77/6.56 % (3201345)dis+21_1_sil=128000:tgt=full:fde=none:e2e=on:si=on:urr=on:uwa=interpreted_only:s2agt=32:sac=on:random_seed=1336995825:s2a=on:i=876:s2at=6:nm=2:rtra=on_1747 on theBenchmark for (1747ds/876Mi) 41.77/6.56 % (3201345)Instruction limit reached! 41.77/6.56 % (3201345)------------------------------ 41.77/6.56 % (3201345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 41.77/6.56 % (3201345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 41.77/6.56 % (3201345)CaDiCaL version: 2.1.3 41.77/6.56 % (3201345)Termination reason: Instruction limit 41.77/6.56 % (3201345)Termination phase: Saturation 41.77/6.56 % (3201345)Time elapsed: 0.229 s 41.77/6.56 % (3201345)Peak memory usage: 17 MB 41.77/6.56 % (3201345)Instructions burned: 878 (million) 41.77/6.56 % (3201351)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=349499612:i=57:ep=R:rtra=on:ntd=on_1745 on theBenchmark for (1745ds/57Mi) 41.77/6.56 % (3201351)Instruction limit reached! 41.77/6.56 % (3201351)------------------------------ 41.77/6.56 % (3201351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 41.77/6.56 % (3201351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 41.77/6.56 % (3201351)CaDiCaL version: 2.1.3 41.77/6.56 % (3201351)Termination reason: Instruction limit 41.77/6.56 % (3201351)Termination phase: Property scanning 41.77/6.56 % (3201351)Time elapsed: 0.022 s 41.77/6.56 % (3201351)Peak memory usage: 10 MB 41.77/6.56 % (3201351)Instructions burned: 59 (million) 41.77/6.56 % (3201354)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on 41.77/6.56 % (3201327)Instruction limit reached! 41.77/6.56 % (3201327)------------------------------ 41.77/6.56 % (3201327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 41.77/6.56 % (3201327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 41.77/6.56 % (3201327)CaDiCaL version: 2.1.3 41.77/6.56 % (3201327)Termination reason: Instruction limit 41.77/6.56 % (3201327)Termination phase: Saturation 41.77/6.56 % (3201327)Time elapsed: 0.607 s 41.77/6.56 % (3201327)Peak memory usage: 18 MB 41.77/6.56 % (3201327)Instructions burned: 1144 (million) 41.77/6.56 % (3201354)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=3161216697:i=306:bd=all:rtra=on_1745 on theBenchmark for (1745ds/306Mi) 41.77/6.56 % (3201355)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=2868153398:i=262:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_1744 on theBenchmark for (1744ds/262Mi) 41.77/6.56 % (3201355)Refutation not found, incomplete strategy 41.77/6.56 % (3201355)------------------------------ 41.77/6.56 % (3201355)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 41.77/6.56 % (3201355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 41.77/6.56 % (3201355)CaDiCaL version: 2.1.3 41.77/6.56 % (3201355)Termination reason: Refutation not found, incomplete strategy 41.77/6.56 % (3201355)Time elapsed: 0.123 s 41.77/6.56 % (3201355)Peak memory usage: 16 MB 41.77/6.56 % (3201355)Instructions burned: 220 (million) 41.77/6.56 % (3201355)------------------------------ 41.77/6.56 % (3201355)------------------------------ 41.77/6.56 % (3201354)Instruction limit reached! 41.77/6.56 % (3201354)------------------------------ 41.77/6.56 % (3201354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 41.77/6.56 % (3201354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 41.77/6.56 % (3201354)CaDiCaL version: 2.1.3 41.77/6.56 % (3201354)Termination reason: Instruction limit 41.77/6.56 % (3201354)Termination phase: Saturation 41.77/6.56 % (3201354)Time elapsed: 0.149 s 41.77/6.56 % (3201354)Peak memory usage: 15 MB 41.77/6.56 % (3201354)Instructions burned: 313 (million) 41.77/6.56 % (3201335)Refutation not found, incomplete strategy 41.77/6.56 % (3201335)------------------------------ 41.77/6.56 % (3201335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 42.34/6.67 % (3201335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 42.34/6.67 % (3201335)CaDiCaL version: 2.1.3 42.34/6.67 % (3201335)Termination reason: Refutation not found, incomplete strategy 42.34/6.67 % (3201335)Time elapsed: 0.563 s 42.34/6.67 % (3201335)Peak memory usage: 18 MB 42.34/6.67 % (3201335)Instructions burned: 791 (million) 42.34/6.67 % (3201335)------------------------------ 42.34/6.67 % (3201335)------------------------------ 42.34/6.67 % (3201334)Instruction limit reached! 42.34/6.67 % (3201334)------------------------------ 42.34/6.67 % (3201334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 42.34/6.67 % (3201334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 42.34/6.67 % (3201334)CaDiCaL version: 2.1.3 42.34/6.67 % (3201334)Termination reason: Instruction limit 42.34/6.67 % (3201334)Termination phase: Saturation 42.34/6.67 % (3201334)Time elapsed: 0.584 s 42.34/6.67 % (3201334)Peak memory usage: 19 MB 42.34/6.67 % (3201334)Instructions burned: 766 (million) 42.34/6.67 % (3201362)dis+10_1_sil=128000:plsq=on:si=on:plsqr=32,1:uwa=off:random_seed=3060439327:s2a=on:i=381:rtra=on_1743 on theBenchmark for (1743ds/381Mi) 42.34/6.67 % (3201361)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on 42.34/6.67 % (3201361)ott+1002_16_sil=128000:si=on:random_seed=2915454051:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_1743 on theBenchmark for (1743ds/409Mi) 42.34/6.67 % (3201364)lrs+10_1_sil=128000:fde=none:si=on:sos=on:spb=goal_then_units:urr=on:random_seed=2658290480:i=240:kws=inv_precedence:rtra=on_1743 on theBenchmark for (1743ds/240Mi) 42.34/6.67 % (3201363)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=868659672:cond=on:i=324:rtra=on:ntd=on_1743 on theBenchmark for (1743ds/324Mi) 42.34/6.67 % (3201362)Instruction limit reached! 42.34/6.67 % (3201362)------------------------------ 42.34/6.67 % (3201362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 42.34/6.67 % (3201362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 42.34/6.67 % (3201362)CaDiCaL version: 2.1.3 42.34/6.67 % (3201362)Termination reason: Instruction limit 42.34/6.67 % (3201362)Termination phase: Saturation 42.34/6.67 % (3201362)Time elapsed: 0.100 s 42.34/6.67 % (3201362)Peak memory usage: 14 MB 42.34/6.67 % (3201362)Instructions burned: 383 (million) 42.34/6.67 % (3201371)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on 42.34/6.67 % (3201371)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=1357958002:cts=off:uwa_fpi=on:i=124:av=off:fsr=off:rtra=on:ntd=on_1741 on theBenchmark for (1741ds/124Mi) 42.34/6.67 % (3201364)Refutation not found, incomplete strategy 42.34/6.67 % (3201364)------------------------------ 42.34/6.67 % (3201364)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 42.34/6.67 % (3201364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 42.34/6.67 % (3201364)CaDiCaL version: 2.1.3 42.34/6.67 % (3201364)Termination reason: Refutation not found, incomplete strategy 42.34/6.67 % (3201364)Time elapsed: 0.108 s 42.34/6.67 % (3201364)Peak memory usage: 15 MB 42.34/6.67 % (3201364)Instructions burned: 151 (million) 42.34/6.67 % (3201371)Instruction limit reached! 42.34/6.67 % (3201371)------------------------------ 42.34/6.67 % (3201371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 42.34/6.67 % (3201371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 42.34/6.67 % (3201371)CaDiCaL version: 2.1.3 42.34/6.67 % (3201371)Termination reason: Instruction limit 42.34/6.67 % (3201371)Termination phase: Property scanning 42.34/6.67 % (3201371)Time elapsed: 0.024 s 42.34/6.67 % (3201371)Peak memory usage: 10 MB 42.34/6.67 % (3201371)Instructions burned: 128 (million) 42.34/6.67 % (3201364)------------------------------ 42.34/6.67 % (3201364)------------------------------ 42.34/6.67 % (3201373)lrs+1010_2_to=lpo:cnfonf=off:e2e=on:si=on:random_seed=2948619299:uwa_fpi=on:i=223:bd=all:rtra=on:fe=abstraction:ntd=on_1741 on theBenchmark for (1741ds/223Mi) 42.34/6.67 % (3201374)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=986384151:s2a=on:i=282:kws=inv_frequency:bd=all:rtra=on_1741 on theBenchmark for (1741ds/282Mi) 42.34/6.67 % (3201373)Instruction limit reached! 42.34/6.67 % (3201373)------------------------------ 42.34/6.67 % (3201373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 45.97/7.12 % (3201373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 45.97/7.12 % (3201373)CaDiCaL version: 2.1.3 45.97/7.12 % (3201373)Termination reason: Instruction limit 45.97/7.12 % (3201373)Termination phase: Saturation 45.97/7.12 % (3201373)Time elapsed: 0.045 s 45.97/7.12 % (3201373)Peak memory usage: 12 MB 45.97/7.12 % (3201373)Instructions burned: 226 (million) 45.97/7.12 % (3201377)lrs+10_1_sil=128000:tgt=ground:cnfonf=conj_eager:si=on:random_seed=1025713443:s2a=on:i=464:kws=frequency:bd=all:rtra=on:ss=axioms_1741 on theBenchmark for (1741ds/464Mi) 45.97/7.12 % (3201377)Refutation not found, incomplete strategy 45.97/7.12 % (3201377)------------------------------ 45.97/7.12 % (3201377)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 45.97/7.12 % (3201377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 45.97/7.12 % (3201377)CaDiCaL version: 2.1.3 45.97/7.12 % (3201377)Termination reason: Refutation not found, incomplete strategy 45.97/7.12 % (3201377)Time elapsed: 0.049 s 45.97/7.12 % (3201377)Peak memory usage: 16 MB 45.97/7.12 % (3201377)Instructions burned: 217 (million) 45.97/7.12 % (3201377)------------------------------ 45.97/7.12 % (3201377)------------------------------ 45.97/7.12 % (3201379)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3534181610:i=88:s2at=3:nm=2:rtra=on:rawr=on_1740 on theBenchmark for (1740ds/88Mi) 45.97/7.12 % (3201379)Instruction limit reached! 45.97/7.12 % (3201379)------------------------------ 45.97/7.12 % (3201379)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 45.97/7.12 % (3201379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 45.97/7.12 % (3201379)CaDiCaL version: 2.1.3 45.97/7.12 % (3201379)Termination reason: Instruction limit 45.97/7.12 % (3201379)Termination phase: Property scanning 45.97/7.12 % (3201379)Time elapsed: 0.018 s 45.97/7.12 % (3201379)Peak memory usage: 11 MB 45.97/7.12 % (3201379)Instructions burned: 89 (million) 45.97/7.12 % (3201363)Instruction limit reached! 45.97/7.12 % (3201363)------------------------------ 45.97/7.12 % (3201363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 45.97/7.12 % (3201363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 45.97/7.12 % (3201363)CaDiCaL version: 2.1.3 45.97/7.12 % (3201363)Termination reason: Instruction limit 45.97/7.12 % (3201363)Termination phase: Saturation 45.97/7.12 % (3201363)Time elapsed: 0.259 s 45.97/7.12 % (3201363)Peak memory usage: 14 MB 45.97/7.12 % (3201363)Instructions burned: 324 (million) 45.97/7.12 % (3201381)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2883398973:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_1740 on theBenchmark for (1740ds/280Mi) 45.97/7.12 % (3201361)Instruction limit reached! 45.97/7.12 % (3201361)------------------------------ 45.97/7.12 % (3201361)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 45.97/7.12 % (3201361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 45.97/7.12 % (3201361)CaDiCaL version: 2.1.3 45.97/7.12 % (3201361)Termination reason: Instruction limit 45.97/7.12 % (3201361)Termination phase: Saturation 45.97/7.12 % (3201361)Time elapsed: 0.294 s 45.97/7.12 % (3201361)Peak memory usage: 14 MB 45.97/7.12 % (3201361)Instructions burned: 410 (million) 45.97/7.12 % (3201382)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on 45.97/7.12 % (3201385)WARNING Broken Constraint: if lookahaed_delay(10) has been set then selection(21) is not lookahead selection 45.97/7.12 % (3201385)WARNING Broken Constraint: if mono_ep(off) has been set then equality_proxy(off) is not equal to off 45.97/7.12 % (3201382)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=487989075:i=4386:hud=10:nm=16:av=off:rtra=on:ntd=on_1740 on theBenchmark for (1740ds/4386Mi) 45.97/7.12 % (3201385)ott+21_3:13_sil=128000:cnfonf=off:sas=cadical:si=on:sp=arity:lma=off:lsd=10:uwa=one_side_interpreted:mep=off:chr=on:random_seed=1152884522:hsq=on:st=2:i=483:sd=1:hsql=off:rtra=on:fe=abstraction:fdi=32:ss=axioms:sgt=20:ntd=on_1739 on theBenchmark for (1739ds/483Mi) 45.97/7.12 % (3201374)Instruction limit reached! 47.28/7.37 % (3201374)------------------------------ 47.28/7.37 % (3201374)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 47.28/7.37 % (3201374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 47.28/7.37 % (3201374)CaDiCaL version: 2.1.3 47.28/7.37 % (3201374)Termination reason: Instruction limit 47.28/7.37 % (3201374)Termination phase: Saturation 47.28/7.37 % (3201374)Time elapsed: 0.211 s 47.28/7.37 % (3201374)Peak memory usage: 17 MB 47.28/7.37 % (3201374)Instructions burned: 283 (million) 47.28/7.37 % (3201388)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=1098324819:i=73:rtra=on_1739 on theBenchmark for (1739ds/73Mi) 47.28/7.37 % (3201388)Instruction limit reached! 47.28/7.37 % (3201388)------------------------------ 47.28/7.37 % (3201388)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 47.28/7.37 % (3201388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 47.28/7.37 % (3201388)CaDiCaL version: 2.1.3 47.28/7.37 % (3201388)Termination reason: Instruction limit 47.28/7.37 % (3201388)Termination phase: Property scanning 47.28/7.37 % (3201388)Time elapsed: 0.014 s 47.28/7.37 % (3201388)Peak memory usage: 10 MB 47.28/7.37 % (3201388)Instructions burned: 75 (million) 47.28/7.37 % (3201390)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2137654130:cts=off:i=176:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_1738 on theBenchmark for (1738ds/176Mi) 47.28/7.37 % (3201390)Instruction limit reached! 47.28/7.37 % (3201390)------------------------------ 47.28/7.37 % (3201390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 47.28/7.37 % (3201390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 47.28/7.37 % (3201390)CaDiCaL version: 2.1.3 47.28/7.37 % (3201390)Termination reason: Instruction limit 47.28/7.37 % (3201390)Termination phase: Saturation 47.28/7.37 % (3201390)Time elapsed: 0.037 s 47.28/7.37 % (3201390)Peak memory usage: 12 MB 47.28/7.37 % (3201390)Instructions burned: 179 (million) 47.28/7.37 % (3201392)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off 47.28/7.37 % (3201381)Instruction limit reached! 47.28/7.37 % (3201381)------------------------------ 47.28/7.37 % (3201381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 47.28/7.37 % (3201381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 47.28/7.37 % (3201381)CaDiCaL version: 2.1.3 47.28/7.37 % (3201381)Termination reason: Instruction limit 47.28/7.37 % (3201381)Termination phase: Saturation 47.28/7.37 % (3201381)Time elapsed: 0.175 s 47.28/7.37 % (3201381)Peak memory usage: 12 MB 47.28/7.37 % (3201381)Instructions burned: 281 (million) 47.28/7.37 % (3201392)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=727286783:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_1738 on theBenchmark for (1738ds/39Mi) 47.28/7.37 % (3201392)Instruction limit reached! 47.28/7.37 % (3201392)------------------------------ 47.28/7.37 % (3201392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 47.28/7.37 % (3201392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 47.28/7.37 % (3201392)CaDiCaL version: 2.1.3 47.28/7.37 % (3201392)Termination reason: Instruction limit 47.28/7.37 % (3201392)Termination phase: Function definition elimination 47.28/7.37 % (3201392)Time elapsed: 0.008 s 47.28/7.37 % (3201392)Peak memory usage: 10 MB 47.28/7.37 % (3201392)Instructions burned: 42 (million) 47.28/7.37 % (3201395)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 47.28/7.37 % (3201395)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=20197042:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_1738 on theBenchmark for (1738ds/252Mi) 47.28/7.37 % (3201385)Instruction limit reached! 47.28/7.37 % (3201385)------------------------------ 47.28/7.37 % (3201385)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 47.28/7.37 % (3201385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 47.28/7.37 % (3201385)CaDiCaL version: 2.1.3 47.28/7.37 % (3201385)Termination reason: Instruction limit 49.64/7.80 % (3201385)Termination phase: Saturation 49.64/7.80 % (3201385)Time elapsed: 0.172 s 49.64/7.80 % (3201385)Peak memory usage: 15 MB 49.64/7.80 % (3201385)Instructions burned: 483 (million) 49.64/7.80 % (3201393)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=776411209:i=708:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_1738 on theBenchmark for (1738ds/708Mi) 49.64/7.80 % (3201398)dis+10_4_sil=128000:tgt=full:fde=unused:cnfonf=lazy_not_gen:sas=cadical:si=on:uwa=off:sac=on:random_seed=3371676380:i=823:fsr=off:rtra=on_1738 on theBenchmark for (1738ds/823Mi) 49.64/7.80 % (3201395)Instruction limit reached! 49.64/7.80 % (3201395)------------------------------ 49.64/7.80 % (3201395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 49.64/7.80 % (3201395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 49.64/7.80 % (3201395)CaDiCaL version: 2.1.3 49.64/7.80 % (3201395)Termination reason: Instruction limit 49.64/7.80 % (3201395)Termination phase: Saturation 49.64/7.80 % (3201395)Time elapsed: 0.065 s 49.64/7.80 % (3201395)Peak memory usage: 12 MB 49.64/7.80 % (3201395)Instructions burned: 253 (million) 49.64/7.80 % (3201402)WARNING Broken Constraint: lrs_first_time_check(100) is less than 100 49.64/7.80 % (3201402)lrs+1010_7_anc=all_dependent:sil=128000:cnfonf=lazy_not_gen:si=on:urr=on:rp=on:sac=on:lftc=100:random_seed=1892950466:lrd=on:st=3:i=16202:add=on:sd=3:kws=frequency:rtra=on:ss=axioms_1737 on theBenchmark for (1737ds/16202Mi) 49.64/7.80 % (3201402)Refutation not found, incomplete strategy 49.64/7.80 % (3201402)------------------------------ 49.64/7.80 % (3201402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 49.64/7.80 % (3201402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 49.64/7.80 % (3201402)CaDiCaL version: 2.1.3 49.64/7.80 % (3201402)Termination reason: Refutation not found, incomplete strategy 49.64/7.80 % (3201402)Time elapsed: 0.097 s 49.64/7.80 % (3201402)Peak memory usage: 15 MB 49.64/7.80 % (3201402)Instructions burned: 250 (million) 49.64/7.80 % (3201402)------------------------------ 49.64/7.80 % (3201402)------------------------------ 49.64/7.80 % (3201404)dis+10_1_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:uwa=off:random_seed=784952119:s2a=on:i=300:s2at=10:bd=all:rtra=on:ntd=on_1736 on theBenchmark for (1736ds/300Mi) 49.64/7.80 % (3201404)Instruction limit reached! 49.64/7.80 % (3201404)------------------------------ 49.64/7.80 % (3201404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 49.64/7.80 % (3201404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 49.64/7.80 % (3201404)CaDiCaL version: 2.1.3 49.64/7.80 % (3201404)Termination reason: Instruction limit 49.64/7.80 % (3201404)Termination phase: Saturation 49.64/7.80 % (3201404)Time elapsed: 0.118 s 49.64/7.80 % (3201404)Peak memory usage: 13 MB 49.64/7.80 % (3201404)Instructions burned: 301 (million) 49.64/7.80 % (3201406)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(2) has been set then positive_literal_split_queue(off) is equal to on 49.64/7.80 % (3201406)WARNING Broken Constraint: if ho_split_queue_lambda_weight(0) has been set then ho_split_queue(off) is equal to on 49.64/7.80 % (3201406)dis+1010_1_anc=none:sil=128000:plsqc=2:sas=cadical:si=on:hsqlw=0:uwa=one_side_interpreted:sac=on:random_seed=4167084003:i=177:add=on:bd=preordered:rtra=on:rawr=on_1734 on theBenchmark for (1734ds/177Mi) 49.64/7.80 % (3201322)Instruction limit reached! 49.64/7.80 % (3201322)------------------------------ 49.64/7.80 % (3201322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 49.64/7.80 % (3201322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 49.64/7.80 % (3201322)CaDiCaL version: 2.1.3 49.64/7.80 % (3201322)Termination reason: Instruction limit 49.64/7.80 % (3201322)Termination phase: Saturation 49.64/7.80 % (3201322)Time elapsed: 1.701 s 49.64/7.80 % (3201322)Peak memory usage: 23 MB 49.64/7.80 % (3201322)Instructions burned: 2241 (million) 49.64/7.80 % (3201408)lrs+10_1_cnfonf=conj_eager:si=on:random_seed=2893828690:st=1.5:s2a=on:i=715:rtra=on:ss=axioms_1734 on theBenchmark for (1734ds/715Mi) 49.64/7.80 % (3201406)Instruction limit reached! 49.64/7.80 % (3201406)------------------------------ 49.64/7.80 % (3201406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 49.64/7.80 % (3201406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 53.89/8.27 % (3201406)CaDiCaL version: 2.1.3 53.89/8.27 % (3201406)Termination reason: Instruction limit 53.89/8.27 % (3201406)Termination phase: Saturation 53.89/8.27 % (3201406)Time elapsed: 0.109 s 53.89/8.27 % (3201406)Peak memory usage: 12 MB 53.89/8.27 % (3201406)Instructions burned: 178 (million) 53.89/8.27 % (3201412)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(3) has been set then positive_literal_split_queue(off) is equal to on 53.89/8.27 % (3201412)WARNING Broken Constraint: if positive_literal_split_queue_ratios(19,3) has been set then positive_literal_split_queue(off) is equal to on 53.89/8.27 % (3201412)dis+11_1_sil=128000:plsqc=3:cnfonf=lazy_gen:si=on:sp=const_max:lma=off:plsqr=19,3:lcm=predicate:uwa=off:fd=preordered:nwc=1:random_seed=1597027621:i=230:add=on:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_1733 on theBenchmark for (1733ds/230Mi) 53.89/8.27 % (3201408)Refutation not found, incomplete strategy 53.89/8.27 % (3201408)------------------------------ 53.89/8.27 % (3201408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 53.89/8.27 % (3201408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 53.89/8.27 % (3201408)CaDiCaL version: 2.1.3 53.89/8.27 % (3201408)Termination reason: Refutation not found, incomplete strategy 53.89/8.27 % (3201408)Time elapsed: 0.112 s 53.89/8.27 % (3201408)Peak memory usage: 15 MB 53.89/8.27 % (3201408)Instructions burned: 164 (million) 53.89/8.27 % (3201408)------------------------------ 53.89/8.27 % (3201408)------------------------------ 53.89/8.27 % (3201416)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=710832847:s2a=on:i=606:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_1733 on theBenchmark for (1733ds/606Mi) 53.89/8.27 % (3201393)Instruction limit reached! 53.89/8.27 % (3201393)------------------------------ 53.89/8.27 % (3201393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 53.89/8.27 % (3201393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 53.89/8.27 % (3201393)CaDiCaL version: 2.1.3 53.89/8.27 % (3201393)Termination reason: Instruction limit 53.89/8.27 % (3201393)Termination phase: Saturation 53.89/8.27 % (3201393)Time elapsed: 0.538 s 53.89/8.27 % (3201393)Peak memory usage: 17 MB 53.89/8.27 % (3201393)Instructions burned: 708 (million) 53.89/8.27 % (3201412)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use 53.89/8.27 % (3201418)WARNING Broken Constraint: if lrs_retroactive_deletes(on) has been set then saturation_algorithm(otter) is equal to lrs 53.89/8.27 % (3201418)ott+2_2:1_sil=128000:tgt=full:drc=off:si=on:lma=off:urr=on:cbe=off:uwa=interpreted_only:random_seed=2459442268:lrd=on:i=841:nm=0:rtra=on_1732 on theBenchmark for (1732ds/841Mi) 53.89/8.27 % (3201412)Instruction limit reached! 53.89/8.27 % (3201412)------------------------------ 53.89/8.27 % (3201412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 53.89/8.27 % (3201412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 53.89/8.27 % (3201412)CaDiCaL version: 2.1.3 53.89/8.27 % (3201412)Termination reason: Instruction limit 53.89/8.27 % (3201412)Termination phase: Saturation 53.89/8.27 % (3201412)Time elapsed: 0.161 s 53.89/8.27 % (3201412)Peak memory usage: 12 MB 53.89/8.27 % (3201412)Instructions burned: 231 (million) 53.89/8.27 % (3201398)Instruction limit reached! 53.89/8.27 % (3201398)------------------------------ 53.89/8.27 % (3201398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 53.89/8.27 % (3201398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 53.89/8.27 % (3201398)CaDiCaL version: 2.1.3 53.89/8.27 % (3201398)Termination reason: Instruction limit 53.89/8.27 % (3201398)Termination phase: Saturation 53.89/8.27 % (3201398)Time elapsed: 0.614 s 53.89/8.27 % (3201398)Peak memory usage: 16 MB 53.89/8.27 % (3201398)Instructions burned: 828 (million) 53.89/8.27 % (3201421)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=2203909472:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_1731 on theBenchmark for (1731ds/71Mi) 53.89/8.27 % (3201420)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1428336637:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1731 on theBenchmark for (1731ds/445Mi) 53.89/8.27 % (3201421)Instruction limit reached! 53.89/8.27 % (3201421)------------------------------ 53.89/8.27 % (3201421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 54.50/8.40 % (3201421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 54.50/8.40 % (3201421)CaDiCaL version: 2.1.3 54.50/8.40 % (3201421)Termination reason: Instruction limit 54.50/8.40 % (3201421)Termination phase: Property scanning 54.50/8.40 % (3201421)Time elapsed: 0.035 s 54.50/8.40 % (3201421)Peak memory usage: 10 MB 54.50/8.40 % (3201421)Instructions burned: 72 (million) 54.50/8.40 % (3201424)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 54.50/8.40 % (3201424)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 54.50/8.40 % (3201424)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2643608383:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1730 on theBenchmark for (1730ds/100Mi) 54.50/8.40 % (3201424)Instruction limit reached! 54.50/8.40 % (3201424)------------------------------ 54.50/8.40 % (3201424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 54.50/8.40 % (3201424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 54.50/8.40 % (3201424)CaDiCaL version: 2.1.3 54.50/8.40 % (3201424)Termination reason: Instruction limit 54.50/8.40 % (3201424)Termination phase: Saturation 54.50/8.40 % (3201424)Time elapsed: 0.075 s 54.50/8.40 % (3201424)Peak memory usage: 11 MB 54.50/8.40 % (3201424)Instructions burned: 101 (million) 54.50/8.40 % (3201429)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(3) has been set then sine_level_split_queue(off) is equal to on 54.50/8.40 % (3201429)lrs+2_128_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=const_max:sos=on:plsqr=32,1:spb=goal:uwa=interpreted_only:slsqc=3:random_seed=2607970755:i=1352:add=on:aac=none:rtra=on_1729 on theBenchmark for (1729ds/1352Mi) 54.50/8.40 % (3201420)Instruction limit reached! 54.50/8.40 % (3201420)------------------------------ 54.50/8.40 % (3201420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 54.50/8.40 % (3201420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 54.50/8.40 % (3201420)CaDiCaL version: 2.1.3 54.50/8.40 % (3201420)Termination reason: Instruction limit 54.50/8.40 % (3201420)Termination phase: Saturation 54.50/8.40 % (3201420)Time elapsed: 0.230 s 54.50/8.40 % (3201420)Peak memory usage: 15 MB 54.50/8.40 % (3201420)Instructions burned: 445 (million) 54.50/8.40 % (3201433)lrs-1002_4:1_sfv=off:to=lpo:plsq=on:prc=on:e2e=on:si=on:hsqlw=5:ser=on:spb=goal:acc=on:uwa=off:foolp=on:s2agt=16:slsqc=1:slsq=on:random_seed=2949854152:hsq=on:hsqr=16,1:s2a=on:i=646:nm=16:rtra=on:gtg=exists_top:proc=on_1728 on theBenchmark for (1728ds/646Mi) 54.50/8.40 % (3201416)Instruction limit reached! 54.50/8.40 % (3201416)------------------------------ 54.50/8.40 % (3201416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 54.50/8.40 % (3201416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 54.50/8.40 % (3201416)CaDiCaL version: 2.1.3 54.50/8.40 % (3201416)Termination reason: Instruction limit 54.50/8.40 % (3201416)Termination phase: Saturation 54.50/8.40 % (3201416)Time elapsed: 0.432 s 54.50/8.40 % (3201416)Peak memory usage: 15 MB 54.50/8.40 % (3201416)Instructions burned: 606 (million) 54.50/8.40 % (3201435)lrs+10_1_sil=128000:si=on:uwa=all:random_seed=1915980696:i=1924:sd=2:kws=precedence:bd=all:rtra=on:ss=axioms:sgt=16_1728 on theBenchmark for (1728ds/1924Mi) 54.50/8.40 % (3201119)Instruction limit reached! 54.50/8.40 % (3201119)------------------------------ 54.50/8.40 % (3201119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 54.50/8.40 % (3201119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 54.50/8.40 % (3201119)CaDiCaL version: 2.1.3 54.50/8.40 % (3201119)Termination reason: Instruction limit 54.50/8.40 % (3201119)Termination phase: Saturation 54.50/8.40 % (3201119)Time elapsed: 5.916 s 54.50/8.40 % (3201119)Peak memory usage: 45 MB 54.50/8.40 % (3201119)Instructions burned: 9840 (million) 54.50/8.40 % (3201438)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=1626635730:hsq=on:i=984:hsqaw=5:rtra=on:fe=abstraction:ntd=on_1727 on theBenchmark for (1727ds/984Mi) 54.50/8.40 % (3201418)Instruction limit reached! 55.47/8.57 % (3201418)------------------------------ 55.47/8.57 % (3201418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 55.47/8.57 % (3201418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 55.47/8.57 % (3201418)CaDiCaL version: 2.1.3 55.47/8.57 % (3201418)Termination reason: Instruction limit 55.47/8.57 % (3201418)Termination phase: Saturation 55.47/8.57 % (3201418)Time elapsed: 0.558 s 55.47/8.57 % (3201418)Peak memory usage: 17 MB 55.47/8.57 % (3201418)Instructions burned: 841 (million) 55.47/8.57 % (3201440)dis+10_128_sil=128000:drc=ordering:fde=unused:si=on:lma=off:uwa=interpreted_only:avsqc=4:random_seed=3442271933:avsq=on:i=592:add=off:kws=inv_frequency:bd=preordered:rtra=on_1726 on theBenchmark for (1726ds/592Mi) 55.47/8.57 % (3201382)Instruction limit reached! 55.47/8.57 % (3201382)------------------------------ 55.47/8.57 % (3201382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 55.47/8.57 % (3201382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 55.47/8.57 % (3201382)CaDiCaL version: 2.1.3 55.47/8.57 % (3201382)Termination reason: Instruction limit 55.47/8.57 % (3201382)Termination phase: Saturation 55.47/8.57 % (3201382)Time elapsed: 1.547 s 55.47/8.57 % (3201382)Peak memory usage: 17 MB 55.47/8.57 % (3201382)Instructions burned: 4386 (million) 55.47/8.57 % (3201443)dis+1010_7_si=on:uwa=off:nwc=1.2:random_seed=4203578711:st=2.5:i=872:sd=4:fsr=off:rtra=on:ss=axioms:c=on:ntd=on_1724 on theBenchmark for (1724ds/872Mi) 55.47/8.57 % (3201433)Instruction limit reached! 55.47/8.57 % (3201433)------------------------------ 55.47/8.57 % (3201433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 55.47/8.57 % (3201433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 55.47/8.57 % (3201433)CaDiCaL version: 2.1.3 55.47/8.57 % (3201433)Termination reason: Instruction limit 55.47/8.57 % (3201433)Termination phase: Saturation 55.47/8.57 % (3201433)Time elapsed: 0.491 s 55.47/8.57 % (3201433)Peak memory usage: 17 MB 55.47/8.57 % (3201433)Instructions burned: 646 (million) 55.47/8.57 % (3201446)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on 55.47/8.57 % (3201446)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=4103655311:i=999:add=on:rtra=on_1723 on theBenchmark for (1723ds/999Mi) 55.47/8.57 % (3201443)Refutation not found, incomplete strategy 55.47/8.57 % (3201443)------------------------------ 55.47/8.57 % (3201443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 55.47/8.57 % (3201443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 55.47/8.57 % (3201443)CaDiCaL version: 2.1.3 55.47/8.57 % (3201443)Termination reason: Refutation not found, incomplete strategy 55.47/8.57 % (3201443)Time elapsed: 0.099 s 55.47/8.57 % (3201443)Peak memory usage: 15 MB 55.47/8.57 % (3201443)Instructions burned: 198 (million) 55.47/8.57 % (3201443)------------------------------ 55.47/8.57 % (3201443)------------------------------ 55.47/8.57 % (3201449)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs 55.47/8.57 % (3201449)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=3453712090:i=244:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_1723 on theBenchmark for (1723ds/244Mi) 55.47/8.57 % (3201429)Refutation not found, incomplete strategy 55.47/8.57 % (3201429)------------------------------ 55.47/8.57 % (3201429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 55.47/8.57 % (3201429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 55.47/8.57 % (3201429)CaDiCaL version: 2.1.3 55.47/8.57 % (3201429)Termination reason: Refutation not found, incomplete strategy 55.47/8.57 % (3201429)Time elapsed: 0.698 s 55.47/8.57 % (3201429)Peak memory usage: 18 MB 55.47/8.57 % (3201429)Instructions burned: 979 (million) 55.47/8.57 % (3201429)------------------------------ 55.47/8.57 % (3201429)------------------------------ 55.47/8.57 % (3201451)ott+1003_1_anc=all:sil=128000:si=on:sos=on:random_seed=645506029:cts=off:i=113:fsr=off:rtra=on:fe=abstraction_1722 on theBenchmark for (1722ds/113Mi) 55.47/8.57 % (3201451)Instruction limit reached! 55.47/8.57 % (3201451)------------------------------ 57.59/8.95 % (3201451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 57.59/8.95 % (3201451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 57.59/8.95 % (3201451)CaDiCaL version: 2.1.3 57.59/8.95 % (3201451)Termination reason: Instruction limit 57.59/8.95 % (3201451)Termination phase: Property scanning 57.59/8.95 % (3201451)Time elapsed: 0.044 s 57.59/8.95 % (3201451)Peak memory usage: 11 MB 57.59/8.95 % (3201451)Instructions burned: 114 (million) 57.59/8.95 % (3201449)Instruction limit reached! 57.59/8.95 % (3201449)------------------------------ 57.59/8.95 % (3201449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 57.59/8.95 % (3201449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 57.59/8.95 % (3201449)CaDiCaL version: 2.1.3 57.59/8.95 % (3201449)Termination reason: Instruction limit 57.59/8.95 % (3201449)Termination phase: Saturation 57.59/8.95 % (3201449)Time elapsed: 0.094 s 57.59/8.95 % (3201449)Peak memory usage: 14 MB 57.59/8.95 % (3201449)Instructions burned: 247 (million) 57.59/8.95 % (3201440)Instruction limit reached! 57.59/8.95 % (3201440)------------------------------ 57.59/8.95 % (3201440)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 57.59/8.95 % (3201440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 57.59/8.95 % (3201440)CaDiCaL version: 2.1.3 57.59/8.95 % (3201440)Termination reason: Instruction limit 57.59/8.95 % (3201440)Termination phase: Saturation 57.59/8.95 % (3201440)Time elapsed: 0.451 s 57.59/8.95 % (3201440)Peak memory usage: 13 MB 57.59/8.95 % (3201440)Instructions burned: 593 (million) 57.59/8.95 % (3201453)lrs+10_1_sil=128000:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3505087524:i=7795:sd=2:nm=16:rtra=on:ss=axioms_1721 on theBenchmark for (1721ds/7795Mi) 57.59/8.95 % (3201454)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4086403506:st=2:i=5026:sd=1:rtra=on:ss=axioms_1721 on theBenchmark for (1721ds/5026Mi) 57.59/8.95 % (3201455)WARNING Broken Constraint: if ho_split_queue_ratios(1,4) has been set then ho_split_queue(off) is equal to on 57.59/8.95 % (3201455)dis+1004_8_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_frequency:sos=on:uwa=off:random_seed=4046563082:hsqr=1,4:i=763:bd=preordered:nm=0:rtra=on:bet=on:ss=axioms_1721 on theBenchmark for (1721ds/763Mi) 57.59/8.95 % (3201454)Refutation not found, incomplete strategy 57.59/8.95 % (3201454)------------------------------ 57.59/8.95 % (3201454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 57.59/8.95 % (3201454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 57.59/8.95 % (3201454)CaDiCaL version: 2.1.3 57.59/8.95 % (3201454)Termination reason: Refutation not found, incomplete strategy 57.59/8.95 % (3201454)Time elapsed: 0.053 s 57.59/8.95 % (3201454)Peak memory usage: 15 MB 57.59/8.95 % (3201454)Instructions burned: 146 (million) 57.59/8.95 % (3201454)------------------------------ 57.59/8.95 % (3201454)------------------------------ 57.59/8.95 % (3201459)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2498721767:hsq=on:st=2:i=1144:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1721 on theBenchmark for (1721ds/1144Mi) 57.59/8.95 % (3201455)Refutation not found, incomplete strategy 57.59/8.95 % (3201455)------------------------------ 57.59/8.95 % (3201455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 57.59/8.95 % (3201455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 57.59/8.95 % (3201455)CaDiCaL version: 2.1.3 57.59/8.95 % (3201455)Termination reason: Refutation not found, incomplete strategy 57.59/8.95 % (3201455)Time elapsed: 0.064 s 57.59/8.95 % (3201455)Peak memory usage: 16 MB 57.59/8.95 % (3201455)Instructions burned: 135 (million) 57.59/8.95 % (3201455)------------------------------ 57.59/8.95 % (3201455)------------------------------ 57.59/8.95 % (3201461)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on 57.59/8.95 % (3201461)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=133111967:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_1720 on theBenchmark for (1720ds/52Mi) 57.59/8.95 % (3201453)Refutation not found, incomplete strategy 57.59/8.95 % (3201453)------------------------------ 57.59/8.95 % (3201453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 62.30/9.50 % (3201453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 62.30/9.50 % (3201453)CaDiCaL version: 2.1.3 62.30/9.50 % (3201453)Termination reason: Refutation not found, incomplete strategy 62.30/9.50 % (3201453)Time elapsed: 0.101 s 62.30/9.50 % (3201453)Peak memory usage: 14 MB 62.30/9.50 % (3201453)Instructions burned: 142 (million) 62.30/9.50 % (3201453)------------------------------ 62.30/9.50 % (3201453)------------------------------ 62.30/9.50 % (3201461)Instruction limit reached! 62.30/9.50 % (3201461)------------------------------ 62.30/9.50 % (3201461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 62.30/9.50 % (3201461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 62.30/9.50 % (3201461)CaDiCaL version: 2.1.3 62.30/9.50 % (3201461)Termination reason: Instruction limit 62.30/9.50 % (3201461)Termination phase: shuffling 62.30/9.50 % (3201461)Time elapsed: 0.019 s 62.30/9.50 % (3201461)Peak memory usage: 10 MB 62.30/9.50 % (3201461)Instructions burned: 53 (million) 62.30/9.50 % (3201438)Instruction limit reached! 62.30/9.50 % (3201438)------------------------------ 62.30/9.50 % (3201438)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 62.30/9.50 % (3201438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 62.30/9.50 % (3201438)CaDiCaL version: 2.1.3 62.30/9.50 % (3201438)Termination reason: Instruction limit 62.30/9.50 % (3201438)Termination phase: Saturation 62.30/9.50 % (3201438)Time elapsed: 0.714 s 62.30/9.50 % (3201438)Peak memory usage: 16 MB 62.30/9.50 % (3201438)Instructions burned: 985 (million) 62.30/9.50 % (3201463)dis+1010_1_sil=128000:si=on:etr=on:uwa=off:random_seed=1556222603:i=1724:fsr=off:rtra=on:fe=abstraction_1720 on theBenchmark for (1720ds/1724Mi) 62.30/9.50 % (3201465)dis-1004_128_to=kbo:sil=128000:tgt=full:si=on:fdtod=off:sp=const_frequency:spb=goal:uwa=off:slsqc=3:slsq=on:random_seed=3238827086:i=439:add=on:slsql=off:rtra=on:ntd=on_1720 on theBenchmark for (1720ds/439Mi) 62.30/9.50 % (3201459)Refutation not found, incomplete strategy 62.30/9.50 % (3201459)------------------------------ 62.30/9.50 % (3201459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 62.30/9.50 % (3201459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 62.30/9.50 % (3201459)CaDiCaL version: 2.1.3 62.30/9.50 % (3201459)Termination reason: Refutation not found, incomplete strategy 62.30/9.50 % (3201459)Time elapsed: 0.077 s 62.30/9.50 % (3201459)Peak memory usage: 14 MB 62.30/9.50 % (3201459)Instructions burned: 203 (million) 62.30/9.50 % (3201459)------------------------------ 62.30/9.50 % (3201459)------------------------------ 62.30/9.50 % (3201470)WARNING Broken Constraint: if ho_split_queue_lambda_weight(5) has been set then ho_split_queue(off) is equal to on 62.30/9.50 % (3201470)ott+2_16:1_sil=128000:si=on:hsqlw=5:sos=on:urr=on:bce=on:uwa=off:random_seed=600932428:i=6762:add=off:bd=all:rtra=on:ss=axioms:ntd=on_1720 on theBenchmark for (1720ds/6762Mi) 62.30/9.50 % (3201468)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=4033825041:i=6395:sd=1:rtra=on:ss=axioms_1720 on theBenchmark for (1720ds/6395Mi) 62.30/9.50 % (3201470)Refutation not found, incomplete strategy 62.30/9.50 % (3201470)------------------------------ 62.30/9.50 % (3201470)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 62.30/9.50 % (3201470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 62.30/9.50 % (3201470)CaDiCaL version: 2.1.3 62.30/9.50 % (3201470)Termination reason: Refutation not found, incomplete strategy 62.30/9.50 % (3201470)Time elapsed: 0.038 s 62.30/9.50 % (3201470)Peak memory usage: 16 MB 62.30/9.50 % (3201470)Instructions burned: 173 (million) 62.30/9.50 % (3201470)------------------------------ 62.30/9.50 % (3201470)------------------------------ 62.30/9.50 % (3201474)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs 62.30/9.50 % (3201474)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=4215776772:s2a=on:i=376:add=on:rtra=on:fe=axiom:fdi=1024_1719 on theBenchmark for (1719ds/376Mi) 62.30/9.50 % (3201468)Refutation not found, incomplete strategy 62.30/9.50 % (3201468)------------------------------ 62.30/9.50 % (3201468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 64.40/9.85 % (3201468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 64.40/9.85 % (3201468)CaDiCaL version: 2.1.3 64.40/9.85 % (3201468)Termination reason: Refutation not found, incomplete strategy 64.40/9.85 % (3201468)Time elapsed: 0.101 s 64.40/9.85 % (3201468)Peak memory usage: 15 MB 64.40/9.85 % (3201468)Instructions burned: 133 (million) 64.40/9.85 % (3201468)------------------------------ 64.40/9.85 % (3201468)------------------------------ 64.40/9.85 % (3201474)Instruction limit reached! 64.40/9.85 % (3201474)------------------------------ 64.40/9.85 % (3201474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 64.40/9.85 % (3201474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 64.40/9.85 % (3201474)CaDiCaL version: 2.1.3 64.40/9.85 % (3201474)Termination reason: Instruction limit 64.40/9.85 % (3201474)Termination phase: Saturation 64.40/9.85 % (3201474)Time elapsed: 0.077 s 64.40/9.85 % (3201474)Peak memory usage: 13 MB 64.40/9.85 % (3201474)Instructions burned: 381 (million) 64.40/9.85 % (3201477)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3566945029:i=5013:sd=1:rtra=on:ss=axioms:sgt=64_1718 on theBenchmark for (1718ds/5013Mi) 64.40/9.85 % (3201476)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=3015951270:i=965:bd=all:ins=4:rtra=on_1718 on theBenchmark for (1718ds/965Mi) 64.40/9.85 % (3201465)Instruction limit reached! 64.40/9.85 % (3201465)------------------------------ 64.40/9.85 % (3201465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 64.40/9.85 % (3201465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 64.40/9.85 % (3201465)CaDiCaL version: 2.1.3 64.40/9.85 % (3201465)Termination reason: Instruction limit 64.40/9.85 % (3201465)Termination phase: Saturation 64.40/9.85 % (3201465)Time elapsed: 0.294 s 64.40/9.85 % (3201465)Peak memory usage: 14 MB 64.40/9.85 % (3201465)Instructions burned: 439 (million) 64.40/9.85 % (3201481)dis+2_1_tgt=full:si=on:uwa=one_side_interpreted:random_seed=4159640677:i=1583:kws=inv_frequency:bd=preordered:nm=0:rtra=on_1717 on theBenchmark for (1717ds/1583Mi) 64.40/9.85 % (3201446)Instruction limit reached! 64.40/9.85 % (3201446)------------------------------ 64.40/9.85 % (3201446)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 64.40/9.85 % (3201446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 64.40/9.85 % (3201446)CaDiCaL version: 2.1.3 64.40/9.85 % (3201446)Termination reason: Instruction limit 64.40/9.85 % (3201446)Termination phase: Saturation 64.40/9.85 % (3201446)Time elapsed: 0.668 s 64.40/9.85 % (3201446)Peak memory usage: 16 MB 64.40/9.85 % (3201446)Instructions burned: 999 (million) 64.40/9.85 % (3201484)WARNING Broken Constraint: if sine_level_split_queue_ratios(1,32) has been set then sine_level_split_queue(off) is equal to on 64.40/9.85 % (3201484)WARNING Broken Constraint: if ho_split_queue_cutoffs(2) has been set then ho_split_queue(off) is equal to on 64.40/9.85 % (3201484)WARNING Broken Constraint: if sine_to_age_generality_threshold(16) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 64.40/9.85 % (3201484)WARNING Broken Constraint: if ho_split_queue_ratios(4,1) has been set then ho_split_queue(off) is equal to on 64.40/9.85 % (3201484)ott+1002_1_slsqr=1,32:sil=128000:fde=none:e2e=on:hsqc=2:si=on:sp=const_min:sos=on:uwa=interpreted_only:s2agt=16:chr=on:random_seed=576500046:hsqr=4,1:avsq=on:cond=on:i=1774:add=on:avsqr=1,16:kws=arity_squared:nm=120:rtra=on:fe=abstraction:ss=axioms_1716 on theBenchmark for (1716ds/1774Mi) 64.40/9.85 % (3201484)Refutation not found, incomplete strategy 64.40/9.85 % (3201484)------------------------------ 64.40/9.85 % (3201484)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 64.40/9.85 % (3201484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 64.40/9.85 % (3201484)CaDiCaL version: 2.1.3 64.40/9.85 % (3201484)Termination reason: Refutation not found, incomplete strategy 64.40/9.85 % (3201484)Time elapsed: 0.096 s 64.40/9.85 % (3201484)Peak memory usage: 14 MB 64.40/9.85 % (3201484)Instructions burned: 137 (million) 64.40/9.85 % (3201484)------------------------------ 64.40/9.85 % (3201484)------------------------------ 64.40/9.85 % (3201486)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=1875907714:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_1715 on theBenchmark for (1715ds/515Mi) 65.68/10.00 % (3201435)Instruction limit reached! 65.68/10.00 % (3201435)------------------------------ 65.68/10.00 % (3201435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 65.68/10.00 % (3201435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 65.68/10.00 % (3201435)CaDiCaL version: 2.1.3 65.68/10.00 % (3201435)Termination reason: Instruction limit 65.68/10.00 % (3201435)Termination phase: Saturation 65.68/10.00 % (3201435)Time elapsed: 1.319 s 65.68/10.00 % (3201435)Peak memory usage: 20 MB 65.68/10.00 % (3201435)Instructions burned: 1925 (million) 65.68/10.00 % (3201489)WARNING Broken Constraint: if sine_to_age_generality_threshold(60) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 65.68/10.00 % (3201489)lrs-30_5:1_sil=128000:drc=off:sas=cadical:si=on:lma=off:cbe=off:uwa=one_side_interpreted:s2agt=60:lwlo=on:random_seed=3605232824:avsq=on:i=1297:add=on:avsqr=1,8:rtra=on:fsd=on_1714 on theBenchmark for (1714ds/1297Mi) 65.68/10.00 % (3201476)Instruction limit reached! 65.68/10.00 % (3201476)------------------------------ 65.68/10.00 % (3201476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 65.68/10.00 % (3201476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 65.68/10.00 % (3201476)CaDiCaL version: 2.1.3 65.68/10.00 % (3201476)Termination reason: Instruction limit 65.68/10.00 % (3201476)Termination phase: Saturation 65.68/10.00 % (3201476)Time elapsed: 0.688 s 65.68/10.00 % (3201476)Peak memory usage: 20 MB 65.68/10.00 % (3201476)Instructions burned: 965 (million) 65.68/10.00 % (3201486)Instruction limit reached! 65.68/10.00 % (3201486)------------------------------ 65.68/10.00 % (3201486)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 65.68/10.00 % (3201486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 65.68/10.00 % (3201486)CaDiCaL version: 2.1.3 65.68/10.00 % (3201486)Termination reason: Instruction limit 65.68/10.00 % (3201486)Termination phase: Saturation 65.68/10.00 % (3201486)Time elapsed: 0.352 s 65.68/10.00 % (3201486)Peak memory usage: 15 MB 65.68/10.00 % (3201486)Instructions burned: 515 (million) 65.68/10.00 % (3201496)dis+1002_1_to=lpo:drc=ordering:fde=none:bsd=on:si=on:ser=on:sp=const_min:cbe=off:uwa=off:flr=on:random_seed=1386150178:s2a=on:i=611:rtra=on:gsp=on_1711 on theBenchmark for (1711ds/611Mi) 65.68/10.00 % (3201497)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on 65.68/10.00 % (3201497)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=677985715:i=72:bd=all:rtra=on_1711 on theBenchmark for (1711ds/72Mi) 65.68/10.00 % (3201496)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 65.68/10.00 % (3201497)Instruction limit reached! 65.68/10.00 % (3201497)------------------------------ 65.68/10.00 % (3201497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 65.68/10.00 % (3201497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 65.68/10.00 % (3201497)CaDiCaL version: 2.1.3 65.68/10.00 % (3201497)Termination reason: Instruction limit 65.68/10.00 % (3201497)Termination phase: Property scanning 65.68/10.00 % (3201497)Time elapsed: 0.026 s 65.68/10.00 % (3201497)Peak memory usage: 10 MB 65.68/10.00 % (3201497)Instructions burned: 74 (million) 65.68/10.00 % (3201501)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=933261663:hsq=on:hsqr=16,1:s2a=on:i=6580:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_1711 on theBenchmark for (1711ds/6580Mi) 65.68/10.00 % (3201481)Instruction limit reached! 65.68/10.00 % (3201481)------------------------------ 65.68/10.00 % (3201481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 65.68/10.00 % (3201481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 65.68/10.00 % (3201481)CaDiCaL version: 2.1.3 65.68/10.00 % (3201481)Termination reason: Instruction limit 65.68/10.00 % (3201481)Termination phase: Saturation 65.68/10.00 % (3201481)Time elapsed: 0.727 s 65.68/10.00 % (3201481)Peak memory usage: 24 MB 65.68/10.00 % (3201481)Instructions burned: 1583 (million) 65.68/10.00 % (3201504)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=3892223419:i=6209:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_1709 on theBenchmark for (1709ds/6209Mi) 68.71/10.34 % (3201496)Instruction limit reached! 68.71/10.34 % (3201496)------------------------------ 68.71/10.34 % (3201496)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 68.71/10.34 % (3201496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 68.71/10.34 % (3201496)CaDiCaL version: 2.1.3 68.71/10.34 % (3201496)Termination reason: Instruction limit 68.71/10.34 % (3201496)Termination phase: Saturation 68.71/10.34 % (3201496)Time elapsed: 0.252 s 68.71/10.34 % (3201496)Peak memory usage: 17 MB 68.71/10.34 % (3201496)Instructions burned: 612 (million) 68.71/10.34 % (3201504)Refutation not found, incomplete strategy 68.71/10.34 % (3201504)------------------------------ 68.71/10.34 % (3201504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 68.71/10.34 % (3201504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 68.71/10.34 % (3201504)CaDiCaL version: 2.1.3 68.71/10.34 % (3201504)Termination reason: Refutation not found, incomplete strategy 68.71/10.35 % (3201504)Time elapsed: 0.095 s 68.71/10.35 % (3201504)Peak memory usage: 16 MB 68.71/10.35 % (3201504)Instructions burned: 220 (million) 68.71/10.35 % (3201504)------------------------------ 68.71/10.35 % (3201504)------------------------------ 68.71/10.35 % (3201506)lrs+1002_14_sil=128000:e2e=on:si=on:urr=on:nwc=1.2:random_seed=2526941638:cond=fast:i=1003:bd=all:fsr=off:rtra=on:sup=off_1709 on theBenchmark for (1709ds/1003Mi) 68.71/10.35 % (3201507)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on 68.71/10.35 % (3201507)ott+1002_16_sil=128000:si=on:random_seed=1934423177:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_1708 on theBenchmark for (1708ds/409Mi) 68.71/10.35 % (3201463)Instruction limit reached! 68.71/10.35 % (3201463)------------------------------ 68.71/10.35 % (3201463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 68.71/10.35 % (3201463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 68.71/10.35 % (3201463)CaDiCaL version: 2.1.3 68.71/10.35 % (3201463)Termination reason: Instruction limit 68.71/10.35 % (3201463)Termination phase: Saturation 68.71/10.35 % (3201463)Time elapsed: 1.334 s 68.71/10.35 % (3201463)Peak memory usage: 19 MB 68.71/10.35 % (3201463)Instructions burned: 1725 (million) 68.71/10.35 % (3201511)ott+10_1024_sil=128000:tgt=ground:cnfonf=lazy_pi_sigma_gen:si=on:sp=const_frequency:sos=on:lma=off:bsr=on:uwa=one_side_interpreted:nwc=20:random_seed=3525627067:cond=on:i=403:kws=precedence:erml=3:bs=unit_only:bd=all:rtra=on:ss=axioms:er=known:ntd=on_1707 on theBenchmark for (1707ds/403Mi) 68.71/10.35 % (3201506)Refutation not found, incomplete strategy 68.71/10.35 % (3201506)------------------------------ 68.71/10.35 % (3201506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 68.71/10.35 % (3201506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 68.71/10.35 % (3201506)CaDiCaL version: 2.1.3 68.71/10.35 % (3201506)Termination reason: Refutation not found, incomplete strategy 68.71/10.35 % (3201506)Time elapsed: 0.212 s 68.71/10.35 % (3201506)Peak memory usage: 15 MB 68.71/10.35 % (3201506)Instructions burned: 466 (million) 68.71/10.35 % (3201506)------------------------------ 68.71/10.35 % (3201506)------------------------------ 68.71/10.35 % (3201507)Instruction limit reached! 68.71/10.35 % (3201507)------------------------------ 68.71/10.35 % (3201507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 68.71/10.35 % (3201507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 68.71/10.35 % (3201507)CaDiCaL version: 2.1.3 68.71/10.35 % (3201507)Termination reason: Instruction limit 68.71/10.35 % (3201507)Termination phase: Saturation 68.71/10.35 % (3201507)Time elapsed: 0.205 s 68.71/10.35 % (3201507)Peak memory usage: 14 MB 68.71/10.35 % (3201507)Instructions burned: 409 (million) 68.71/10.35 % (3201513)lrs+10_1_sil=128000:fde=none:cnfonf=lazy_pi_sigma_gen:si=on:random_seed=1444754456:st=2:i=6843:sd=2:bd=all:rtra=on:sup=off:ss=axioms_1706 on theBenchmark for (1706ds/6843Mi) 68.71/10.35 % (3201514)lrs+10_2:1_si=on:random_seed=1160191910:s2a=on:i=506:rtra=on:fe=abstraction_1706 on theBenchmark for (1706ds/506Mi) 68.71/10.35 % (3201511)Refutation not found, incomplete strategy 68.71/10.35 % (3201511)------------------------------ 68.71/10.35 % (3201511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.62 % (3201511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.62 % (3201511)CaDiCaL version: 2.1.3 70.10/10.62 % (3201511)Termination reason: Refutation not found, incomplete strategy 70.10/10.62 % (3201511)Time elapsed: 0.066 s 70.10/10.62 % (3201511)Peak memory usage: 16 MB 70.10/10.62 % (3201511)Instructions burned: 151 (million) 70.10/10.62 % (3201511)------------------------------ 70.10/10.62 % (3201511)------------------------------ 70.10/10.62 % (3201513)Refutation not found, incomplete strategy 70.10/10.62 % (3201513)------------------------------ 70.10/10.62 % (3201513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.62 % (3201513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.62 % (3201513)CaDiCaL version: 2.1.3 70.10/10.62 % (3201513)Termination reason: Refutation not found, incomplete strategy 70.10/10.62 % (3201513)Time elapsed: 0.025 s 70.10/10.62 % (3201513)Peak memory usage: 15 MB 70.10/10.62 % (3201513)Instructions burned: 105 (million) 70.10/10.62 % (3201513)------------------------------ 70.10/10.62 % (3201513)------------------------------ 70.10/10.62 % (3201518)WARNING Broken Constraint: if positive_literal_split_queue_ratios(32,1) has been set then positive_literal_split_queue(off) is equal to on 70.10/10.62 % (3201518)ott+1002_3:2_to=kbo:sil=128000:cnfonf=lazy_gen:si=on:sp=reverse_frequency:lma=off:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=1.5:random_seed=1427438216:cond=fast:i=416:fgj=on:bd=preordered:rtra=on_1706 on theBenchmark for (1706ds/416Mi) 70.10/10.62 % (3201489)Instruction limit reached! 70.10/10.62 % (3201489)------------------------------ 70.10/10.62 % (3201489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.62 % (3201489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.62 % (3201489)CaDiCaL version: 2.1.3 70.10/10.62 % (3201489)Termination reason: Instruction limit 70.10/10.62 % (3201489)Termination phase: Saturation 70.10/10.62 % (3201489)Time elapsed: 0.865 s 70.10/10.62 % (3201489)Peak memory usage: 15 MB 70.10/10.62 % (3201489)Instructions burned: 1298 (million) 70.10/10.62 % (3201517)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=901848908:uwa_fpi=on:i=888:doe=on:bd=preordered:rtra=on:fsd=on_1706 on theBenchmark for (1706ds/888Mi) 70.10/10.62 % (3201520)dis+10_3:2_sfv=off:to=kbo:plsq=on:fde=unused:e2e=on:si=on:sp=reverse_frequency:acc=on:uwa=off:fd=preordered:slsqc=1:pe=on:slsq=on:random_seed=934707457:hsq=on:hsqr=16,1:avsq=on:s2a=on:i=13534:hsql=off:nm=16:nicw=on:ins=20:rtra=on:ss=axioms:ntd=on_1706 on theBenchmark for (1706ds/13534Mi) 70.10/10.62 % (3201518)Instruction limit reached! 70.10/10.62 % (3201518)------------------------------ 70.10/10.62 % (3201518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.62 % (3201518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.62 % (3201518)CaDiCaL version: 2.1.3 70.10/10.62 % (3201518)Termination reason: Instruction limit 70.10/10.62 % (3201518)Termination phase: Saturation 70.10/10.62 % (3201518)Time elapsed: 0.095 s 70.10/10.62 % (3201518)Peak memory usage: 17 MB 70.10/10.62 % (3201518)Instructions burned: 418 (million) 70.10/10.62 % (3201533)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(10) has been set then forward_subsumption_demodulation(off) is equal to on 70.10/10.62 % (3201533)dis+1002_3_tgt=ground:cnfonf=lazy_simp:si=on:sp=unary_first:cbe=off:uwa=ground:updr=off:random_seed=4019764569:i=206:fgj=on:hud=10:nm=30:rtra=on:fsdmm=10_1705 on theBenchmark for (1705ds/206Mi) 70.10/10.62 % (3201520)Refutation not found, incomplete strategy 70.10/10.62 % (3201520)------------------------------ 70.10/10.62 % (3201520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.62 % (3201520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.62 % (3201520)CaDiCaL version: 2.1.3 70.10/10.62 % (3201520)Termination reason: Refutation not found, incomplete strategy 70.10/10.62 % (3201520)Time elapsed: 0.095 s 70.10/10.62 % (3201520)Peak memory usage: 15 MB 70.10/10.62 % (3201520)Instructions burned: 220 (million) 70.10/10.62 % (3201520)------------------------------ 70.10/10.62 % (3201520)------------------------------ 70.10/10.62 % (3201545)dis+1010_1_sfv=off:slsqr=2,1:to=kbo:plsq=on:cnfonf=lazy_simp:si=on:cbe=off:uwa=hol:nwc=2:s2agt=16:slsq=on:random_seed=253285602:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2295:avsqr=1,16:aac=none:hud=3:rtra=on_1704 on theBenchmark for (1704ds/2295Mi) 70.10/10.62 % (3201533)Instruction limit reached! 70.10/10.62 % (3201533)------------------------------ 70.10/10.62 % (3201533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.62 % (3201533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.62 % (3201533)CaDiCaL version: 2.1.3 70.10/10.62 % (3201533)Termination reason: Instruction limit 70.10/10.62 % (3201533)Termination phase: Saturation 70.10/10.62 % (3201533)Time elapsed: 0.043 s 70.10/10.62 % (3201533)Peak memory usage: 12 MB 70.10/10.62 % (3201533)Instructions burned: 210 (million) 70.10/10.62 % (3201562)ott+1010_1_to=lpo:sil=128000:fde=none:si=on:sp=unary_first:uwa=off:nwc=1:random_seed=3847849435:i=637:piset=not:ep=RST:bd=all:av=off:rtra=on_1704 on theBenchmark for (1704ds/637Mi) 70.10/10.62 % (3201514)Instruction limit reached! 70.10/10.62 % (3201514)------------------------------ 70.10/10.62 % (3201514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.62 % (3201514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.62 % (3201514)CaDiCaL version: 2.1.3 70.10/10.62 % (3201514)Termination reason: Instruction limit 70.10/10.62 % (3201514)Termination phase: Saturation 70.10/10.62 % (3201514)Time elapsed: 0.204 s 70.10/10.62 % (3201514)Peak memory usage: 15 MB 70.10/10.62 % (3201514)Instructions burned: 508 (million) 70.10/10.62 % (3201574)dis+1002_15:31_sil=128000:cnfonf=lazy_not_gen:si=on:cbe=off:uwa=off:random_seed=3948623563:hsq=on:i=667:rtra=on:ixr=off_1704 on theBenchmark for (1704ds/667Mi) 70.10/10.62 % (3201562)Instruction limit reached! 70.10/10.62 % (3201562)------------------------------ 70.10/10.62 % (3201562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.62 % (3201562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.62 % (3201562)CaDiCaL version: 2.1.3 70.10/10.62 % (3201562)Termination reason: Instruction limit 70.10/10.62 % (3201562)Termination phase: Saturation 70.10/10.62 % (3201562)Time elapsed: 0.149 s 70.10/10.62 % (3201562)Peak memory usage: 18 MB 70.10/10.62 % (3201562)Instructions burned: 638 (million) 70.10/10.62 % (3201621)lrs-1004_16_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:lma=off:uwa=off:random_seed=155693765:i=1801:bd=preordered:nm=32:rtra=on:fdi=1024_1702 on theBenchmark for (1702ds/1801Mi) 70.10/10.62 % (3201517)Instruction limit reached! 70.10/10.62 % (3201517)------------------------------ 70.10/10.62 % (3201517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.62 % (3201517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.62 % (3201517)CaDiCaL version: 2.1.3 70.10/10.62 % (3201517)Termination reason: Instruction limit 70.10/10.62 % (3201517)Termination phase: Saturation 70.10/10.62 % (3201517)Time elapsed: 0.406 s 70.10/10.62 % (3201517)Peak memory usage: 14 MB 70.10/10.62 % (3201517)Instructions burned: 889 (million) 70.10/10.62 % (3201651)lrs+1002_1024_anc=all_dependent:sil=128000:drc=off:cnfonf=lazy_not_be_gen:si=on:cbe=off:cs=on:random_seed=1498337117:i=555:aac=none:rtra=on:fe=abstraction:ntd=on_1701 on theBenchmark for (1701ds/555Mi) 70.10/10.62 % (3201574)Instruction limit reached! 70.10/10.62 % (3201574)------------------------------ 70.10/10.62 % (3201574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.62 % (3201574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.62 % (3201574)CaDiCaL version: 2.1.3 70.10/10.62 % (3201574)Termination reason: Instruction limit 70.10/10.62 % (3201574)Termination phase: Saturation 70.10/10.62 % (3201574)Time elapsed: 0.262 s 70.10/10.62 % (3201574)Peak memory usage: 14 MB 70.10/10.62 % (3201574)Instructions burned: 669 (million) 70.10/10.62 % (3201336)Instruction limit reached! 70.10/10.62 % (3201336)------------------------------ 70.10/10.62 % (3201336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.62 % (3201336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.62 % (3201336)CaDiCaL version: 2.1.3 70.10/10.62 % (3201336)Termination reason: Instruction limit 70.10/10.62 % (3201336)Termination phase: Saturation 70.10/10.62 % (3201336)Time elapsed: 4.741 s 70.10/10.62 % (3201336)Peak memory usage: 42 MB 70.10/10.62 % (3201336)Instructions burned: 6360 (million) 70.10/10.62 % (3201677)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=2478521416:i=88:s2at=3:nm=2:rtra=on:rawr=on_1701 on theBenchmark for (1701ds/88Mi) 70.10/10.62 % (3201691)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=1033256368:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_1701 on theBenchmark for (1701ds/280Mi) 70.10/10.62 % (3201677)Instruction limit reached! 70.10/10.62 % (3201677)------------------------------ 70.10/10.62 % (3201677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.62 % (3201677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.62 % (3201677)CaDiCaL version: 2.1.3 70.10/10.62 % (3201677)Termination reason: Instruction limit 70.10/10.62 % (3201677)Termination phase: Property scanning 70.10/10.62 % (3201677)Time elapsed: 0.034 s 70.10/10.62 % (3201677)Peak memory usage: 11 MB 70.10/10.62 % (3201677)Instructions burned: 88 (million) 70.10/10.62 % (3201545) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3200883-3201545"... 70.10/10.62 % (3201699)dis+10_5:4_e2e=on:si=on:urr=on:uwa=interpreted_only:nwc=3:random_seed=1785808602:s2a=on:i=3166:bd=preordered:rtra=on_1700 on theBenchmark for (1700ds/3166Mi) 70.10/10.62 % (3201691)Instruction limit reached! 70.10/10.62 % (3201691)------------------------------ 70.10/10.62 % (3201691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.62 % (3201691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.62 % (3201691)CaDiCaL version: 2.1.3 70.10/10.62 % (3201691)Termination reason: Instruction limit 70.10/10.62 % (3201691)Termination phase: Saturation 70.10/10.62 % (3201691)Time elapsed: 0.107 s 70.10/10.62 % (3201691)Peak memory usage: 13 MB 70.10/10.62 % (3201691)Instructions burned: 280 (million) 70.10/10.62 % (3201701)WARNING Broken Constraint: if avatar_split_queue_ratios(1,2) has been set then avatar_split_queue(off) is equal to on 70.10/10.62 % (3201701)lrs+1010_128_to=kbo:plsq=on:plsqc=4:cnfonf=lazy_pi_sigma_gen:bsd=on:si=on:sp=occurrence:sos=on:plsql=on:random_seed=3178890788:i=4201:add=off:avsqr=1,2:bsdmm=10:fsr=off:rtra=on:fe=axiom_1699 on theBenchmark for (1699ds/4201Mi) 70.10/10.62 % (3201651)Instruction limit reached! 70.10/10.62 % (3201651)------------------------------ 70.10/10.62 % (3201651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.62 % (3201651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.62 % (3201651)CaDiCaL version: 2.1.3 70.10/10.62 % (3201651)Termination reason: Instruction limit 70.10/10.62 % (3201651)Termination phase: Saturation 70.10/10.62 % (3201651)Time elapsed: 0.211 s 70.10/10.62 % (3201651)Peak memory usage: 12 MB 70.10/10.62 % (3201651)Instructions burned: 555 (million) 70.10/10.62 % (3201703)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=561730941:i=2352:rtra=on:ixr=off_1699 on theBenchmark for (1699ds/2352Mi) 70.10/10.62 % (3201545)...printing done. 70.10/10.62 % (3201545)Refutation found. Thanks to Tanya! 70.10/10.62 % SZS status Theorem for theBenchmark 70.10/10.62 % SZS output start Proof for theBenchmark 70.10/10.62 thf(type_def_5, type, mworld: $tType). 70.10/10.62 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType). 70.10/10.62 thf(func_def_0, type, mrel: (mworld > mworld > $o)). 70.10/10.62 thf(func_def_1, type, mactual: mworld). 70.10/10.62 thf(func_def_2, type, mlocal: ((mworld > $o) > $o)). 70.10/10.62 thf(func_def_4, type, mnot: ((mworld > $o) > mworld > $o)). 70.10/10.62 thf(func_def_5, type, mand: ((mworld > $o) > (mworld > $o) > mworld > $o)). 70.10/10.62 thf(func_def_6, type, mor: ((mworld > $o) > (mworld > $o) > mworld > $o)). 70.10/10.62 thf(func_def_7, type, mimplies: ((mworld > $o) > (mworld > $o) > mworld > $o)). 70.10/10.62 thf(func_def_8, type, mequiv: ((mworld > $o) > (mworld > $o) > mworld > $o)). 70.10/10.62 thf(func_def_9, type, mbox: ((mworld > $o) > mworld > $o)). 70.10/10.62 thf(func_def_10, type, mdia: ((mworld > $o) > mworld > $o)). 70.10/10.62 thf(func_def_11, type, mforall_di: (($i > mworld > $o) > mworld > $o)). 70.10/10.62 thf(func_def_12, type, mexists_di: (($i > mworld > $o) > mworld > $o)). 70.10/10.62 thf(func_def_18, type, qmltpeq: ($i > $i > mworld > $o)). 70.10/10.62 thf(func_def_19, type, inv: ($i > $i)). 70.10/10.62 thf(func_def_20, type, op: ($i > $i > $i)). 70.10/10.62 thf(func_def_23, type, vIMP: ($o > $o > $o)). 70.10/10.62 thf(func_def_24, type, db2: !>[X0: $tType]:(X0)). 70.10/10.62 thf(func_def_25, type, db0: !>[X0: $tType]:(X0)). 70.10/10.62 thf(func_def_26, type, db1: !>[X0: $tType]:(X0)). 70.10/10.62 thf(func_def_27, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))). 70.10/10.62 thf(func_def_28, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))). 70.10/10.62 thf(func_def_29, type, vAND: ($o > $o > $o)). 70.10/10.62 thf(func_def_30, type, vIFF: ($o > $o > $o)). 70.10/10.62 thf(func_def_31, type, vOR: ($o > $o > $o)). 70.10/10.62 thf(func_def_32, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))). 70.10/10.62 thf(func_def_33, type, vNOT: ($o > $o)). 70.10/10.62 thf(func_def_34, type, db4: !>[X0: $tType]:(X0)). 70.10/10.62 thf(func_def_35, type, db3: !>[X0: $tType]:(X0)). 70.10/10.62 thf(func_def_36, type, db5: !>[X0: $tType]:(X0)). 70.10/10.62 thf(func_def_37, type, db6: !>[X0: $tType]:(X0)). 70.10/10.62 thf(func_def_38, type, db7: !>[X0: $tType]:(X0)). 70.10/10.62 thf(func_def_39, type, sK0: mworld). 70.10/10.62 thf(func_def_40, type, sK1: (mworld > mworld)). 70.10/10.62 thf(func_def_41, type, sK2: (mworld > mworld)). 70.10/10.62 thf(func_def_42, type, sK3: (mworld > mworld)). 70.10/10.62 thf(func_def_43, type, sK4: (mworld > mworld)). 70.10/10.62 thf(func_def_44, type, sK5: mworld). 70.10/10.62 thf(func_def_45, type, sK6: mworld). 70.10/10.62 thf(func_def_46, type, sK7: mworld). 70.10/10.62 thf(func_def_47, type, sK8: (mworld > mworld)). 70.10/10.62 thf(func_def_48, type, sK9: (mworld > mworld)). 70.10/10.62 thf(func_def_49, type, sK10: (mworld > mworld)). 70.10/10.62 thf(func_def_50, type, sK11: mworld). 70.10/10.62 thf(func_def_51, type, sK12: mworld). 70.10/10.62 thf(func_def_52, type, sK13: (mworld > mworld)). 70.10/10.62 thf(func_def_53, type, sK14: (mworld > mworld)). 70.10/10.62 thf(func_def_54, type, sK15: (mworld > mworld)). 70.10/10.62 thf(func_def_55, type, sK16: (mworld > mworld)). 70.10/10.62 thf(func_def_56, type, sK17: mworld). 70.10/10.62 thf(func_def_57, type, sK18: mworld). 70.10/10.62 thf(func_def_58, type, sK19: (mworld > mworld)). 70.10/10.62 thf(func_def_59, type, sK20: (mworld > mworld)). 70.10/10.62 thf(func_def_60, type, sK21: (mworld > mworld)). 70.10/10.62 thf(func_def_61, type, sK22: (mworld > mworld)). 70.10/10.62 thf(func_def_62, type, sK23: (mworld > mworld)). 70.10/10.62 thf(func_def_63, type, sK24: (mworld > mworld)). 70.10/10.62 thf(func_def_64, type, sK25: mworld). 70.10/10.62 thf(func_def_65, type, sK26: (mworld > mworld)). 70.10/10.62 thf(func_def_66, type, sK27: (mworld > mworld)). 70.10/10.62 thf(func_def_67, type, sK28: (mworld > mworld)). 70.10/10.62 thf(func_def_68, type, sK29: mworld). 70.10/10.62 thf(func_def_69, type, sK30: mworld). 70.10/10.62 thf(func_def_70, type, sK31: mworld). 70.10/10.62 thf(func_def_71, type, sK32: (mworld > mworld)). 70.10/10.62 thf(func_def_72, type, sK33: (mworld > mworld)). 70.10/10.62 thf(func_def_73, type, sK34: mworld). 70.10/10.62 thf(func_def_74, type, sK35: mworld). 70.10/10.62 thf(func_def_75, type, sK36: ($i > mworld > $i > mworld)). 70.10/10.62 thf(f1,axiom,( 70.10/10.62 (mlocal = (^[X0 : (mworld > $o)] : ((X0 @ mactual))))), 70.10/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def)). 70.10/10.62 thf(f2,axiom,( 70.10/10.62 ((^[X0 : (mworld > $o), X1 : mworld] : (~(X0 @ X1))) = mnot)), 70.10/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def)). 70.10/10.62 thf(f3,axiom,( 70.10/10.62 (mand = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))), 70.10/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def)). 70.10/10.62 thf(f4,axiom,( 70.10/10.62 (mor = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X1 @ X2) | (X0 @ X2))))), 70.10/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def)). 70.10/10.62 thf(f7,axiom,( 70.10/10.62 (mbox = (^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))), 70.10/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def)). 70.10/10.62 thf(f18,conjecture,( 70.10/10.62 (mlocal @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ (mbox @ (mnot @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))))))))), 70.10/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1)). 70.10/10.62 thf(f19,negated_conjecture,( 70.10/10.62 ~(mlocal @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ (mbox @ (mnot @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))))))))), 70.10/10.62 inference(negated_conjecture,[status(cth)],[f18])). 70.10/10.62 thf(f29,axiom,( 70.10/10.62 ! [X1 : mworld,X2 : mworld,X0 : mworld] : (((mrel @ X0 @ X2) & (mrel @ X0 @ X1)) => (mrel @ X2 @ X1))), 70.10/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_euclidean)). 70.10/10.62 thf(f42,plain,( 70.10/10.62 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))), 70.10/10.62 inference(fool_elimination,[],[f1])). 70.10/10.62 thf(f51,plain,( 70.10/10.62 (mor = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X1 @ X2) | (X0 @ X2))))), 70.10/10.62 inference(rectify,[],[f4])). 70.10/10.62 thf(f52,plain,( 70.10/10.62 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))))), 70.10/10.62 inference(fool_elimination,[],[f51])). 70.10/10.62 thf(f63,plain,( 70.10/10.62 (mand = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))), 70.10/10.62 inference(rectify,[],[f3])). 70.10/10.62 thf(f64,plain,( 70.10/10.62 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))), 70.10/10.62 inference(fool_elimination,[],[f63])). 70.10/10.62 thf(f65,plain,( 70.10/10.62 ((^[X0 : (mworld > $o), X1 : mworld] : (~(X0 @ X1))) = mnot)), 70.10/10.62 inference(rectify,[],[f2])). 70.10/10.62 thf(f66,plain,( 70.10/10.62 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))), 70.10/10.62 inference(fool_elimination,[],[f65])). 70.10/10.62 thf(f73,plain,( 70.10/10.62 (mbox = (^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))), 70.10/10.62 inference(rectify,[],[f7])). 70.10/10.62 thf(f74,plain,( 70.10/10.62 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))), 70.10/10.62 inference(fool_elimination,[],[f73])). 70.10/10.62 thf(f81,plain,( 70.10/10.62 ~(mlocal @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ (mbox @ (mnot @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3)))))))))))))))), 70.10/10.62 inference(rectify,[],[f19])). 70.10/10.62 thf(f82,plain,( 70.10/10.62 ($true = ((~ (mlocal @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ (mbox @ (mnot @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))))))))))), 70.10/10.62 inference(fool_elimination,[],[f81])). 70.10/10.62 thf(f83,plain,( 70.10/10.62 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((mrel @ X2 @ X1) & (mrel @ X2 @ X0)) => (mrel @ X1 @ X0))), 70.10/10.62 inference(rectify,[],[f29])). 70.10/10.62 thf(f84,plain,( 70.10/10.62 ($true = ((!! @ mworld @ (^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: (((mrel @ Y0 @ Y2) & (mrel @ Y0 @ Y1)) => (mrel @ Y1 @ Y2))))))))))), 70.10/10.62 inference(fool_elimination,[],[f83])). 70.10/10.62 thf(f92,plain,( 70.10/10.62 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))), 70.10/10.62 inference(cnf_transformation,[],[f42])). 70.10/10.62 thf(f97,plain,( 70.10/10.62 ($true = ((!! @ mworld @ (^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: (((mrel @ Y0 @ Y2) & (mrel @ Y0 @ Y1)) => (mrel @ Y1 @ Y2))))))))))), 70.10/10.62 inference(cnf_transformation,[],[f84])). 70.10/10.62 thf(f104,plain,( 70.10/10.62 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))), 70.10/10.62 inference(cnf_transformation,[],[f64])). 70.10/10.62 thf(f108,plain,( 70.10/10.62 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))))), 70.10/10.62 inference(cnf_transformation,[],[f52])). 70.10/10.62 thf(f110,plain,( 70.10/10.62 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))), 70.10/10.62 inference(cnf_transformation,[],[f66])). 70.10/10.62 thf(f111,plain,( 70.10/10.62 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))), 70.10/10.62 inference(cnf_transformation,[],[f74])). 70.10/10.62 thf(f115,plain,( 70.10/10.62 ($true = ((~ (mlocal @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ (mbox @ (mnot @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ (mor @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ (mand @ (mbox @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ (mand @ (mbox @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ (mbox @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))))))))))), 70.10/10.62 inference(cnf_transformation,[],[f82])). 70.10/10.62 thf(f136,plain,( 70.10/10.62 ($true = ((~ ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e3 @ e3) @ e3))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e0 @ e0) @ e0)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e1 @ e1) @ e0)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e2 @ e2) @ e0)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e3 @ e3) @ e0))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e0 @ e0) @ e1)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e1 @ e1) @ e1)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e2 @ e2) @ e1)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e3 @ e3) @ e1))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e0 @ e0) @ e2)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e1 @ e1) @ e2)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e2 @ e2) @ e2)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e3 @ e3) @ e2))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e0 @ e0) @ e3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e1 @ e1) @ e3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e2 @ e2) @ e3)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ (qmltpeq @ (op @ e3 @ e3) @ e3))))))))))))))))))), 70.10/10.62 inference(definition_unfolding,[],[f115,f92,f108,f104,f111,f104,f111,f104,f111,f111,f108,f104,f111,f104,f111,f104,f111,f111,f108,f104,f111,f104,f111,f104,f111,f111,f108,f104,f111,f104,f111,f104,f111,f111,f111,f110,f108,f104,f111,f104,f111,f104,f111,f111,f108,f104,f111,f104,f111,f104,f111,f111,f108,f104,f111,f104,f111,f104,f111,f111,f104,f111,f104,f111,f104,f111,f111])). 70.10/10.62 thf(f143,plain,( 70.10/10.62 (((~ (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))) | (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))) | (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))) | ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1)))))))))))))))))))) = $true)), 70.10/10.62 inference(beta-eta_normalization,[],[f136])). 70.10/10.62 thf(f171,plain,( 70.10/10.62 ($false = ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))) | (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))) | (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))) | ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1))))))))))))))))))))), 70.10/10.62 inference(not_proxy_clausification,[],[f143])). 70.10/10.62 thf(f200,plain,( 70.10/10.62 ( ! [X1 : mworld] : (((((^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: (((mrel @ Y0 @ Y2) & (mrel @ Y0 @ Y1)) => (mrel @ Y1 @ Y2))))))) @ X1)) = $true)) )), 70.10/10.62 inference(pi_proxy_clausification,[],[f97])). 70.10/10.62 thf(f201,plain,( 70.10/10.62 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (((mrel @ X1 @ Y1) & (mrel @ X1 @ Y0)) => (mrel @ Y0 @ Y1))))))))) )), 70.10/10.62 inference(beta-eta_normalization,[],[f200])). 70.10/10.62 thf(f211,plain,( 70.10/10.62 ($false = ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))) | (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))) | (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))) | ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1)))))))))))))))))))), 70.10/10.62 inference(or_proxy_clausification,[],[f171])). 70.10/10.62 thf(f212,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))))), 70.10/10.62 inference(or_proxy_clausification,[],[f171])). 70.10/10.62 thf(f246,plain,( 70.10/10.62 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (((mrel @ X1 @ Y1) & (mrel @ X1 @ Y0)) => (mrel @ Y0 @ Y1))))) @ X2)))) )), 70.10/10.62 inference(pi_proxy_clausification,[],[f201])). 70.10/10.62 thf(f247,plain,( 70.10/10.62 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: (((mrel @ X1 @ Y0) & (mrel @ X1 @ X2)) => (mrel @ X2 @ Y0))))) = $true)) )), 70.10/10.62 inference(beta-eta_normalization,[],[f246])). 70.10/10.62 thf(f260,plain,( 70.10/10.62 ($false = ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))) | (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))) | (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))) | ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1))))))))))))))))))), 70.10/10.62 inference(or_proxy_clausification,[],[f211])). 70.10/10.62 thf(f261,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))))), 70.10/10.62 inference(or_proxy_clausification,[],[f211])). 70.10/10.62 thf(f262,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f212])). 70.10/10.62 thf(f306,plain,( 70.10/10.62 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: (((mrel @ X1 @ Y0) & (mrel @ X1 @ X2)) => (mrel @ X2 @ Y0))) @ X3)))) )), 70.10/10.62 inference(pi_proxy_clausification,[],[f247])). 70.10/10.62 thf(f307,plain,( 70.10/10.62 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((((mrel @ X1 @ X3) & (mrel @ X1 @ X2)) => (mrel @ X2 @ X3))) = $true)) )), 70.10/10.62 inference(beta-eta_normalization,[],[f306])). 70.10/10.62 thf(f321,plain,( 70.10/10.62 ($false = ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))) | (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))) | (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))) | ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1)))))))))))))))))), 70.10/10.62 inference(or_proxy_clausification,[],[f260])). 70.10/10.62 thf(f322,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))), 70.10/10.62 inference(or_proxy_clausification,[],[f260])). 70.10/10.62 thf(f323,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f261])). 70.10/10.62 thf(f324,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ sK0)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f262])). 70.10/10.62 thf(f325,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0)))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))), 70.10/10.62 inference(beta-eta_normalization,[],[f324])). 70.10/10.62 thf(f374,plain,( 70.10/10.62 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = (((mrel @ X1 @ X3) & (mrel @ X1 @ X2)))) | ($true = ((mrel @ X2 @ X3)))) )), 70.10/10.62 inference(imp_proxy_clausification,[],[f307])). 70.10/10.62 thf(f389,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))) | (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))) | (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))) | ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1))))))))))))))))), 70.10/10.62 inference(or_proxy_clausification,[],[f321])). 70.10/10.62 thf(f390,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))), 70.10/10.62 inference(or_proxy_clausification,[],[f321])). 70.10/10.62 thf(f391,plain,( 70.10/10.62 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $false) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f322])). 70.10/10.62 thf(f392,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f323])). 70.10/10.62 thf(f393,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f325])). 70.10/10.62 thf(f394,plain,( 70.10/10.62 (((mrel @ mactual @ sK0)) = $true) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f325])). 70.10/10.62 thf(f441,plain,( 70.10/10.62 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((mrel @ X2 @ X3))) | ($false = ((mrel @ X1 @ X3))) | (((mrel @ X1 @ X2)) = $false)) )), 70.10/10.62 inference(and_proxy_clausification,[],[f374])). 70.10/10.62 thf(f459,plain,( 70.10/10.62 ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (~ (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y1))))))) | (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y1))))))) | (((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y1))))))) | ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y1)))) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y1)))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y1))))))))))))) @ sK5)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f389])). 70.10/10.62 thf(f460,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK5) => (~ (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))))))), 70.10/10.62 inference(beta-eta_normalization,[],[f459])). 70.10/10.62 thf(f461,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f390])). 70.10/10.62 thf(f462,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ sK6)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f391])). 70.10/10.62 thf(f463,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) | ($false = (((mrel @ mactual @ sK6) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))))), 70.10/10.62 inference(beta-eta_normalization,[],[f462])). 70.10/10.62 thf(f464,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ sK7))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f392])). 70.10/10.62 thf(f465,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = (((mrel @ mactual @ sK7) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7)))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))), 70.10/10.62 inference(beta-eta_normalization,[],[f464])). 70.10/10.62 thf(f466,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | (((mrel @ mactual @ sK0)) = $true)), 70.10/10.62 inference(and_proxy_clausification,[],[f394])). 70.10/10.62 thf(f467,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f393])). 70.10/10.62 thf(f536,plain,( 70.10/10.62 ($false = ((~ (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f460])). 70.10/10.62 thf(f537,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK5)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f460])). 70.10/10.62 thf(f538,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f461])). 70.10/10.62 thf(f539,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = (((mrel @ mactual @ sK6) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6)))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f463])). 70.10/10.62 thf(f540,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ sK11))) | ($false = (((mrel @ mactual @ sK7) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f465])). 70.10/10.62 thf(f541,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK7) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7)))) | ($false = (((mrel @ mactual @ sK11) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11)))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))), 70.10/10.62 inference(beta-eta_normalization,[],[f540])). 70.10/10.62 thf(f542,plain,( 70.10/10.62 (((mrel @ mactual @ sK0)) = $true) | ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ sK12)) = $false) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f466])). 70.10/10.62 thf(f543,plain,( 70.10/10.62 ((((mrel @ mactual @ sK12) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) = $false) | (((mrel @ mactual @ sK0)) = $true) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))), 70.10/10.62 inference(beta-eta_normalization,[],[f542])). 70.10/10.62 thf(f544,plain,( 70.10/10.62 ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ sK12)) = $false) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f467])). 70.10/10.62 thf(f545,plain,( 70.10/10.62 ((((mrel @ mactual @ sK12) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) = $false) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0)))), 70.10/10.62 inference(beta-eta_normalization,[],[f544])). 70.10/10.62 thf(f616,plain,( 70.10/10.62 (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))))) = $true)), 70.10/10.62 inference(not_proxy_clausification,[],[f536])). 70.10/10.62 thf(f617,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ sK17))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f538])). 70.10/10.62 thf(f618,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) | ($false = (((mrel @ mactual @ sK17) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))))), 70.10/10.62 inference(beta-eta_normalization,[],[f617])). 70.10/10.62 thf(f619,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK6) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6)))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ sK18)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f539])). 70.10/10.62 thf(f620,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK6) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6)))) | ($false = (((mrel @ mactual @ sK18) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))), 70.10/10.62 inference(beta-eta_normalization,[],[f619])). 70.10/10.62 thf(f621,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | ($false = (((mrel @ mactual @ sK11) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f541])). 70.10/10.62 thf(f622,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($false = (((mrel @ mactual @ sK11) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11)))) | (((mrel @ mactual @ sK7)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f541])). 70.10/10.62 thf(f623,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | (((mrel @ mactual @ sK0)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f543])). 70.10/10.62 thf(f624,plain,( 70.10/10.62 (((mrel @ mactual @ sK0)) = $true) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | ($true = ((mrel @ mactual @ sK12)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f543])). 70.10/10.62 thf(f625,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f545])). 70.10/10.62 thf(f626,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($true = ((mrel @ mactual @ sK12)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f545])). 70.10/10.62 thf(f689,plain,( 70.10/10.62 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))))) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) = $true)), 70.10/10.62 inference(or_proxy_clausification,[],[f616])). 70.10/10.62 thf(f690,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK17) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17)))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ sK25)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f618])). 70.10/10.62 thf(f691,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK17) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17)))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25))))), 70.10/10.62 inference(beta-eta_normalization,[],[f690])). 70.10/10.62 thf(f692,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK18) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f620])). 70.10/10.62 thf(f693,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((mrel @ mactual @ sK6))) | ($false = (((mrel @ mactual @ sK18) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f620])). 70.10/10.62 thf(f694,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | ($false = (((mrel @ mactual @ sK11) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11)))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f621])). 70.10/10.62 thf(f695,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK11) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11)))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | (((mrel @ mactual @ sK7)) = $true) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f622])). 70.10/10.62 thf(f696,plain,( 70.10/10.62 (((mrel @ mactual @ sK0)) = $true) | ($true = ((mrel @ mactual @ sK12))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f624])). 70.10/10.62 thf(f697,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | (((mrel @ mactual @ sK0)) = $true)), 70.10/10.62 inference(and_proxy_clausification,[],[f623])). 70.10/10.62 thf(f698,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($true = ((mrel @ mactual @ sK12))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f626])). 70.10/10.62 thf(f699,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12)))), 70.10/10.62 inference(and_proxy_clausification,[],[f625])). 70.10/10.62 thf(f769,plain,( 70.10/10.62 ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) = $true) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) = $true)), 70.10/10.62 inference(and_proxy_clausification,[],[f689])). 70.10/10.62 thf(f770,plain,( 70.10/10.62 (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true)), 70.10/10.62 inference(and_proxy_clausification,[],[f689])). 70.10/10.62 thf(f771,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f691])). 70.10/10.62 thf(f772,plain,( 70.10/10.62 (((mrel @ mactual @ sK17)) = $true) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f691])). 70.10/10.62 thf(f773,plain,( 70.10/10.62 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) = $false) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((mrel @ mactual @ sK6))) | ($false = (((mrel @ mactual @ sK18) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18))))), 70.10/10.62 inference(and_proxy_clausification,[],[f693])). 70.10/10.62 thf(f774,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f692])). 70.10/10.62 thf(f775,plain,( 70.10/10.62 ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | (((mrel @ mactual @ sK18)) = $true) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f692])). 70.10/10.62 thf(f776,plain,( 70.10/10.62 ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ sK29))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = (((mrel @ mactual @ sK11) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f694])). 70.10/10.62 thf(f777,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = (((mrel @ mactual @ sK29) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29)))) | ($false = (((mrel @ mactual @ sK11) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11)))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7)))), 70.10/10.62 inference(beta-eta_normalization,[],[f776])). 70.10/10.62 thf(f778,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | (((mrel @ mactual @ sK7)) = $true) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f695])). 70.10/10.62 thf(f779,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK11))) | (((mrel @ mactual @ sK7)) = $true) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f695])). 70.10/10.62 thf(f780,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ sK30))) | ($true = ((mrel @ mactual @ sK12))) | (((mrel @ mactual @ sK0)) = $true)), 70.10/10.62 inference(sigma_proxy_clausification,[],[f696])). 70.10/10.62 thf(f781,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | ($false = (((mrel @ mactual @ sK30) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30)))) | (((mrel @ mactual @ sK0)) = $true) | ($true = ((mrel @ mactual @ sK12)))), 70.10/10.62 inference(beta-eta_normalization,[],[f780])). 70.10/10.62 thf(f782,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ sK31))) | (((mrel @ mactual @ sK0)) = $true) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f697])). 70.10/10.62 thf(f783,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | (((mrel @ mactual @ sK0)) = $true) | ((((mrel @ mactual @ sK31) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) = $false) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12)))), 70.10/10.62 inference(beta-eta_normalization,[],[f782])). 70.10/10.62 thf(f784,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK12))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ sK31))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f698])). 70.10/10.62 thf(f785,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($true = ((mrel @ mactual @ sK12))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ((((mrel @ mactual @ sK31) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) = $false)), 70.10/10.62 inference(beta-eta_normalization,[],[f784])). 70.10/10.62 thf(f786,plain,( 70.10/10.62 ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ sK31))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f699])). 70.10/10.62 thf(f787,plain,( 70.10/10.62 ((((mrel @ mactual @ sK31) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) = $false) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0)))), 70.10/10.62 inference(beta-eta_normalization,[],[f786])). 70.10/10.62 thf(f852,plain,( 70.10/10.62 (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f769])). 70.10/10.62 thf(f853,plain,( 70.10/10.62 (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) = $true)), 70.10/10.62 inference(and_proxy_clausification,[],[f769])). 70.10/10.62 thf(f854,plain,( 70.10/10.62 ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true)), 70.10/10.62 inference(or_proxy_clausification,[],[f770])). 70.10/10.62 thf(f855,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17)))), 70.10/10.62 inference(and_proxy_clausification,[],[f771])). 70.10/10.62 thf(f856,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | (((mrel @ mactual @ sK17)) = $true)), 70.10/10.62 inference(and_proxy_clausification,[],[f772])). 70.10/10.62 thf(f857,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = (((mrel @ mactual @ sK18) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ sK34))) | ($true = ((mrel @ mactual @ sK6)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f773])). 70.10/10.62 thf(f858,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK18) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((mrel @ mactual @ sK6))) | ($false = (((mrel @ mactual @ sK34) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))))), 70.10/10.62 inference(beta-eta_normalization,[],[f857])). 70.10/10.62 thf(f859,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) = $false) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6)))), 70.10/10.62 inference(and_proxy_clausification,[],[f774])). 70.10/10.62 thf(f860,plain,( 70.10/10.62 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) = $false) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((mrel @ mactual @ sK18)) = $true) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6)))), 70.10/10.62 inference(and_proxy_clausification,[],[f775])). 70.10/10.62 thf(f861,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK29) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29)))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ sK35))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | ($false = (((mrel @ mactual @ sK11) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f777])). 70.10/10.62 thf(f862,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK11) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11)))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | ($false = (((mrel @ mactual @ sK35) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35)))) | ($false = (((mrel @ mactual @ sK29) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29))))), 70.10/10.62 inference(beta-eta_normalization,[],[f861])). 70.10/10.62 thf(f863,plain,( 70.10/10.62 (((mrel @ mactual @ sK7)) = $true) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ sK35))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f778])). 70.10/10.62 thf(f864,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = (((mrel @ mactual @ sK35) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35)))) | (((mrel @ mactual @ sK7)) = $true) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11)))), 70.10/10.62 inference(beta-eta_normalization,[],[f863])). 70.10/10.62 thf(f865,plain,( 70.10/10.62 ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ sK35))) | (((mrel @ mactual @ sK7)) = $true) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((mrel @ mactual @ sK11)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f779])). 70.10/10.62 thf(f866,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = (((mrel @ mactual @ sK35) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35)))) | (((mrel @ mactual @ sK7)) = $true) | ($true = ((mrel @ mactual @ sK11)))), 70.10/10.62 inference(beta-eta_normalization,[],[f865])). 70.10/10.62 thf(f867,plain,( 70.10/10.62 ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ sK31))) | ($false = (((mrel @ mactual @ sK30) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30)))) | ($true = ((mrel @ mactual @ sK12))) | (((mrel @ mactual @ sK0)) = $true)), 70.10/10.62 inference(sigma_proxy_clausification,[],[f781])). 70.10/10.62 thf(f868,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK12))) | (((mrel @ mactual @ sK0)) = $true) | ($false = (((mrel @ mactual @ sK30) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30)))) | ((((mrel @ mactual @ sK31) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) = $false)), 70.10/10.62 inference(beta-eta_normalization,[],[f867])). 70.10/10.62 thf(f869,plain,( 70.10/10.62 ((((mrel @ mactual @ sK31) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) = $false) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ sK30))) | (((mrel @ mactual @ sK0)) = $true) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f783])). 70.10/10.62 thf(f870,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK30) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30)))) | ((((mrel @ mactual @ sK31) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) = $false) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | (((mrel @ mactual @ sK0)) = $true)), 70.10/10.62 inference(beta-eta_normalization,[],[f869])). 70.10/10.62 thf(f871,plain,( 70.10/10.62 ((((mrel @ mactual @ sK31) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) = $false) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ sK30))) | ($true = ((mrel @ mactual @ sK12))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f785])). 70.10/10.62 thf(f872,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ((((mrel @ mactual @ sK31) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) = $false) | ($true = ((mrel @ mactual @ sK12))) | ($false = (((mrel @ mactual @ sK30) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30))))), 70.10/10.62 inference(beta-eta_normalization,[],[f871])). 70.10/10.62 thf(f873,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f787])). 70.10/10.62 thf(f874,plain,( 70.10/10.62 (((mrel @ mactual @ sK31)) = $true) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f787])). 70.10/10.62 thf(f930,plain,( 70.10/10.62 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) = $true)), 70.10/10.62 inference(or_proxy_clausification,[],[f852])). 70.10/10.62 thf(f931,plain,( 70.10/10.62 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) = $true) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true)), 70.10/10.62 inference(or_proxy_clausification,[],[f853])). 70.10/10.62 thf(f932,plain,( 70.10/10.62 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true)), 70.10/10.62 inference(and_proxy_clausification,[],[f854])). 70.10/10.62 thf(f933,plain,( 70.10/10.62 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true)), 70.10/10.62 inference(and_proxy_clausification,[],[f854])). 70.10/10.62 thf(f934,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))) = $false) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f855])). 70.10/10.62 thf(f935,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($false = (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))), 70.10/10.62 inference(beta-eta_normalization,[],[f934])). 70.10/10.62 thf(f936,plain,( 70.10/10.62 (((mrel @ mactual @ sK17)) = $true) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f856])). 70.10/10.62 thf(f937,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | (((mrel @ mactual @ sK17)) = $true) | ($false = (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))))), 70.10/10.62 inference(beta-eta_normalization,[],[f936])). 70.10/10.62 thf(f938,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK6))) | ($false = (((mrel @ mactual @ sK34) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34)))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false)), 70.10/10.62 inference(imp_proxy_clausification,[],[f858])). 70.10/10.62 thf(f939,plain,( 70.10/10.62 (((mrel @ mactual @ sK18)) = $true) | ($false = (((mrel @ mactual @ sK34) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34)))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((mrel @ mactual @ sK6)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f858])). 70.10/10.62 thf(f940,plain,( 70.10/10.62 (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) = $false) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f859])). 70.10/10.62 thf(f941,plain,( 70.10/10.62 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))) = $false) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | ($false = (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))))), 70.10/10.62 inference(beta-eta_normalization,[],[f940])). 70.10/10.62 thf(f942,plain,( 70.10/10.62 (((mrel @ mactual @ sK18)) = $true) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ sK34))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f860])). 70.10/10.62 thf(f943,plain,( 70.10/10.62 (((mrel @ mactual @ sK18)) = $true) | ($false = (((mrel @ mactual @ sK34) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34)))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6)))), 70.10/10.62 inference(beta-eta_normalization,[],[f942])). 70.10/10.62 thf(f944,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))) | ($false = (((mrel @ mactual @ sK29) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29)))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | ($false = (((mrel @ mactual @ sK35) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f862])). 70.10/10.62 thf(f945,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK35) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35)))) | ($false = (((mrel @ mactual @ sK29) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29)))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | ($true = ((mrel @ mactual @ sK11)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f862])). 70.10/10.62 thf(f946,plain,( 70.10/10.62 ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ sK29))) | (((mrel @ mactual @ sK7)) = $true) | ($false = (((mrel @ mactual @ sK35) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f864])). 70.10/10.62 thf(f947,plain,( 70.10/10.62 (((mrel @ mactual @ sK7)) = $true) | ($false = (((mrel @ mactual @ sK29) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))) | ($false = (((mrel @ mactual @ sK35) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35))))), 70.10/10.62 inference(beta-eta_normalization,[],[f946])). 70.10/10.62 thf(f948,plain,( 70.10/10.62 (((mrel @ mactual @ sK7)) = $true) | ($false = (((mrel @ mactual @ sK35) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35)))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ sK29))) | ($true = ((mrel @ mactual @ sK11)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f866])). 70.10/10.62 thf(f949,plain,( 70.10/10.62 (((mrel @ mactual @ sK7)) = $true) | ($false = (((mrel @ mactual @ sK35) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35)))) | ($true = ((mrel @ mactual @ sK11))) | ($false = (((mrel @ mactual @ sK29) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29))))), 70.10/10.62 inference(beta-eta_normalization,[],[f948])). 70.10/10.62 thf(f950,plain,( 70.10/10.62 ((((mrel @ mactual @ sK31) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) = $false) | (((mrel @ mactual @ sK0)) = $true) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30))) | ($true = ((mrel @ mactual @ sK12)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f868])). 70.10/10.62 thf(f951,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK30))) | ($true = ((mrel @ mactual @ sK12))) | ((((mrel @ mactual @ sK31) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) = $false) | (((mrel @ mactual @ sK0)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f868])). 70.10/10.62 thf(f952,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | ((((mrel @ mactual @ sK31) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) = $false) | (((mrel @ mactual @ sK0)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f870])). 70.10/10.62 thf(f953,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK30))) | (((mrel @ mactual @ sK0)) = $true) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | ((((mrel @ mactual @ sK31) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) = $false)), 70.10/10.62 inference(imp_proxy_clausification,[],[f870])). 70.10/10.62 thf(f954,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK12))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = (((mrel @ mactual @ sK30) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f872])). 70.10/10.62 thf(f955,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | (((mrel @ mactual @ sK31)) = $true) | ($false = (((mrel @ mactual @ sK30) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30)))) | ($true = ((mrel @ mactual @ sK12)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f872])). 70.10/10.62 thf(f956,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | (((mrel @ mactual @ sK31)) = $true) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ sK30))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f874])). 70.10/10.62 thf(f957,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | (((mrel @ mactual @ sK31)) = $true) | ($false = (((mrel @ mactual @ sK30) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30)))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0)))), 70.10/10.62 inference(beta-eta_normalization,[],[f956])). 70.10/10.62 thf(f958,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ sK30)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f873])). 70.10/10.62 thf(f959,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) | ($false = (((mrel @ mactual @ sK30) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30))))), 70.10/10.62 inference(beta-eta_normalization,[],[f958])). 70.10/10.62 thf(f1017,plain,( 70.10/10.62 ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) = $true) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f930])). 70.10/10.62 thf(f1018,plain,( 70.10/10.62 (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f930])). 70.10/10.62 thf(f1019,plain,( 70.10/10.62 ( ! [X1 : mworld] : ((((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ Y0))) @ X1)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) = $true)) )), 70.10/10.62 inference(pi_proxy_clausification,[],[f931])). 70.10/10.62 thf(f1020,plain,( 70.10/10.62 ( ! [X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) = $true) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true)) )), 70.10/10.62 inference(beta-eta_normalization,[],[f1019])). 70.10/10.62 thf(f1021,plain,( 70.10/10.62 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X1)) = $true) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true)) )), 70.10/10.62 inference(pi_proxy_clausification,[],[f933])). 70.10/10.62 thf(f1022,plain,( 70.10/10.62 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X1))) = $true) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true)) )), 70.10/10.62 inference(beta-eta_normalization,[],[f1021])). 70.10/10.62 thf(f1023,plain,( 70.10/10.62 (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true)), 70.10/10.62 inference(and_proxy_clausification,[],[f932])). 70.10/10.62 thf(f1024,plain,( 70.10/10.62 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true)), 70.10/10.62 inference(and_proxy_clausification,[],[f932])). 70.10/10.62 thf(f1025,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f935])). 70.10/10.62 thf(f1026,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f935])). 70.10/10.62 thf(f1027,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))) = $false) | (((mrel @ mactual @ sK17)) = $true)), 70.10/10.62 inference(sigma_proxy_clausification,[],[f937])). 70.10/10.62 thf(f1028,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))))) | (((mrel @ mactual @ sK17)) = $true) | ($false = (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25))))), 70.10/10.62 inference(beta-eta_normalization,[],[f1027])). 70.10/10.62 thf(f1029,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | ($true = ((mrel @ mactual @ sK6))) | (((mrel @ mactual @ sK18)) = $true) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f939])). 70.10/10.62 thf(f1030,plain,( 70.10/10.62 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((mrel @ mactual @ sK6))) | (((mrel @ mactual @ sK18)) = $true) | ($true = ((mrel @ mactual @ sK34)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f939])). 70.10/10.62 thf(f1031,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK6))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false)), 70.10/10.62 inference(imp_proxy_clausification,[],[f938])). 70.10/10.62 thf(f1032,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK6))) | ($true = ((mrel @ mactual @ sK34))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false)), 70.10/10.62 inference(imp_proxy_clausification,[],[f938])). 70.10/10.62 thf(f1033,plain,( 70.10/10.62 (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | ($false = (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ sK34)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f941])). 70.10/10.62 thf(f1034,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | ($false = (((mrel @ mactual @ sK34) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34)))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | ($false = (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))))), 70.10/10.62 inference(beta-eta_normalization,[],[f1033])). 70.10/10.62 thf(f1035,plain,( 70.10/10.62 (((mrel @ mactual @ sK18)) = $true) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f943])). 70.10/10.62 thf(f1036,plain,( 70.10/10.62 (((mrel @ mactual @ sK18)) = $true) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | ($true = ((mrel @ mactual @ sK34)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f943])). 70.10/10.62 thf(f1037,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK29) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29)))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35))) | ($true = ((mrel @ mactual @ sK11)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f945])). 70.10/10.62 thf(f1038,plain,( 70.10/10.62 (((mrel @ mactual @ sK35)) = $true) | ($false = (((mrel @ mactual @ sK29) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29)))) | ($true = ((mrel @ mactual @ sK11))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f945])). 70.10/10.62 thf(f1039,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))) | ($false = (((mrel @ mactual @ sK35) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f944])). 70.10/10.62 thf(f1040,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK35) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35)))) | (((mrel @ mactual @ sK29)) = $true) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f944])). 70.10/10.62 thf(f1041,plain,( 70.10/10.62 (((mrel @ mactual @ sK7)) = $true) | ($false = (((mrel @ mactual @ sK35) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f947])). 70.10/10.62 thf(f1042,plain,( 70.10/10.62 (((mrel @ mactual @ sK29)) = $true) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))) | ($false = (((mrel @ mactual @ sK35) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35)))) | (((mrel @ mactual @ sK7)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f947])). 70.10/10.62 thf(f1043,plain,( 70.10/10.62 (((mrel @ mactual @ sK7)) = $true) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35))) | ($false = (((mrel @ mactual @ sK29) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29)))) | ($true = ((mrel @ mactual @ sK11)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f949])). 70.10/10.62 thf(f1044,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK11))) | (((mrel @ mactual @ sK35)) = $true) | ($false = (((mrel @ mactual @ sK29) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29)))) | (((mrel @ mactual @ sK7)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f949])). 70.10/10.62 thf(f1045,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) | (((mrel @ mactual @ sK0)) = $true) | ($true = ((mrel @ mactual @ sK12))) | ($true = ((mrel @ mactual @ sK30)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f951])). 70.10/10.62 thf(f1046,plain,( 70.10/10.62 (((mrel @ mactual @ sK31)) = $true) | ($true = ((mrel @ mactual @ sK30))) | (((mrel @ mactual @ sK0)) = $true) | ($true = ((mrel @ mactual @ sK12)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f951])). 70.10/10.62 thf(f1047,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30))) | ($true = ((mrel @ mactual @ sK12))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) | (((mrel @ mactual @ sK0)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f950])). 70.10/10.62 thf(f1048,plain,( 70.10/10.62 (((mrel @ mactual @ sK31)) = $true) | (((mrel @ mactual @ sK0)) = $true) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30))) | ($true = ((mrel @ mactual @ sK12)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f950])). 70.10/10.62 thf(f1049,plain,( 70.10/10.62 (((mrel @ mactual @ sK0)) = $true) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) | ($true = ((mrel @ mactual @ sK30))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f953])). 70.10/10.62 thf(f1050,plain,( 70.10/10.62 (((mrel @ mactual @ sK31)) = $true) | ($true = ((mrel @ mactual @ sK30))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | (((mrel @ mactual @ sK0)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f953])). 70.10/10.62 thf(f1051,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30))) | (((mrel @ mactual @ sK0)) = $true) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f952])). 70.10/10.62 thf(f1052,plain,( 70.10/10.62 (((mrel @ mactual @ sK0)) = $true) | (((mrel @ mactual @ sK31)) = $true) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f952])). 70.10/10.62 thf(f1053,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($true = ((mrel @ mactual @ sK12)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f954])). 70.10/10.62 thf(f1054,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK30))) | ($true = ((mrel @ mactual @ sK12))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f954])). 70.10/10.62 thf(f1055,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30))) | (((mrel @ mactual @ sK31)) = $true) | ($true = ((mrel @ mactual @ sK12)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f955])). 70.10/10.62 thf(f1056,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK30))) | (((mrel @ mactual @ sK31)) = $true) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($true = ((mrel @ mactual @ sK12)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f955])). 70.10/10.62 thf(f1057,plain,( 70.10/10.62 (((mrel @ mactual @ sK31)) = $true) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f957])). 70.10/10.62 thf(f1058,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($true = ((mrel @ mactual @ sK30))) | (((mrel @ mactual @ sK31)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f957])). 70.10/10.62 thf(f1059,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f959])). 70.10/10.62 thf(f1060,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK30))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f959])). 70.10/10.62 thf(f1132,plain,( 70.10/10.62 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true)), 70.10/10.62 inference(and_proxy_clausification,[],[f1017])). 70.10/10.62 thf(f1133,plain,( 70.10/10.62 (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f1017])). 70.10/10.62 thf(f1134,plain,( 70.10/10.62 ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))), 70.10/10.62 inference(or_proxy_clausification,[],[f1018])). 70.10/10.62 thf(f1135,plain,( 70.10/10.62 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) = $true) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.62 inference(imp_proxy_clausification,[],[f1020])). 70.10/10.62 thf(f1136,plain,( 70.10/10.62 ( ! [X2 : mworld,X1 : mworld] : ((((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X1))) = $true)) )), 70.10/10.62 inference(pi_proxy_clausification,[],[f1022])). 70.10/10.62 thf(f1137,plain,( 70.10/10.62 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X1))) = $true) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))))) )), 70.10/10.62 inference(beta-eta_normalization,[],[f1136])). 70.10/10.62 thf(f1138,plain,( 70.10/10.62 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))), 70.10/10.62 inference(or_proxy_clausification,[],[f1023])). 70.10/10.62 thf(f1139,plain,( 70.10/10.62 ( ! [X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X1)) = $true) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.62 inference(pi_proxy_clausification,[],[f1024])). 70.10/10.62 thf(f1140,plain,( 70.10/10.62 ( ! [X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X1))) = $true) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.62 inference(beta-eta_normalization,[],[f1139])). 70.10/10.62 thf(f1141,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f1025])). 70.10/10.62 thf(f1142,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($false = (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17)))), 70.10/10.62 inference(beta-eta_normalization,[],[f1141])). 70.10/10.62 thf(f1143,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f1026])). 70.10/10.62 thf(f1144,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17)))), 70.10/10.62 inference(beta-eta_normalization,[],[f1143])). 70.10/10.62 thf(f1145,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))) | (((mrel @ mactual @ sK17)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1028])). 70.10/10.62 thf(f1146,plain,( 70.10/10.62 (((mrel @ mactual @ sK17)) = $true) | ($false = (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1028])). 70.10/10.62 thf(f1147,plain,( 70.10/10.62 (((mrel @ mactual @ sK18)) = $true) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | ($true = ((mrel @ mactual @ sK6))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f1029])). 70.10/10.62 thf(f1148,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))))) | (((mrel @ mactual @ sK18)) = $true) | ($true = ((mrel @ mactual @ sK6))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34)))), 70.10/10.62 inference(beta-eta_normalization,[],[f1147])). 70.10/10.62 thf(f1149,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK34))) | ($true = ((mrel @ mactual @ sK6))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | (((mrel @ mactual @ sK18)) = $true)), 70.10/10.62 inference(sigma_proxy_clausification,[],[f1030])). 70.10/10.62 thf(f1150,plain,( 70.10/10.62 (((mrel @ mactual @ sK18)) = $true) | ($true = ((mrel @ mactual @ sK6))) | ($true = ((mrel @ mactual @ sK34))) | ($false = (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))))), 70.10/10.62 inference(beta-eta_normalization,[],[f1149])). 70.10/10.62 thf(f1151,plain,( 70.10/10.62 ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | ($true = ((mrel @ mactual @ sK6))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false)), 70.10/10.62 inference(sigma_proxy_clausification,[],[f1031])). 70.10/10.62 thf(f1152,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))))) | ($true = ((mrel @ mactual @ sK6))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34)))), 70.10/10.62 inference(beta-eta_normalization,[],[f1151])). 70.10/10.62 thf(f1153,plain,( 70.10/10.62 ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | ($true = ((mrel @ mactual @ sK6))) | ($true = ((mrel @ mactual @ sK34)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f1032])). 70.10/10.62 thf(f1154,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | ($true = ((mrel @ mactual @ sK6))) | ($true = ((mrel @ mactual @ sK34)))), 70.10/10.62 inference(beta-eta_normalization,[],[f1153])). 70.10/10.62 thf(f1155,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1034])). 70.10/10.62 thf(f1156,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK34))) | ($false = (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1034])). 70.10/10.62 thf(f1157,plain,( 70.10/10.62 (((mrel @ mactual @ sK18)) = $true) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | ($true = ((mrel @ mactual @ sK34)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f1036])). 70.10/10.62 thf(f1158,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | (((mrel @ mactual @ sK18)) = $true) | ($false = (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))))) | ($true = ((mrel @ mactual @ sK34)))), 70.10/10.62 inference(beta-eta_normalization,[],[f1157])). 70.10/10.62 thf(f1159,plain,( 70.10/10.62 ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | (((mrel @ mactual @ sK18)) = $true) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34)))), 70.10/10.62 inference(sigma_proxy_clausification,[],[f1035])). 70.10/10.62 thf(f1160,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | (((mrel @ mactual @ sK18)) = $true) | ($false = (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))))), 70.10/10.62 inference(beta-eta_normalization,[],[f1159])). 70.10/10.62 thf(f1161,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35))) | ($true = ((mrel @ mactual @ sK11)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1037])). 70.10/10.62 thf(f1162,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK11))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | (((mrel @ mactual @ sK29)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1037])). 70.10/10.62 thf(f1163,plain,( 70.10/10.62 (((mrel @ mactual @ sK35)) = $true) | ($true = ((mrel @ mactual @ sK11))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1038])). 70.10/10.62 thf(f1164,plain,( 70.10/10.62 (((mrel @ mactual @ sK35)) = $true) | ($true = ((mrel @ mactual @ sK11))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | (((mrel @ mactual @ sK29)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1038])). 70.10/10.62 thf(f1165,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1039])). 70.10/10.62 thf(f1166,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | (((mrel @ mactual @ sK35)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1039])). 70.10/10.62 thf(f1167,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | (((mrel @ mactual @ sK29)) = $true) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1040])). 70.10/10.62 thf(f1168,plain,( 70.10/10.62 (((mrel @ mactual @ sK29)) = $true) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | (((mrel @ mactual @ sK35)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1040])). 70.10/10.62 thf(f1169,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35))) | (((mrel @ mactual @ sK7)) = $true) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))) | (((mrel @ mactual @ sK29)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1042])). 70.10/10.62 thf(f1170,plain,( 70.10/10.62 (((mrel @ mactual @ sK29)) = $true) | (((mrel @ mactual @ sK35)) = $true) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))) | (((mrel @ mactual @ sK7)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1042])). 70.10/10.62 thf(f1171,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))) | (((mrel @ mactual @ sK7)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1041])). 70.10/10.62 thf(f1172,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29))) | (((mrel @ mactual @ sK7)) = $true) | (((mrel @ mactual @ sK35)) = $true) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1041])). 70.10/10.62 thf(f1173,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK11))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29))) | (((mrel @ mactual @ sK7)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1043])). 70.10/10.62 thf(f1174,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK11))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35))) | (((mrel @ mactual @ sK7)) = $true) | (((mrel @ mactual @ sK29)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1043])). 70.10/10.62 thf(f1175,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29))) | ($true = ((mrel @ mactual @ sK11))) | (((mrel @ mactual @ sK7)) = $true) | (((mrel @ mactual @ sK35)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1044])). 70.10/10.62 thf(f1176,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK11))) | (((mrel @ mactual @ sK7)) = $true) | (((mrel @ mactual @ sK29)) = $true) | (((mrel @ mactual @ sK35)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1044])). 70.10/10.62 thf(f1178,definition,( 70.10/10.62 spl37_5 <=> ($true = ((mrel @ mactual @ sK12)))), 70.10/10.62 introduced(definition,[new_symbols(definition,[spl37_5])],[avatar_definition])). 70.10/10.62 thf(f1179,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK12))) | ~spl37_5), 70.10/10.62 inference(avatar_component_clause,[],[f1178])). 70.10/10.62 thf(f1181,definition,( 70.10/10.62 spl37_6 <=> ($true = ((mrel @ mactual @ sK30)))), 70.10/10.62 introduced(definition,[new_symbols(definition,[spl37_6])],[avatar_definition])). 70.10/10.62 thf(f1182,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK30))) | ~spl37_6), 70.10/10.62 inference(avatar_component_clause,[],[f1181])). 70.10/10.62 thf(f1184,definition,( 70.10/10.62 spl37_7 <=> (((mrel @ mactual @ sK0)) = $true)), 70.10/10.62 introduced(definition,[new_symbols(definition,[spl37_7])],[avatar_definition])). 70.10/10.62 thf(f1185,plain,( 70.10/10.62 (((mrel @ mactual @ sK0)) = $true) | ~spl37_7), 70.10/10.62 inference(avatar_component_clause,[],[f1184])). 70.10/10.62 thf(f1187,definition,( 70.10/10.62 spl37_8 <=> (((mrel @ mactual @ sK31)) = $true)), 70.10/10.62 introduced(definition,[new_symbols(definition,[spl37_8])],[avatar_definition])). 70.10/10.62 thf(f1188,plain,( 70.10/10.62 (((mrel @ mactual @ sK31)) = $true) | ~spl37_8), 70.10/10.62 inference(avatar_component_clause,[],[f1187])). 70.10/10.62 thf(f1189,plain,( 70.10/10.62 spl37_5 | spl37_6 | spl37_7 | spl37_8), 70.10/10.62 inference(avatar_split_clause,[],[f1046,f1187,f1184,f1181,f1178])). 70.10/10.62 thf(f1191,definition,( 70.10/10.62 spl37_9 <=> ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31)))), 70.10/10.62 introduced(definition,[new_symbols(definition,[spl37_9])],[avatar_definition])). 70.10/10.62 thf(f1192,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ sK31))) | ~spl37_9), 70.10/10.62 inference(avatar_component_clause,[],[f1191])). 70.10/10.62 thf(f1193,plain,( 70.10/10.62 spl37_6 | spl37_5 | spl37_7 | spl37_9), 70.10/10.62 inference(avatar_split_clause,[],[f1045,f1191,f1184,f1178,f1181])). 70.10/10.62 thf(f1195,definition,( 70.10/10.62 spl37_10 <=> ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30)))), 70.10/10.62 introduced(definition,[new_symbols(definition,[spl37_10])],[avatar_definition])). 70.10/10.62 thf(f1196,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ sK30))) | ~spl37_10), 70.10/10.62 inference(avatar_component_clause,[],[f1195])). 70.10/10.62 thf(f1197,plain,( 70.10/10.62 spl37_10 | spl37_5 | spl37_9 | spl37_7), 70.10/10.62 inference(avatar_split_clause,[],[f1047,f1184,f1191,f1178,f1195])). 70.10/10.62 thf(f1198,plain,( 70.10/10.62 spl37_8 | spl37_7 | spl37_10 | spl37_5), 70.10/10.62 inference(avatar_split_clause,[],[f1048,f1178,f1195,f1184,f1187])). 70.10/10.62 thf(f1200,definition,( 70.10/10.62 spl37_11 <=> ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12)))), 70.10/10.62 introduced(definition,[new_symbols(definition,[spl37_11])],[avatar_definition])). 70.10/10.62 thf(f1201,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ sK12))) | ~spl37_11), 70.10/10.62 inference(avatar_component_clause,[],[f1200])). 70.10/10.62 thf(f1202,plain,( 70.10/10.62 spl37_8 | spl37_7 | spl37_11 | spl37_6), 70.10/10.62 inference(avatar_split_clause,[],[f1050,f1181,f1200,f1184,f1187])). 70.10/10.62 thf(f1203,plain,( 70.10/10.62 spl37_7 | spl37_9 | spl37_6 | spl37_11), 70.10/10.62 inference(avatar_split_clause,[],[f1049,f1200,f1181,f1191,f1184])). 70.10/10.62 thf(f1204,plain,( 70.10/10.62 spl37_11 | spl37_7 | spl37_9 | spl37_10), 70.10/10.62 inference(avatar_split_clause,[],[f1051,f1195,f1191,f1184,f1200])). 70.10/10.62 thf(f1205,plain,( 70.10/10.62 spl37_10 | spl37_8 | spl37_7 | spl37_11), 70.10/10.62 inference(avatar_split_clause,[],[f1052,f1200,f1184,f1187,f1195])). 70.10/10.62 thf(f1207,definition,( 70.10/10.62 spl37_12 <=> ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0)))), 70.10/10.62 introduced(definition,[new_symbols(definition,[spl37_12])],[avatar_definition])). 70.10/10.62 thf(f1208,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ sK0))) | ~spl37_12), 70.10/10.62 inference(avatar_component_clause,[],[f1207])). 70.10/10.62 thf(f1209,plain,( 70.10/10.62 spl37_5 | spl37_9 | spl37_10 | spl37_12), 70.10/10.62 inference(avatar_split_clause,[],[f1053,f1207,f1195,f1191,f1178])). 70.10/10.62 thf(f1210,plain,( 70.10/10.62 spl37_12 | spl37_9 | spl37_6 | spl37_5), 70.10/10.62 inference(avatar_split_clause,[],[f1054,f1178,f1181,f1191,f1207])). 70.10/10.62 thf(f1211,plain,( 70.10/10.62 spl37_12 | spl37_5 | spl37_6 | spl37_8), 70.10/10.62 inference(avatar_split_clause,[],[f1056,f1187,f1181,f1178,f1207])). 70.10/10.62 thf(f1212,plain,( 70.10/10.62 spl37_5 | spl37_12 | spl37_10 | spl37_8), 70.10/10.62 inference(avatar_split_clause,[],[f1055,f1187,f1195,f1207,f1178])). 70.10/10.62 thf(f1213,plain,( 70.10/10.62 spl37_12 | spl37_10 | spl37_8 | spl37_11), 70.10/10.62 inference(avatar_split_clause,[],[f1057,f1200,f1187,f1195,f1207])). 70.10/10.62 thf(f1214,plain,( 70.10/10.62 spl37_12 | spl37_6 | spl37_11 | spl37_8), 70.10/10.62 inference(avatar_split_clause,[],[f1058,f1187,f1200,f1181,f1207])). 70.10/10.62 thf(f1215,plain,( 70.10/10.62 spl37_9 | spl37_11 | spl37_6 | spl37_12), 70.10/10.62 inference(avatar_split_clause,[],[f1060,f1207,f1181,f1200,f1191])). 70.10/10.62 thf(f1216,plain,( 70.10/10.62 spl37_10 | spl37_12 | spl37_9 | spl37_11), 70.10/10.62 inference(avatar_split_clause,[],[f1059,f1200,f1191,f1207,f1195])). 70.10/10.62 thf(f1287,plain,( 70.10/10.62 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))), 70.10/10.62 inference(or_proxy_clausification,[],[f1133])). 70.10/10.62 thf(f1288,plain,( 70.10/10.62 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f1132])). 70.10/10.62 thf(f1289,plain,( 70.10/10.62 (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f1132])). 70.10/10.62 thf(f1290,plain,( 70.10/10.62 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f1134])). 70.10/10.62 thf(f1291,plain,( 70.10/10.62 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f1134])). 70.10/10.62 thf(f1292,plain,( 70.10/10.62 ( ! [X1 : mworld] : ((((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) )), 70.10/10.62 inference(and_proxy_clausification,[],[f1135])). 70.10/10.62 thf(f1293,plain,( 70.10/10.62 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.62 inference(and_proxy_clausification,[],[f1135])). 70.10/10.62 thf(f1294,plain,( 70.10/10.62 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.62 inference(imp_proxy_clausification,[],[f1137])). 70.10/10.62 thf(f1295,plain,( 70.10/10.62 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true)), 70.10/10.62 inference(and_proxy_clausification,[],[f1138])). 70.10/10.62 thf(f1296,plain,( 70.10/10.62 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))), 70.10/10.62 inference(and_proxy_clausification,[],[f1138])). 70.10/10.62 thf(f1297,plain,( 70.10/10.62 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.62 inference(imp_proxy_clausification,[],[f1140])). 70.10/10.62 thf(f1298,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25))) | ($false = (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1142])). 70.10/10.62 thf(f1299,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($true = ((mrel @ mactual @ sK25))) | ($false = (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1142])). 70.10/10.62 thf(f1300,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1144])). 70.10/10.62 thf(f1301,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1144])). 70.10/10.62 thf(f1302,plain,( 70.10/10.62 (((mrel @ mactual @ sK17)) = $true) | (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))) = $true) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1146])). 70.10/10.62 thf(f1303,plain,( 70.10/10.62 ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))) = $true) | (((mrel @ mactual @ sK17)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1146])). 70.10/10.62 thf(f1304,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | (((mrel @ mactual @ sK17)) = $true) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1145])). 70.10/10.62 thf(f1305,plain,( 70.10/10.62 (((mrel @ mactual @ sK17)) = $true) | ($false = (((mrel @ mactual @ sK25) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))) | ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1145])). 70.10/10.62 thf(f1306,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK6))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | (((mrel @ mactual @ sK18)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1148])). 70.10/10.62 thf(f1307,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | (((mrel @ mactual @ sK18)) = $true) | (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))) = $true) | ($true = ((mrel @ mactual @ sK6)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1148])). 70.10/10.62 thf(f1308,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK34))) | (((mrel @ mactual @ sK18)) = $true) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | ($true = ((mrel @ mactual @ sK6)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1150])). 70.10/10.62 thf(f1309,plain,( 70.10/10.62 (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))) = $true) | ($true = ((mrel @ mactual @ sK34))) | ($true = ((mrel @ mactual @ sK6))) | (((mrel @ mactual @ sK18)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1150])). 70.10/10.62 thf(f1310,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | ($true = ((mrel @ mactual @ sK6))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1152])). 70.10/10.62 thf(f1311,plain,( 70.10/10.62 (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))) = $true) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | ($true = ((mrel @ mactual @ sK6))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1152])). 70.10/10.62 thf(f1312,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK6))) | ($true = ((mrel @ mactual @ sK34))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1154])). 70.10/10.62 thf(f1313,plain,( 70.10/10.62 ($true = ((mrel @ mactual @ sK34))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))) = $true) | ($true = ((mrel @ mactual @ sK6)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1154])). 70.10/10.62 thf(f1314,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | ($true = ((mrel @ mactual @ sK34)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1156])). 70.10/10.62 thf(f1315,plain,( 70.10/10.62 (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | ($true = ((mrel @ mactual @ sK34))) | (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))) = $true) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1156])). 70.10/10.62 thf(f1316,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1155])). 70.10/10.62 thf(f1317,plain,( 70.10/10.62 (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))) = $true) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1155])). 70.10/10.62 thf(f1318,plain,( 70.10/10.62 (((mrel @ mactual @ sK18)) = $true) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | ($true = ((mrel @ mactual @ sK34)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1158])). 70.10/10.62 thf(f1319,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))) = $true) | (((mrel @ mactual @ sK18)) = $true) | ($true = ((mrel @ mactual @ sK34)))), 70.10/10.62 inference(imp_proxy_clausification,[],[f1158])). 70.10/10.62 thf(f1320,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | (((mrel @ mactual @ sK18)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1160])). 70.10/10.62 thf(f1321,plain,( 70.10/10.62 (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))) = $true) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | (((mrel @ mactual @ sK18)) = $true)), 70.10/10.62 inference(imp_proxy_clausification,[],[f1160])). 70.10/10.62 thf(f1323,definition,( 70.10/10.62 spl37_17 <=> ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7)))), 70.10/10.62 introduced(definition,[new_symbols(definition,[spl37_17])],[avatar_definition])). 70.10/10.62 thf(f1324,plain,( 70.10/10.62 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ sK7))) | ~spl37_17), 70.10/10.63 inference(avatar_component_clause,[],[f1323])). 70.10/10.63 thf(f1326,definition,( 70.10/10.63 spl37_18 <=> ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29)))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_18])],[avatar_definition])). 70.10/10.63 thf(f1327,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ sK29))) | ~spl37_18), 70.10/10.63 inference(avatar_component_clause,[],[f1326])). 70.10/10.63 thf(f1329,definition,( 70.10/10.63 spl37_19 <=> ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35)))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_19])],[avatar_definition])). 70.10/10.63 thf(f1330,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e3 @ e3) @ e1 @ sK35))) | ~spl37_19), 70.10/10.63 inference(avatar_component_clause,[],[f1329])). 70.10/10.63 thf(f1332,definition,( 70.10/10.63 spl37_20 <=> ($true = ((mrel @ mactual @ sK11)))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_20])],[avatar_definition])). 70.10/10.63 thf(f1333,plain,( 70.10/10.63 ($true = ((mrel @ mactual @ sK11))) | ~spl37_20), 70.10/10.63 inference(avatar_component_clause,[],[f1332])). 70.10/10.63 thf(f1334,plain,( 70.10/10.63 spl37_17 | spl37_18 | spl37_19 | spl37_20), 70.10/10.63 inference(avatar_split_clause,[],[f1161,f1332,f1329,f1326,f1323])). 70.10/10.63 thf(f1336,definition,( 70.10/10.63 spl37_21 <=> (((mrel @ mactual @ sK29)) = $true)), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_21])],[avatar_definition])). 70.10/10.63 thf(f1337,plain,( 70.10/10.63 (((mrel @ mactual @ sK29)) = $true) | ~spl37_21), 70.10/10.63 inference(avatar_component_clause,[],[f1336])). 70.10/10.63 thf(f1338,plain,( 70.10/10.63 spl37_17 | spl37_20 | spl37_19 | spl37_21), 70.10/10.63 inference(avatar_split_clause,[],[f1162,f1336,f1329,f1332,f1323])). 70.10/10.63 thf(f1340,definition,( 70.10/10.63 spl37_22 <=> (((mrel @ mactual @ sK35)) = $true)), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_22])],[avatar_definition])). 70.10/10.63 thf(f1341,plain,( 70.10/10.63 (((mrel @ mactual @ sK35)) = $true) | ~spl37_22), 70.10/10.63 inference(avatar_component_clause,[],[f1340])). 70.10/10.63 thf(f1342,plain,( 70.10/10.63 spl37_17 | spl37_18 | spl37_22 | spl37_20), 70.10/10.63 inference(avatar_split_clause,[],[f1163,f1332,f1340,f1326,f1323])). 70.10/10.63 thf(f1343,plain,( 70.10/10.63 spl37_21 | spl37_22 | spl37_17 | spl37_20), 70.10/10.63 inference(avatar_split_clause,[],[f1164,f1332,f1323,f1340,f1336])). 70.10/10.63 thf(f1345,definition,( 70.10/10.63 spl37_23 <=> ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11)))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_23])],[avatar_definition])). 70.10/10.63 thf(f1346,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ sK11))) | ~spl37_23), 70.10/10.63 inference(avatar_component_clause,[],[f1345])). 70.10/10.63 thf(f1347,plain,( 70.10/10.63 spl37_17 | spl37_19 | spl37_18 | spl37_23), 70.10/10.63 inference(avatar_split_clause,[],[f1165,f1345,f1326,f1329,f1323])). 70.10/10.63 thf(f1348,plain,( 70.10/10.63 spl37_18 | spl37_23 | spl37_17 | spl37_22), 70.10/10.63 inference(avatar_split_clause,[],[f1166,f1340,f1323,f1345,f1326])). 70.10/10.63 thf(f1349,plain,( 70.10/10.63 spl37_21 | spl37_17 | spl37_22 | spl37_23), 70.10/10.63 inference(avatar_split_clause,[],[f1168,f1345,f1340,f1323,f1336])). 70.10/10.63 thf(f1350,plain,( 70.10/10.63 spl37_19 | spl37_23 | spl37_21 | spl37_17), 70.10/10.63 inference(avatar_split_clause,[],[f1167,f1323,f1336,f1345,f1329])). 70.10/10.63 thf(f1352,definition,( 70.10/10.63 spl37_24 <=> (((mrel @ mactual @ sK7)) = $true)), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_24])],[avatar_definition])). 70.10/10.63 thf(f1353,plain,( 70.10/10.63 (((mrel @ mactual @ sK7)) = $true) | ~spl37_24), 70.10/10.63 inference(avatar_component_clause,[],[f1352])). 70.10/10.63 thf(f1354,plain,( 70.10/10.63 spl37_23 | spl37_19 | spl37_24 | spl37_21), 70.10/10.63 inference(avatar_split_clause,[],[f1169,f1336,f1352,f1329,f1345])). 70.10/10.63 thf(f1355,plain,( 70.10/10.63 spl37_24 | spl37_21 | spl37_22 | spl37_23), 70.10/10.63 inference(avatar_split_clause,[],[f1170,f1345,f1340,f1336,f1352])). 70.10/10.63 thf(f1356,plain,( 70.10/10.63 spl37_24 | spl37_19 | spl37_23 | spl37_18), 70.10/10.63 inference(avatar_split_clause,[],[f1171,f1326,f1345,f1329,f1352])). 70.10/10.63 thf(f1357,plain,( 70.10/10.63 spl37_22 | spl37_24 | spl37_23 | spl37_18), 70.10/10.63 inference(avatar_split_clause,[],[f1172,f1326,f1345,f1352,f1340])). 70.10/10.63 thf(f1358,plain,( 70.10/10.63 spl37_21 | spl37_24 | spl37_19 | spl37_20), 70.10/10.63 inference(avatar_split_clause,[],[f1174,f1332,f1329,f1352,f1336])). 70.10/10.63 thf(f1359,plain,( 70.10/10.63 spl37_24 | spl37_19 | spl37_20 | spl37_18), 70.10/10.63 inference(avatar_split_clause,[],[f1173,f1326,f1332,f1329,f1352])). 70.10/10.63 thf(f1360,plain,( 70.10/10.63 spl37_21 | spl37_20 | spl37_24 | spl37_22), 70.10/10.63 inference(avatar_split_clause,[],[f1176,f1340,f1352,f1332,f1336])). 70.10/10.63 thf(f1361,plain,( 70.10/10.63 spl37_20 | spl37_22 | spl37_24 | spl37_18), 70.10/10.63 inference(avatar_split_clause,[],[f1175,f1326,f1352,f1340,f1332])). 70.10/10.63 thf(f1433,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1287])). 70.10/10.63 thf(f1434,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1433])). 70.10/10.63 thf(f1435,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))), 70.10/10.63 inference(or_proxy_clausification,[],[f1289])). 70.10/10.63 thf(f1436,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1288])). 70.10/10.63 thf(f1437,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1436])). 70.10/10.63 thf(f1438,plain,( 70.10/10.63 ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1290])). 70.10/10.63 thf(f1439,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1290])). 70.10/10.63 thf(f1440,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X1)) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1291])). 70.10/10.63 thf(f1441,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1440])). 70.10/10.63 thf(f1442,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X2))) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1293])). 70.10/10.63 thf(f1443,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1442])). 70.10/10.63 thf(f1444,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(or_proxy_clausification,[],[f1292])). 70.10/10.63 thf(f1445,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1294])). 70.10/10.63 thf(f1446,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1295])). 70.10/10.63 thf(f1447,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1446])). 70.10/10.63 thf(f1448,plain,( 70.10/10.63 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1296])). 70.10/10.63 thf(f1449,plain,( 70.10/10.63 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true)), 70.10/10.63 inference(and_proxy_clausification,[],[f1296])). 70.10/10.63 thf(f1450,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.63 inference(or_proxy_clausification,[],[f1297])). 70.10/10.63 thf(f1451,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))) | ($true = ((mrel @ mactual @ sK25)))), 70.10/10.63 inference(imp_proxy_clausification,[],[f1299])). 70.10/10.63 thf(f1452,plain,( 70.10/10.63 ($true = ((mrel @ mactual @ sK25))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))) = $true) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17)))), 70.10/10.63 inference(imp_proxy_clausification,[],[f1299])). 70.10/10.63 thf(f1453,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))))), 70.10/10.63 inference(imp_proxy_clausification,[],[f1298])). 70.10/10.63 thf(f1454,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25))) | (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))) = $true)), 70.10/10.63 inference(imp_proxy_clausification,[],[f1298])). 70.10/10.63 thf(f1455,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))) = $true) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))), 70.10/10.63 inference(imp_proxy_clausification,[],[f1301])). 70.10/10.63 thf(f1456,plain,( 70.10/10.63 ($true = ((mrel @ mactual @ sK25))) | ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))) = $true)), 70.10/10.63 inference(imp_proxy_clausification,[],[f1301])). 70.10/10.63 thf(f1457,plain,( 70.10/10.63 ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))), 70.10/10.63 inference(imp_proxy_clausification,[],[f1300])). 70.10/10.63 thf(f1458,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ($true = ((mrel @ mactual @ sK25))) | ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))))), 70.10/10.63 inference(imp_proxy_clausification,[],[f1300])). 70.10/10.63 thf(f1459,plain,( 70.10/10.63 ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))) = $true) | (((mrel @ mactual @ sK17)) = $true) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))), 70.10/10.63 inference(imp_proxy_clausification,[],[f1303])). 70.10/10.63 thf(f1460,plain,( 70.10/10.63 ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($true = ((mrel @ mactual @ sK25))) | (((mrel @ mactual @ sK17)) = $true) | (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))) = $true)), 70.10/10.63 inference(imp_proxy_clausification,[],[f1303])). 70.10/10.63 thf(f1461,plain,( 70.10/10.63 (((mrel @ mactual @ sK17)) = $true) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25))) | (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))) = $true) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))))), 70.10/10.63 inference(imp_proxy_clausification,[],[f1302])). 70.10/10.63 thf(f1462,plain,( 70.10/10.63 (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))) = $true) | (((mrel @ mactual @ sK17)) = $true) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($true = ((mrel @ mactual @ sK25)))), 70.10/10.63 inference(imp_proxy_clausification,[],[f1302])). 70.10/10.63 thf(f1463,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25))) | (((mrel @ mactual @ sK17)) = $true) | ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))))), 70.10/10.63 inference(imp_proxy_clausification,[],[f1305])). 70.10/10.63 thf(f1464,plain,( 70.10/10.63 ($true = ((mrel @ mactual @ sK25))) | (((mrel @ mactual @ sK17)) = $true) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))) | ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))))), 70.10/10.63 inference(imp_proxy_clausification,[],[f1305])). 70.10/10.63 thf(f1465,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))) | ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25))) | (((mrel @ mactual @ sK17)) = $true) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))))), 70.10/10.63 inference(imp_proxy_clausification,[],[f1304])). 70.10/10.63 thf(f1466,plain,( 70.10/10.63 ($true = ((mrel @ mactual @ sK25))) | ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))) | (((mrel @ mactual @ sK17)) = $true)), 70.10/10.63 inference(imp_proxy_clausification,[],[f1304])). 70.10/10.63 thf(f1468,definition,( 70.10/10.63 spl37_29 <=> ($true = ((mrel @ mactual @ sK6)))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_29])],[avatar_definition])). 70.10/10.63 thf(f1469,plain,( 70.10/10.63 ($true = ((mrel @ mactual @ sK6))) | ~spl37_29), 70.10/10.63 inference(avatar_component_clause,[],[f1468])). 70.10/10.63 thf(f1471,definition,( 70.10/10.63 spl37_30 <=> ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_30])],[avatar_definition])). 70.10/10.63 thf(f1472,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | ~spl37_30), 70.10/10.63 inference(avatar_component_clause,[],[f1471])). 70.10/10.63 thf(f1474,definition,( 70.10/10.63 spl37_31 <=> (((mrel @ mactual @ sK18)) = $true)), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_31])],[avatar_definition])). 70.10/10.63 thf(f1475,plain,( 70.10/10.63 (((mrel @ mactual @ sK18)) = $true) | ~spl37_31), 70.10/10.63 inference(avatar_component_clause,[],[f1474])). 70.10/10.63 thf(f1477,definition,( 70.10/10.63 spl37_32 <=> ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34)))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_32])],[avatar_definition])). 70.10/10.63 thf(f1478,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ sK34))) | ~spl37_32), 70.10/10.63 inference(avatar_component_clause,[],[f1477])). 70.10/10.63 thf(f1479,plain,( 70.10/10.63 spl37_29 | spl37_30 | spl37_31 | spl37_32), 70.10/10.63 inference(avatar_split_clause,[],[f1306,f1477,f1474,f1471,f1468])). 70.10/10.63 thf(f1481,definition,( 70.10/10.63 spl37_33 <=> (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))) = $true)), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_33])],[avatar_definition])). 70.10/10.63 thf(f1482,plain,( 70.10/10.63 (((mrel @ mactual @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))) = $true) | ~spl37_33), 70.10/10.63 inference(avatar_component_clause,[],[f1481])). 70.10/10.63 thf(f1483,plain,( 70.10/10.63 spl37_33 | spl37_31 | spl37_29 | spl37_32), 70.10/10.63 inference(avatar_split_clause,[],[f1307,f1477,f1468,f1474,f1481])). 70.10/10.63 thf(f1485,definition,( 70.10/10.63 spl37_34 <=> ($true = ((mrel @ mactual @ sK34)))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_34])],[avatar_definition])). 70.10/10.63 thf(f1486,plain,( 70.10/10.63 ($true = ((mrel @ mactual @ sK34))) | ~spl37_34), 70.10/10.63 inference(avatar_component_clause,[],[f1485])). 70.10/10.63 thf(f1487,plain,( 70.10/10.63 spl37_29 | spl37_34 | spl37_33 | spl37_31), 70.10/10.63 inference(avatar_split_clause,[],[f1309,f1474,f1481,f1485,f1468])). 70.10/10.63 thf(f1488,plain,( 70.10/10.63 spl37_30 | spl37_29 | spl37_31 | spl37_34), 70.10/10.63 inference(avatar_split_clause,[],[f1308,f1485,f1474,f1468,f1471])). 70.10/10.63 thf(f1490,definition,( 70.10/10.63 spl37_35 <=> (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false)), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_35])],[avatar_definition])). 70.10/10.63 thf(f1491,plain,( 70.10/10.63 (((qmltpeq @ (op @ e1 @ e1) @ e2 @ sK18)) = $false) | ~spl37_35), 70.10/10.63 inference(avatar_component_clause,[],[f1490])). 70.10/10.63 thf(f1492,plain,( 70.10/10.63 spl37_30 | spl37_35 | spl37_29 | spl37_32), 70.10/10.63 inference(avatar_split_clause,[],[f1310,f1477,f1468,f1490,f1471])). 70.10/10.63 thf(f1493,plain,( 70.10/10.63 spl37_35 | spl37_32 | spl37_33 | spl37_29), 70.10/10.63 inference(avatar_split_clause,[],[f1311,f1468,f1481,f1477,f1490])). 70.10/10.63 thf(f1494,plain,( 70.10/10.63 spl37_35 | spl37_29 | spl37_34 | spl37_33), 70.10/10.63 inference(avatar_split_clause,[],[f1313,f1481,f1485,f1468,f1490])). 70.10/10.63 thf(f1495,plain,( 70.10/10.63 spl37_34 | spl37_35 | spl37_30 | spl37_29), 70.10/10.63 inference(avatar_split_clause,[],[f1312,f1468,f1471,f1490,f1485])). 70.10/10.63 thf(f1497,definition,( 70.10/10.63 spl37_36 <=> ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6)))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_36])],[avatar_definition])). 70.10/10.63 thf(f1498,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ sK6))) | ~spl37_36), 70.10/10.63 inference(avatar_component_clause,[],[f1497])). 70.10/10.63 thf(f1499,plain,( 70.10/10.63 spl37_36 | spl37_33 | spl37_35 | spl37_34), 70.10/10.63 inference(avatar_split_clause,[],[f1315,f1485,f1490,f1481,f1497])). 70.10/10.63 thf(f1500,plain,( 70.10/10.63 spl37_36 | spl37_34 | spl37_35 | spl37_30), 70.10/10.63 inference(avatar_split_clause,[],[f1314,f1471,f1490,f1485,f1497])). 70.10/10.63 thf(f1501,plain,( 70.10/10.63 spl37_35 | spl37_30 | spl37_32 | spl37_36), 70.10/10.63 inference(avatar_split_clause,[],[f1316,f1497,f1477,f1471,f1490])). 70.10/10.63 thf(f1502,plain,( 70.10/10.63 spl37_33 | spl37_36 | spl37_32 | spl37_35), 70.10/10.63 inference(avatar_split_clause,[],[f1317,f1490,f1477,f1497,f1481])). 70.10/10.63 thf(f1503,plain,( 70.10/10.63 spl37_33 | spl37_34 | spl37_31 | spl37_36), 70.10/10.63 inference(avatar_split_clause,[],[f1319,f1497,f1474,f1485,f1481])). 70.10/10.63 thf(f1504,plain,( 70.10/10.63 spl37_36 | spl37_31 | spl37_34 | spl37_30), 70.10/10.63 inference(avatar_split_clause,[],[f1318,f1471,f1485,f1474,f1497])). 70.10/10.63 thf(f1505,plain,( 70.10/10.63 spl37_36 | spl37_32 | spl37_31 | spl37_30), 70.10/10.63 inference(avatar_split_clause,[],[f1320,f1471,f1474,f1477,f1497])). 70.10/10.63 thf(f1506,plain,( 70.10/10.63 spl37_36 | spl37_33 | spl37_32 | spl37_31), 70.10/10.63 inference(avatar_split_clause,[],[f1321,f1474,f1477,f1481,f1497])). 70.10/10.63 thf(f1577,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1434])). 70.10/10.63 thf(f1578,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1577])). 70.10/10.63 thf(f1579,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ Y0))) @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1435])). 70.10/10.63 thf(f1580,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1579])). 70.10/10.63 thf(f1581,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1437])). 70.10/10.63 thf(f1582,plain,( 70.10/10.63 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1438])). 70.10/10.63 thf(f1583,plain,( 70.10/10.63 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1438])). 70.10/10.63 thf(f1584,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X1)) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1439])). 70.10/10.63 thf(f1585,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1584])). 70.10/10.63 thf(f1586,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1441])). 70.10/10.63 thf(f1587,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1441])). 70.10/10.63 thf(f1588,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )), 70.10/10.63 inference(or_proxy_clausification,[],[f1443])). 70.10/10.63 thf(f1589,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1444])). 70.10/10.63 thf(f1590,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1444])). 70.10/10.63 thf(f1591,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(or_proxy_clausification,[],[f1445])). 70.10/10.63 thf(f1592,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1447])). 70.10/10.63 thf(f1593,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1592])). 70.10/10.63 thf(f1594,plain,( 70.10/10.63 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)), 70.10/10.63 inference(and_proxy_clausification,[],[f1448])). 70.10/10.63 thf(f1595,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true)), 70.10/10.63 inference(and_proxy_clausification,[],[f1448])). 70.10/10.63 thf(f1596,plain,( 70.10/10.63 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)), 70.10/10.63 inference(and_proxy_clausification,[],[f1449])). 70.10/10.63 thf(f1597,plain,( 70.10/10.63 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)), 70.10/10.63 inference(and_proxy_clausification,[],[f1449])). 70.10/10.63 thf(f1598,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1450])). 70.10/10.63 thf(f1599,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1450])). 70.10/10.63 thf(f1601,definition,( 70.10/10.63 spl37_41 <=> (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))) = $true)), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_41])],[avatar_definition])). 70.10/10.63 thf(f1602,plain,( 70.10/10.63 (((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))) = $true) | ~spl37_41), 70.10/10.63 inference(avatar_component_clause,[],[f1601])). 70.10/10.63 thf(f1604,definition,( 70.10/10.63 spl37_42 <=> ($true = ((mrel @ mactual @ sK25)))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_42])],[avatar_definition])). 70.10/10.63 thf(f1605,plain,( 70.10/10.63 ($true = ((mrel @ mactual @ sK25))) | ~spl37_42), 70.10/10.63 inference(avatar_component_clause,[],[f1604])). 70.10/10.63 thf(f1607,definition,( 70.10/10.63 spl37_43 <=> ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17)))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_43])],[avatar_definition])). 70.10/10.63 thf(f1608,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ sK17))) | ~spl37_43), 70.10/10.63 inference(avatar_component_clause,[],[f1607])). 70.10/10.63 thf(f1610,definition,( 70.10/10.63 spl37_44 <=> ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_44])],[avatar_definition])). 70.10/10.63 thf(f1611,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ~spl37_44), 70.10/10.63 inference(avatar_component_clause,[],[f1610])). 70.10/10.63 thf(f1612,plain,( 70.10/10.63 spl37_41 | spl37_42 | spl37_43 | spl37_44), 70.10/10.63 inference(avatar_split_clause,[],[f1452,f1610,f1607,f1604,f1601])). 70.10/10.63 thf(f1614,definition,( 70.10/10.63 spl37_45 <=> ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3)))))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_45])],[avatar_definition])). 70.10/10.63 thf(f1615,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))) | ~spl37_45), 70.10/10.63 inference(avatar_component_clause,[],[f1614])). 70.10/10.63 thf(f1616,plain,( 70.10/10.63 spl37_43 | spl37_45 | spl37_44 | spl37_42), 70.10/10.63 inference(avatar_split_clause,[],[f1451,f1604,f1610,f1614,f1607])). 70.10/10.63 thf(f1618,definition,( 70.10/10.63 spl37_46 <=> ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25)))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_46])],[avatar_definition])). 70.10/10.63 thf(f1619,plain,( 70.10/10.63 ($false = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ sK25))) | ~spl37_46), 70.10/10.63 inference(avatar_component_clause,[],[f1618])). 70.10/10.63 thf(f1620,plain,( 70.10/10.63 spl37_46 | spl37_43 | spl37_41 | spl37_44), 70.10/10.63 inference(avatar_split_clause,[],[f1454,f1610,f1601,f1607,f1618])). 70.10/10.63 thf(f1621,plain,( 70.10/10.63 spl37_43 | spl37_45 | spl37_46 | spl37_44), 70.10/10.63 inference(avatar_split_clause,[],[f1453,f1610,f1618,f1614,f1607])). 70.10/10.63 thf(f1623,definition,( 70.10/10.63 spl37_47 <=> ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))))), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_47])],[avatar_definition])). 70.10/10.63 thf(f1624,plain,( 70.10/10.63 ($true = ((mrel @ mactual @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ~spl37_47), 70.10/10.63 inference(avatar_component_clause,[],[f1623])). 70.10/10.63 thf(f1625,plain,( 70.10/10.63 spl37_46 | spl37_47 | spl37_41 | spl37_43), 70.10/10.63 inference(avatar_split_clause,[],[f1455,f1607,f1601,f1623,f1618])). 70.10/10.63 thf(f1626,plain,( 70.10/10.63 spl37_47 | spl37_43 | spl37_42 | spl37_41), 70.10/10.63 inference(avatar_split_clause,[],[f1456,f1601,f1604,f1607,f1623])). 70.10/10.63 thf(f1627,plain,( 70.10/10.63 spl37_45 | spl37_47 | spl37_42 | spl37_43), 70.10/10.63 inference(avatar_split_clause,[],[f1458,f1607,f1604,f1623,f1614])). 70.10/10.63 thf(f1628,plain,( 70.10/10.63 spl37_45 | spl37_47 | spl37_46 | spl37_43), 70.10/10.63 inference(avatar_split_clause,[],[f1457,f1607,f1618,f1623,f1614])). 70.10/10.63 thf(f1630,definition,( 70.10/10.63 spl37_48 <=> (((mrel @ mactual @ sK17)) = $true)), 70.10/10.63 introduced(definition,[new_symbols(definition,[spl37_48])],[avatar_definition])). 70.10/10.63 thf(f1631,plain,( 70.10/10.63 (((mrel @ mactual @ sK17)) = $true) | ~spl37_48), 70.10/10.63 inference(avatar_component_clause,[],[f1630])). 70.10/10.63 thf(f1632,plain,( 70.10/10.63 spl37_48 | spl37_41 | spl37_47 | spl37_42), 70.10/10.63 inference(avatar_split_clause,[],[f1460,f1604,f1623,f1601,f1630])). 70.10/10.63 thf(f1633,plain,( 70.10/10.63 spl37_41 | spl37_48 | spl37_46 | spl37_47), 70.10/10.63 inference(avatar_split_clause,[],[f1459,f1623,f1618,f1630,f1601])). 70.10/10.63 thf(f1634,plain,( 70.10/10.63 spl37_41 | spl37_44 | spl37_42 | spl37_48), 70.10/10.63 inference(avatar_split_clause,[],[f1462,f1630,f1604,f1610,f1601])). 70.10/10.63 thf(f1635,plain,( 70.10/10.63 spl37_48 | spl37_41 | spl37_44 | spl37_46), 70.10/10.63 inference(avatar_split_clause,[],[f1461,f1618,f1610,f1601,f1630])). 70.10/10.63 thf(f1636,plain,( 70.10/10.63 spl37_48 | spl37_47 | spl37_45 | spl37_42), 70.10/10.63 inference(avatar_split_clause,[],[f1464,f1604,f1614,f1623,f1630])). 70.10/10.63 thf(f1637,plain,( 70.10/10.63 spl37_47 | spl37_48 | spl37_45 | spl37_46), 70.10/10.63 inference(avatar_split_clause,[],[f1463,f1618,f1614,f1630,f1623])). 70.10/10.63 thf(f1638,plain,( 70.10/10.63 spl37_44 | spl37_48 | spl37_42 | spl37_45), 70.10/10.63 inference(avatar_split_clause,[],[f1466,f1614,f1604,f1630,f1610])). 70.10/10.63 thf(f1639,plain,( 70.10/10.63 spl37_46 | spl37_48 | spl37_45 | spl37_44), 70.10/10.63 inference(avatar_split_clause,[],[f1465,f1610,f1614,f1630,f1618])). 70.10/10.63 thf(f1700,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1578])). 70.10/10.63 thf(f1701,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X2)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1580])). 70.10/10.63 thf(f1702,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1701])). 70.10/10.63 thf(f1703,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) )), 70.10/10.63 inference(or_proxy_clausification,[],[f1581])). 70.10/10.63 thf(f1704,plain,( 70.10/10.63 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1582])). 70.10/10.63 thf(f1705,plain,( 70.10/10.63 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1582])). 70.10/10.63 thf(f1706,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1583])). 70.10/10.63 thf(f1707,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1583])). 70.10/10.63 thf(f1708,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1585])). 70.10/10.63 thf(f1709,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1708])). 70.10/10.63 thf(f1710,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1587])). 70.10/10.63 thf(f1711,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1586])). 70.10/10.63 thf(f1712,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1586])). 70.10/10.63 thf(f1713,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1588])). 70.10/10.63 thf(f1714,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1588])). 70.10/10.63 thf(f1715,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1589])). 70.10/10.63 thf(f1716,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1589])). 70.10/10.63 thf(f1717,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1590])). 70.10/10.63 thf(f1718,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1590])). 70.10/10.63 thf(f1719,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1591])). 70.10/10.63 thf(f1720,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1591])). 70.10/10.63 thf(f1721,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1593])). 70.10/10.63 thf(f1722,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1593])). 70.10/10.63 thf(f1723,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1595])). 70.10/10.63 thf(f1724,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1723])). 70.10/10.63 thf(f1725,plain,( 70.10/10.63 ( ! [X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X1)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1594])). 70.10/10.63 thf(f1726,plain,( 70.10/10.63 ( ! [X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X1))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1725])). 70.10/10.63 thf(f1727,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X1)) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1597])). 70.10/10.63 thf(f1728,plain,( 70.10/10.63 ( ! [X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X1))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1727])). 70.10/10.63 thf(f1729,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X1)) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1596])). 70.10/10.63 thf(f1730,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X1))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1729])). 70.10/10.63 thf(f1731,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1599])). 70.10/10.63 thf(f1732,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1731])). 70.10/10.63 thf(f1733,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1598])). 70.10/10.63 thf(f1734,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1733])). 70.10/10.63 thf(f1795,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1700])). 70.10/10.63 thf(f1796,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1700])). 70.10/10.63 thf(f1797,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1702])). 70.10/10.63 thf(f1798,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1702])). 70.10/10.63 thf(f1799,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1703])). 70.10/10.63 thf(f1800,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1703])). 70.10/10.63 thf(f1801,plain,( 70.10/10.63 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1704])). 70.10/10.63 thf(f1802,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1704])). 70.10/10.63 thf(f1803,plain,( 70.10/10.63 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1705])). 70.10/10.63 thf(f1804,plain,( 70.10/10.63 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1705])). 70.10/10.63 thf(f1805,plain,( 70.10/10.63 ( ! [X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1707])). 70.10/10.63 thf(f1806,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1805])). 70.10/10.63 thf(f1807,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X1)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1706])). 70.10/10.63 thf(f1808,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1807])). 70.10/10.63 thf(f1809,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1709])). 70.10/10.63 thf(f1810,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1709])). 70.10/10.63 thf(f1811,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1710])). 70.10/10.63 thf(f1812,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1710])). 70.10/10.63 thf(f1813,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1712])). 70.10/10.63 thf(f1814,plain,( 70.10/10.63 ( ! [X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1711])). 70.10/10.63 thf(f1815,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1713])). 70.10/10.63 thf(f1816,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1713])). 70.10/10.63 thf(f1817,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1714])). 70.10/10.63 thf(f1818,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1716])). 70.10/10.63 thf(f1819,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1716])). 70.10/10.63 thf(f1820,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1715])). 70.10/10.63 thf(f1821,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1715])). 70.10/10.63 thf(f1822,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1718])). 70.10/10.63 thf(f1823,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1718])). 70.10/10.63 thf(f1824,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1717])). 70.10/10.63 thf(f1825,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1717])). 70.10/10.63 thf(f1826,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1719])). 70.10/10.63 thf(f1827,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1719])). 70.10/10.63 thf(f1828,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1720])). 70.10/10.63 thf(f1829,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1720])). 70.10/10.63 thf(f1830,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1722])). 70.10/10.63 thf(f1831,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1830])). 70.10/10.63 thf(f1832,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1721])). 70.10/10.63 thf(f1833,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1721])). 70.10/10.63 thf(f1834,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ Y0))) @ X2)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1724])). 70.10/10.63 thf(f1835,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1834])). 70.10/10.63 thf(f1836,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1726])). 70.10/10.63 thf(f1837,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1728])). 70.10/10.63 thf(f1838,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X1))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1730])). 70.10/10.63 thf(f1839,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X1))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1838])). 70.10/10.63 thf(f1840,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1732])). 70.10/10.63 thf(f1841,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1732])). 70.10/10.63 thf(f1842,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1734])). 70.10/10.63 thf(f1843,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1734])). 70.10/10.63 thf(f1905,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1795])). 70.10/10.63 thf(f1906,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1795])). 70.10/10.63 thf(f1907,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1796])). 70.10/10.63 thf(f1908,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1796])). 70.10/10.63 thf(f1909,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1798])). 70.10/10.63 thf(f1910,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1798])). 70.10/10.63 thf(f1911,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1797])). 70.10/10.63 thf(f1912,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1799])). 70.10/10.63 thf(f1913,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1799])). 70.10/10.63 thf(f1914,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1800])). 70.10/10.63 thf(f1915,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1914])). 70.10/10.63 thf(f1916,plain,( 70.10/10.63 ( ! [X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X1)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1802])). 70.10/10.63 thf(f1917,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1916])). 70.10/10.63 thf(f1918,plain,( 70.10/10.63 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1801])). 70.10/10.63 thf(f1919,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1801])). 70.10/10.63 thf(f1920,plain,( 70.10/10.63 ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1803])). 70.10/10.63 thf(f1921,plain,( 70.10/10.63 ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1803])). 70.10/10.63 thf(f1922,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1804])). 70.10/10.63 thf(f1923,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1804])). 70.10/10.63 thf(f1924,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1806])). 70.10/10.63 thf(f1925,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1806])). 70.10/10.63 thf(f1926,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1808])). 70.10/10.63 thf(f1927,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1808])). 70.10/10.63 thf(f1928,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1809])). 70.10/10.63 thf(f1929,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1810])). 70.10/10.63 thf(f1930,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1811])). 70.10/10.63 thf(f1931,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1930])). 70.10/10.63 thf(f1932,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1812])). 70.10/10.63 thf(f1933,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1932])). 70.10/10.63 thf(f1934,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1813])). 70.10/10.63 thf(f1935,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1934])). 70.10/10.63 thf(f1936,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1814])). 70.10/10.63 thf(f1937,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1814])). 70.10/10.63 thf(f1938,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1816])). 70.10/10.63 thf(f1939,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1815])). 70.10/10.63 thf(f1940,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1815])). 70.10/10.63 thf(f1941,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1817])). 70.10/10.63 thf(f1942,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1817])). 70.10/10.63 thf(f1943,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1818])). 70.10/10.63 thf(f1944,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1818])). 70.10/10.63 thf(f1945,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1819])). 70.10/10.63 thf(f1946,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1945])). 70.10/10.63 thf(f1947,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1821])). 70.10/10.63 thf(f1948,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1821])). 70.10/10.63 thf(f1949,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1820])). 70.10/10.63 thf(f1950,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1820])). 70.10/10.63 thf(f1951,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X2)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1823])). 70.10/10.63 thf(f1952,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1951])). 70.10/10.63 thf(f1953,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1822])). 70.10/10.63 thf(f1954,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1822])). 70.10/10.63 thf(f1955,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1825])). 70.10/10.63 thf(f1956,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1955])). 70.10/10.63 thf(f1957,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1824])). 70.10/10.63 thf(f1958,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1824])). 70.10/10.63 thf(f1959,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1827])). 70.10/10.63 thf(f1960,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1827])). 70.10/10.63 thf(f1961,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1826])). 70.10/10.63 thf(f1962,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1826])). 70.10/10.63 thf(f1963,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1828])). 70.10/10.63 thf(f1964,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1963])). 70.10/10.63 thf(f1965,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1829])). 70.10/10.63 thf(f1966,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1965])). 70.10/10.63 thf(f1967,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1831])). 70.10/10.63 thf(f1968,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1833])). 70.10/10.63 thf(f1969,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1832])). 70.10/10.63 thf(f1970,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) = $true)) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1835])). 70.10/10.63 thf(f1971,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1836])). 70.10/10.63 thf(f1972,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1836])). 70.10/10.63 thf(f1973,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1837])). 70.10/10.63 thf(f1974,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1973])). 70.10/10.63 thf(f1975,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X1))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1839])). 70.10/10.63 thf(f1976,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1840])). 70.10/10.63 thf(f1977,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1840])). 70.10/10.63 thf(f1978,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1841])). 70.10/10.63 thf(f1979,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1978])). 70.10/10.63 thf(f1980,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1843])). 70.10/10.63 thf(f1981,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f1980])). 70.10/10.63 thf(f1982,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1842])). 70.10/10.63 thf(f1983,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1842])). 70.10/10.63 thf(f2043,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1906])). 70.10/10.63 thf(f2044,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1906])). 70.10/10.63 thf(f2045,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1905])). 70.10/10.63 thf(f2046,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1905])). 70.10/10.63 thf(f2047,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1908])). 70.10/10.63 thf(f2048,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1907])). 70.10/10.63 thf(f2049,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1910])). 70.10/10.63 thf(f2050,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2049])). 70.10/10.63 thf(f2051,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1909])). 70.10/10.63 thf(f2052,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1911])). 70.10/10.63 thf(f2053,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1911])). 70.10/10.63 thf(f2054,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1912])). 70.10/10.63 thf(f2055,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2054])). 70.10/10.63 thf(f2056,plain,( 70.10/10.63 ( ! [X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1913])). 70.10/10.63 thf(f2057,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1913])). 70.10/10.63 thf(f2058,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1915])). 70.10/10.63 thf(f2059,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1915])). 70.10/10.63 thf(f2060,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1917])). 70.10/10.63 thf(f2061,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1917])). 70.10/10.63 thf(f2062,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1918])). 70.10/10.63 thf(f2063,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1918])). 70.10/10.63 thf(f2064,plain,( 70.10/10.63 ( ! [X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X1)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1919])). 70.10/10.63 thf(f2065,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2064])). 70.10/10.63 thf(f2066,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1921])). 70.10/10.63 thf(f2067,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1921])). 70.10/10.63 thf(f2068,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1920])). 70.10/10.63 thf(f2069,plain,( 70.10/10.63 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))), 70.10/10.63 inference(and_proxy_clausification,[],[f1920])). 70.10/10.63 thf(f2070,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X1)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1923])). 70.10/10.63 thf(f2071,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2070])). 70.10/10.63 thf(f2072,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X1)) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1922])). 70.10/10.63 thf(f2073,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2072])). 70.10/10.63 thf(f2074,plain,( 70.10/10.63 ( ! [X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1924])). 70.10/10.63 thf(f2075,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1924])). 70.10/10.63 thf(f2076,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1925])). 70.10/10.63 thf(f2077,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2076])). 70.10/10.63 thf(f2078,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1926])). 70.10/10.63 thf(f2079,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1927])). 70.10/10.63 thf(f2080,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1928])). 70.10/10.63 thf(f2081,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1928])). 70.10/10.63 thf(f2082,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1929])). 70.10/10.63 thf(f2083,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1931])). 70.10/10.63 thf(f2084,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2083])). 70.10/10.63 thf(f2085,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1933])). 70.10/10.63 thf(f2086,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2085])). 70.10/10.63 thf(f2087,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1935])). 70.10/10.63 thf(f2088,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2087])). 70.10/10.63 thf(f2089,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1936])). 70.10/10.63 thf(f2090,plain,( 70.10/10.63 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1936])). 70.10/10.63 thf(f2091,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X2)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1937])). 70.10/10.63 thf(f2092,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2091])). 70.10/10.63 thf(f2093,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1938])). 70.10/10.63 thf(f2094,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1938])). 70.10/10.63 thf(f2095,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1939])). 70.10/10.63 thf(f2096,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1939])). 70.10/10.63 thf(f2097,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1940])). 70.10/10.63 thf(f2098,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2097])). 70.10/10.63 thf(f2099,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1941])). 70.10/10.63 thf(f2100,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2099])). 70.10/10.63 thf(f2101,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1942])). 70.10/10.63 thf(f2102,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2101])). 70.10/10.63 thf(f2103,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1943])). 70.10/10.63 thf(f2104,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1943])). 70.10/10.63 thf(f2105,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1944])). 70.10/10.63 thf(f2106,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2105])). 70.10/10.63 thf(f2107,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1946])). 70.10/10.63 thf(f2108,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1948])). 70.10/10.63 thf(f2109,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2108])). 70.10/10.63 thf(f2110,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1947])). 70.10/10.63 thf(f2111,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2110])). 70.10/10.63 thf(f2112,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1949])). 70.10/10.63 thf(f2113,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1949])). 70.10/10.63 thf(f2114,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1950])). 70.10/10.63 thf(f2115,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2114])). 70.10/10.63 thf(f2116,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X3)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1952])). 70.10/10.63 thf(f2117,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2116])). 70.10/10.63 thf(f2118,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X2)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1953])). 70.10/10.63 thf(f2119,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2118])). 70.10/10.63 thf(f2120,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X2)) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1954])). 70.10/10.63 thf(f2121,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2120])). 70.10/10.63 thf(f2122,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1956])). 70.10/10.63 thf(f2123,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1956])). 70.10/10.63 thf(f2124,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X2)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1957])). 70.10/10.63 thf(f2125,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2124])). 70.10/10.63 thf(f2126,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1958])). 70.10/10.63 thf(f2127,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2126])). 70.10/10.63 thf(f2128,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1959])). 70.10/10.63 thf(f2129,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1959])). 70.10/10.63 thf(f2130,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1960])). 70.10/10.63 thf(f2131,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2130])). 70.10/10.63 thf(f2132,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1962])). 70.10/10.63 thf(f2133,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2132])). 70.10/10.63 thf(f2134,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1961])). 70.10/10.63 thf(f2135,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1961])). 70.10/10.63 thf(f2136,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1964])). 70.10/10.63 thf(f2137,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1966])). 70.10/10.63 thf(f2138,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2137])). 70.10/10.63 thf(f2139,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1967])). 70.10/10.63 thf(f2140,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1967])). 70.10/10.63 thf(f2141,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1968])). 70.10/10.63 thf(f2142,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2141])). 70.10/10.63 thf(f2143,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1969])). 70.10/10.63 thf(f2144,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1969])). 70.10/10.63 thf(f2145,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1970])). 70.10/10.63 thf(f2146,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1970])). 70.10/10.63 thf(f2147,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1972])). 70.10/10.63 thf(f2148,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2147])). 70.10/10.63 thf(f2149,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X2)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1971])). 70.10/10.63 thf(f2150,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2149])). 70.10/10.63 thf(f2151,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1974])). 70.10/10.63 thf(f2152,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f1975])). 70.10/10.63 thf(f2153,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1976])). 70.10/10.63 thf(f2154,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1976])). 70.10/10.63 thf(f2155,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X3)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1977])). 70.10/10.63 thf(f2156,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2155])). 70.10/10.63 thf(f2157,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f1979])). 70.10/10.63 thf(f2158,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2157])). 70.10/10.63 thf(f2159,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1981])). 70.10/10.63 thf(f2160,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1981])). 70.10/10.63 thf(f2161,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1983])). 70.10/10.63 thf(f2162,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1983])). 70.10/10.63 thf(f2163,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1982])). 70.10/10.63 thf(f2164,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f1982])). 70.10/10.63 thf(f2226,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2044])). 70.10/10.63 thf(f2227,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2226])). 70.10/10.63 thf(f2228,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2043])). 70.10/10.63 thf(f2229,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2228])). 70.10/10.63 thf(f2230,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f2046])). 70.10/10.63 thf(f2231,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2045])). 70.10/10.63 thf(f2232,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2045])). 70.10/10.63 thf(f2233,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2047])). 70.10/10.63 thf(f2234,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2233])). 70.10/10.63 thf(f2235,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2048])). 70.10/10.63 thf(f2236,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2235])). 70.10/10.63 thf(f2237,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f2050])). 70.10/10.63 thf(f2238,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2051])). 70.10/10.63 thf(f2239,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2238])). 70.10/10.63 thf(f2240,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2052])). 70.10/10.63 thf(f2241,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2052])). 70.10/10.63 thf(f2242,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f2053])). 70.10/10.63 thf(f2243,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2055])). 70.10/10.63 thf(f2244,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2055])). 70.10/10.63 thf(f2245,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2057])). 70.10/10.63 thf(f2246,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2245])). 70.10/10.63 thf(f2247,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2056])). 70.10/10.63 thf(f2248,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2056])). 70.10/10.63 thf(f2249,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2059])). 70.10/10.63 thf(f2250,plain,( 70.10/10.63 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2249])). 70.10/10.63 thf(f2251,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2058])). 70.10/10.63 thf(f2252,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2058])). 70.10/10.63 thf(f2253,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2061])). 70.10/10.63 thf(f2254,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2061])). 70.10/10.63 thf(f2255,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X2)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2060])). 70.10/10.63 thf(f2256,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2255])). 70.10/10.63 thf(f2257,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2062])). 70.10/10.63 thf(f2258,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2257])). 70.10/10.63 thf(f2259,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X1)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2063])). 70.10/10.63 thf(f2260,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2259])). 70.10/10.63 thf(f2261,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f2065])). 70.10/10.63 thf(f2262,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2067])). 70.10/10.63 thf(f2263,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X1))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2262])). 70.10/10.63 thf(f2264,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2066])). 70.10/10.63 thf(f2265,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2264])). 70.10/10.63 thf(f2266,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2068])). 70.10/10.63 thf(f2267,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2266])). 70.10/10.63 thf(f2268,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2069])). 70.10/10.63 thf(f2269,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2268])). 70.10/10.63 thf(f2270,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f2071])). 70.10/10.63 thf(f2271,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X2)) = $true)) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2073])). 70.10/10.63 thf(f2272,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2271])). 70.10/10.63 thf(f2273,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2075])). 70.10/10.63 thf(f2274,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) = $true)) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2273])). 70.10/10.63 thf(f2275,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2074])). 70.10/10.63 thf(f2276,plain,( 70.10/10.63 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2074])). 70.10/10.63 thf(f2277,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f2077])). 70.10/10.63 thf(f2278,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2078])). 70.10/10.63 thf(f2279,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2))))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2278])). 70.10/10.63 thf(f2280,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X2)))) )), 70.10/10.63 inference(pi_proxy_clausification,[],[f2079])). 70.10/10.63 thf(f2281,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.63 inference(beta-eta_normalization,[],[f2280])). 70.10/10.63 thf(f2282,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.63 inference(imp_proxy_clausification,[],[f2080])). 70.10/10.63 thf(f2283,plain,( 70.10/10.63 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.63 inference(and_proxy_clausification,[],[f2081])). 70.10/10.64 thf(f2284,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2081])). 70.10/10.64 thf(f2285,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2082])). 70.10/10.64 thf(f2286,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2285])). 70.10/10.64 thf(f2287,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2084])). 70.10/10.64 thf(f2288,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X4)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2086])). 70.10/10.64 thf(f2289,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X4)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2288])). 70.10/10.64 thf(f2290,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2088])). 70.10/10.64 thf(f2291,plain,( 70.10/10.64 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2089])). 70.10/10.64 thf(f2292,plain,( 70.10/10.64 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2089])). 70.10/10.64 thf(f2293,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2090])). 70.10/10.64 thf(f2294,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2293])). 70.10/10.64 thf(f2295,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X3)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2092])). 70.10/10.64 thf(f2296,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2295])). 70.10/10.64 thf(f2297,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2093])). 70.10/10.64 thf(f2298,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2093])). 70.10/10.64 thf(f2299,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2094])). 70.10/10.64 thf(f2300,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2299])). 70.10/10.64 thf(f2301,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2095])). 70.10/10.64 thf(f2302,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2095])). 70.10/10.64 thf(f2303,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2096])). 70.10/10.64 thf(f2304,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2096])). 70.10/10.64 thf(f2305,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2098])). 70.10/10.64 thf(f2306,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2100])). 70.10/10.64 thf(f2307,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2100])). 70.10/10.64 thf(f2308,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2102])). 70.10/10.64 thf(f2309,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2103])). 70.10/10.64 thf(f2310,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2309])). 70.10/10.64 thf(f2311,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2104])). 70.10/10.64 thf(f2312,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2311])). 70.10/10.64 thf(f2313,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X3))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2106])). 70.10/10.64 thf(f2314,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2313])). 70.10/10.64 thf(f2315,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2107])). 70.10/10.64 thf(f2316,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2107])). 70.10/10.64 thf(f2317,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2109])). 70.10/10.64 thf(f2318,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2111])). 70.10/10.64 thf(f2319,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2111])). 70.10/10.64 thf(f2320,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2112])). 70.10/10.64 thf(f2321,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2112])). 70.10/10.64 thf(f2322,plain,( 70.10/10.64 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2113])). 70.10/10.64 thf(f2323,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2113])). 70.10/10.64 thf(f2324,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2115])). 70.10/10.64 thf(f2325,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2117])). 70.10/10.64 thf(f2326,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2119])). 70.10/10.64 thf(f2327,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2119])). 70.10/10.64 thf(f2328,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3)) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2121])). 70.10/10.64 thf(f2329,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2328])). 70.10/10.64 thf(f2330,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2122])). 70.10/10.64 thf(f2331,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2122])). 70.10/10.64 thf(f2332,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2123])). 70.10/10.64 thf(f2333,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2332])). 70.10/10.64 thf(f2334,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2125])). 70.10/10.64 thf(f2335,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X3)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2127])). 70.10/10.64 thf(f2336,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2335])). 70.10/10.64 thf(f2337,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2129])). 70.10/10.64 thf(f2338,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2337])). 70.10/10.64 thf(f2339,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2128])). 70.10/10.64 thf(f2340,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2339])). 70.10/10.64 thf(f2341,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2131])). 70.10/10.64 thf(f2342,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2133])). 70.10/10.64 thf(f2343,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2133])). 70.10/10.64 thf(f2344,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2134])). 70.10/10.64 thf(f2345,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2134])). 70.10/10.64 thf(f2346,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2135])). 70.10/10.64 thf(f2347,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2135])). 70.10/10.64 thf(f2348,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2136])). 70.10/10.64 thf(f2349,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2136])). 70.10/10.64 thf(f2350,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2138])). 70.10/10.64 thf(f2351,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2140])). 70.10/10.64 thf(f2352,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2139])). 70.10/10.64 thf(f2353,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2139])). 70.10/10.64 thf(f2354,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2142])). 70.10/10.64 thf(f2355,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2142])). 70.10/10.64 thf(f2356,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2143])). 70.10/10.64 thf(f2357,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2356])). 70.10/10.64 thf(f2358,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2144])). 70.10/10.64 thf(f2359,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2358])). 70.10/10.64 thf(f2360,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2145])). 70.10/10.64 thf(f2361,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2146])). 70.10/10.64 thf(f2362,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2148])). 70.10/10.64 thf(f2363,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2148])). 70.10/10.64 thf(f2364,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2150])). 70.10/10.64 thf(f2365,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2151])). 70.10/10.64 thf(f2366,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2365])). 70.10/10.64 thf(f2367,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2152])). 70.10/10.64 thf(f2368,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2152])). 70.10/10.64 thf(f2369,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2154])). 70.10/10.64 thf(f2370,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2153])). 70.10/10.64 thf(f2371,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2156])). 70.10/10.64 thf(f2372,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2371])). 70.10/10.64 thf(f2373,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2158])). 70.10/10.64 thf(f2374,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2159])). 70.10/10.64 thf(f2375,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2160])). 70.10/10.64 thf(f2376,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2161])). 70.10/10.64 thf(f2377,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2161])). 70.10/10.64 thf(f2378,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2162])). 70.10/10.64 thf(f2379,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2378])). 70.10/10.64 thf(f2380,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2163])). 70.10/10.64 thf(f2381,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2164])). 70.10/10.64 thf(f2382,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2164])). 70.10/10.64 thf(f2438,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2227])). 70.10/10.64 thf(f2439,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2438])). 70.10/10.64 thf(f2440,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2229])). 70.10/10.64 thf(f2441,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2230])). 70.10/10.64 thf(f2442,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2230])). 70.10/10.64 thf(f2443,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2232])). 70.10/10.64 thf(f2444,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2443])). 70.10/10.64 thf(f2445,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2231])). 70.10/10.64 thf(f2446,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2231])). 70.10/10.64 thf(f2447,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2234])). 70.10/10.64 thf(f2448,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2236])). 70.10/10.64 thf(f2449,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2237])). 70.10/10.64 thf(f2450,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2239])). 70.10/10.64 thf(f2451,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2239])). 70.10/10.64 thf(f2452,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2241])). 70.10/10.64 thf(f2453,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2452])). 70.10/10.64 thf(f2454,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2240])). 70.10/10.64 thf(f2455,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2240])). 70.10/10.64 thf(f2456,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2242])). 70.10/10.64 thf(f2457,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2456])). 70.10/10.64 thf(f2458,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2244])). 70.10/10.64 thf(f2459,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2458])). 70.10/10.64 thf(f2460,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2243])). 70.10/10.64 thf(f2461,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2246])). 70.10/10.64 thf(f2462,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2246])). 70.10/10.64 thf(f2463,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2248])). 70.10/10.64 thf(f2464,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2463])). 70.10/10.64 thf(f2465,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2247])). 70.10/10.64 thf(f2466,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2247])). 70.10/10.64 thf(f2467,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2250])). 70.10/10.64 thf(f2468,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2250])). 70.10/10.64 thf(f2469,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2252])). 70.10/10.64 thf(f2470,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2251])). 70.10/10.64 thf(f2471,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2254])). 70.10/10.64 thf(f2472,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2253])). 70.10/10.64 thf(f2473,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2472])). 70.10/10.64 thf(f2474,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2256])). 70.10/10.64 thf(f2475,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2258])). 70.10/10.64 thf(f2476,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2475])). 70.10/10.64 thf(f2477,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X1)))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2260])). 70.10/10.64 thf(f2478,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2260])). 70.10/10.64 thf(f2479,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X2)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2261])). 70.10/10.64 thf(f2480,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2479])). 70.10/10.64 thf(f2481,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X1))) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2263])). 70.10/10.64 thf(f2482,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X1))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2481])). 70.10/10.64 thf(f2483,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2265])). 70.10/10.64 thf(f2484,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2483])). 70.10/10.64 thf(f2485,plain,( 70.10/10.64 ( ! [X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2267])). 70.10/10.64 thf(f2486,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2269])). 70.10/10.64 thf(f2487,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2486])). 70.10/10.64 thf(f2488,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2270])). 70.10/10.64 thf(f2489,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2488])). 70.10/10.64 thf(f2490,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2272])). 70.10/10.64 thf(f2491,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2274])). 70.10/10.64 thf(f2492,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2491])). 70.10/10.64 thf(f2493,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2276])). 70.10/10.64 thf(f2494,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2493])). 70.10/10.64 thf(f2495,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2275])). 70.10/10.64 thf(f2496,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2495])). 70.10/10.64 thf(f2497,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2277])). 70.10/10.64 thf(f2498,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2497])). 70.10/10.64 thf(f2499,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2279])). 70.10/10.64 thf(f2500,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2499])). 70.10/10.64 thf(f2501,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2281])). 70.10/10.64 thf(f2502,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2282])). 70.10/10.64 thf(f2503,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2282])). 70.10/10.64 thf(f2504,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2283])). 70.10/10.64 thf(f2505,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2504])). 70.10/10.64 thf(f2506,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2284])). 70.10/10.64 thf(f2507,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2506])). 70.10/10.64 thf(f2508,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2286])). 70.10/10.64 thf(f2509,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2287])). 70.10/10.64 thf(f2510,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2287])). 70.10/10.64 thf(f2511,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2289])). 70.10/10.64 thf(f2512,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2290])). 70.10/10.64 thf(f2513,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2292])). 70.10/10.64 thf(f2514,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2513])). 70.10/10.64 thf(f2515,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ Y0))) @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2291])). 70.10/10.64 thf(f2516,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2515])). 70.10/10.64 thf(f2517,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2294])). 70.10/10.64 thf(f2518,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2517])). 70.10/10.64 thf(f2519,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2296])). 70.10/10.64 thf(f2520,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2297])). 70.10/10.64 thf(f2521,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2520])). 70.10/10.64 thf(f2522,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2298])). 70.10/10.64 thf(f2523,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2522])). 70.10/10.64 thf(f2524,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2300])). 70.10/10.64 thf(f2525,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2524])). 70.10/10.64 thf(f2526,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2302])). 70.10/10.64 thf(f2527,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2526])). 70.10/10.64 thf(f2528,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2301])). 70.10/10.64 thf(f2529,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2304])). 70.10/10.64 thf(f2530,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2529])). 70.10/10.64 thf(f2531,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2303])). 70.10/10.64 thf(f2532,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2305])). 70.10/10.64 thf(f2533,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2307])). 70.10/10.64 thf(f2534,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2533])). 70.10/10.64 thf(f2535,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2306])). 70.10/10.64 thf(f2536,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2308])). 70.10/10.64 thf(f2537,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2536])). 70.10/10.64 thf(f2538,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X3)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2310])). 70.10/10.64 thf(f2539,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2538])). 70.10/10.64 thf(f2540,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2312])). 70.10/10.64 thf(f2541,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2312])). 70.10/10.64 thf(f2542,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2314])). 70.10/10.64 thf(f2543,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2315])). 70.10/10.64 thf(f2544,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2315])). 70.10/10.64 thf(f2545,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2316])). 70.10/10.64 thf(f2546,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2545])). 70.10/10.64 thf(f2547,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2317])). 70.10/10.64 thf(f2548,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2317])). 70.10/10.64 thf(f2549,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2319])). 70.10/10.64 thf(f2550,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2549])). 70.10/10.64 thf(f2551,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X3)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2318])). 70.10/10.64 thf(f2552,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2551])). 70.10/10.64 thf(f2553,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2321])). 70.10/10.64 thf(f2554,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2553])). 70.10/10.64 thf(f2555,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2320])). 70.10/10.64 thf(f2556,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2320])). 70.10/10.64 thf(f2557,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2322])). 70.10/10.64 thf(f2558,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2557])). 70.10/10.64 thf(f2559,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2323])). 70.10/10.64 thf(f2560,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2559])). 70.10/10.64 thf(f2561,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2324])). 70.10/10.64 thf(f2562,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2324])). 70.10/10.64 thf(f2563,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2325])). 70.10/10.64 thf(f2564,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2327])). 70.10/10.64 thf(f2565,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2564])). 70.10/10.64 thf(f2566,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2326])). 70.10/10.64 thf(f2567,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2566])). 70.10/10.64 thf(f2568,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2329])). 70.10/10.64 thf(f2569,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2568])). 70.10/10.64 thf(f2570,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2330])). 70.10/10.64 thf(f2571,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2570])). 70.10/10.64 thf(f2572,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2331])). 70.10/10.64 thf(f2573,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2572])). 70.10/10.64 thf(f2574,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2333])). 70.10/10.64 thf(f2575,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2334])). 70.10/10.64 thf(f2576,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2334])). 70.10/10.64 thf(f2577,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2336])). 70.10/10.64 thf(f2578,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2577])). 70.10/10.64 thf(f2579,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2338])). 70.10/10.64 thf(f2580,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2340])). 70.10/10.64 thf(f2581,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2580])). 70.10/10.64 thf(f2582,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2341])). 70.10/10.64 thf(f2583,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2582])). 70.10/10.64 thf(f2584,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2343])). 70.10/10.64 thf(f2585,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2584])). 70.10/10.64 thf(f2586,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2342])). 70.10/10.64 thf(f2587,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2342])). 70.10/10.64 thf(f2588,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2345])). 70.10/10.64 thf(f2589,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2345])). 70.10/10.64 thf(f2590,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2344])). 70.10/10.64 thf(f2591,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2344])). 70.10/10.64 thf(f2592,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2347])). 70.10/10.64 thf(f2593,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2592])). 70.10/10.64 thf(f2594,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2346])). 70.10/10.64 thf(f2595,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2594])). 70.10/10.64 thf(f2596,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2349])). 70.10/10.64 thf(f2597,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2596])). 70.10/10.64 thf(f2598,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2348])). 70.10/10.64 thf(f2599,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2348])). 70.10/10.64 thf(f2600,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2350])). 70.10/10.64 thf(f2601,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2351])). 70.10/10.64 thf(f2602,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2353])). 70.10/10.64 thf(f2603,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2352])). 70.10/10.64 thf(f2604,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2355])). 70.10/10.64 thf(f2605,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2604])). 70.10/10.64 thf(f2606,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2354])). 70.10/10.64 thf(f2607,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2354])). 70.10/10.64 thf(f2608,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2357])). 70.10/10.64 thf(f2609,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2357])). 70.10/10.64 thf(f2610,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2359])). 70.10/10.64 thf(f2611,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2360])). 70.10/10.64 thf(f2612,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2611])). 70.10/10.64 thf(f2613,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2361])). 70.10/10.64 thf(f2614,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2613])). 70.10/10.64 thf(f2615,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2363])). 70.10/10.64 thf(f2616,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2615])). 70.10/10.64 thf(f2617,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2362])). 70.10/10.64 thf(f2618,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2617])). 70.10/10.64 thf(f2619,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2364])). 70.10/10.64 thf(f2620,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2364])). 70.10/10.64 thf(f2621,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2366])). 70.10/10.64 thf(f2622,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2621])). 70.10/10.64 thf(f2623,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2368])). 70.10/10.64 thf(f2624,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2623])). 70.10/10.64 thf(f2625,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2367])). 70.10/10.64 thf(f2626,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2367])). 70.10/10.64 thf(f2627,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2369])). 70.10/10.64 thf(f2628,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2627])). 70.10/10.64 thf(f2629,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X3)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2370])). 70.10/10.64 thf(f2630,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2629])). 70.10/10.64 thf(f2631,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2372])). 70.10/10.64 thf(f2632,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2373])). 70.10/10.64 thf(f2633,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2374])). 70.10/10.64 thf(f2634,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2375])). 70.10/10.64 thf(f2635,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2377])). 70.10/10.64 thf(f2636,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2635])). 70.10/10.64 thf(f2637,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2376])). 70.10/10.64 thf(f2638,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2379])). 70.10/10.64 thf(f2639,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2638])). 70.10/10.64 thf(f2640,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2380])). 70.10/10.64 thf(f2641,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2640])). 70.10/10.64 thf(f2642,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2382])). 70.10/10.64 thf(f2643,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2642])). 70.10/10.64 thf(f2644,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2381])). 70.10/10.64 thf(f2645,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2644])). 70.10/10.64 thf(f2705,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2439])). 70.10/10.64 thf(f2706,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2440])). 70.10/10.64 thf(f2707,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2441])). 70.10/10.64 thf(f2708,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2441])). 70.10/10.64 thf(f2709,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2442])). 70.10/10.64 thf(f2710,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2709])). 70.10/10.64 thf(f2711,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2444])). 70.10/10.64 thf(f2712,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2711])). 70.10/10.64 thf(f2713,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2446])). 70.10/10.64 thf(f2714,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2713])). 70.10/10.64 thf(f2715,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2445])). 70.10/10.64 thf(f2716,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2715])). 70.10/10.64 thf(f2717,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2447])). 70.10/10.64 thf(f2718,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2717])). 70.10/10.64 thf(f2719,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2448])). 70.10/10.64 thf(f2720,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2448])). 70.10/10.64 thf(f2721,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2449])). 70.10/10.64 thf(f2722,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2721])). 70.10/10.64 thf(f2723,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2450])). 70.10/10.64 thf(f2724,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2451])). 70.10/10.64 thf(f2725,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2453])). 70.10/10.64 thf(f2726,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X3))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2455])). 70.10/10.64 thf(f2727,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2726])). 70.10/10.64 thf(f2728,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2454])). 70.10/10.64 thf(f2729,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2457])). 70.10/10.64 thf(f2730,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2459])). 70.10/10.64 thf(f2731,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2460])). 70.10/10.64 thf(f2732,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2460])). 70.10/10.64 thf(f2733,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2462])). 70.10/10.64 thf(f2734,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2461])). 70.10/10.64 thf(f2735,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2734])). 70.10/10.64 thf(f2736,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X3)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2464])). 70.10/10.64 thf(f2737,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2736])). 70.10/10.64 thf(f2738,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2466])). 70.10/10.64 thf(f2739,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2738])). 70.10/10.64 thf(f2740,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2465])). 70.10/10.64 thf(f2741,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2465])). 70.10/10.64 thf(f2742,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2468])). 70.10/10.64 thf(f2743,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2742])). 70.10/10.64 thf(f2744,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X4)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2467])). 70.10/10.64 thf(f2745,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2744])). 70.10/10.64 thf(f2746,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2469])). 70.10/10.64 thf(f2747,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2746])). 70.10/10.64 thf(f2748,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2470])). 70.10/10.64 thf(f2749,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2470])). 70.10/10.64 thf(f2750,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2471])). 70.10/10.64 thf(f2751,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2750])). 70.10/10.64 thf(f2752,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2473])). 70.10/10.64 thf(f2753,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2474])). 70.10/10.64 thf(f2754,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2474])). 70.10/10.64 thf(f2755,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) = $true)) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2476])). 70.10/10.64 thf(f2756,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2478])). 70.10/10.64 thf(f2757,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2477])). 70.10/10.64 thf(f2758,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2480])). 70.10/10.64 thf(f2759,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2480])). 70.10/10.64 thf(f2760,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2482])). 70.10/10.64 thf(f2761,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2484])). 70.10/10.64 thf(f2762,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2485])). 70.10/10.64 thf(f2763,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2485])). 70.10/10.64 thf(f2764,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2487])). 70.10/10.64 thf(f2765,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2487])). 70.10/10.64 thf(f2766,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2489])). 70.10/10.64 thf(f2767,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2490])). 70.10/10.64 thf(f2768,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2767])). 70.10/10.64 thf(f2769,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2492])). 70.10/10.64 thf(f2770,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2494])). 70.10/10.64 thf(f2771,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2496])). 70.10/10.64 thf(f2772,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2498])). 70.10/10.64 thf(f2773,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2772])). 70.10/10.64 thf(f2774,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2500])). 70.10/10.64 thf(f2775,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2501])). 70.10/10.64 thf(f2776,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2775])). 70.10/10.64 thf(f2777,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2503])). 70.10/10.64 thf(f2778,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2503])). 70.10/10.64 thf(f2779,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2502])). 70.10/10.64 thf(f2780,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2502])). 70.10/10.64 thf(f2781,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2505])). 70.10/10.64 thf(f2782,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2507])). 70.10/10.64 thf(f2783,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2508])). 70.10/10.64 thf(f2784,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2508])). 70.10/10.64 thf(f2785,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2509])). 70.10/10.64 thf(f2786,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2509])). 70.10/10.64 thf(f2787,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2510])). 70.10/10.64 thf(f2788,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2511])). 70.10/10.64 thf(f2789,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2512])). 70.10/10.64 thf(f2790,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2512])). 70.10/10.64 thf(f2791,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2514])). 70.10/10.64 thf(f2792,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2791])). 70.10/10.64 thf(f2793,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X3)) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2516])). 70.10/10.64 thf(f2794,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2793])). 70.10/10.64 thf(f2795,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2518])). 70.10/10.64 thf(f2796,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2518])). 70.10/10.64 thf(f2797,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2519])). 70.10/10.64 thf(f2798,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2519])). 70.10/10.64 thf(f2799,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2521])). 70.10/10.64 thf(f2800,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2799])). 70.10/10.64 thf(f2801,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2523])). 70.10/10.64 thf(f2802,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2801])). 70.10/10.64 thf(f2803,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2525])). 70.10/10.64 thf(f2804,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2527])). 70.10/10.64 thf(f2805,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2527])). 70.10/10.64 thf(f2806,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2528])). 70.10/10.64 thf(f2807,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2806])). 70.10/10.64 thf(f2808,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2530])). 70.10/10.64 thf(f2809,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2808])). 70.10/10.64 thf(f2810,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2531])). 70.10/10.64 thf(f2811,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2810])). 70.10/10.64 thf(f2812,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2532])). 70.10/10.64 thf(f2813,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2532])). 70.10/10.64 thf(f2814,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2534])). 70.10/10.64 thf(f2815,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2535])). 70.10/10.64 thf(f2816,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2535])). 70.10/10.64 thf(f2817,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2537])). 70.10/10.64 thf(f2818,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2539])). 70.10/10.64 thf(f2819,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2541])). 70.10/10.64 thf(f2820,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2540])). 70.10/10.64 thf(f2821,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2542])). 70.10/10.64 thf(f2822,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2542])). 70.10/10.64 thf(f2823,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2544])). 70.10/10.64 thf(f2824,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2823])). 70.10/10.64 thf(f2825,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2543])). 70.10/10.64 thf(f2826,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2543])). 70.10/10.64 thf(f2827,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2546])). 70.10/10.64 thf(f2828,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2827])). 70.10/10.64 thf(f2829,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2548])). 70.10/10.64 thf(f2830,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2829])). 70.10/10.64 thf(f2831,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2547])). 70.10/10.64 thf(f2832,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2831])). 70.10/10.64 thf(f2833,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2550])). 70.10/10.64 thf(f2834,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2552])). 70.10/10.64 thf(f2835,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2552])). 70.10/10.64 thf(f2836,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2554])). 70.10/10.64 thf(f2837,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2555])). 70.10/10.64 thf(f2838,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2837])). 70.10/10.64 thf(f2839,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2556])). 70.10/10.64 thf(f2840,plain,( 70.10/10.64 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2556])). 70.10/10.64 thf(f2841,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X3)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2558])). 70.10/10.64 thf(f2842,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2841])). 70.10/10.64 thf(f2843,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2560])). 70.10/10.64 thf(f2844,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2843])). 70.10/10.64 thf(f2845,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2561])). 70.10/10.64 thf(f2846,plain,( 70.10/10.64 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.64 inference(and_proxy_clausification,[],[f2561])). 70.10/10.64 thf(f2847,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2562])). 70.10/10.64 thf(f2848,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2847])). 70.10/10.64 thf(f2849,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2563])). 70.10/10.64 thf(f2850,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2849])). 70.10/10.64 thf(f2851,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2565])). 70.10/10.64 thf(f2852,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2851])). 70.10/10.64 thf(f2853,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2567])). 70.10/10.64 thf(f2854,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2853])). 70.10/10.64 thf(f2855,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2569])). 70.10/10.64 thf(f2856,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2571])). 70.10/10.64 thf(f2857,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2573])). 70.10/10.64 thf(f2858,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2857])). 70.10/10.64 thf(f2859,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2574])). 70.10/10.64 thf(f2860,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2859])). 70.10/10.64 thf(f2861,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2576])). 70.10/10.64 thf(f2862,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2861])). 70.10/10.64 thf(f2863,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X3))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2575])). 70.10/10.64 thf(f2864,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2863])). 70.10/10.64 thf(f2865,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2578])). 70.10/10.64 thf(f2866,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2579])). 70.10/10.64 thf(f2867,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2866])). 70.10/10.64 thf(f2868,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2581])). 70.10/10.64 thf(f2869,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2583])). 70.10/10.64 thf(f2870,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2585])). 70.10/10.64 thf(f2871,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2587])). 70.10/10.64 thf(f2872,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2871])). 70.10/10.64 thf(f2873,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2586])). 70.10/10.64 thf(f2874,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2873])). 70.10/10.64 thf(f2875,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2589])). 70.10/10.64 thf(f2876,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2875])). 70.10/10.64 thf(f2877,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2588])). 70.10/10.64 thf(f2878,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2877])). 70.10/10.64 thf(f2879,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2591])). 70.10/10.64 thf(f2880,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2879])). 70.10/10.64 thf(f2881,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2590])). 70.10/10.64 thf(f2882,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2881])). 70.10/10.64 thf(f2883,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2593])). 70.10/10.64 thf(f2884,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2883])). 70.10/10.64 thf(f2885,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2595])). 70.10/10.64 thf(f2886,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2597])). 70.10/10.64 thf(f2887,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2598])). 70.10/10.64 thf(f2888,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2887])). 70.10/10.64 thf(f2889,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2599])). 70.10/10.64 thf(f2890,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2889])). 70.10/10.64 thf(f2892,definition,( 70.10/10.64 spl37_97 <=> ! [X2 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))))), 70.10/10.64 introduced(definition,[new_symbols(definition,[spl37_97])],[avatar_definition])). 70.10/10.64 thf(f2893,plain,( 70.10/10.64 ( ! [X2 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) ) | ~spl37_97), 70.10/10.64 inference(avatar_component_clause,[],[f2892])). 70.10/10.64 thf(f2895,definition,( 70.10/10.64 spl37_98 <=> ! [X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4))))), 70.10/10.64 introduced(definition,[new_symbols(definition,[spl37_98])],[avatar_definition])). 70.10/10.64 thf(f2896,plain,( 70.10/10.64 ( ! [X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4)))) ) | ~spl37_98), 70.10/10.64 inference(avatar_component_clause,[],[f2895])). 70.10/10.64 thf(f2898,definition,( 70.10/10.64 spl37_99 <=> ! [X3 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))))), 70.10/10.64 introduced(definition,[new_symbols(definition,[spl37_99])],[avatar_definition])). 70.10/10.64 thf(f2899,plain,( 70.10/10.64 ( ! [X3 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3)))) ) | ~spl37_99), 70.10/10.64 inference(avatar_component_clause,[],[f2898])). 70.10/10.64 thf(f2901,definition,( 70.10/10.64 spl37_100 <=> ! [X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))))), 70.10/10.64 introduced(definition,[new_symbols(definition,[spl37_100])],[avatar_definition])). 70.10/10.64 thf(f2902,plain,( 70.10/10.64 ( ! [X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) ) | ~spl37_100), 70.10/10.64 inference(avatar_component_clause,[],[f2901])). 70.10/10.64 thf(f2903,plain,( 70.10/10.64 spl37_97 | spl37_98 | spl37_99 | spl37_100), 70.10/10.64 inference(avatar_split_clause,[],[f2600,f2901,f2898,f2895,f2892])). 70.10/10.64 thf(f2904,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2601])). 70.10/10.64 thf(f2905,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2904])). 70.10/10.64 thf(f2906,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.64 inference(pi_proxy_clausification,[],[f2602])). 70.10/10.64 thf(f2907,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )), 70.10/10.64 inference(beta-eta_normalization,[],[f2906])). 70.10/10.64 thf(f2908,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2603])). 70.10/10.64 thf(f2909,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2605])). 70.10/10.64 thf(f2910,plain,( 70.10/10.64 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.64 inference(imp_proxy_clausification,[],[f2607])). 70.10/10.65 thf(f2911,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2606])). 70.10/10.65 thf(f2912,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2606])). 70.10/10.65 thf(f2913,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2608])). 70.10/10.65 thf(f2914,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2608])). 70.10/10.65 thf(f2915,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2609])). 70.10/10.65 thf(f2916,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2610])). 70.10/10.65 thf(f2917,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2612])). 70.10/10.65 thf(f2918,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2612])). 70.10/10.65 thf(f2919,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2614])). 70.10/10.65 thf(f2920,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2616])). 70.10/10.65 thf(f2921,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2618])). 70.10/10.65 thf(f2922,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2619])). 70.10/10.65 thf(f2923,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2619])). 70.10/10.65 thf(f2924,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2620])). 70.10/10.65 thf(f2925,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f2924])). 70.10/10.65 thf(f2926,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2622])). 70.10/10.65 thf(f2927,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2624])). 70.10/10.65 thf(f2928,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f2927])). 70.10/10.65 thf(f2929,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2626])). 70.10/10.65 thf(f2930,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f2929])). 70.10/10.65 thf(f2931,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2625])). 70.10/10.65 thf(f2932,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f2931])). 70.10/10.65 thf(f2933,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2628])). 70.10/10.65 thf(f2934,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2630])). 70.10/10.65 thf(f2935,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f2934])). 70.10/10.65 thf(f2936,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2631])). 70.10/10.65 thf(f2937,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2632])). 70.10/10.65 thf(f2938,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2633])). 70.10/10.65 thf(f2939,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2633])). 70.10/10.65 thf(f2940,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2634])). 70.10/10.65 thf(f2941,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f2940])). 70.10/10.65 thf(f2942,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2636])). 70.10/10.65 thf(f2943,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2637])). 70.10/10.65 thf(f2944,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f2943])). 70.10/10.65 thf(f2945,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2639])). 70.10/10.65 thf(f2946,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2641])). 70.10/10.65 thf(f2947,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2643])). 70.10/10.65 thf(f2948,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f2947])). 70.10/10.65 thf(f2949,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2645])). 70.10/10.65 thf(f2984,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2705])). 70.10/10.65 thf(f2985,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2706])). 70.10/10.65 thf(f2986,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2706])). 70.10/10.65 thf(f2987,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2707])). 70.10/10.65 thf(f2988,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2707])). 70.10/10.65 thf(f2989,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2708])). 70.10/10.65 thf(f2990,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f2989])). 70.10/10.65 thf(f2991,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2710])). 70.10/10.65 thf(f2992,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2712])). 70.10/10.65 thf(f2993,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2714])). 70.10/10.65 thf(f2994,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f2993])). 70.10/10.65 thf(f2995,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2716])). 70.10/10.65 thf(f2996,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2718])). 70.10/10.65 thf(f2997,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2719])). 70.10/10.65 thf(f2998,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2719])). 70.10/10.65 thf(f2999,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2720])). 70.10/10.65 thf(f3000,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f2999])). 70.10/10.65 thf(f3001,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2722])). 70.10/10.65 thf(f3002,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2723])). 70.10/10.65 thf(f3003,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2723])). 70.10/10.65 thf(f3004,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2724])). 70.10/10.65 thf(f3005,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2725])). 70.10/10.65 thf(f3006,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2727])). 70.10/10.65 thf(f3007,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2728])). 70.10/10.65 thf(f3008,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2728])). 70.10/10.65 thf(f3009,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2729])). 70.10/10.65 thf(f3010,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2729])). 70.10/10.65 thf(f3011,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2730])). 70.10/10.65 thf(f3012,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2730])). 70.10/10.65 thf(f3013,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2732])). 70.10/10.65 thf(f3014,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2732])). 70.10/10.65 thf(f3015,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2731])). 70.10/10.65 thf(f3016,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2731])). 70.10/10.65 thf(f3017,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X3)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2733])). 70.10/10.65 thf(f3018,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3017])). 70.10/10.65 thf(f3019,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2735])). 70.10/10.65 thf(f3020,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2735])). 70.10/10.65 thf(f3021,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2737])). 70.10/10.65 thf(f3022,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2737])). 70.10/10.65 thf(f3023,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2739])). 70.10/10.65 thf(f3024,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2739])). 70.10/10.65 thf(f3025,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2741])). 70.10/10.65 thf(f3026,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3025])). 70.10/10.65 thf(f3027,plain,( 70.10/10.65 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2740])). 70.10/10.65 thf(f3028,plain,( 70.10/10.65 ( ! [X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2740])). 70.10/10.65 thf(f3029,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2743])). 70.10/10.65 thf(f3030,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2745])). 70.10/10.65 thf(f3031,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2747])). 70.10/10.65 thf(f3032,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2747])). 70.10/10.65 thf(f3033,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2749])). 70.10/10.65 thf(f3034,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2749])). 70.10/10.65 thf(f3035,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2748])). 70.10/10.65 thf(f3036,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2748])). 70.10/10.65 thf(f3037,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2751])). 70.10/10.65 thf(f3038,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3037])). 70.10/10.65 thf(f3039,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2752])). 70.10/10.65 thf(f3040,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2752])). 70.10/10.65 thf(f3041,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2754])). 70.10/10.65 thf(f3042,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3041])). 70.10/10.65 thf(f3043,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2753])). 70.10/10.65 thf(f3044,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2753])). 70.10/10.65 thf(f3045,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2755])). 70.10/10.65 thf(f3046,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2755])). 70.10/10.65 thf(f3047,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2756])). 70.10/10.65 thf(f3048,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3047])). 70.10/10.65 thf(f3049,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2757])). 70.10/10.65 thf(f3050,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2))) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3049])). 70.10/10.65 thf(f3051,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2758])). 70.10/10.65 thf(f3052,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2759])). 70.10/10.65 thf(f3053,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3052])). 70.10/10.65 thf(f3054,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X1))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2760])). 70.10/10.65 thf(f3055,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3054])). 70.10/10.65 thf(f3056,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2761])). 70.10/10.65 thf(f3057,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3056])). 70.10/10.65 thf(f3058,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2762])). 70.10/10.65 thf(f3059,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3058])). 70.10/10.65 thf(f3060,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2763])). 70.10/10.65 thf(f3061,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3060])). 70.10/10.65 thf(f3062,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2764])). 70.10/10.65 thf(f3063,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3062])). 70.10/10.65 thf(f3064,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2765])). 70.10/10.65 thf(f3065,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3064])). 70.10/10.65 thf(f3066,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2766])). 70.10/10.65 thf(f3067,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3066])). 70.10/10.65 thf(f3068,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2768])). 70.10/10.65 thf(f3069,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2769])). 70.10/10.65 thf(f3070,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2770])). 70.10/10.65 thf(f3071,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3070])). 70.10/10.65 thf(f3072,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2771])). 70.10/10.65 thf(f3073,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2773])). 70.10/10.65 thf(f3074,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2774])). 70.10/10.65 thf(f3075,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2774])). 70.10/10.65 thf(f3076,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2776])). 70.10/10.65 thf(f3077,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2777])). 70.10/10.65 thf(f3078,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3077])). 70.10/10.65 thf(f3079,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2778])). 70.10/10.65 thf(f3080,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3079])). 70.10/10.65 thf(f3081,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2779])). 70.10/10.65 thf(f3082,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2779])). 70.10/10.65 thf(f3083,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2780])). 70.10/10.65 thf(f3084,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3083])). 70.10/10.65 thf(f3085,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X4)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2781])). 70.10/10.65 thf(f3086,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3085])). 70.10/10.65 thf(f3087,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2782])). 70.10/10.65 thf(f3088,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3087])). 70.10/10.65 thf(f3089,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2783])). 70.10/10.65 thf(f3090,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2783])). 70.10/10.65 thf(f3091,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2784])). 70.10/10.65 thf(f3092,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3091])). 70.10/10.65 thf(f3093,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2785])). 70.10/10.65 thf(f3094,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3093])). 70.10/10.65 thf(f3095,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2786])). 70.10/10.65 thf(f3096,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2787])). 70.10/10.65 thf(f3097,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3096])). 70.10/10.65 thf(f3098,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X4))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2788])). 70.10/10.65 thf(f3099,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2790])). 70.10/10.65 thf(f3100,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3099])). 70.10/10.65 thf(f3101,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2789])). 70.10/10.65 thf(f3102,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2789])). 70.10/10.65 thf(f3103,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2792])). 70.10/10.65 thf(f3104,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2794])). 70.10/10.65 thf(f3105,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2796])). 70.10/10.65 thf(f3106,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2795])). 70.10/10.65 thf(f3107,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2797])). 70.10/10.65 thf(f3108,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2797])). 70.10/10.65 thf(f3109,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2798])). 70.10/10.65 thf(f3110,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3109])). 70.10/10.65 thf(f3111,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2800])). 70.10/10.65 thf(f3112,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2802])). 70.10/10.65 thf(f3113,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2803])). 70.10/10.65 thf(f3114,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2804])). 70.10/10.65 thf(f3115,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3114])). 70.10/10.65 thf(f3116,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2805])). 70.10/10.65 thf(f3117,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3116])). 70.10/10.65 thf(f3118,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2807])). 70.10/10.65 thf(f3119,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2809])). 70.10/10.65 thf(f3120,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2811])). 70.10/10.65 thf(f3121,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2812])). 70.10/10.65 thf(f3122,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2812])). 70.10/10.65 thf(f3123,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2813])). 70.10/10.65 thf(f3124,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3123])). 70.10/10.65 thf(f3125,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2814])). 70.10/10.65 thf(f3126,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2815])). 70.10/10.65 thf(f3127,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3126])). 70.10/10.65 thf(f3128,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2816])). 70.10/10.65 thf(f3129,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3128])). 70.10/10.65 thf(f3131,definition,( 70.10/10.65 spl37_105 <=> ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))))), 70.10/10.65 introduced(definition,[new_symbols(definition,[spl37_105])],[avatar_definition])). 70.10/10.65 thf(f3132,plain,( 70.10/10.65 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) ) | ~spl37_105), 70.10/10.65 inference(avatar_component_clause,[],[f3131])). 70.10/10.65 thf(f3133,plain,( 70.10/10.65 spl37_99 | spl37_105 | spl37_98 | spl37_97), 70.10/10.65 inference(avatar_split_clause,[],[f2817,f2892,f2895,f3131,f2898])). 70.10/10.65 thf(f3134,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2818])). 70.10/10.65 thf(f3135,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2818])). 70.10/10.65 thf(f3136,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X3)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2819])). 70.10/10.65 thf(f3137,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3136])). 70.10/10.65 thf(f3138,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2820])). 70.10/10.65 thf(f3139,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3138])). 70.10/10.65 thf(f3140,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2821])). 70.10/10.65 thf(f3141,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3140])). 70.10/10.65 thf(f3142,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2822])). 70.10/10.65 thf(f3143,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2824])). 70.10/10.65 thf(f3144,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3143])). 70.10/10.65 thf(f3145,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2826])). 70.10/10.65 thf(f3146,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3145])). 70.10/10.65 thf(f3147,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2825])). 70.10/10.65 thf(f3148,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3147])). 70.10/10.65 thf(f3149,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2828])). 70.10/10.65 thf(f3150,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2830])). 70.10/10.65 thf(f3151,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2832])). 70.10/10.65 thf(f3152,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2833])). 70.10/10.65 thf(f3153,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2835])). 70.10/10.65 thf(f3154,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3153])). 70.10/10.65 thf(f3155,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2834])). 70.10/10.65 thf(f3156,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2834])). 70.10/10.65 thf(f3157,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2836])). 70.10/10.65 thf(f3158,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3157])). 70.10/10.65 thf(f3159,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2838])). 70.10/10.65 thf(f3160,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3159])). 70.10/10.65 thf(f3161,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2840])). 70.10/10.65 thf(f3162,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X2))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3161])). 70.10/10.65 thf(f3163,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2839])). 70.10/10.65 thf(f3164,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3163])). 70.10/10.65 thf(f3165,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2842])). 70.10/10.65 thf(f3166,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2844])). 70.10/10.65 thf(f3167,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2846])). 70.10/10.65 thf(f3168,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3167])). 70.10/10.65 thf(f3169,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X3)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2845])). 70.10/10.65 thf(f3170,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3169])). 70.10/10.65 thf(f3171,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2848])). 70.10/10.65 thf(f3172,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2848])). 70.10/10.65 thf(f3173,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2850])). 70.10/10.65 thf(f3174,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2852])). 70.10/10.65 thf(f3175,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2854])). 70.10/10.65 thf(f3176,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2855])). 70.10/10.65 thf(f3177,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2856])). 70.10/10.65 thf(f3178,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2856])). 70.10/10.65 thf(f3179,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2858])). 70.10/10.65 thf(f3180,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2860])). 70.10/10.65 thf(f3181,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2862])). 70.10/10.65 thf(f3182,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2864])). 70.10/10.65 thf(f3183,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2864])). 70.10/10.65 thf(f3184,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2865])). 70.10/10.65 thf(f3185,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2867])). 70.10/10.65 thf(f3186,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2868])). 70.10/10.65 thf(f3188,definition,( 70.10/10.65 spl37_106 <=> ! [X3 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))))), 70.10/10.65 introduced(definition,[new_symbols(definition,[spl37_106])],[avatar_definition])). 70.10/10.65 thf(f3189,plain,( 70.10/10.65 ( ! [X3 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3)))) ) | ~spl37_106), 70.10/10.65 inference(avatar_component_clause,[],[f3188])). 70.10/10.65 thf(f3190,plain,( 70.10/10.65 spl37_106 | spl37_98 | spl37_97 | spl37_100), 70.10/10.65 inference(avatar_split_clause,[],[f2869,f2901,f2892,f2895,f3188])). 70.10/10.65 thf(f3191,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2870])). 70.10/10.65 thf(f3192,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2872])). 70.10/10.65 thf(f3193,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2874])). 70.10/10.65 thf(f3194,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2876])). 70.10/10.65 thf(f3195,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2878])). 70.10/10.65 thf(f3196,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2880])). 70.10/10.65 thf(f3197,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2882])). 70.10/10.65 thf(f3198,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2884])). 70.10/10.65 thf(f3199,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2885])). 70.10/10.65 thf(f3200,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3199])). 70.10/10.65 thf(f3202,definition,( 70.10/10.65 spl37_107 <=> ! [X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true))), 70.10/10.65 introduced(definition,[new_symbols(definition,[spl37_107])],[avatar_definition])). 70.10/10.65 thf(f3203,plain,( 70.10/10.65 ( ! [X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4)))) ) | ~spl37_107), 70.10/10.65 inference(avatar_component_clause,[],[f3202])). 70.10/10.65 thf(f3204,plain,( 70.10/10.65 spl37_97 | spl37_107 | spl37_99 | spl37_100), 70.10/10.65 inference(avatar_split_clause,[],[f2886,f2901,f2898,f3202,f2892])). 70.10/10.65 thf(f3205,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2888])). 70.10/10.65 thf(f3206,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2890])). 70.10/10.65 thf(f3207,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2905])). 70.10/10.65 thf(f3208,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2907])). 70.10/10.65 thf(f3209,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2908])). 70.10/10.65 thf(f3210,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2908])). 70.10/10.65 thf(f3211,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2909])). 70.10/10.65 thf(f3212,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2910])). 70.10/10.65 thf(f3213,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2911])). 70.10/10.65 thf(f3214,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2912])). 70.10/10.65 thf(f3215,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2913])). 70.10/10.65 thf(f3216,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2913])). 70.10/10.65 thf(f3217,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2914])). 70.10/10.65 thf(f3218,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2915])). 70.10/10.65 thf(f3219,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2916])). 70.10/10.65 thf(f3220,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2916])). 70.10/10.65 thf(f3221,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2917])). 70.10/10.65 thf(f3222,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2918])). 70.10/10.65 thf(f3223,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3222])). 70.10/10.65 thf(f3224,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2919])). 70.10/10.65 thf(f3225,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3224])). 70.10/10.65 thf(f3226,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2920])). 70.10/10.65 thf(f3227,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2921])). 70.10/10.65 thf(f3228,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2923])). 70.10/10.65 thf(f3229,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3228])). 70.10/10.65 thf(f3230,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2922])). 70.10/10.65 thf(f3231,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3230])). 70.10/10.65 thf(f3232,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2925])). 70.10/10.65 thf(f3233,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2926])). 70.10/10.65 thf(f3234,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2928])). 70.10/10.65 thf(f3235,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2930])). 70.10/10.65 thf(f3236,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2932])). 70.10/10.65 thf(f3237,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2933])). 70.10/10.65 thf(f3238,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3237])). 70.10/10.65 thf(f3239,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2935])). 70.10/10.65 thf(f3240,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2936])). 70.10/10.65 thf(f3242,definition,( 70.10/10.65 spl37_108 <=> ! [X2 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))))), 70.10/10.65 introduced(definition,[new_symbols(definition,[spl37_108])],[avatar_definition])). 70.10/10.65 thf(f3243,plain,( 70.10/10.65 ( ! [X2 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2)))) ) | ~spl37_108), 70.10/10.65 inference(avatar_component_clause,[],[f3242])). 70.10/10.65 thf(f3244,plain,( 70.10/10.65 spl37_98 | spl37_100 | spl37_99 | spl37_108), 70.10/10.65 inference(avatar_split_clause,[],[f2937,f3242,f2898,f2901,f2895])). 70.10/10.65 thf(f3245,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2938])). 70.10/10.65 thf(f3246,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3245])). 70.10/10.65 thf(f3247,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2939])). 70.10/10.65 thf(f3248,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3247])). 70.10/10.65 thf(f3249,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2941])). 70.10/10.65 thf(f3250,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2942])). 70.10/10.65 thf(f3251,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3250])). 70.10/10.65 thf(f3252,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2944])). 70.10/10.65 thf(f3253,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2945])). 70.10/10.65 thf(f3254,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2946])). 70.10/10.65 thf(f3255,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2946])). 70.10/10.65 thf(f3256,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2948])). 70.10/10.65 thf(f3257,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2949])). 70.10/10.65 thf(f3290,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2984])). 70.10/10.65 thf(f3291,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2986])). 70.10/10.65 thf(f3292,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3291])). 70.10/10.65 thf(f3293,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2985])). 70.10/10.65 thf(f3294,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2985])). 70.10/10.65 thf(f3295,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2988])). 70.10/10.65 thf(f3296,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3295])). 70.10/10.65 thf(f3297,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2987])). 70.10/10.65 thf(f3298,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3297])). 70.10/10.65 thf(f3299,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2990])). 70.10/10.65 thf(f3300,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3299])). 70.10/10.65 thf(f3301,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2991])). 70.10/10.65 thf(f3302,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3301])). 70.10/10.65 thf(f3303,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2992])). 70.10/10.65 thf(f3304,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f2994])). 70.10/10.65 thf(f3305,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2995])). 70.10/10.65 thf(f3306,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f2995])). 70.10/10.65 thf(f3308,definition,( 70.10/10.65 spl37_113 <=> ! [X2 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))))), 70.10/10.65 introduced(definition,[new_symbols(definition,[spl37_113])],[avatar_definition])). 70.10/10.65 thf(f3309,plain,( 70.10/10.65 ( ! [X2 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) ) | ~spl37_113), 70.10/10.65 inference(avatar_component_clause,[],[f3308])). 70.10/10.65 thf(f3310,plain,( 70.10/10.65 spl37_98 | spl37_97 | spl37_113 | spl37_99), 70.10/10.65 inference(avatar_split_clause,[],[f2996,f2898,f3308,f2892,f2895])). 70.10/10.65 thf(f3311,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2997])). 70.10/10.65 thf(f3312,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3311])). 70.10/10.65 thf(f3313,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f2998])). 70.10/10.65 thf(f3314,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3313])). 70.10/10.65 thf(f3315,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3000])). 70.10/10.65 thf(f3316,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3001])). 70.10/10.65 thf(f3317,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3002])). 70.10/10.65 thf(f3318,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3003])). 70.10/10.65 thf(f3319,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3004])). 70.10/10.65 thf(f3320,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3319])). 70.10/10.65 thf(f3321,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3005])). 70.10/10.65 thf(f3322,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3005])). 70.10/10.65 thf(f3323,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3006])). 70.10/10.65 thf(f3324,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3006])). 70.10/10.65 thf(f3325,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3007])). 70.10/10.65 thf(f3326,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3325])). 70.10/10.65 thf(f3327,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3008])). 70.10/10.65 thf(f3328,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3327])). 70.10/10.65 thf(f3329,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3010])). 70.10/10.65 thf(f3330,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3329])). 70.10/10.65 thf(f3331,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3009])). 70.10/10.65 thf(f3332,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3009])). 70.10/10.65 thf(f3333,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3011])). 70.10/10.65 thf(f3334,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3012])). 70.10/10.65 thf(f3335,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3334])). 70.10/10.65 thf(f3336,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3014])). 70.10/10.65 thf(f3337,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3336])). 70.10/10.65 thf(f3338,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3013])). 70.10/10.65 thf(f3339,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3338])). 70.10/10.65 thf(f3340,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3015])). 70.10/10.65 thf(f3341,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3015])). 70.10/10.65 thf(f3342,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3016])). 70.10/10.65 thf(f3343,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3016])). 70.10/10.65 thf(f3344,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3018])). 70.10/10.65 thf(f3345,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3020])). 70.10/10.65 thf(f3346,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3345])). 70.10/10.65 thf(f3347,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3019])). 70.10/10.65 thf(f3348,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3347])). 70.10/10.65 thf(f3349,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3022])). 70.10/10.65 thf(f3350,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3021])). 70.10/10.65 thf(f3351,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X3)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3024])). 70.10/10.65 thf(f3352,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3351])). 70.10/10.65 thf(f3353,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3023])). 70.10/10.65 thf(f3354,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3023])). 70.10/10.65 thf(f3355,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3026])). 70.10/10.65 thf(f3356,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3355])). 70.10/10.65 thf(f3357,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3027])). 70.10/10.65 thf(f3358,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3357])). 70.10/10.65 thf(f3359,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3028])). 70.10/10.65 thf(f3360,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3359])). 70.10/10.65 thf(f3361,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3029])). 70.10/10.65 thf(f3362,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3030])). 70.10/10.65 thf(f3363,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3032])). 70.10/10.65 thf(f3364,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X4)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3031])). 70.10/10.65 thf(f3365,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3364])). 70.10/10.65 thf(f3366,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3033])). 70.10/10.65 thf(f3367,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3366])). 70.10/10.65 thf(f3368,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3034])). 70.10/10.65 thf(f3369,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3368])). 70.10/10.65 thf(f3370,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3036])). 70.10/10.65 thf(f3371,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3370])). 70.10/10.65 thf(f3372,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3035])). 70.10/10.65 thf(f3373,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3372])). 70.10/10.65 thf(f3374,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X4)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3038])). 70.10/10.65 thf(f3375,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3374])). 70.10/10.65 thf(f3376,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3040])). 70.10/10.65 thf(f3377,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3376])). 70.10/10.65 thf(f3378,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3039])). 70.10/10.65 thf(f3379,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3042])). 70.10/10.65 thf(f3380,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3379])). 70.10/10.65 thf(f3381,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3043])). 70.10/10.65 thf(f3382,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3043])). 70.10/10.65 thf(f3383,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3044])). 70.10/10.65 thf(f3384,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3383])). 70.10/10.65 thf(f3385,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3046])). 70.10/10.65 thf(f3386,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X3))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3045])). 70.10/10.65 thf(f3387,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3386])). 70.10/10.65 thf(f3388,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3048])). 70.10/10.65 thf(f3389,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2))) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3050])). 70.10/10.65 thf(f3390,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3389])). 70.10/10.65 thf(f3391,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3051])). 70.10/10.65 thf(f3392,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3391])). 70.10/10.65 thf(f3393,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2))) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3053])). 70.10/10.65 thf(f3394,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X1))) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3055])). 70.10/10.65 thf(f3395,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X1))) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3394])). 70.10/10.65 thf(f3396,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3057])). 70.10/10.65 thf(f3397,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3059])). 70.10/10.65 thf(f3398,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X2))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3061])). 70.10/10.65 thf(f3399,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3398])). 70.10/10.65 thf(f3400,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3063])). 70.10/10.65 thf(f3401,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3065])). 70.10/10.65 thf(f3402,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3067])). 70.10/10.65 thf(f3403,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X4)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3402])). 70.10/10.65 thf(f3404,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3068])). 70.10/10.65 thf(f3405,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3069])). 70.10/10.65 thf(f3406,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3071])). 70.10/10.65 thf(f3407,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3072])). 70.10/10.65 thf(f3408,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3407])). 70.10/10.65 thf(f3409,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3073])). 70.10/10.65 thf(f3410,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3075])). 70.10/10.65 thf(f3411,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3074])). 70.10/10.65 thf(f3412,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3074])). 70.10/10.65 thf(f3413,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3076])). 70.10/10.65 thf(f3414,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3076])). 70.10/10.65 thf(f3415,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3078])). 70.10/10.65 thf(f3416,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3080])). 70.10/10.65 thf(f3417,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3416])). 70.10/10.65 thf(f3418,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3082])). 70.10/10.65 thf(f3419,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3418])). 70.10/10.65 thf(f3420,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3081])). 70.10/10.65 thf(f3421,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3420])). 70.10/10.65 thf(f3422,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X4)) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3084])). 70.10/10.65 thf(f3423,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3422])). 70.10/10.65 thf(f3424,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3086])). 70.10/10.65 thf(f3425,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3088])). 70.10/10.65 thf(f3426,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3089])). 70.10/10.65 thf(f3427,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3089])). 70.10/10.65 thf(f3428,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3090])). 70.10/10.65 thf(f3429,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3428])). 70.10/10.65 thf(f3430,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3092])). 70.10/10.65 thf(f3431,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3094])). 70.10/10.65 thf(f3432,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3095])). 70.10/10.65 thf(f3433,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3432])). 70.10/10.65 thf(f3434,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3097])). 70.10/10.65 thf(f3436,definition,( 70.10/10.65 spl37_114 <=> ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))))), 70.10/10.65 introduced(definition,[new_symbols(definition,[spl37_114])],[avatar_definition])). 70.10/10.65 thf(f3437,plain,( 70.10/10.65 ( ! [X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) ) | ~spl37_114), 70.10/10.65 inference(avatar_component_clause,[],[f3436])). 70.10/10.65 thf(f3438,plain,( 70.10/10.65 spl37_114 | spl37_98 | spl37_97 | spl37_99), 70.10/10.65 inference(avatar_split_clause,[],[f3098,f2898,f2892,f2895,f3436])). 70.10/10.65 thf(f3439,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3100])). 70.10/10.65 thf(f3440,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3102])). 70.10/10.65 thf(f3441,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3440])). 70.10/10.65 thf(f3442,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3101])). 70.10/10.65 thf(f3443,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3442])). 70.10/10.65 thf(f3444,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3103])). 70.10/10.65 thf(f3445,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3444])). 70.10/10.65 thf(f3446,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3104])). 70.10/10.65 thf(f3447,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3105])). 70.10/10.65 thf(f3448,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3106])). 70.10/10.65 thf(f3449,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3107])). 70.10/10.65 thf(f3450,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3449])). 70.10/10.65 thf(f3451,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3108])). 70.10/10.65 thf(f3452,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true)) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3451])). 70.10/10.65 thf(f3453,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3110])). 70.10/10.65 thf(f3454,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3111])). 70.10/10.65 thf(f3455,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3112])). 70.10/10.65 thf(f3456,plain,( 70.10/10.65 spl37_105 | spl37_97 | spl37_107 | spl37_99), 70.10/10.65 inference(avatar_split_clause,[],[f3113,f2898,f3202,f2892,f3131])). 70.10/10.65 thf(f3457,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3115])). 70.10/10.65 thf(f3458,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3117])). 70.10/10.65 thf(f3459,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3118])). 70.10/10.65 thf(f3460,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3118])). 70.10/10.65 thf(f3461,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3119])). 70.10/10.65 thf(f3462,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3120])). 70.10/10.65 thf(f3463,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3462])). 70.10/10.65 thf(f3464,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3121])). 70.10/10.65 thf(f3465,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3464])). 70.10/10.65 thf(f3466,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3122])). 70.10/10.65 thf(f3467,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3466])). 70.10/10.65 thf(f3468,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3124])). 70.10/10.65 thf(f3469,plain,( 70.10/10.65 spl37_98 | spl37_97 | spl37_106 | spl37_105), 70.10/10.65 inference(avatar_split_clause,[],[f3125,f3131,f3188,f2892,f2895])). 70.10/10.65 thf(f3470,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3127])). 70.10/10.65 thf(f3471,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3129])). 70.10/10.65 thf(f3472,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3134])). 70.10/10.65 thf(f3473,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3134])). 70.10/10.65 thf(f3474,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3135])). 70.10/10.65 thf(f3475,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3))))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3137])). 70.10/10.65 thf(f3476,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3475])). 70.10/10.65 thf(f3477,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3139])). 70.10/10.65 thf(f3478,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3139])). 70.10/10.65 thf(f3479,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3141])). 70.10/10.65 thf(f3480,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X4)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3142])). 70.10/10.65 thf(f3481,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3480])). 70.10/10.65 thf(f3482,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3144])). 70.10/10.65 thf(f3483,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3146])). 70.10/10.65 thf(f3484,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3483])). 70.10/10.65 thf(f3485,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3148])). 70.10/10.65 thf(f3486,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3149])). 70.10/10.65 thf(f3487,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3150])). 70.10/10.65 thf(f3488,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3487])). 70.10/10.65 thf(f3489,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3151])). 70.10/10.65 thf(f3490,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3489])). 70.10/10.65 thf(f3491,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3152])). 70.10/10.65 thf(f3492,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.65 inference(and_proxy_clausification,[],[f3152])). 70.10/10.65 thf(f3493,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3154])). 70.10/10.65 thf(f3494,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3155])). 70.10/10.65 thf(f3495,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3156])). 70.10/10.65 thf(f3496,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3495])). 70.10/10.65 thf(f3497,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3158])). 70.10/10.65 thf(f3498,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3160])). 70.10/10.65 thf(f3499,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))))))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3162])). 70.10/10.65 thf(f3500,plain,( 70.10/10.65 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3164])). 70.10/10.65 thf(f3501,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3165])). 70.10/10.65 thf(f3502,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3166])). 70.10/10.65 thf(f3503,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3502])). 70.10/10.65 thf(f3504,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))))) = $true)) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3168])). 70.10/10.65 thf(f3505,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3170])). 70.10/10.65 thf(f3506,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true)) )), 70.10/10.65 inference(pi_proxy_clausification,[],[f3172])). 70.10/10.65 thf(f3507,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))))) )), 70.10/10.65 inference(beta-eta_normalization,[],[f3506])). 70.10/10.65 thf(f3508,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.65 inference(imp_proxy_clausification,[],[f3171])). 70.10/10.65 thf(f3509,plain,( 70.10/10.65 spl37_99 | spl37_105 | spl37_108 | spl37_98), 70.10/10.65 inference(avatar_split_clause,[],[f3173,f2895,f3242,f3131,f2898])). 70.10/10.65 thf(f3510,plain,( 70.10/10.65 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3174])). 70.10/10.66 thf(f3511,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3175])). 70.10/10.66 thf(f3512,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3176])). 70.10/10.66 thf(f3513,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3178])). 70.10/10.66 thf(f3514,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3177])). 70.10/10.66 thf(f3515,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3514])). 70.10/10.66 thf(f3516,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3179])). 70.10/10.66 thf(f3517,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3180])). 70.10/10.66 thf(f3518,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3181])). 70.10/10.66 thf(f3519,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3518])). 70.10/10.66 thf(f3520,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3183])). 70.10/10.66 thf(f3521,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3182])). 70.10/10.66 thf(f3522,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3184])). 70.10/10.66 thf(f3524,definition,( 70.10/10.66 spl37_115 <=> ! [X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X4))))), 70.10/10.66 introduced(definition,[new_symbols(definition,[spl37_115])],[avatar_definition])). 70.10/10.66 thf(f3525,plain,( 70.10/10.66 ( ! [X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X4)))) ) | ~spl37_115), 70.10/10.66 inference(avatar_component_clause,[],[f3524])). 70.10/10.66 thf(f3526,plain,( 70.10/10.66 spl37_97 | spl37_100 | spl37_115 | spl37_98), 70.10/10.66 inference(avatar_split_clause,[],[f3185,f2895,f3524,f2901,f2892])). 70.10/10.66 thf(f3528,definition,( 70.10/10.66 spl37_116 <=> ! [X3 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))))), 70.10/10.66 introduced(definition,[new_symbols(definition,[spl37_116])],[avatar_definition])). 70.10/10.66 thf(f3529,plain,( 70.10/10.66 ( ! [X3 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3)))) ) | ~spl37_116), 70.10/10.66 inference(avatar_component_clause,[],[f3528])). 70.10/10.66 thf(f3530,plain,( 70.10/10.66 spl37_100 | spl37_98 | spl37_97 | spl37_116), 70.10/10.66 inference(avatar_split_clause,[],[f3186,f3528,f2892,f2895,f2901])). 70.10/10.66 thf(f3531,plain,( 70.10/10.66 spl37_107 | spl37_97 | spl37_106 | spl37_100), 70.10/10.66 inference(avatar_split_clause,[],[f3191,f2901,f3188,f2892,f3202])). 70.10/10.66 thf(f3532,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3192])). 70.10/10.66 thf(f3533,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3193])). 70.10/10.66 thf(f3534,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3194])). 70.10/10.66 thf(f3535,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3534])). 70.10/10.66 thf(f3536,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3195])). 70.10/10.66 thf(f3537,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3536])). 70.10/10.66 thf(f3538,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3196])). 70.10/10.66 thf(f3539,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3538])). 70.10/10.66 thf(f3540,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3197])). 70.10/10.66 thf(f3541,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3540])). 70.10/10.66 thf(f3542,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3198])). 70.10/10.66 thf(f3543,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3200])). 70.10/10.66 thf(f3545,definition,( 70.10/10.66 spl37_117 <=> ! [X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true))), 70.10/10.66 introduced(definition,[new_symbols(definition,[spl37_117])],[avatar_definition])). 70.10/10.66 thf(f3546,plain,( 70.10/10.66 ( ! [X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4)))) ) | ~spl37_117), 70.10/10.66 inference(avatar_component_clause,[],[f3545])). 70.10/10.66 thf(f3547,plain,( 70.10/10.66 spl37_99 | spl37_97 | spl37_100 | spl37_117), 70.10/10.66 inference(avatar_split_clause,[],[f3205,f3545,f2901,f2892,f2898])). 70.10/10.66 thf(f3549,definition,( 70.10/10.66 spl37_118 <=> ! [X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4))))), 70.10/10.66 introduced(definition,[new_symbols(definition,[spl37_118])],[avatar_definition])). 70.10/10.66 thf(f3550,plain,( 70.10/10.66 ( ! [X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4)))) ) | ~spl37_118), 70.10/10.66 inference(avatar_component_clause,[],[f3549])). 70.10/10.66 thf(f3551,plain,( 70.10/10.66 spl37_118 | spl37_99 | spl37_100 | spl37_97), 70.10/10.66 inference(avatar_split_clause,[],[f3206,f2892,f2901,f2898,f3549])). 70.10/10.66 thf(f3553,definition,( 70.10/10.66 spl37_119 <=> ! [X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))))), 70.10/10.66 introduced(definition,[new_symbols(definition,[spl37_119])],[avatar_definition])). 70.10/10.66 thf(f3554,plain,( 70.10/10.66 ( ! [X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) ) | ~spl37_119), 70.10/10.66 inference(avatar_component_clause,[],[f3553])). 70.10/10.66 thf(f3555,plain,( 70.10/10.66 spl37_99 | spl37_119 | spl37_100 | spl37_98), 70.10/10.66 inference(avatar_split_clause,[],[f3207,f2895,f2901,f3553,f2898])). 70.10/10.66 thf(f3556,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3208])). 70.10/10.66 thf(f3557,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3209])). 70.10/10.66 thf(f3558,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3557])). 70.10/10.66 thf(f3559,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3210])). 70.10/10.66 thf(f3560,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3559])). 70.10/10.66 thf(f3561,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3211])). 70.10/10.66 thf(f3562,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3212])). 70.10/10.66 thf(f3563,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3562])). 70.10/10.66 thf(f3564,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3213])). 70.10/10.66 thf(f3565,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3214])). 70.10/10.66 thf(f3566,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3216])). 70.10/10.66 thf(f3567,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3215])). 70.10/10.66 thf(f3568,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3567])). 70.10/10.66 thf(f3569,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3217])). 70.10/10.66 thf(f3570,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3569])). 70.10/10.66 thf(f3571,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3218])). 70.10/10.66 thf(f3572,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3571])). 70.10/10.66 thf(f3573,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3219])). 70.10/10.66 thf(f3574,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3219])). 70.10/10.66 thf(f3575,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3220])). 70.10/10.66 thf(f3576,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3575])). 70.10/10.66 thf(f3577,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3221])). 70.10/10.66 thf(f3578,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3221])). 70.10/10.66 thf(f3579,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3223])). 70.10/10.66 thf(f3580,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3225])). 70.10/10.66 thf(f3581,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3226])). 70.10/10.66 thf(f3582,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3581])). 70.10/10.66 thf(f3583,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3227])). 70.10/10.66 thf(f3584,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3583])). 70.10/10.66 thf(f3585,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3229])). 70.10/10.66 thf(f3586,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3231])). 70.10/10.66 thf(f3587,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3232])). 70.10/10.66 thf(f3588,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3232])). 70.10/10.66 thf(f3590,definition,( 70.10/10.66 spl37_120 <=> ! [X2 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))))), 70.10/10.66 introduced(definition,[new_symbols(definition,[spl37_120])],[avatar_definition])). 70.10/10.66 thf(f3591,plain,( 70.10/10.66 ( ! [X2 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) ) | ~spl37_120), 70.10/10.66 inference(avatar_component_clause,[],[f3590])). 70.10/10.66 thf(f3592,plain,( 70.10/10.66 spl37_98 | spl37_120 | spl37_99 | spl37_100), 70.10/10.66 inference(avatar_split_clause,[],[f3233,f2901,f2898,f3590,f2895])). 70.10/10.66 thf(f3593,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3234])). 70.10/10.66 thf(f3594,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X4)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3235])). 70.10/10.66 thf(f3595,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3594])). 70.10/10.66 thf(f3596,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X4)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3236])). 70.10/10.66 thf(f3597,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3596])). 70.10/10.66 thf(f3598,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3238])). 70.10/10.66 thf(f3599,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3239])). 70.10/10.66 thf(f3600,plain,( 70.10/10.66 spl37_98 | spl37_106 | spl37_108 | spl37_100), 70.10/10.66 inference(avatar_split_clause,[],[f3240,f2901,f3242,f3188,f2895])). 70.10/10.66 thf(f3601,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3246])). 70.10/10.66 thf(f3602,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3248])). 70.10/10.66 thf(f3603,plain,( 70.10/10.66 spl37_99 | spl37_108 | spl37_100 | spl37_107), 70.10/10.66 inference(avatar_split_clause,[],[f3249,f3202,f2901,f3242,f2898])). 70.10/10.66 thf(f3604,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3251])). 70.10/10.66 thf(f3605,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3252])). 70.10/10.66 thf(f3606,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3605])). 70.10/10.66 thf(f3607,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3253])). 70.10/10.66 thf(f3608,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3254])). 70.10/10.66 thf(f3609,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3254])). 70.10/10.66 thf(f3610,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3255])). 70.10/10.66 thf(f3611,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3610])). 70.10/10.66 thf(f3612,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3256])). 70.10/10.66 thf(f3613,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3257])). 70.10/10.66 thf(f3614,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3257])). 70.10/10.66 thf(f3645,plain,( 70.10/10.66 spl37_113 | spl37_99 | spl37_107 | spl37_97), 70.10/10.66 inference(avatar_split_clause,[],[f3290,f2892,f3202,f2898,f3308])). 70.10/10.66 thf(f3646,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3292])). 70.10/10.66 thf(f3647,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3293])). 70.10/10.66 thf(f3648,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3647])). 70.10/10.66 thf(f3649,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3294])). 70.10/10.66 thf(f3650,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3649])). 70.10/10.66 thf(f3651,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3296])). 70.10/10.66 thf(f3652,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3651])). 70.10/10.66 thf(f3653,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3298])). 70.10/10.66 thf(f3654,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3653])). 70.10/10.66 thf(f3655,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3300])). 70.10/10.66 thf(f3656,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3302])). 70.10/10.66 thf(f3657,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3303])). 70.10/10.66 thf(f3658,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3304])). 70.10/10.66 thf(f3659,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3306])). 70.10/10.66 thf(f3660,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3305])). 70.10/10.66 thf(f3661,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3660])). 70.10/10.66 thf(f3662,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3312])). 70.10/10.66 thf(f3663,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3314])). 70.10/10.66 thf(f3664,plain,( 70.10/10.66 spl37_98 | spl37_113 | spl37_97 | spl37_106), 70.10/10.66 inference(avatar_split_clause,[],[f3315,f3188,f2892,f3308,f2895])). 70.10/10.66 thf(f3665,plain,( 70.10/10.66 spl37_113 | spl37_98 | spl37_108 | spl37_99), 70.10/10.66 inference(avatar_split_clause,[],[f3316,f2898,f3242,f2895,f3308])). 70.10/10.66 thf(f3666,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3317])). 70.10/10.66 thf(f3667,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3666])). 70.10/10.66 thf(f3668,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3318])). 70.10/10.66 thf(f3669,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3668])). 70.10/10.66 thf(f3670,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3320])). 70.10/10.66 thf(f3671,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3322])). 70.10/10.66 thf(f3672,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3671])). 70.10/10.66 thf(f3673,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3321])). 70.10/10.66 thf(f3674,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3673])). 70.10/10.66 thf(f3675,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3324])). 70.10/10.66 thf(f3676,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3323])). 70.10/10.66 thf(f3677,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3676])). 70.10/10.66 thf(f3678,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3326])). 70.10/10.66 thf(f3679,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3328])). 70.10/10.66 thf(f3680,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3328])). 70.10/10.66 thf(f3681,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3330])). 70.10/10.66 thf(f3682,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3331])). 70.10/10.66 thf(f3683,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3331])). 70.10/10.66 thf(f3684,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3332])). 70.10/10.66 thf(f3685,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3684])). 70.10/10.66 thf(f3686,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3333])). 70.10/10.66 thf(f3687,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3333])). 70.10/10.66 thf(f3688,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3335])). 70.10/10.66 thf(f3689,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3337])). 70.10/10.66 thf(f3690,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3689])). 70.10/10.66 thf(f3691,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3339])). 70.10/10.66 thf(f3692,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3341])). 70.10/10.66 thf(f3693,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3692])). 70.10/10.66 thf(f3694,plain,( 70.10/10.66 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3340])). 70.10/10.66 thf(f3695,plain,( 70.10/10.66 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3340])). 70.10/10.66 thf(f3696,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3343])). 70.10/10.66 thf(f3697,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3696])). 70.10/10.66 thf(f3698,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3342])). 70.10/10.66 thf(f3699,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3698])). 70.10/10.66 thf(f3700,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3344])). 70.10/10.66 thf(f3701,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3700])). 70.10/10.66 thf(f3702,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3346])). 70.10/10.66 thf(f3703,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3348])). 70.10/10.66 thf(f3704,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3349])). 70.10/10.66 thf(f3705,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3350])). 70.10/10.66 thf(f3706,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3352])). 70.10/10.66 thf(f3707,plain,( 70.10/10.66 ( ! [X2 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3353])). 70.10/10.66 thf(f3708,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3354])). 70.10/10.66 thf(f3709,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3708])). 70.10/10.66 thf(f3710,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3356])). 70.10/10.66 thf(f3711,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3358])). 70.10/10.66 thf(f3712,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3711])). 70.10/10.66 thf(f3713,plain,( 70.10/10.66 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3360])). 70.10/10.66 thf(f3714,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3361])). 70.10/10.66 thf(f3715,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3362])). 70.10/10.66 thf(f3716,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3363])). 70.10/10.66 thf(f3717,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3716])). 70.10/10.66 thf(f3718,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3365])). 70.10/10.66 thf(f3719,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3367])). 70.10/10.66 thf(f3720,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3369])). 70.10/10.66 thf(f3721,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3371])). 70.10/10.66 thf(f3722,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3373])). 70.10/10.66 thf(f3723,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3375])). 70.10/10.66 thf(f3724,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3377])). 70.10/10.66 thf(f3725,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3724])). 70.10/10.66 thf(f3726,plain,( 70.10/10.66 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3378])). 70.10/10.66 thf(f3727,plain,( 70.10/10.66 ( ! [X2 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))))))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3378])). 70.10/10.66 thf(f3728,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3380])). 70.10/10.66 thf(f3729,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2))))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3382])). 70.10/10.66 thf(f3730,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3729])). 70.10/10.66 thf(f3731,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3381])). 70.10/10.66 thf(f3732,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3731])). 70.10/10.66 thf(f3733,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3384])). 70.10/10.66 thf(f3734,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))))))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3385])). 70.10/10.66 thf(f3735,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3734])). 70.10/10.66 thf(f3736,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3387])). 70.10/10.66 thf(f3737,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3388])). 70.10/10.66 thf(f3738,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3737])). 70.10/10.66 thf(f3739,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3390])). 70.10/10.66 thf(f3740,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3392])). 70.10/10.66 thf(f3741,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3393])). 70.10/10.66 thf(f3742,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3741])). 70.10/10.66 thf(f3743,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X4))) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3395])). 70.10/10.66 thf(f3744,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X4)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3396])). 70.10/10.66 thf(f3745,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X4))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3744])). 70.10/10.66 thf(f3746,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3397])). 70.10/10.66 thf(f3747,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3746])). 70.10/10.66 thf(f3748,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3399])). 70.10/10.66 thf(f3749,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3400])). 70.10/10.66 thf(f3750,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3749])). 70.10/10.66 thf(f3751,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3401])). 70.10/10.66 thf(f3752,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3403])). 70.10/10.66 thf(f3753,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3404])). 70.10/10.66 thf(f3754,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3753])). 70.10/10.66 thf(f3755,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3405])). 70.10/10.66 thf(f3756,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3755])). 70.10/10.66 thf(f3757,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3406])). 70.10/10.66 thf(f3758,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3757])). 70.10/10.66 thf(f3759,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3408])). 70.10/10.66 thf(f3760,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3409])). 70.10/10.66 thf(f3761,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3410])). 70.10/10.66 thf(f3762,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3761])). 70.10/10.66 thf(f3763,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3412])). 70.10/10.66 thf(f3764,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3))))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3411])). 70.10/10.66 thf(f3765,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3))))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3411])). 70.10/10.66 thf(f3766,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3414])). 70.10/10.66 thf(f3767,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3766])). 70.10/10.66 thf(f3768,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3413])). 70.10/10.66 thf(f3769,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3413])). 70.10/10.66 thf(f3770,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3415])). 70.10/10.66 thf(f3771,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3415])). 70.10/10.66 thf(f3772,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3417])). 70.10/10.66 thf(f3773,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3419])). 70.10/10.66 thf(f3774,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3773])). 70.10/10.66 thf(f3775,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3421])). 70.10/10.66 thf(f3776,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3775])). 70.10/10.66 thf(f3777,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3423])). 70.10/10.66 thf(f3778,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3424])). 70.10/10.66 thf(f3779,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3425])). 70.10/10.66 thf(f3780,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3426])). 70.10/10.66 thf(f3781,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3780])). 70.10/10.66 thf(f3782,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3427])). 70.10/10.66 thf(f3783,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3782])). 70.10/10.66 thf(f3784,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3429])). 70.10/10.66 thf(f3785,plain,( 70.10/10.66 spl37_108 | spl37_99 | spl37_114 | spl37_98), 70.10/10.66 inference(avatar_split_clause,[],[f3430,f2895,f3436,f2898,f3242])). 70.10/10.66 thf(f3786,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3431])). 70.10/10.66 thf(f3787,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3433])). 70.10/10.66 thf(f3788,plain,( 70.10/10.66 spl37_106 | spl37_98 | spl37_97 | spl37_114), 70.10/10.66 inference(avatar_split_clause,[],[f3434,f3436,f2892,f2895,f3188])). 70.10/10.66 thf(f3789,plain,( 70.10/10.66 spl37_97 | spl37_114 | spl37_107 | spl37_99), 70.10/10.66 inference(avatar_split_clause,[],[f3439,f2898,f3202,f3436,f2892])). 70.10/10.66 thf(f3790,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3441])). 70.10/10.66 thf(f3791,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3443])). 70.10/10.66 thf(f3792,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3445])). 70.10/10.66 thf(f3793,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3446])). 70.10/10.66 thf(f3794,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3446])). 70.10/10.66 thf(f3795,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3447])). 70.10/10.66 thf(f3796,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3795])). 70.10/10.66 thf(f3797,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3448])). 70.10/10.66 thf(f3798,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3448])). 70.10/10.66 thf(f3799,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3450])). 70.10/10.66 thf(f3800,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3452])). 70.10/10.66 thf(f3801,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3453])). 70.10/10.66 thf(f3802,plain,( 70.10/10.66 spl37_97 | spl37_99 | spl37_105 | spl37_117), 70.10/10.66 inference(avatar_split_clause,[],[f3454,f3545,f3131,f2898,f2892])). 70.10/10.66 thf(f3803,plain,( 70.10/10.66 spl37_99 | spl37_118 | spl37_97 | spl37_105), 70.10/10.66 inference(avatar_split_clause,[],[f3455,f3131,f2892,f3549,f2898])). 70.10/10.66 thf(f3804,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3457])). 70.10/10.66 thf(f3805,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3458])). 70.10/10.66 thf(f3806,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3459])). 70.10/10.66 thf(f3807,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3806])). 70.10/10.66 thf(f3808,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3460])). 70.10/10.66 thf(f3809,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3808])). 70.10/10.66 thf(f3810,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3461])). 70.10/10.66 thf(f3811,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3463])). 70.10/10.66 thf(f3812,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3465])). 70.10/10.66 thf(f3813,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3467])). 70.10/10.66 thf(f3814,plain,( 70.10/10.66 spl37_106 | spl37_97 | spl37_107 | spl37_105), 70.10/10.66 inference(avatar_split_clause,[],[f3468,f3131,f3202,f2892,f3188])). 70.10/10.66 thf(f3815,plain,( 70.10/10.66 spl37_98 | spl37_116 | spl37_105 | spl37_97), 70.10/10.66 inference(avatar_split_clause,[],[f3470,f2892,f3131,f3528,f2895])). 70.10/10.66 thf(f3816,plain,( 70.10/10.66 spl37_97 | spl37_98 | spl37_105 | spl37_115), 70.10/10.66 inference(avatar_split_clause,[],[f3471,f3524,f3131,f2895,f2892])). 70.10/10.66 thf(f3817,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3473])). 70.10/10.66 thf(f3818,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3817])). 70.10/10.66 thf(f3819,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3472])). 70.10/10.66 thf(f3820,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3474])). 70.10/10.66 thf(f3821,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3820])). 70.10/10.66 thf(f3822,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3476])). 70.10/10.66 thf(f3823,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3478])). 70.10/10.66 thf(f3824,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3823])). 70.10/10.66 thf(f3825,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3477])). 70.10/10.66 thf(f3826,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3825])). 70.10/10.66 thf(f3827,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3479])). 70.10/10.66 thf(f3828,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3481])). 70.10/10.66 thf(f3829,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3482])). 70.10/10.66 thf(f3830,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3484])). 70.10/10.66 thf(f3831,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3485])). 70.10/10.66 thf(f3832,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3831])). 70.10/10.66 thf(f3833,plain,( 70.10/10.66 spl37_106 | spl37_108 | spl37_105 | spl37_98), 70.10/10.66 inference(avatar_split_clause,[],[f3486,f2895,f3131,f3242,f3188])). 70.10/10.66 thf(f3834,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3488])). 70.10/10.66 thf(f3835,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3490])). 70.10/10.66 thf(f3836,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3492])). 70.10/10.66 thf(f3837,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3836])). 70.10/10.66 thf(f3838,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3491])). 70.10/10.66 thf(f3839,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3491])). 70.10/10.66 thf(f3840,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3493])). 70.10/10.66 thf(f3841,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3494])). 70.10/10.66 thf(f3842,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X2))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3841])). 70.10/10.66 thf(f3843,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3496])). 70.10/10.66 thf(f3844,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3497])). 70.10/10.66 thf(f3845,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3497])). 70.10/10.66 thf(f3846,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3498])). 70.10/10.66 thf(f3847,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3499])). 70.10/10.66 thf(f3848,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0)))))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X2)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3847])). 70.10/10.66 thf(f3849,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3500])). 70.10/10.66 thf(f3850,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3849])). 70.10/10.66 thf(f3851,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3501])). 70.10/10.66 thf(f3852,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3851])). 70.10/10.66 thf(f3853,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3503])). 70.10/10.66 thf(f3854,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3504])). 70.10/10.66 thf(f3855,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3854])). 70.10/10.66 thf(f3856,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3505])). 70.10/10.66 thf(f3857,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))))))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3505])). 70.10/10.66 thf(f3858,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3507])). 70.10/10.66 thf(f3859,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3508])). 70.10/10.66 thf(f3860,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3508])). 70.10/10.66 thf(f3861,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3510])). 70.10/10.66 thf(f3862,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3511])). 70.10/10.66 thf(f3863,plain,( 70.10/10.66 spl37_99 | spl37_108 | spl37_105 | spl37_107), 70.10/10.66 inference(avatar_split_clause,[],[f3512,f3202,f3131,f3242,f2898])). 70.10/10.66 thf(f3864,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3513])). 70.10/10.66 thf(f3865,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3864])). 70.10/10.66 thf(f3866,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3515])). 70.10/10.66 thf(f3867,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3516])). 70.10/10.66 thf(f3868,plain,( 70.10/10.66 spl37_99 | spl37_105 | spl37_120 | spl37_98), 70.10/10.66 inference(avatar_split_clause,[],[f3517,f2895,f3590,f3131,f2898])). 70.10/10.66 thf(f3869,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3519])). 70.10/10.66 thf(f3870,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3520])). 70.10/10.66 thf(f3871,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3870])). 70.10/10.66 thf(f3872,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3521])). 70.10/10.66 thf(f3873,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3872])). 70.10/10.66 thf(f3874,plain,( 70.10/10.66 spl37_99 | spl37_98 | spl37_119 | spl37_105), 70.10/10.66 inference(avatar_split_clause,[],[f3522,f3131,f3553,f2895,f2898])). 70.10/10.66 thf(f3875,plain,( 70.10/10.66 spl37_107 | spl37_97 | spl37_100 | spl37_115), 70.10/10.66 inference(avatar_split_clause,[],[f3532,f3524,f2901,f2892,f3202])). 70.10/10.66 thf(f3876,plain,( 70.10/10.66 spl37_100 | spl37_97 | spl37_107 | spl37_116), 70.10/10.66 inference(avatar_split_clause,[],[f3533,f3528,f3202,f2892,f2901])). 70.10/10.66 thf(f3877,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3535])). 70.10/10.66 thf(f3878,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3537])). 70.10/10.66 thf(f3879,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3539])). 70.10/10.66 thf(f3880,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3541])). 70.10/10.66 thf(f3881,plain,( 70.10/10.66 spl37_106 | spl37_97 | spl37_118 | spl37_100), 70.10/10.66 inference(avatar_split_clause,[],[f3542,f2901,f3549,f2892,f3188])). 70.10/10.66 thf(f3882,plain,( 70.10/10.66 spl37_106 | spl37_97 | spl37_117 | spl37_100), 70.10/10.66 inference(avatar_split_clause,[],[f3543,f2901,f3545,f2892,f3188])). 70.10/10.66 thf(f3883,plain,( 70.10/10.66 spl37_100 | spl37_106 | spl37_98 | spl37_119), 70.10/10.66 inference(avatar_split_clause,[],[f3556,f3553,f2895,f3188,f2901])). 70.10/10.66 thf(f3884,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3558])). 70.10/10.66 thf(f3885,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3560])). 70.10/10.66 thf(f3886,plain,( 70.10/10.66 spl37_119 | spl37_100 | spl37_107 | spl37_99), 70.10/10.66 inference(avatar_split_clause,[],[f3561,f2898,f3202,f2901,f3553])). 70.10/10.66 thf(f3887,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3563])). 70.10/10.66 thf(f3888,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3564])). 70.10/10.66 thf(f3889,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3888])). 70.10/10.66 thf(f3890,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3565])). 70.10/10.66 thf(f3891,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3890])). 70.10/10.66 thf(f3892,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3566])). 70.10/10.66 thf(f3893,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3892])). 70.10/10.66 thf(f3894,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3568])). 70.10/10.66 thf(f3895,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3570])). 70.10/10.66 thf(f3896,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3572])). 70.10/10.66 thf(f3897,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3573])). 70.10/10.66 thf(f3898,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3573])). 70.10/10.66 thf(f3899,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3574])). 70.10/10.66 thf(f3900,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3899])). 70.10/10.66 thf(f3901,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3576])). 70.10/10.66 thf(f3902,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3577])). 70.10/10.66 thf(f3903,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3902])). 70.10/10.66 thf(f3904,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3578])). 70.10/10.66 thf(f3905,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3904])). 70.10/10.66 thf(f3906,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3579])). 70.10/10.66 thf(f3907,plain,( 70.10/10.66 spl37_107 | spl37_120 | spl37_100 | spl37_99), 70.10/10.66 inference(avatar_split_clause,[],[f3580,f2898,f2901,f3590,f3202])). 70.10/10.66 thf(f3908,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3582])). 70.10/10.66 thf(f3909,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3584])). 70.10/10.66 thf(f3910,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3585])). 70.10/10.66 thf(f3911,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3910])). 70.10/10.66 thf(f3912,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))))))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3586])). 70.10/10.66 thf(f3913,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3586])). 70.10/10.66 thf(f3914,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3588])). 70.10/10.66 thf(f3915,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3914])). 70.10/10.66 thf(f3916,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3587])). 70.10/10.66 thf(f3917,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3587])). 70.10/10.66 thf(f3918,plain,( 70.10/10.66 spl37_106 | spl37_100 | spl37_98 | spl37_120), 70.10/10.66 inference(avatar_split_clause,[],[f3593,f3590,f2895,f2901,f3188])). 70.10/10.66 thf(f3919,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3595])). 70.10/10.66 thf(f3920,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3597])). 70.10/10.66 thf(f3921,plain,( 70.10/10.66 spl37_98 | spl37_108 | spl37_100 | spl37_115), 70.10/10.66 inference(avatar_split_clause,[],[f3598,f3524,f2901,f3242,f2895])). 70.10/10.66 thf(f3922,plain,( 70.10/10.66 spl37_100 | spl37_116 | spl37_98 | spl37_108), 70.10/10.66 inference(avatar_split_clause,[],[f3599,f3242,f2895,f3528,f2901])). 70.10/10.66 thf(f3923,plain,( 70.10/10.66 spl37_108 | spl37_117 | spl37_99 | spl37_100), 70.10/10.66 inference(avatar_split_clause,[],[f3601,f2901,f2898,f3545,f3242])). 70.10/10.66 thf(f3924,plain,( 70.10/10.66 spl37_108 | spl37_100 | spl37_99 | spl37_118), 70.10/10.66 inference(avatar_split_clause,[],[f3602,f3549,f2898,f2901,f3242])). 70.10/10.66 thf(f3925,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3604])). 70.10/10.66 thf(f3926,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3606])). 70.10/10.66 thf(f3927,plain,( 70.10/10.66 spl37_106 | spl37_100 | spl37_107 | spl37_108), 70.10/10.66 inference(avatar_split_clause,[],[f3607,f3242,f3202,f2901,f3188])). 70.10/10.66 thf(f3928,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3609])). 70.10/10.66 thf(f3929,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3928])). 70.10/10.66 thf(f3930,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3608])). 70.10/10.66 thf(f3931,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3930])). 70.10/10.66 thf(f3932,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3611])). 70.10/10.66 thf(f3933,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3612])). 70.10/10.66 thf(f3934,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3613])). 70.10/10.66 thf(f3935,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3934])). 70.10/10.66 thf(f3936,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3614])). 70.10/10.66 thf(f3937,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3936])). 70.10/10.66 thf(f3979,plain,( 70.10/10.66 spl37_97 | spl37_106 | spl37_107 | spl37_113), 70.10/10.66 inference(avatar_split_clause,[],[f3646,f3308,f3202,f3188,f2892])). 70.10/10.66 thf(f3980,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3648])). 70.10/10.66 thf(f3981,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3650])). 70.10/10.66 thf(f3982,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3))))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3652])). 70.10/10.66 thf(f3983,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3654])). 70.10/10.66 thf(f3984,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3655])). 70.10/10.66 thf(f3985,plain,( 70.10/10.66 spl37_118 | spl37_113 | spl37_99 | spl37_97), 70.10/10.66 inference(avatar_split_clause,[],[f3656,f2892,f2898,f3308,f3549])). 70.10/10.66 thf(f3986,plain,( 70.10/10.66 spl37_113 | spl37_99 | spl37_117 | spl37_97), 70.10/10.66 inference(avatar_split_clause,[],[f3657,f2892,f3545,f2898,f3308])). 70.10/10.66 thf(f3987,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3658])). 70.10/10.66 thf(f3988,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3659])). 70.10/10.66 thf(f3989,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3988])). 70.10/10.66 thf(f3990,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e0 @ e0) @ e1 @ X1))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3661])). 70.10/10.66 thf(f3991,plain,( 70.10/10.66 spl37_116 | spl37_113 | spl37_97 | spl37_98), 70.10/10.66 inference(avatar_split_clause,[],[f3662,f2895,f2892,f3308,f3528])). 70.10/10.66 thf(f3992,plain,( 70.10/10.66 spl37_113 | spl37_98 | spl37_97 | spl37_115), 70.10/10.66 inference(avatar_split_clause,[],[f3663,f3524,f2892,f2895,f3308])). 70.10/10.66 thf(f3993,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3667])). 70.10/10.66 thf(f3994,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3669])). 70.10/10.66 thf(f3995,plain,( 70.10/10.66 spl37_108 | spl37_98 | spl37_113 | spl37_106), 70.10/10.66 inference(avatar_split_clause,[],[f3670,f3188,f3308,f2895,f3242])). 70.10/10.66 thf(f3996,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3672])). 70.10/10.66 thf(f3997,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3674])). 70.10/10.66 thf(f3998,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3675])). 70.10/10.66 thf(f3999,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f3998])). 70.10/10.66 thf(f4000,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3677])). 70.10/10.66 thf(f4001,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3678])). 70.10/10.66 thf(f4002,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3678])). 70.10/10.66 thf(f4003,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3680])). 70.10/10.66 thf(f4004,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3679])). 70.10/10.66 thf(f4005,plain,( 70.10/10.66 spl37_99 | spl37_107 | spl37_113 | spl37_108), 70.10/10.66 inference(avatar_split_clause,[],[f3681,f3242,f3308,f3202,f2898])). 70.10/10.66 thf(f4006,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3683])). 70.10/10.66 thf(f4007,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4006])). 70.10/10.66 thf(f4008,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3682])). 70.10/10.66 thf(f4009,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4008])). 70.10/10.66 thf(f4010,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3685])). 70.10/10.66 thf(f4011,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3686])). 70.10/10.66 thf(f4012,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4011])). 70.10/10.66 thf(f4013,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3687])). 70.10/10.66 thf(f4014,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4013])). 70.10/10.66 thf(f4015,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3688])). 70.10/10.66 thf(f4016,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3690])). 70.10/10.66 thf(f4017,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3691])). 70.10/10.66 thf(f4018,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3691])). 70.10/10.66 thf(f4019,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3693])). 70.10/10.66 thf(f4020,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3695])). 70.10/10.66 thf(f4021,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4020])). 70.10/10.66 thf(f4022,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3694])). 70.10/10.66 thf(f4023,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4022])). 70.10/10.66 thf(f4024,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3697])). 70.10/10.66 thf(f4025,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3699])). 70.10/10.66 thf(f4026,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4025])). 70.10/10.66 thf(f4027,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3701])). 70.10/10.66 thf(f4028,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3702])). 70.10/10.66 thf(f4029,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ((((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3703])). 70.10/10.66 thf(f4030,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3704])). 70.10/10.66 thf(f4031,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4030])). 70.10/10.66 thf(f4032,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3705])). 70.10/10.66 thf(f4033,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3705])). 70.10/10.66 thf(f4034,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3706])). 70.10/10.66 thf(f4035,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3707])). 70.10/10.66 thf(f4036,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4035])). 70.10/10.66 thf(f4037,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3709])). 70.10/10.66 thf(f4038,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3710])). 70.10/10.66 thf(f4039,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3712])). 70.10/10.66 thf(f4040,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4039])). 70.10/10.66 thf(f4041,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3713])). 70.10/10.66 thf(f4042,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4041])). 70.10/10.66 thf(f4043,plain,( 70.10/10.66 spl37_99 | spl37_98 | spl37_113 | spl37_120), 70.10/10.66 inference(avatar_split_clause,[],[f3714,f3590,f3308,f2895,f2898])). 70.10/10.66 thf(f4044,plain,( 70.10/10.66 spl37_99 | spl37_113 | spl37_119 | spl37_98), 70.10/10.66 inference(avatar_split_clause,[],[f3715,f2895,f3553,f3308,f2898])). 70.10/10.66 thf(f4045,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3717])). 70.10/10.66 thf(f4046,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3718])). 70.10/10.66 thf(f4047,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3719])). 70.10/10.66 thf(f4048,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4047])). 70.10/10.66 thf(f4049,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3720])). 70.10/10.66 thf(f4050,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4049])). 70.10/10.66 thf(f4051,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X4)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3721])). 70.10/10.66 thf(f4052,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4051])). 70.10/10.66 thf(f4053,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3722])). 70.10/10.66 thf(f4054,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4053])). 70.10/10.66 thf(f4055,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3723])). 70.10/10.66 thf(f4056,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3725])). 70.10/10.66 thf(f4057,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3726])). 70.10/10.66 thf(f4058,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4057])). 70.10/10.66 thf(f4059,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X3)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3727])). 70.10/10.66 thf(f4060,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4059])). 70.10/10.66 thf(f4061,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3728])). 70.10/10.66 thf(f4062,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3730])). 70.10/10.66 thf(f4063,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2))))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3732])). 70.10/10.66 thf(f4064,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3733])). 70.10/10.66 thf(f4065,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4064])). 70.10/10.66 thf(f4066,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3735])). 70.10/10.66 thf(f4067,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4066])). 70.10/10.66 thf(f4068,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3736])). 70.10/10.66 thf(f4069,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3736])). 70.10/10.66 thf(f4070,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3738])). 70.10/10.66 thf(f4071,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4070])). 70.10/10.66 thf(f4072,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true)) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3739])). 70.10/10.66 thf(f4073,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))))))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3739])). 70.10/10.66 thf(f4074,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3740])). 70.10/10.66 thf(f4075,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4074])). 70.10/10.66 thf(f4076,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3742])). 70.10/10.66 thf(f4077,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e2 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3))))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3743])). 70.10/10.66 thf(f4078,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X4)))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3745])). 70.10/10.66 thf(f4079,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3747])). 70.10/10.66 thf(f4080,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3748])). 70.10/10.66 thf(f4081,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3750])). 70.10/10.66 thf(f4082,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3751])). 70.10/10.66 thf(f4083,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3752])). 70.10/10.66 thf(f4084,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3754])). 70.10/10.66 thf(f4085,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3756])). 70.10/10.66 thf(f4086,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3758])). 70.10/10.66 thf(f4087,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3759])). 70.10/10.66 thf(f4088,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4087])). 70.10/10.66 thf(f4089,plain,( 70.10/10.66 spl37_98 | spl37_106 | spl37_108 | spl37_114), 70.10/10.66 inference(avatar_split_clause,[],[f3760,f3436,f3242,f3188,f2895])). 70.10/10.66 thf(f4090,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3762])). 70.10/10.66 thf(f4091,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3763])). 70.10/10.66 thf(f4092,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4091])). 70.10/10.66 thf(f4093,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3764])). 70.10/10.66 thf(f4094,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4093])). 70.10/10.66 thf(f4095,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3765])). 70.10/10.66 thf(f4096,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4095])). 70.10/10.66 thf(f4097,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3767])). 70.10/10.66 thf(f4098,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3768])). 70.10/10.66 thf(f4099,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(and_proxy_clausification,[],[f3768])). 70.10/10.66 thf(f4100,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3769])). 70.10/10.66 thf(f4101,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4100])). 70.10/10.66 thf(f4102,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3770])). 70.10/10.66 thf(f4103,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4102])). 70.10/10.66 thf(f4104,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3771])). 70.10/10.66 thf(f4105,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true)) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4104])). 70.10/10.66 thf(f4106,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3772])). 70.10/10.66 thf(f4107,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3774])). 70.10/10.66 thf(f4108,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3776])). 70.10/10.66 thf(f4109,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3777])). 70.10/10.66 thf(f4110,plain,( 70.10/10.66 spl37_114 | spl37_98 | spl37_119 | spl37_99), 70.10/10.66 inference(avatar_split_clause,[],[f3778,f2898,f3553,f2895,f3436])). 70.10/10.66 thf(f4111,plain,( 70.10/10.66 spl37_114 | spl37_98 | spl37_120 | spl37_99), 70.10/10.66 inference(avatar_split_clause,[],[f3779,f2898,f3590,f2895,f3436])). 70.10/10.66 thf(f4112,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3781])). 70.10/10.66 thf(f4113,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3783])). 70.10/10.66 thf(f4114,plain,( 70.10/10.66 spl37_107 | spl37_99 | spl37_108 | spl37_114), 70.10/10.66 inference(avatar_split_clause,[],[f3784,f3436,f3242,f2898,f3202])). 70.10/10.66 thf(f4115,plain,( 70.10/10.66 spl37_114 | spl37_98 | spl37_116 | spl37_97), 70.10/10.66 inference(avatar_split_clause,[],[f3786,f2892,f3528,f2895,f3436])). 70.10/10.66 thf(f4116,plain,( 70.10/10.66 spl37_98 | spl37_97 | spl37_115 | spl37_114), 70.10/10.66 inference(avatar_split_clause,[],[f3787,f3436,f3524,f2892,f2895])). 70.10/10.66 thf(f4117,plain,( 70.10/10.66 spl37_97 | spl37_99 | spl37_114 | spl37_118), 70.10/10.66 inference(avatar_split_clause,[],[f3790,f3549,f3436,f2898,f2892])). 70.10/10.66 thf(f4118,plain,( 70.10/10.66 spl37_99 | spl37_114 | spl37_117 | spl37_97), 70.10/10.66 inference(avatar_split_clause,[],[f3791,f2892,f3545,f3436,f2898])). 70.10/10.66 thf(f4119,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.66 inference(imp_proxy_clausification,[],[f3792])). 70.10/10.66 thf(f4120,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3793])). 70.10/10.66 thf(f4121,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4))))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4120])). 70.10/10.66 thf(f4122,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3)))) )), 70.10/10.66 inference(pi_proxy_clausification,[],[f3794])). 70.10/10.66 thf(f4123,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.66 inference(beta-eta_normalization,[],[f4122])). 70.10/10.66 thf(f4124,plain,( 70.10/10.66 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3796])). 70.10/10.67 thf(f4125,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3797])). 70.10/10.67 thf(f4126,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4125])). 70.10/10.67 thf(f4127,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3798])). 70.10/10.67 thf(f4128,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true)) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4127])). 70.10/10.67 thf(f4129,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3799])). 70.10/10.67 thf(f4130,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X3)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3800])). 70.10/10.67 thf(f4131,plain,( 70.10/10.67 spl37_106 | spl37_114 | spl37_97 | spl37_107), 70.10/10.67 inference(avatar_split_clause,[],[f3801,f3202,f2892,f3436,f3188])). 70.10/10.67 thf(f4132,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3804])). 70.10/10.67 thf(f4133,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3805])). 70.10/10.67 thf(f4134,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3807])). 70.10/10.67 thf(f4135,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3809])). 70.10/10.67 thf(f4136,plain,( 70.10/10.67 spl37_97 | spl37_107 | spl37_105 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f3810,f3524,f3131,f3202,f2892])). 70.10/10.67 thf(f4137,plain,( 70.10/10.67 spl37_105 | spl37_97 | spl37_116 | spl37_107), 70.10/10.67 inference(avatar_split_clause,[],[f3811,f3202,f3528,f2892,f3131])). 70.10/10.67 thf(f4138,plain,( 70.10/10.67 spl37_106 | spl37_105 | spl37_97 | spl37_117), 70.10/10.67 inference(avatar_split_clause,[],[f3812,f3545,f2892,f3131,f3188])). 70.10/10.67 thf(f4139,plain,( 70.10/10.67 spl37_97 | spl37_106 | spl37_105 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f3813,f3549,f3131,f3188,f2892])). 70.10/10.67 thf(f4140,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3818])). 70.10/10.67 thf(f4141,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3819])). 70.10/10.67 thf(f4142,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4141])). 70.10/10.67 thf(f4143,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3821])). 70.10/10.67 thf(f4144,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3822])). 70.10/10.67 thf(f4145,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3824])). 70.10/10.67 thf(f4146,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3826])). 70.10/10.67 thf(f4147,plain,( 70.10/10.67 spl37_106 | spl37_98 | spl37_105 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f3827,f3553,f3131,f2895,f3188])). 70.10/10.67 thf(f4148,plain,( 70.10/10.67 spl37_120 | spl37_105 | spl37_106 | spl37_98), 70.10/10.67 inference(avatar_split_clause,[],[f3828,f2895,f3188,f3131,f3590])). 70.10/10.67 thf(f4149,plain,( 70.10/10.67 spl37_105 | spl37_108 | spl37_106 | spl37_107), 70.10/10.67 inference(avatar_split_clause,[],[f3829,f3202,f3188,f3242,f3131])). 70.10/10.67 thf(f4150,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3830])). 70.10/10.67 thf(f4151,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3832])). 70.10/10.67 thf(f4152,plain,( 70.10/10.67 spl37_115 | spl37_108 | spl37_105 | spl37_98), 70.10/10.67 inference(avatar_split_clause,[],[f3834,f2895,f3131,f3242,f3524])). 70.10/10.67 thf(f4153,plain,( 70.10/10.67 spl37_116 | spl37_98 | spl37_108 | spl37_105), 70.10/10.67 inference(avatar_split_clause,[],[f3835,f3131,f3242,f2895,f3528])). 70.10/10.67 thf(f4154,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3837])). 70.10/10.67 thf(f4155,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3838])). 70.10/10.67 thf(f4156,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4155])). 70.10/10.67 thf(f4157,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3839])). 70.10/10.67 thf(f4158,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4157])). 70.10/10.67 thf(f4159,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3840])). 70.10/10.67 thf(f4160,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4))))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3842])). 70.10/10.67 thf(f4161,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3843])). 70.10/10.67 thf(f4162,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3844])). 70.10/10.67 thf(f4163,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true)) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4162])). 70.10/10.67 thf(f4164,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3845])). 70.10/10.67 thf(f4165,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4164])). 70.10/10.67 thf(f4166,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.67 inference(and_proxy_clausification,[],[f3846])). 70.10/10.67 thf(f4167,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(and_proxy_clausification,[],[f3846])). 70.10/10.67 thf(f4168,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e3 @ X2)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ Y0))) @ X4)) = $true)) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3848])). 70.10/10.67 thf(f4169,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4168])). 70.10/10.67 thf(f4170,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3850])). 70.10/10.67 thf(f4171,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3852])). 70.10/10.67 thf(f4172,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3853])). 70.10/10.67 thf(f4173,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3855])). 70.10/10.67 thf(f4174,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.67 inference(and_proxy_clausification,[],[f3856])). 70.10/10.67 thf(f4175,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3)))) )), 70.10/10.67 inference(and_proxy_clausification,[],[f3856])). 70.10/10.67 thf(f4176,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3857])). 70.10/10.67 thf(f4177,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4176])). 70.10/10.67 thf(f4178,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3858])). 70.10/10.67 thf(f4179,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.67 inference(and_proxy_clausification,[],[f3859])). 70.10/10.67 thf(f4180,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.67 inference(and_proxy_clausification,[],[f3859])). 70.10/10.67 thf(f4181,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3860])). 70.10/10.67 thf(f4182,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4181])). 70.10/10.67 thf(f4183,plain,( 70.10/10.67 spl37_108 | spl37_99 | spl37_105 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f3861,f3549,f3131,f2898,f3242])). 70.10/10.67 thf(f4184,plain,( 70.10/10.67 spl37_105 | spl37_99 | spl37_117 | spl37_108), 70.10/10.67 inference(avatar_split_clause,[],[f3862,f3242,f3545,f2898,f3131])). 70.10/10.67 thf(f4185,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3865])). 70.10/10.67 thf(f4186,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3866])). 70.10/10.67 thf(f4187,plain,( 70.10/10.67 spl37_105 | spl37_99 | spl37_107 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f3867,f3590,f3202,f2898,f3131])). 70.10/10.67 thf(f4188,plain,( 70.10/10.67 spl37_105 | spl37_99 | spl37_119 | spl37_107), 70.10/10.67 inference(avatar_split_clause,[],[f3869,f3202,f3553,f2898,f3131])). 70.10/10.67 thf(f4189,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3871])). 70.10/10.67 thf(f4190,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3873])). 70.10/10.67 thf(f4191,plain,( 70.10/10.67 spl37_97 | spl37_100 | spl37_118 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f3877,f3524,f3549,f2901,f2892])). 70.10/10.67 thf(f4192,plain,( 70.10/10.67 spl37_97 | spl37_115 | spl37_117 | spl37_100), 70.10/10.67 inference(avatar_split_clause,[],[f3878,f2901,f3545,f3524,f2892])). 70.10/10.67 thf(f4193,plain,( 70.10/10.67 spl37_116 | spl37_118 | spl37_97 | spl37_100), 70.10/10.67 inference(avatar_split_clause,[],[f3879,f2901,f2892,f3549,f3528])). 70.10/10.67 thf(f4194,plain,( 70.10/10.67 spl37_117 | spl37_97 | spl37_116 | spl37_100), 70.10/10.67 inference(avatar_split_clause,[],[f3880,f2901,f3528,f2892,f3545])). 70.10/10.67 thf(f4195,plain,( 70.10/10.67 spl37_119 | spl37_116 | spl37_98 | spl37_100), 70.10/10.67 inference(avatar_split_clause,[],[f3884,f2901,f2895,f3528,f3553])). 70.10/10.67 thf(f4196,plain,( 70.10/10.67 spl37_98 | spl37_100 | spl37_119 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f3885,f3524,f3553,f2901,f2895])). 70.10/10.67 thf(f4197,plain,( 70.10/10.67 spl37_100 | spl37_106 | spl37_107 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f3887,f3553,f3202,f3188,f2901])). 70.10/10.67 thf(f4198,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3889])). 70.10/10.67 thf(f4199,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3891])). 70.10/10.67 thf(f4200,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3893])). 70.10/10.67 thf(f4201,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X1))) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3894])). 70.10/10.67 thf(f4202,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3895])). 70.10/10.67 thf(f4203,plain,( 70.10/10.67 spl37_117 | spl37_99 | spl37_100 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f3896,f3553,f2901,f2898,f3545])). 70.10/10.67 thf(f4204,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3898])). 70.10/10.67 thf(f4205,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true)) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4204])). 70.10/10.67 thf(f4206,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3897])). 70.10/10.67 thf(f4207,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4206])). 70.10/10.67 thf(f4208,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3900])). 70.10/10.67 thf(f4209,plain,( 70.10/10.67 spl37_99 | spl37_118 | spl37_100 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f3901,f3553,f2901,f3549,f2898])). 70.10/10.67 thf(f4210,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3903])). 70.10/10.67 thf(f4211,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e3 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3905])). 70.10/10.67 thf(f4212,plain,( 70.10/10.67 spl37_100 | spl37_120 | spl37_106 | spl37_107), 70.10/10.67 inference(avatar_split_clause,[],[f3906,f3202,f3188,f3590,f2901])). 70.10/10.67 thf(f4213,plain,( 70.10/10.67 spl37_99 | spl37_100 | spl37_118 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f3908,f3590,f3549,f2901,f2898])). 70.10/10.67 thf(f4214,plain,( 70.10/10.67 spl37_99 | spl37_117 | spl37_100 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f3909,f3590,f2901,f3545,f2898])). 70.10/10.67 thf(f4215,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3911])). 70.10/10.67 thf(f4216,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3912])). 70.10/10.67 thf(f4217,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4216])). 70.10/10.67 thf(f4218,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3913])). 70.10/10.67 thf(f4219,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4218])). 70.10/10.67 thf(f4220,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3915])). 70.10/10.67 thf(f4221,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3917])). 70.10/10.67 thf(f4222,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4221])). 70.10/10.67 thf(f4223,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f3916])). 70.10/10.67 thf(f4224,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4223])). 70.10/10.67 thf(f4225,plain,( 70.10/10.67 spl37_115 | spl37_98 | spl37_100 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f3919,f3590,f2901,f2895,f3524])). 70.10/10.67 thf(f4226,plain,( 70.10/10.67 spl37_98 | spl37_120 | spl37_100 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f3920,f3528,f2901,f3590,f2895])). 70.10/10.67 thf(f4227,plain,( 70.10/10.67 spl37_108 | spl37_100 | spl37_107 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f3925,f3524,f3202,f2901,f3242])). 70.10/10.67 thf(f4228,plain,( 70.10/10.67 spl37_116 | spl37_100 | spl37_108 | spl37_107), 70.10/10.67 inference(avatar_split_clause,[],[f3926,f3202,f3242,f2901,f3528])). 70.10/10.67 thf(f4229,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3929])). 70.10/10.67 thf(f4230,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3931])). 70.10/10.67 thf(f4231,plain,( 70.10/10.67 spl37_106 | spl37_108 | spl37_100 | spl37_117), 70.10/10.67 inference(avatar_split_clause,[],[f3932,f3545,f2901,f3242,f3188])). 70.10/10.67 thf(f4232,plain,( 70.10/10.67 spl37_106 | spl37_100 | spl37_108 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f3933,f3549,f3242,f2901,f3188])). 70.10/10.67 thf(f4233,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3935])). 70.10/10.67 thf(f4234,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3937])). 70.10/10.67 thf(f4250,plain,( 70.10/10.67 spl37_116 | spl37_107 | spl37_113 | spl37_97), 70.10/10.67 inference(avatar_split_clause,[],[f3980,f2892,f3308,f3202,f3528])). 70.10/10.67 thf(f4251,plain,( 70.10/10.67 spl37_97 | spl37_115 | spl37_107 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f3981,f3308,f3202,f3524,f2892])). 70.10/10.67 thf(f4252,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3982])). 70.10/10.67 thf(f4253,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3983])). 70.10/10.67 thf(f4254,plain,( 70.10/10.67 spl37_97 | spl37_118 | spl37_106 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f3984,f3308,f3188,f3549,f2892])). 70.10/10.67 thf(f4255,plain,( 70.10/10.67 spl37_113 | spl37_97 | spl37_117 | spl37_106), 70.10/10.67 inference(avatar_split_clause,[],[f3987,f3188,f3545,f2892,f3308])). 70.10/10.67 thf(f4256,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3989])). 70.10/10.67 thf(f4257,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3990])). 70.10/10.67 thf(f4258,plain,( 70.10/10.67 spl37_98 | spl37_108 | spl37_116 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f3993,f3308,f3528,f3242,f2895])). 70.10/10.67 thf(f4259,plain,( 70.10/10.67 spl37_98 | spl37_108 | spl37_113 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f3994,f3524,f3308,f3242,f2895])). 70.10/10.67 thf(f4260,plain,( 70.10/10.67 spl37_118 | spl37_113 | spl37_108 | spl37_99), 70.10/10.67 inference(avatar_split_clause,[],[f3996,f2898,f3242,f3308,f3549])). 70.10/10.67 thf(f4261,plain,( 70.10/10.67 spl37_108 | spl37_117 | spl37_99 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f3997,f3308,f2898,f3545,f3242])). 70.10/10.67 thf(f4262,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f3999])). 70.10/10.67 thf(f4263,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4000])). 70.10/10.67 thf(f4264,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4002])). 70.10/10.67 thf(f4265,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4264])). 70.10/10.67 thf(f4266,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4001])). 70.10/10.67 thf(f4267,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4))))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4266])). 70.10/10.67 thf(f4268,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4003])). 70.10/10.67 thf(f4269,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4268])). 70.10/10.67 thf(f4270,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4004])). 70.10/10.67 thf(f4271,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4270])). 70.10/10.67 thf(f4272,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4007])). 70.10/10.67 thf(f4273,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4009])). 70.10/10.67 thf(f4274,plain,( 70.10/10.67 spl37_106 | spl37_108 | spl37_107 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f4010,f3308,f3202,f3242,f3188])). 70.10/10.67 thf(f4275,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4012])). 70.10/10.67 thf(f4276,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4014])). 70.10/10.67 thf(f4277,plain,( 70.10/10.67 spl37_113 | spl37_119 | spl37_106 | spl37_98), 70.10/10.67 inference(avatar_split_clause,[],[f4015,f2895,f3188,f3553,f3308])). 70.10/10.67 thf(f4278,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4016])). 70.10/10.67 thf(f4279,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4018])). 70.10/10.67 thf(f4280,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4279])). 70.10/10.67 thf(f4281,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true)) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4017])). 70.10/10.67 thf(f4282,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4281])). 70.10/10.67 thf(f4283,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))))))) )), 70.10/10.67 inference(and_proxy_clausification,[],[f4019])). 70.10/10.67 thf(f4284,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(and_proxy_clausification,[],[f4019])). 70.10/10.67 thf(f4285,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4021])). 70.10/10.67 thf(f4286,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4023])). 70.10/10.67 thf(f4287,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4286])). 70.10/10.67 thf(f4288,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4024])). 70.10/10.67 thf(f4289,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4288])). 70.10/10.67 thf(f4290,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4026])). 70.10/10.67 thf(f4291,plain,( 70.10/10.67 spl37_106 | spl37_113 | spl37_98 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4027,f3590,f2895,f3308,f3188])). 70.10/10.67 thf(f4292,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4028])). 70.10/10.67 thf(f4293,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4029])). 70.10/10.67 thf(f4294,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4031])). 70.10/10.67 thf(f4295,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4033])). 70.10/10.67 thf(f4296,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4295])). 70.10/10.67 thf(f4297,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4032])). 70.10/10.67 thf(f4298,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4297])). 70.10/10.67 thf(f4299,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4034])). 70.10/10.67 thf(f4300,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4299])). 70.10/10.67 thf(f4301,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4036])). 70.10/10.67 thf(f4302,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4301])). 70.10/10.67 thf(f4303,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))))))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4037])). 70.10/10.67 thf(f4304,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4038])). 70.10/10.67 thf(f4305,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4304])). 70.10/10.67 thf(f4306,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4040])). 70.10/10.67 thf(f4307,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4042])). 70.10/10.67 thf(f4308,plain,( 70.10/10.67 spl37_107 | spl37_99 | spl37_113 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4045,f3590,f3308,f2898,f3202])). 70.10/10.67 thf(f4309,plain,( 70.10/10.67 spl37_119 | spl37_99 | spl37_107 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f4046,f3308,f3202,f2898,f3553])). 70.10/10.67 thf(f4310,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4048])). 70.10/10.67 thf(f4311,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4050])). 70.10/10.67 thf(f4312,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4052])). 70.10/10.67 thf(f4313,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4054])). 70.10/10.67 thf(f4314,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4055])). 70.10/10.67 thf(f4315,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4056])). 70.10/10.67 thf(f4316,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4058])). 70.10/10.67 thf(f4317,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ Y0))) @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4060])). 70.10/10.67 thf(f4318,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4317])). 70.10/10.67 thf(f4319,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4061])). 70.10/10.67 thf(f4320,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4062])). 70.10/10.67 thf(f4321,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4320])). 70.10/10.67 thf(f4322,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4063])). 70.10/10.67 thf(f4323,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((mrel @ sK5 @ X2) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4322])). 70.10/10.67 thf(f4324,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4065])). 70.10/10.67 thf(f4325,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4067])). 70.10/10.67 thf(f4326,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4068])). 70.10/10.67 thf(f4327,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4069])). 70.10/10.67 thf(f4328,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4327])). 70.10/10.67 thf(f4329,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4071])). 70.10/10.67 thf(f4330,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4073])). 70.10/10.67 thf(f4331,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0)))))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4072])). 70.10/10.67 thf(f4332,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4075])). 70.10/10.67 thf(f4333,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e0 @ e0) @ e3 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4076])). 70.10/10.67 thf(f4334,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e2 @ X1)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4077])). 70.10/10.67 thf(f4335,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4078])). 70.10/10.67 thf(f4336,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4079])). 70.10/10.67 thf(f4337,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true)) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4336])). 70.10/10.67 thf(f4338,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4080])). 70.10/10.67 thf(f4339,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4338])). 70.10/10.67 thf(f4340,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = (((mrel @ sK5 @ X1) => (qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4081])). 70.10/10.67 thf(f4341,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true)) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4082])). 70.10/10.67 thf(f4342,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true)) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4341])). 70.10/10.67 thf(f4343,plain,( 70.10/10.67 spl37_114 | spl37_98 | spl37_115 | spl37_108), 70.10/10.67 inference(avatar_split_clause,[],[f4083,f3242,f3524,f2895,f3436])). 70.10/10.67 thf(f4344,plain,( 70.10/10.67 spl37_98 | spl37_108 | spl37_116 | spl37_114), 70.10/10.67 inference(avatar_split_clause,[],[f4084,f3436,f3528,f3242,f2895])). 70.10/10.67 thf(f4345,plain,( 70.10/10.67 spl37_108 | spl37_107 | spl37_106 | spl37_114), 70.10/10.67 inference(avatar_split_clause,[],[f4085,f3436,f3188,f3202,f3242])). 70.10/10.67 thf(f4346,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e1 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4086])). 70.10/10.67 thf(f4347,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4088])). 70.10/10.67 thf(f4348,plain,( 70.10/10.67 spl37_98 | spl37_114 | spl37_119 | spl37_106), 70.10/10.67 inference(avatar_split_clause,[],[f4090,f3188,f3553,f3436,f2895])). 70.10/10.67 thf(f4349,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4092])). 70.10/10.67 thf(f4350,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4094])). 70.10/10.67 thf(f4351,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($true = (((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4096])). 70.10/10.67 thf(f4352,plain,( 70.10/10.67 spl37_114 | spl37_106 | spl37_98 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4097,f3590,f2895,f3188,f3436])). 70.10/10.67 thf(f4353,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4099])). 70.10/10.67 thf(f4354,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4353])). 70.10/10.67 thf(f4355,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4098])). 70.10/10.67 thf(f4356,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4355])). 70.10/10.67 thf(f4357,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4101])). 70.10/10.67 thf(f4358,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4103])). 70.10/10.67 thf(f4359,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4105])). 70.10/10.67 thf(f4360,plain,( 70.10/10.67 spl37_107 | spl37_120 | spl37_114 | spl37_99), 70.10/10.67 inference(avatar_split_clause,[],[f4106,f2898,f3436,f3590,f3202])). 70.10/10.67 thf(f4361,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4107])). 70.10/10.67 thf(f4362,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e2 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4108])). 70.10/10.67 thf(f4363,plain,( 70.10/10.67 spl37_99 | spl37_119 | spl37_107 | spl37_114), 70.10/10.67 inference(avatar_split_clause,[],[f4109,f3436,f3202,f3553,f2898])). 70.10/10.67 thf(f4364,plain,( 70.10/10.67 spl37_117 | spl37_99 | spl37_114 | spl37_108), 70.10/10.67 inference(avatar_split_clause,[],[f4112,f3242,f3436,f2898,f3545])). 70.10/10.67 thf(f4365,plain,( 70.10/10.67 spl37_99 | spl37_118 | spl37_114 | spl37_108), 70.10/10.67 inference(avatar_split_clause,[],[f4113,f3242,f3436,f3549,f2898])). 70.10/10.67 thf(f4366,plain,( 70.10/10.67 spl37_114 | spl37_116 | spl37_97 | spl37_107), 70.10/10.67 inference(avatar_split_clause,[],[f4119,f3202,f2892,f3528,f3436])). 70.10/10.67 thf(f4367,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4121])). 70.10/10.67 thf(f4368,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4123])). 70.10/10.67 thf(f4369,plain,( 70.10/10.67 spl37_114 | spl37_97 | spl37_107 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f4124,f3524,f3202,f2892,f3436])). 70.10/10.67 thf(f4370,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4126])). 70.10/10.67 thf(f4371,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4128])). 70.10/10.67 thf(f4372,plain,( 70.10/10.67 spl37_106 | spl37_117 | spl37_97 | spl37_114), 70.10/10.67 inference(avatar_split_clause,[],[f4129,f3436,f2892,f3545,f3188])). 70.10/10.67 thf(f4373,plain,( 70.10/10.67 spl37_118 | spl37_114 | spl37_106 | spl37_97), 70.10/10.67 inference(avatar_split_clause,[],[f4130,f2892,f3188,f3436,f3549])). 70.10/10.67 thf(f4374,plain,( 70.10/10.67 spl37_105 | spl37_116 | spl37_97 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f4132,f3549,f2892,f3528,f3131])). 70.10/10.67 thf(f4375,plain,( 70.10/10.67 spl37_97 | spl37_118 | spl37_115 | spl37_105), 70.10/10.67 inference(avatar_split_clause,[],[f4133,f3131,f3524,f3549,f2892])). 70.10/10.67 thf(f4376,plain,( 70.10/10.67 spl37_97 | spl37_116 | spl37_105 | spl37_117), 70.10/10.67 inference(avatar_split_clause,[],[f4134,f3545,f3131,f3528,f2892])). 70.10/10.67 thf(f4377,plain,( 70.10/10.67 spl37_105 | spl37_117 | spl37_115 | spl37_97), 70.10/10.67 inference(avatar_split_clause,[],[f4135,f2892,f3524,f3545,f3131])). 70.10/10.67 thf(f4378,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4140])). 70.10/10.67 thf(f4379,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4142])). 70.10/10.67 thf(f4380,plain,( 70.10/10.67 spl37_107 | spl37_105 | spl37_106 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f4143,f3553,f3188,f3131,f3202])). 70.10/10.67 thf(f4381,plain,( 70.10/10.67 spl37_105 | spl37_107 | spl37_120 | spl37_106), 70.10/10.67 inference(avatar_split_clause,[],[f4144,f3188,f3590,f3202,f3131])). 70.10/10.67 thf(f4382,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4145])). 70.10/10.67 thf(f4383,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4146])). 70.10/10.67 thf(f4384,plain,( 70.10/10.67 spl37_105 | spl37_106 | spl37_118 | spl37_108), 70.10/10.67 inference(avatar_split_clause,[],[f4150,f3242,f3549,f3188,f3131])). 70.10/10.67 thf(f4385,plain,( 70.10/10.67 spl37_105 | spl37_108 | spl37_117 | spl37_106), 70.10/10.67 inference(avatar_split_clause,[],[f4151,f3188,f3545,f3242,f3131])). 70.10/10.67 thf(f4386,plain,( 70.10/10.67 spl37_107 | spl37_115 | spl37_105 | spl37_108), 70.10/10.67 inference(avatar_split_clause,[],[f4154,f3242,f3131,f3524,f3202])). 70.10/10.67 thf(f4387,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4156])). 70.10/10.67 thf(f4388,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4158])). 70.10/10.67 thf(f4389,plain,( 70.10/10.67 spl37_107 | spl37_105 | spl37_108 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4159,f3528,f3242,f3131,f3202])). 70.10/10.67 thf(f4390,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4160])). 70.10/10.67 thf(f4391,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4161])). 70.10/10.67 thf(f4392,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4163])). 70.10/10.67 thf(f4393,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4165])). 70.10/10.67 thf(f4394,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4167])). 70.10/10.67 thf(f4395,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4394])). 70.10/10.67 thf(f4396,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4166])). 70.10/10.67 thf(f4397,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4396])). 70.10/10.67 thf(f4398,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e1 @ X4))))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4169])). 70.10/10.67 thf(f4399,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ Y0))) @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4170])). 70.10/10.67 thf(f4400,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4399])). 70.10/10.67 thf(f4401,plain,( 70.10/10.67 spl37_105 | spl37_98 | spl37_119 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4171,f3528,f3553,f2895,f3131])). 70.10/10.67 thf(f4402,plain,( 70.10/10.67 spl37_119 | spl37_98 | spl37_105 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f4172,f3524,f3131,f2895,f3553])). 70.10/10.67 thf(f4403,plain,( 70.10/10.67 spl37_105 | spl37_116 | spl37_98 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4173,f3590,f2895,f3528,f3131])). 70.10/10.67 thf(f4404,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4175])). 70.10/10.67 thf(f4405,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4404])). 70.10/10.67 thf(f4406,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4174])). 70.10/10.67 thf(f4407,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4406])). 70.10/10.67 thf(f4408,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4177])). 70.10/10.67 thf(f4409,plain,( 70.10/10.67 spl37_105 | spl37_120 | spl37_115 | spl37_98), 70.10/10.67 inference(avatar_split_clause,[],[f4178,f2895,f3524,f3590,f3131])). 70.10/10.67 thf(f4410,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4180])). 70.10/10.67 thf(f4411,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4410])). 70.10/10.67 thf(f4412,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4179])). 70.10/10.67 thf(f4413,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4412])). 70.10/10.67 thf(f4414,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4182])). 70.10/10.67 thf(f4415,plain,( 70.10/10.67 spl37_105 | spl37_118 | spl37_120 | spl37_99), 70.10/10.67 inference(avatar_split_clause,[],[f4185,f2898,f3590,f3549,f3131])). 70.10/10.67 thf(f4416,plain,( 70.10/10.67 spl37_99 | spl37_117 | spl37_120 | spl37_105), 70.10/10.67 inference(avatar_split_clause,[],[f4186,f3131,f3590,f3545,f2898])). 70.10/10.67 thf(f4417,plain,( 70.10/10.67 spl37_119 | spl37_118 | spl37_105 | spl37_99), 70.10/10.67 inference(avatar_split_clause,[],[f4189,f2898,f3131,f3549,f3553])). 70.10/10.67 thf(f4418,plain,( 70.10/10.67 spl37_117 | spl37_99 | spl37_119 | spl37_105), 70.10/10.67 inference(avatar_split_clause,[],[f4190,f3131,f3553,f2898,f3545])). 70.10/10.67 thf(f4419,plain,( 70.10/10.67 spl37_107 | spl37_100 | spl37_119 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4198,f3528,f3553,f2901,f3202])). 70.10/10.67 thf(f4420,plain,( 70.10/10.67 spl37_100 | spl37_107 | spl37_119 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f4199,f3524,f3553,f3202,f2901])). 70.10/10.67 thf(f4421,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4200])). 70.10/10.67 thf(f4422,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4201])). 70.10/10.67 thf(f4423,plain,( 70.10/10.67 spl37_106 | spl37_117 | spl37_119 | spl37_100), 70.10/10.67 inference(avatar_split_clause,[],[f4202,f2901,f3553,f3545,f3188])). 70.10/10.67 thf(f4424,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4205])). 70.10/10.67 thf(f4425,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e0 @ e0) @ e0 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4207])). 70.10/10.67 thf(f4426,plain,( 70.10/10.67 spl37_106 | spl37_119 | spl37_118 | spl37_100), 70.10/10.67 inference(avatar_split_clause,[],[f4208,f2901,f3549,f3553,f3188])). 70.10/10.67 thf(f4427,plain,( 70.10/10.67 spl37_116 | spl37_100 | spl37_107 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4210,f3590,f3202,f2901,f3528])). 70.10/10.67 thf(f4428,plain,( 70.10/10.67 spl37_107 | spl37_120 | spl37_100 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f4211,f3524,f2901,f3590,f3202])). 70.10/10.67 thf(f4429,plain,( 70.10/10.67 spl37_117 | spl37_106 | spl37_100 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4215,f3590,f2901,f3188,f3545])). 70.10/10.67 thf(f4430,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4217])). 70.10/10.67 thf(f4431,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4219])). 70.10/10.67 thf(f4432,plain,( 70.10/10.67 spl37_106 | spl37_118 | spl37_120 | spl37_100), 70.10/10.67 inference(avatar_split_clause,[],[f4220,f2901,f3590,f3549,f3188])). 70.10/10.67 thf(f4433,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4222])). 70.10/10.67 thf(f4434,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e0 @ e0) @ e0 @ X1)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4224])). 70.10/10.67 thf(f4435,plain,( 70.10/10.67 spl37_100 | spl37_108 | spl37_117 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f4229,f3524,f3545,f3242,f2901])). 70.10/10.67 thf(f4436,plain,( 70.10/10.67 spl37_117 | spl37_116 | spl37_100 | spl37_108), 70.10/10.67 inference(avatar_split_clause,[],[f4230,f3242,f2901,f3528,f3545])). 70.10/10.67 thf(f4437,plain,( 70.10/10.67 spl37_100 | spl37_118 | spl37_108 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4233,f3528,f3242,f3549,f2901])). 70.10/10.67 thf(f4438,plain,( 70.10/10.67 spl37_108 | spl37_115 | spl37_100 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f4234,f3549,f2901,f3524,f3242])). 70.10/10.67 thf(f4454,plain,( 70.10/10.67 spl37_115 | spl37_113 | spl37_97 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f4252,f3549,f2892,f3308,f3524])). 70.10/10.67 thf(f4455,plain,( 70.10/10.67 spl37_113 | spl37_118 | spl37_97 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4253,f3528,f2892,f3549,f3308])). 70.10/10.67 thf(f4456,plain,( 70.10/10.67 spl37_115 | spl37_117 | spl37_97 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f4256,f3308,f2892,f3545,f3524])). 70.10/10.67 thf(f4457,plain,( 70.10/10.67 spl37_97 | spl37_116 | spl37_113 | spl37_117), 70.10/10.67 inference(avatar_split_clause,[],[f4257,f3545,f3308,f3528,f2892])). 70.10/10.67 thf(f4458,plain,( 70.10/10.67 spl37_113 | spl37_106 | spl37_118 | spl37_108), 70.10/10.67 inference(avatar_split_clause,[],[f4262,f3242,f3549,f3188,f3308])). 70.10/10.67 thf(f4459,plain,( 70.10/10.67 spl37_113 | spl37_106 | spl37_117 | spl37_108), 70.10/10.67 inference(avatar_split_clause,[],[f4263,f3242,f3545,f3188,f3308])). 70.10/10.67 thf(f4460,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4265])). 70.10/10.67 thf(f4461,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4267])). 70.10/10.67 thf(f4462,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4269])). 70.10/10.67 thf(f4463,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4271])). 70.10/10.67 thf(f4464,plain,( 70.10/10.67 spl37_108 | spl37_107 | spl37_115 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f4272,f3308,f3524,f3202,f3242])). 70.10/10.67 thf(f4465,plain,( 70.10/10.67 spl37_113 | spl37_108 | spl37_107 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4273,f3528,f3202,f3242,f3308])). 70.10/10.67 thf(f4466,plain,( 70.10/10.67 spl37_119 | spl37_116 | spl37_98 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f4275,f3308,f2895,f3528,f3553])). 70.10/10.67 thf(f4467,plain,( 70.10/10.67 spl37_113 | spl37_119 | spl37_98 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f4276,f3524,f2895,f3553,f3308])). 70.10/10.67 thf(f4468,plain,( 70.10/10.67 spl37_119 | spl37_107 | spl37_106 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f4278,f3308,f3188,f3202,f3553])). 70.10/10.67 thf(f4469,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4280])). 70.10/10.67 thf(f4470,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4282])). 70.10/10.67 thf(f4471,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4283])). 70.10/10.67 thf(f4472,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4471])). 70.10/10.67 thf(f4473,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4284])). 70.10/10.67 thf(f4474,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4473])). 70.10/10.67 thf(f4475,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4285])). 70.10/10.67 thf(f4476,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4475])). 70.10/10.67 thf(f4477,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4287])). 70.10/10.67 thf(f4478,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4289])). 70.10/10.67 thf(f4479,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e2 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4290])). 70.10/10.67 thf(f4480,plain,( 70.10/10.67 spl37_115 | spl37_113 | spl37_98 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4292,f3590,f2895,f3308,f3524])). 70.10/10.67 thf(f4481,plain,( 70.10/10.67 spl37_116 | spl37_98 | spl37_113 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4293,f3590,f3308,f2895,f3528])). 70.10/10.67 thf(f4482,plain,( 70.10/10.67 spl37_120 | spl37_106 | spl37_107 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f4294,f3308,f3202,f3188,f3590])). 70.10/10.67 thf(f4483,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4296])). 70.10/10.67 thf(f4484,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4298])). 70.10/10.67 thf(f4485,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4300])). 70.10/10.67 thf(f4486,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4302])). 70.10/10.67 thf(f4487,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4303])). 70.10/10.67 thf(f4488,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4487])). 70.10/10.67 thf(f4489,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4305])). 70.10/10.67 thf(f4490,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) = $true) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4306])). 70.10/10.67 thf(f4491,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4307])). 70.10/10.67 thf(f4492,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true)) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4491])). 70.10/10.67 thf(f4493,plain,( 70.10/10.67 spl37_119 | spl37_118 | spl37_99 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f4310,f3308,f2898,f3549,f3553])). 70.10/10.67 thf(f4494,plain,( 70.10/10.67 spl37_113 | spl37_99 | spl37_120 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f4311,f3549,f3590,f2898,f3308])). 70.10/10.67 thf(f4495,plain,( 70.10/10.67 spl37_117 | spl37_99 | spl37_113 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4312,f3590,f3308,f2898,f3545])). 70.10/10.67 thf(f4496,plain,( 70.10/10.67 spl37_99 | spl37_113 | spl37_117 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f4313,f3553,f3545,f3308,f2898])). 70.10/10.67 thf(f4497,plain,( 70.10/10.67 spl37_115 | spl37_114 | spl37_120 | spl37_98), 70.10/10.67 inference(avatar_split_clause,[],[f4314,f2895,f3590,f3436,f3524])). 70.10/10.67 thf(f4498,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4315])). 70.10/10.67 thf(f4499,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4316])). 70.10/10.67 thf(f4500,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4499])). 70.10/10.67 thf(f4501,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4318])). 70.10/10.67 thf(f4502,plain,( 70.10/10.67 spl37_119 | spl37_115 | spl37_114 | spl37_98), 70.10/10.67 inference(avatar_split_clause,[],[f4319,f2895,f3436,f3524,f3553])). 70.10/10.67 thf(f4503,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ((((mrel @ sK5 @ X3) => (qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4321])). 70.10/10.67 thf(f4504,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4323])). 70.10/10.67 thf(f4505,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4324])). 70.10/10.67 thf(f4506,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X4)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4325])). 70.10/10.67 thf(f4507,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4326])). 70.10/10.67 thf(f4508,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4507])). 70.10/10.67 thf(f4509,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4328])). 70.10/10.67 thf(f4510,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e3 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4329])). 70.10/10.67 thf(f4511,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4330])). 70.10/10.67 thf(f4512,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ((((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4511])). 70.10/10.67 thf(f4513,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK5 @ Y0) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ Y0))) @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true)) )), 70.10/10.67 inference(pi_proxy_clausification,[],[f4331])). 70.10/10.67 thf(f4514,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = (((mrel @ sK5 @ X4) => (qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) )), 70.10/10.67 inference(beta-eta_normalization,[],[f4513])). 70.10/10.67 thf(f4515,plain,( 70.10/10.67 spl37_98 | spl37_116 | spl37_119 | spl37_114), 70.10/10.67 inference(avatar_split_clause,[],[f4332,f3436,f3553,f3528,f2895])). 70.10/10.67 thf(f4516,plain,( 70.10/10.67 spl37_98 | spl37_114 | spl37_116 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4333,f3590,f3528,f3436,f2895])). 70.10/10.67 thf(f4517,plain,( 70.10/10.67 spl37_108 | spl37_114 | spl37_115 | spl37_107), 70.10/10.67 inference(avatar_split_clause,[],[f4334,f3202,f3524,f3436,f3242])). 70.10/10.67 thf(f4518,plain,( 70.10/10.67 spl37_114 | spl37_107 | spl37_108 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4335,f3528,f3242,f3202,f3436])). 70.10/10.67 thf(f4519,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4337])). 70.10/10.67 thf(f4520,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4339])). 70.10/10.67 thf(f4521,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4340])). 70.10/10.67 thf(f4522,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e1 @ e1) @ e1 @ X1)) = $true) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e2 @ e2) @ e0 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4342])). 70.10/10.67 thf(f4523,plain,( 70.10/10.67 spl37_118 | spl37_108 | spl37_106 | spl37_114), 70.10/10.67 inference(avatar_split_clause,[],[f4346,f3436,f3188,f3242,f3549])). 70.10/10.67 thf(f4524,plain,( 70.10/10.67 spl37_106 | spl37_117 | spl37_108 | spl37_114), 70.10/10.67 inference(avatar_split_clause,[],[f4347,f3436,f3242,f3545,f3188])). 70.10/10.67 thf(f4525,plain,( 70.10/10.67 spl37_114 | spl37_106 | spl37_119 | spl37_107), 70.10/10.67 inference(avatar_split_clause,[],[f4349,f3202,f3553,f3188,f3436])). 70.10/10.67 thf(f4526,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4350])). 70.10/10.67 thf(f4527,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4351])). 70.10/10.67 thf(f4528,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4354])). 70.10/10.67 thf(f4529,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e1 @ e1) @ e2 @ X3)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4356])). 70.10/10.67 thf(f4530,plain,( 70.10/10.67 spl37_106 | spl37_114 | spl37_107 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4357,f3590,f3202,f3436,f3188])). 70.10/10.67 thf(f4531,plain,( 70.10/10.67 spl37_114 | spl37_120 | spl37_117 | spl37_99), 70.10/10.67 inference(avatar_split_clause,[],[f4358,f2898,f3545,f3590,f3436])). 70.10/10.67 thf(f4532,plain,( 70.10/10.67 spl37_120 | spl37_99 | spl37_118 | spl37_114), 70.10/10.67 inference(avatar_split_clause,[],[f4359,f3436,f3549,f2898,f3590])). 70.10/10.67 thf(f4533,plain,( 70.10/10.67 spl37_99 | spl37_118 | spl37_114 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f4361,f3553,f3436,f3549,f2898])). 70.10/10.67 thf(f4534,plain,( 70.10/10.67 spl37_99 | spl37_114 | spl37_117 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f4362,f3553,f3545,f3436,f2898])). 70.10/10.67 thf(f4535,plain,( 70.10/10.67 spl37_114 | spl37_116 | spl37_117 | spl37_97), 70.10/10.67 inference(avatar_split_clause,[],[f4367,f2892,f3545,f3528,f3436])). 70.10/10.67 thf(f4536,plain,( 70.10/10.67 spl37_97 | spl37_118 | spl37_114 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4368,f3528,f3436,f3549,f2892])). 70.10/10.67 thf(f4537,plain,( 70.10/10.67 spl37_97 | spl37_117 | spl37_114 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f4370,f3524,f3436,f3545,f2892])). 70.10/10.67 thf(f4538,plain,( 70.10/10.67 spl37_97 | spl37_114 | spl37_115 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f4371,f3549,f3524,f3436,f2892])). 70.10/10.67 thf(f4539,plain,( 70.10/10.67 spl37_105 | spl37_118 | spl37_119 | spl37_106), 70.10/10.67 inference(avatar_split_clause,[],[f4378,f3188,f3553,f3549,f3131])). 70.10/10.67 thf(f4540,plain,( 70.10/10.67 spl37_106 | spl37_117 | spl37_119 | spl37_105), 70.10/10.67 inference(avatar_split_clause,[],[f4379,f3131,f3553,f3545,f3188])). 70.10/10.67 thf(f4541,plain,( 70.10/10.67 spl37_120 | spl37_118 | spl37_105 | spl37_106), 70.10/10.67 inference(avatar_split_clause,[],[f4382,f3188,f3131,f3549,f3590])). 70.10/10.67 thf(f4542,plain,( 70.10/10.67 spl37_117 | spl37_120 | spl37_106 | spl37_105), 70.10/10.67 inference(avatar_split_clause,[],[f4383,f3131,f3188,f3590,f3545])). 70.10/10.67 thf(f4543,plain,( 70.10/10.67 spl37_117 | spl37_105 | spl37_108 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f4387,f3524,f3242,f3131,f3545])). 70.10/10.67 thf(f4544,plain,( 70.10/10.67 spl37_108 | spl37_105 | spl37_118 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f4388,f3524,f3549,f3131,f3242])). 70.10/10.67 thf(f4545,plain,( 70.10/10.67 spl37_108 | spl37_105 | spl37_117 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4390,f3528,f3545,f3131,f3242])). 70.10/10.67 thf(f4546,plain,( 70.10/10.67 spl37_116 | spl37_108 | spl37_105 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f4391,f3549,f3131,f3242,f3528])). 70.10/10.67 thf(f4547,plain,( 70.10/10.67 spl37_116 | spl37_119 | spl37_105 | spl37_107), 70.10/10.67 inference(avatar_split_clause,[],[f4392,f3202,f3131,f3553,f3528])). 70.10/10.67 thf(f4548,plain,( 70.10/10.67 spl37_107 | spl37_115 | spl37_105 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f4393,f3553,f3131,f3524,f3202])). 70.10/10.67 thf(f4549,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4395])). 70.10/10.67 thf(f4550,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4397])). 70.10/10.67 thf(f4551,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4398])). 70.10/10.67 thf(f4552,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4400])). 70.10/10.67 thf(f4553,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4405])). 70.10/10.67 thf(f4554,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4407])). 70.10/10.67 thf(f4555,plain,( 70.10/10.67 spl37_107 | spl37_120 | spl37_105 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4408,f3528,f3131,f3590,f3202])). 70.10/10.67 thf(f4556,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4411])). 70.10/10.67 thf(f4557,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($true = ((qmltpeq @ (op @ e1 @ e1) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4413])). 70.10/10.67 thf(f4558,plain,( 70.10/10.67 spl37_115 | spl37_105 | spl37_120 | spl37_107), 70.10/10.67 inference(avatar_split_clause,[],[f4414,f3202,f3590,f3131,f3524])). 70.10/10.67 thf(f4559,plain,( 70.10/10.67 spl37_117 | spl37_119 | spl37_100 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f4421,f3524,f2901,f3553,f3545])). 70.10/10.67 thf(f4560,plain,( 70.10/10.67 spl37_116 | spl37_119 | spl37_100 | spl37_117), 70.10/10.67 inference(avatar_split_clause,[],[f4422,f3545,f2901,f3553,f3528])). 70.10/10.67 thf(f4561,plain,( 70.10/10.67 spl37_118 | spl37_119 | spl37_115 | spl37_100), 70.10/10.67 inference(avatar_split_clause,[],[f4424,f2901,f3524,f3553,f3549])). 70.10/10.67 thf(f4562,plain,( 70.10/10.67 spl37_118 | spl37_100 | spl37_116 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f4425,f3553,f3528,f2901,f3549])). 70.10/10.67 thf(f4563,plain,( 70.10/10.67 spl37_120 | spl37_117 | spl37_116 | spl37_100), 70.10/10.67 inference(avatar_split_clause,[],[f4430,f2901,f3528,f3545,f3590])). 70.10/10.67 thf(f4564,plain,( 70.10/10.67 spl37_100 | spl37_117 | spl37_120 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f4431,f3524,f3590,f3545,f2901])). 70.10/10.67 thf(f4565,plain,( 70.10/10.67 spl37_118 | spl37_115 | spl37_120 | spl37_100), 70.10/10.67 inference(avatar_split_clause,[],[f4433,f2901,f3590,f3524,f3549])). 70.10/10.67 thf(f4566,plain,( 70.10/10.67 spl37_116 | spl37_120 | spl37_100 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f4434,f3549,f2901,f3590,f3528])). 70.10/10.67 thf(f4582,plain,( 70.10/10.67 spl37_108 | spl37_115 | spl37_117 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f4460,f3308,f3545,f3524,f3242])). 70.10/10.67 thf(f4583,plain,( 70.10/10.67 spl37_116 | spl37_108 | spl37_113 | spl37_117), 70.10/10.67 inference(avatar_split_clause,[],[f4461,f3545,f3308,f3242,f3528])). 70.10/10.67 thf(f4584,plain,( 70.10/10.67 spl37_108 | spl37_118 | spl37_113 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f4462,f3524,f3308,f3549,f3242])). 70.10/10.67 thf(f4585,plain,( 70.10/10.67 spl37_108 | spl37_113 | spl37_118 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4463,f3528,f3549,f3308,f3242])). 70.10/10.67 thf(f4586,plain,( 70.10/10.67 spl37_119 | spl37_107 | spl37_113 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f4469,f3524,f3308,f3202,f3553])). 70.10/10.67 thf(f4587,plain,( 70.10/10.67 spl37_116 | spl37_113 | spl37_107 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f4470,f3553,f3202,f3308,f3528])). 70.10/10.67 thf(f4588,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4472])). 70.10/10.67 thf(f4589,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4474])). 70.10/10.67 thf(f4590,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4476])). 70.10/10.67 thf(f4591,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4477])). 70.10/10.67 thf(f4592,plain,( 70.10/10.67 spl37_119 | spl37_118 | spl37_113 | spl37_106), 70.10/10.67 inference(avatar_split_clause,[],[f4478,f3188,f3308,f3549,f3553])). 70.10/10.67 thf(f4593,plain,( 70.10/10.67 spl37_119 | spl37_113 | spl37_106 | spl37_117), 70.10/10.67 inference(avatar_split_clause,[],[f4479,f3545,f3188,f3308,f3553])). 70.10/10.67 thf(f4594,plain,( 70.10/10.67 spl37_113 | spl37_118 | spl37_120 | spl37_106), 70.10/10.67 inference(avatar_split_clause,[],[f4483,f3188,f3590,f3549,f3308])). 70.10/10.67 thf(f4595,plain,( 70.10/10.67 spl37_106 | spl37_117 | spl37_120 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f4484,f3308,f3590,f3545,f3188])). 70.10/10.67 thf(f4596,plain,( 70.10/10.67 spl37_113 | spl37_115 | spl37_120 | spl37_107), 70.10/10.67 inference(avatar_split_clause,[],[f4485,f3202,f3590,f3524,f3308])). 70.10/10.67 thf(f4597,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true)) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4486])). 70.10/10.67 thf(f4598,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | (((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4488])). 70.10/10.67 thf(f4599,plain,( 70.10/10.67 spl37_107 | spl37_120 | spl37_113 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4489,f3528,f3308,f3590,f3202])). 70.10/10.67 thf(f4600,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e3 @ e3) @ e2 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e3 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4490])). 70.10/10.67 thf(f4601,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X3))) | ($true = ((qmltpeq @ (op @ e3 @ e3) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4492])). 70.10/10.67 thf(f4602,plain,( 70.10/10.67 spl37_115 | spl37_107 | spl37_114 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4498,f3590,f3436,f3202,f3524])). 70.10/10.67 thf(f4603,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4500])). 70.10/10.67 thf(f4604,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : ((((qmltpeq @ (op @ e2 @ e2) @ e3 @ X3)) = $true) | ($false = ((mrel @ sK5 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X2))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X4))) | ($false = ((mrel @ sK5 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4501])). 70.10/10.67 thf(f4605,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4503])). 70.10/10.67 thf(f4606,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e2 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4504])). 70.10/10.67 thf(f4607,plain,( 70.10/10.67 spl37_115 | spl37_114 | spl37_107 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f4505,f3553,f3202,f3436,f3524])). 70.10/10.67 thf(f4608,plain,( 70.10/10.67 spl37_119 | spl37_116 | spl37_114 | spl37_107), 70.10/10.67 inference(avatar_split_clause,[],[f4506,f3202,f3436,f3528,f3553])). 70.10/10.67 thf(f4609,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | ($false = ((mrel @ sK5 @ X1))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X2))) | ($false = ((mrel @ sK5 @ X4))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4508])). 70.10/10.67 thf(f4610,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e3 @ e3) @ e2 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e1 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($false = ((mrel @ sK5 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4509])). 70.10/10.67 thf(f4611,plain,( 70.10/10.67 spl37_120 | spl37_114 | spl37_107 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4510,f3528,f3202,f3436,f3590])). 70.10/10.67 thf(f4612,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e3 @ X4))) | ($false = ((mrel @ sK5 @ X4))) | ($false = ((mrel @ sK5 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4512])). 70.10/10.67 thf(f4613,plain,( 70.10/10.67 ( ! [X2 : mworld,X3 : mworld,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK5 @ X1))) | ($false = ((mrel @ sK5 @ X3))) | (((qmltpeq @ (op @ e3 @ e3) @ e2 @ X2)) = $true) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e0 @ X3))) | ($true = ((qmltpeq @ (op @ e2 @ e2) @ e1 @ X1))) | ($false = ((mrel @ sK5 @ X2))) | (((qmltpeq @ (op @ e3 @ e3) @ e3 @ X4)) = $true) | ($false = ((mrel @ sK5 @ X4)))) )), 70.10/10.67 inference(imp_proxy_clausification,[],[f4514])). 70.10/10.67 thf(f4614,plain,( 70.10/10.67 spl37_116 | spl37_117 | spl37_108 | spl37_114), 70.10/10.67 inference(avatar_split_clause,[],[f4519,f3436,f3242,f3545,f3528])). 70.10/10.67 thf(f4615,plain,( 70.10/10.67 spl37_108 | spl37_115 | spl37_114 | spl37_117), 70.10/10.67 inference(avatar_split_clause,[],[f4520,f3545,f3436,f3524,f3242])). 70.10/10.67 thf(f4616,plain,( 70.10/10.67 spl37_118 | spl37_114 | spl37_108 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4521,f3528,f3242,f3436,f3549])). 70.10/10.67 thf(f4617,plain,( 70.10/10.67 spl37_114 | spl37_115 | spl37_118 | spl37_108), 70.10/10.67 inference(avatar_split_clause,[],[f4522,f3242,f3549,f3524,f3436])). 70.10/10.67 thf(f4618,plain,( 70.10/10.67 spl37_106 | spl37_117 | spl37_114 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f4526,f3553,f3436,f3545,f3188])). 70.10/10.67 thf(f4619,plain,( 70.10/10.67 spl37_119 | spl37_106 | spl37_114 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f4527,f3549,f3436,f3188,f3553])). 70.10/10.67 thf(f4620,plain,( 70.10/10.67 spl37_106 | spl37_114 | spl37_120 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f4528,f3549,f3590,f3436,f3188])). 70.10/10.67 thf(f4621,plain,( 70.10/10.67 spl37_120 | spl37_114 | spl37_106 | spl37_117), 70.10/10.67 inference(avatar_split_clause,[],[f4529,f3545,f3188,f3436,f3590])). 70.10/10.67 thf(f4622,plain,( 70.10/10.67 spl37_105 | spl37_115 | spl37_119 | spl37_117), 70.10/10.67 inference(avatar_split_clause,[],[f4549,f3545,f3553,f3524,f3131])). 70.10/10.67 thf(f4623,plain,( 70.10/10.67 spl37_119 | spl37_117 | spl37_105 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4550,f3528,f3131,f3545,f3553])). 70.10/10.67 thf(f4624,plain,( 70.10/10.67 spl37_119 | spl37_118 | spl37_115 | spl37_105), 70.10/10.67 inference(avatar_split_clause,[],[f4551,f3131,f3524,f3549,f3553])). 70.10/10.67 thf(f4625,plain,( 70.10/10.67 spl37_119 | spl37_116 | spl37_118 | spl37_105), 70.10/10.67 inference(avatar_split_clause,[],[f4552,f3131,f3549,f3528,f3553])). 70.10/10.67 thf(f4626,plain,( 70.10/10.67 spl37_116 | spl37_118 | spl37_120 | spl37_105), 70.10/10.67 inference(avatar_split_clause,[],[f4553,f3131,f3590,f3549,f3528])). 70.10/10.67 thf(f4627,plain,( 70.10/10.67 spl37_117 | spl37_116 | spl37_105 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4554,f3590,f3131,f3528,f3545])). 70.10/10.67 thf(f4628,plain,( 70.10/10.67 spl37_105 | spl37_118 | spl37_115 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4556,f3590,f3524,f3549,f3131])). 70.10/10.67 thf(f4629,plain,( 70.10/10.67 spl37_115 | spl37_105 | spl37_120 | spl37_117), 70.10/10.67 inference(avatar_split_clause,[],[f4557,f3545,f3590,f3131,f3524])). 70.10/10.67 thf(f4645,plain,( 70.10/10.67 spl37_113 | spl37_117 | spl37_115 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f4588,f3553,f3524,f3545,f3308])). 70.10/10.67 thf(f4646,plain,( 70.10/10.67 spl37_118 | spl37_113 | spl37_115 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f4589,f3553,f3524,f3308,f3549])). 70.10/10.67 thf(f4647,plain,( 70.10/10.67 spl37_116 | spl37_119 | spl37_113 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f4590,f3549,f3308,f3553,f3528])). 70.10/10.67 thf(f4648,plain,( 70.10/10.67 spl37_119 | spl37_116 | spl37_117 | spl37_113), 70.10/10.67 inference(avatar_split_clause,[],[f4591,f3308,f3545,f3528,f3553])). 70.10/10.67 thf(f4649,plain,( 70.10/10.67 spl37_117 | spl37_113 | spl37_115 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4597,f3590,f3524,f3308,f3545])). 70.10/10.67 thf(f4650,plain,( 70.10/10.67 spl37_115 | spl37_113 | spl37_120 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f4598,f3549,f3590,f3308,f3524])). 70.10/10.67 thf(f4651,plain,( 70.10/10.67 spl37_117 | spl37_113 | spl37_116 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4600,f3590,f3528,f3308,f3545])). 70.10/10.67 thf(f4652,plain,( 70.10/10.67 spl37_116 | spl37_120 | spl37_113 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f4601,f3549,f3308,f3590,f3528])). 70.10/10.67 thf(f4653,plain,( 70.10/10.67 spl37_120 | spl37_117 | spl37_114 | spl37_115), 70.10/10.67 inference(avatar_split_clause,[],[f4603,f3524,f3436,f3545,f3590])). 70.10/10.67 thf(f4654,plain,( 70.10/10.67 spl37_118 | spl37_115 | spl37_120 | spl37_114), 70.10/10.67 inference(avatar_split_clause,[],[f4604,f3436,f3590,f3524,f3549])). 70.10/10.67 thf(f4655,plain,( 70.10/10.67 spl37_114 | spl37_119 | spl37_115 | spl37_118), 70.10/10.67 inference(avatar_split_clause,[],[f4605,f3549,f3524,f3553,f3436])). 70.10/10.67 thf(f4656,plain,( 70.10/10.67 spl37_115 | spl37_114 | spl37_117 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f4606,f3553,f3545,f3436,f3524])). 70.10/10.67 thf(f4657,plain,( 70.10/10.67 spl37_116 | spl37_117 | spl37_114 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f4609,f3553,f3436,f3545,f3528])). 70.10/10.67 thf(f4658,plain,( 70.10/10.67 spl37_116 | spl37_114 | spl37_118 | spl37_119), 70.10/10.67 inference(avatar_split_clause,[],[f4610,f3553,f3549,f3436,f3528])). 70.10/10.67 thf(f4659,plain,( 70.10/10.67 spl37_116 | spl37_118 | spl37_114 | spl37_120), 70.10/10.67 inference(avatar_split_clause,[],[f4612,f3590,f3436,f3549,f3528])). 70.10/10.67 thf(f4660,plain,( 70.10/10.67 spl37_120 | spl37_117 | spl37_114 | spl37_116), 70.10/10.67 inference(avatar_split_clause,[],[f4613,f3528,f3436,f3545,f3590])). 70.10/10.67 thf(f5031,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK31))) | ($false = $true) | (~spl37_9 | ~spl37_113)), 70.10/10.67 inference(constrained_superposition,[],[f1192,f3309])). 70.10/10.67 thf(f5032,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK31))) | (~spl37_9 | ~spl37_113)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5031])). 70.10/10.67 thf(f5045,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK5))) | ($false = ((mrel @ X0 @ sK31))) | ($false = $true)) ) | (~spl37_9 | ~spl37_113)), 70.10/10.67 inference(constrained_superposition,[],[f441,f5032])). 70.10/10.67 thf(f5050,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK31))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_9 | ~spl37_113)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5045])). 70.10/10.67 thf(f5056,plain,( 70.10/10.67 ($false = $true) | ($false = ((mrel @ mactual @ sK5))) | (~spl37_8 | ~spl37_9 | ~spl37_113)), 70.10/10.67 inference(constrained_superposition,[],[f1188,f5050])). 70.10/10.67 thf(f5059,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | (~spl37_8 | ~spl37_9 | ~spl37_113)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5056])). 70.10/10.67 thf(f5065,plain,( 70.10/10.67 ($false = $true) | (~spl37_8 | ~spl37_9 | ~spl37_113)), 70.10/10.67 inference(constrained_superposition,[],[f5059,f537])). 70.10/10.67 thf(f5073,plain,( 70.10/10.67 $false | (~spl37_8 | ~spl37_9 | ~spl37_113)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5065])). 70.10/10.67 thf(f5074,plain,( 70.10/10.67 ~spl37_8 | ~spl37_9 | ~spl37_113), 70.10/10.67 inference(avatar_contradiction_clause,[],[f5073])). 70.10/10.67 thf(f5076,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK0))) | ($false = $true) | (~spl37_12 | ~spl37_100)), 70.10/10.67 inference(constrained_superposition,[],[f2902,f1208])). 70.10/10.67 thf(f5077,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK0))) | (~spl37_12 | ~spl37_100)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5076])). 70.10/10.67 thf(f5079,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK0))) | ($false = ((mrel @ X0 @ sK5))) | ($false = $true)) ) | (~spl37_12 | ~spl37_100)), 70.10/10.67 inference(constrained_superposition,[],[f5077,f441])). 70.10/10.67 thf(f5081,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK5))) | ($false = ((mrel @ X0 @ sK0)))) ) | (~spl37_12 | ~spl37_100)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5079])). 70.10/10.67 thf(f5086,plain,( 70.10/10.67 ($false = $true) | ($false = ((mrel @ mactual @ sK0))) | (~spl37_12 | ~spl37_100)), 70.10/10.67 inference(constrained_superposition,[],[f537,f5081])). 70.10/10.67 thf(f5092,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK0))) | (~spl37_12 | ~spl37_100)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5086])). 70.10/10.67 thf(f5097,plain,( 70.10/10.67 ($false = $true) | (~spl37_7 | ~spl37_12 | ~spl37_100)), 70.10/10.67 inference(constrained_superposition,[],[f1185,f5092])). 70.10/10.67 thf(f5101,plain,( 70.10/10.67 $false | (~spl37_7 | ~spl37_12 | ~spl37_100)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5097])). 70.10/10.67 thf(f5102,plain,( 70.10/10.67 ~spl37_7 | ~spl37_12 | ~spl37_100), 70.10/10.67 inference(avatar_contradiction_clause,[],[f5101])). 70.10/10.67 thf(f5105,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK34))) | ($false = $true) | (~spl37_32 | ~spl37_115)), 70.10/10.67 inference(constrained_superposition,[],[f3525,f1478])). 70.10/10.67 thf(f5107,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK34))) | (~spl37_32 | ~spl37_115)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5105])). 70.10/10.67 thf(f5110,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK5))) | ($false = $true) | ($false = ((mrel @ X0 @ sK34)))) ) | (~spl37_32 | ~spl37_115)), 70.10/10.67 inference(constrained_superposition,[],[f441,f5107])). 70.10/10.67 thf(f5111,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK34))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_32 | ~spl37_115)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5110])). 70.10/10.67 thf(f5113,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | ($false = $true) | (~spl37_32 | ~spl37_34 | ~spl37_115)), 70.10/10.67 inference(constrained_superposition,[],[f5111,f1486])). 70.10/10.67 thf(f5120,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | (~spl37_32 | ~spl37_34 | ~spl37_115)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5113])). 70.10/10.67 thf(f5127,plain,( 70.10/10.67 ($false = $true) | (~spl37_32 | ~spl37_34 | ~spl37_115)), 70.10/10.67 inference(constrained_superposition,[],[f537,f5120])). 70.10/10.67 thf(f5132,plain,( 70.10/10.67 $false | (~spl37_32 | ~spl37_34 | ~spl37_115)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5127])). 70.10/10.67 thf(f5133,plain,( 70.10/10.67 ~spl37_32 | ~spl37_34 | ~spl37_115), 70.10/10.67 inference(avatar_contradiction_clause,[],[f5132])). 70.10/10.67 thf(f5136,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))) | ($false = $true) | (~spl37_45 | ~spl37_117)), 70.10/10.67 inference(constrained_superposition,[],[f1615,f3546])). 70.10/10.67 thf(f5137,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))) | (~spl37_45 | ~spl37_117)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5136])). 70.10/10.67 thf(f5140,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))) | ($false = $true) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_45 | ~spl37_117)), 70.10/10.67 inference(constrained_superposition,[],[f441,f5137])). 70.10/10.67 thf(f5141,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ (sK36 @ e3 @ mactual @ (op @ e3 @ e3))))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_45 | ~spl37_117)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5140])). 70.10/10.67 thf(f5146,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | ($false = $true) | (~spl37_41 | ~spl37_45 | ~spl37_117)), 70.10/10.67 inference(constrained_superposition,[],[f1602,f5141])). 70.10/10.67 thf(f5151,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | (~spl37_41 | ~spl37_45 | ~spl37_117)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5146])). 70.10/10.67 thf(f5155,plain,( 70.10/10.67 ($false = $true) | (~spl37_41 | ~spl37_45 | ~spl37_117)), 70.10/10.67 inference(constrained_superposition,[],[f5151,f537])). 70.10/10.67 thf(f5162,plain,( 70.10/10.67 $false | (~spl37_41 | ~spl37_45 | ~spl37_117)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5155])). 70.10/10.67 thf(f5163,plain,( 70.10/10.67 ~spl37_41 | ~spl37_45 | ~spl37_117), 70.10/10.67 inference(avatar_contradiction_clause,[],[f5162])). 70.10/10.67 thf(f5165,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK17))) | ($false = $true) | (~spl37_43 | ~spl37_107)), 70.10/10.67 inference(constrained_superposition,[],[f1608,f3203])). 70.10/10.67 thf(f5167,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK17))) | (~spl37_43 | ~spl37_107)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5165])). 70.10/10.67 thf(f5169,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK17))) | ($false = $true) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_43 | ~spl37_107)), 70.10/10.67 inference(constrained_superposition,[],[f5167,f441])). 70.10/10.67 thf(f5171,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK17))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_43 | ~spl37_107)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5169])). 70.10/10.67 thf(f5176,plain,( 70.10/10.67 ($false = $true) | ($false = ((mrel @ mactual @ sK5))) | (~spl37_43 | ~spl37_48 | ~spl37_107)), 70.10/10.67 inference(constrained_superposition,[],[f1631,f5171])). 70.10/10.67 thf(f5179,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | (~spl37_43 | ~spl37_48 | ~spl37_107)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5176])). 70.10/10.67 thf(f5187,plain,( 70.10/10.67 ($false = $true) | (~spl37_43 | ~spl37_48 | ~spl37_107)), 70.10/10.67 inference(constrained_superposition,[],[f537,f5179])). 70.10/10.67 thf(f5193,plain,( 70.10/10.67 $false | (~spl37_43 | ~spl37_48 | ~spl37_107)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5187])). 70.10/10.67 thf(f5194,plain,( 70.10/10.67 ~spl37_43 | ~spl37_48 | ~spl37_107), 70.10/10.67 inference(avatar_contradiction_clause,[],[f5193])). 70.10/10.67 thf(f5196,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK29))) | ($false = $true) | (~spl37_18 | ~spl37_120)), 70.10/10.67 inference(constrained_superposition,[],[f1327,f3591])). 70.10/10.67 thf(f5197,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK29))) | (~spl37_18 | ~spl37_120)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5196])). 70.10/10.67 thf(f5200,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK5))) | (((mrel @ X0 @ sK29)) = $false) | ($false = $true)) ) | (~spl37_18 | ~spl37_120)), 70.10/10.67 inference(constrained_superposition,[],[f441,f5197])). 70.10/10.67 thf(f5201,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK5))) | (((mrel @ X0 @ sK29)) = $false)) ) | (~spl37_18 | ~spl37_120)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5200])). 70.10/10.67 thf(f5206,plain,( 70.10/10.67 ($false = $true) | ($false = ((mrel @ mactual @ sK29))) | (~spl37_18 | ~spl37_120)), 70.10/10.67 inference(constrained_superposition,[],[f537,f5201])). 70.10/10.67 thf(f5210,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK29))) | (~spl37_18 | ~spl37_120)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5206])). 70.10/10.67 thf(f5217,plain,( 70.10/10.67 ($false = $true) | (~spl37_18 | ~spl37_21 | ~spl37_120)), 70.10/10.67 inference(constrained_superposition,[],[f1337,f5210])). 70.10/10.67 thf(f5222,plain,( 70.10/10.67 $false | (~spl37_18 | ~spl37_21 | ~spl37_120)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5217])). 70.10/10.67 thf(f5223,plain,( 70.10/10.67 ~spl37_18 | ~spl37_21 | ~spl37_120), 70.10/10.67 inference(avatar_contradiction_clause,[],[f5222])). 70.10/10.67 thf(f5225,plain,( 70.10/10.67 ($false = $true) | ($false = ((mrel @ sK5 @ sK35))) | (~spl37_19 | ~spl37_119)), 70.10/10.67 inference(constrained_superposition,[],[f1330,f3554])). 70.10/10.67 thf(f5227,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK35))) | (~spl37_19 | ~spl37_119)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5225])). 70.10/10.67 thf(f5229,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK5))) | ($false = ((mrel @ X0 @ sK35))) | ($false = $true)) ) | (~spl37_19 | ~spl37_119)), 70.10/10.67 inference(constrained_superposition,[],[f5227,f441])). 70.10/10.67 thf(f5231,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK35))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_19 | ~spl37_119)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5229])). 70.10/10.67 thf(f5233,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | ($false = $true) | (~spl37_19 | ~spl37_22 | ~spl37_119)), 70.10/10.67 inference(constrained_superposition,[],[f5231,f1341])). 70.10/10.67 thf(f5242,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | (~spl37_19 | ~spl37_22 | ~spl37_119)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5233])). 70.10/10.67 thf(f5250,plain,( 70.10/10.67 ($false = $true) | (~spl37_19 | ~spl37_22 | ~spl37_119)), 70.10/10.67 inference(constrained_superposition,[],[f5242,f537])). 70.10/10.67 thf(f5257,plain,( 70.10/10.67 $false | (~spl37_19 | ~spl37_22 | ~spl37_119)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5250])). 70.10/10.67 thf(f5258,plain,( 70.10/10.67 ~spl37_19 | ~spl37_22 | ~spl37_119), 70.10/10.67 inference(avatar_contradiction_clause,[],[f5257])). 70.10/10.67 thf(f5260,plain,( 70.10/10.67 ($false = $true) | ($false = ((mrel @ sK5 @ sK6))) | (~spl37_36 | ~spl37_99)), 70.10/10.67 inference(constrained_superposition,[],[f2899,f1498])). 70.10/10.67 thf(f5261,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK6))) | (~spl37_36 | ~spl37_99)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5260])). 70.10/10.67 thf(f5264,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK6))) | ($false = ((mrel @ X0 @ sK5))) | ($false = $true)) ) | (~spl37_36 | ~spl37_99)), 70.10/10.67 inference(constrained_superposition,[],[f441,f5261])). 70.10/10.67 thf(f5265,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK6))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_36 | ~spl37_99)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5264])). 70.10/10.67 thf(f5272,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | ($false = $true) | (~spl37_29 | ~spl37_36 | ~spl37_99)), 70.10/10.67 inference(constrained_superposition,[],[f1469,f5265])). 70.10/10.67 thf(f5273,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | (~spl37_29 | ~spl37_36 | ~spl37_99)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5272])). 70.10/10.67 thf(f5282,plain,( 70.10/10.67 ($false = $true) | (~spl37_29 | ~spl37_36 | ~spl37_99)), 70.10/10.67 inference(constrained_superposition,[],[f537,f5273])). 70.10/10.67 thf(f5286,plain,( 70.10/10.67 $false | (~spl37_29 | ~spl37_36 | ~spl37_99)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5282])). 70.10/10.67 thf(f5287,plain,( 70.10/10.67 ~spl37_29 | ~spl37_36 | ~spl37_99), 70.10/10.67 inference(avatar_contradiction_clause,[],[f5286])). 70.10/10.67 thf(f5293,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK18))) | ($false = $true) | (~spl37_35 | ~spl37_106)), 70.10/10.67 inference(constrained_superposition,[],[f1491,f3189])). 70.10/10.67 thf(f5297,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK18))) | (~spl37_35 | ~spl37_106)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5293])). 70.10/10.67 thf(f5325,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK5))) | ($false = ((mrel @ X0 @ sK18))) | ($false = $true)) ) | (~spl37_35 | ~spl37_106)), 70.10/10.67 inference(constrained_superposition,[],[f5297,f441])). 70.10/10.67 thf(f5327,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK18))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_35 | ~spl37_106)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5325])). 70.10/10.67 thf(f5334,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | ($false = $true) | (~spl37_31 | ~spl37_35 | ~spl37_106)), 70.10/10.67 inference(constrained_superposition,[],[f1475,f5327])). 70.10/10.67 thf(f5335,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | (~spl37_31 | ~spl37_35 | ~spl37_106)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5334])). 70.10/10.67 thf(f5344,plain,( 70.10/10.67 ($false = $true) | (~spl37_31 | ~spl37_35 | ~spl37_106)), 70.10/10.67 inference(constrained_superposition,[],[f537,f5335])). 70.10/10.67 thf(f5349,plain,( 70.10/10.67 $false | (~spl37_31 | ~spl37_35 | ~spl37_106)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5344])). 70.10/10.67 thf(f5350,plain,( 70.10/10.67 ~spl37_31 | ~spl37_35 | ~spl37_106), 70.10/10.67 inference(avatar_contradiction_clause,[],[f5349])). 70.10/10.67 thf(f5351,plain,( 70.10/10.67 ($false = $true) | ($false = ((mrel @ sK5 @ sK30))) | (~spl37_10 | ~spl37_114)), 70.10/10.67 inference(constrained_superposition,[],[f1196,f3437])). 70.10/10.67 thf(f5353,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK30))) | (~spl37_10 | ~spl37_114)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5351])). 70.10/10.67 thf(f5355,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK30))) | ($false = $true) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_10 | ~spl37_114)), 70.10/10.67 inference(constrained_superposition,[],[f5353,f441])). 70.10/10.67 thf(f5357,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK30))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_10 | ~spl37_114)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5355])). 70.10/10.67 thf(f5364,plain,( 70.10/10.67 ($false = $true) | ($false = ((mrel @ mactual @ sK5))) | (~spl37_6 | ~spl37_10 | ~spl37_114)), 70.10/10.67 inference(constrained_superposition,[],[f1182,f5357])). 70.10/10.67 thf(f5366,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | (~spl37_6 | ~spl37_10 | ~spl37_114)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5364])). 70.10/10.67 thf(f5388,plain,( 70.10/10.67 ($false = $true) | (~spl37_6 | ~spl37_10 | ~spl37_114)), 70.10/10.67 inference(constrained_superposition,[],[f537,f5366])). 70.10/10.67 thf(f5393,plain,( 70.10/10.67 $false | (~spl37_6 | ~spl37_10 | ~spl37_114)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5388])). 70.10/10.67 thf(f5394,plain,( 70.10/10.67 ~spl37_6 | ~spl37_10 | ~spl37_114), 70.10/10.67 inference(avatar_contradiction_clause,[],[f5393])). 70.10/10.67 thf(f5397,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK25))) | ($false = $true) | (~spl37_46 | ~spl37_98)), 70.10/10.67 inference(constrained_superposition,[],[f2896,f1619])). 70.10/10.67 thf(f5399,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK25))) | (~spl37_46 | ~spl37_98)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5397])). 70.10/10.67 thf(f5413,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK5))) | ($false = ((mrel @ X0 @ sK25))) | ($false = $true)) ) | (~spl37_46 | ~spl37_98)), 70.10/10.67 inference(constrained_superposition,[],[f5399,f441])). 70.10/10.67 thf(f5415,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK25))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_46 | ~spl37_98)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5413])). 70.10/10.67 thf(f5419,plain,( 70.10/10.67 ($false = $true) | ($false = ((mrel @ mactual @ sK5))) | (~spl37_42 | ~spl37_46 | ~spl37_98)), 70.10/10.67 inference(constrained_superposition,[],[f5415,f1605])). 70.10/10.67 thf(f5423,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | (~spl37_42 | ~spl37_46 | ~spl37_98)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5419])). 70.10/10.67 thf(f5432,plain,( 70.10/10.67 ($false = $true) | (~spl37_42 | ~spl37_46 | ~spl37_98)), 70.10/10.67 inference(constrained_superposition,[],[f537,f5423])). 70.10/10.67 thf(f5437,plain,( 70.10/10.67 $false | (~spl37_42 | ~spl37_46 | ~spl37_98)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5432])). 70.10/10.67 thf(f5438,plain,( 70.10/10.67 ~spl37_42 | ~spl37_46 | ~spl37_98), 70.10/10.67 inference(avatar_contradiction_clause,[],[f5437])). 70.10/10.67 thf(f5449,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK11))) | ($false = $true) | (~spl37_23 | ~spl37_108)), 70.10/10.67 inference(constrained_superposition,[],[f1346,f3243])). 70.10/10.67 thf(f5451,plain,( 70.10/10.67 ($false = ((mrel @ sK5 @ sK11))) | (~spl37_23 | ~spl37_108)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5449])). 70.10/10.67 thf(f5454,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = $true) | ($false = ((mrel @ X0 @ sK5))) | ($false = ((mrel @ X0 @ sK11)))) ) | (~spl37_23 | ~spl37_108)), 70.10/10.67 inference(constrained_superposition,[],[f441,f5451])). 70.10/10.67 thf(f5455,plain,( 70.10/10.67 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK11))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_23 | ~spl37_108)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5454])). 70.10/10.67 thf(f5470,plain,( 70.10/10.67 ($false = $true) | ($false = ((mrel @ mactual @ sK5))) | (~spl37_20 | ~spl37_23 | ~spl37_108)), 70.10/10.67 inference(constrained_superposition,[],[f1333,f5455])). 70.10/10.67 thf(f5475,plain,( 70.10/10.67 ($false = ((mrel @ mactual @ sK5))) | (~spl37_20 | ~spl37_23 | ~spl37_108)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5470])). 70.10/10.67 thf(f5484,plain,( 70.10/10.67 ($false = $true) | (~spl37_20 | ~spl37_23 | ~spl37_108)), 70.10/10.67 inference(constrained_superposition,[],[f537,f5475])). 70.10/10.67 thf(f5487,plain,( 70.10/10.67 $false | (~spl37_20 | ~spl37_23 | ~spl37_108)), 70.10/10.67 inference(trivial_inequality_removal,[],[f5484])). 70.10/10.67 thf(f5488,plain,( 70.10/10.67 ~spl37_20 | ~spl37_23 | ~spl37_108), 70.10/10.67 inference(avatar_contradiction_clause,[],[f5487])). 70.10/10.67 thf(f5491,plain,( 70.10/10.67 ($false = $true) | ($false = ((mrel @ sK5 @ sK7))) | (~spl37_17 | ~spl37_97)), 70.10/10.68 inference(constrained_superposition,[],[f1324,f2893])). 70.10/10.68 thf(f5493,plain,( 70.10/10.68 ($false = ((mrel @ sK5 @ sK7))) | (~spl37_17 | ~spl37_97)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5491])). 70.10/10.68 thf(f5495,plain,( 70.10/10.68 ( ! [X0 : mworld] : (($false = $true) | ($false = ((mrel @ X0 @ sK7))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_17 | ~spl37_97)), 70.10/10.68 inference(constrained_superposition,[],[f5493,f441])). 70.10/10.68 thf(f5497,plain,( 70.10/10.68 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK7))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_17 | ~spl37_97)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5495])). 70.10/10.68 thf(f5508,plain,( 70.10/10.68 ($false = ((mrel @ mactual @ sK5))) | ($false = $true) | (~spl37_17 | ~spl37_24 | ~spl37_97)), 70.10/10.68 inference(constrained_superposition,[],[f1353,f5497])). 70.10/10.68 thf(f5510,plain,( 70.10/10.68 ($false = ((mrel @ mactual @ sK5))) | (~spl37_17 | ~spl37_24 | ~spl37_97)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5508])). 70.10/10.68 thf(f5520,plain,( 70.10/10.68 ($false = $true) | (~spl37_17 | ~spl37_24 | ~spl37_97)), 70.10/10.68 inference(constrained_superposition,[],[f5510,f537])). 70.10/10.68 thf(f5526,plain,( 70.10/10.68 $false | (~spl37_17 | ~spl37_24 | ~spl37_97)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5520])). 70.10/10.68 thf(f5527,plain,( 70.10/10.68 ~spl37_17 | ~spl37_24 | ~spl37_97), 70.10/10.68 inference(avatar_contradiction_clause,[],[f5526])). 70.10/10.68 thf(f5543,plain,( 70.10/10.68 ($false = ((mrel @ sK5 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | ($false = $true) | (~spl37_30 | ~spl37_116)), 70.10/10.68 inference(constrained_superposition,[],[f1472,f3529])). 70.10/10.68 thf(f5545,plain,( 70.10/10.68 ($false = ((mrel @ sK5 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | (~spl37_30 | ~spl37_116)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5543])). 70.10/10.68 thf(f5548,plain,( 70.10/10.68 ( ! [X0 : mworld] : (($false = $true) | ($false = ((mrel @ X0 @ sK5))) | ($false = ((mrel @ X0 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3)))))) ) | (~spl37_30 | ~spl37_116)), 70.10/10.68 inference(constrained_superposition,[],[f441,f5545])). 70.10/10.68 thf(f5549,plain,( 70.10/10.68 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ (sK36 @ e2 @ mactual @ (op @ e3 @ e3))))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_30 | ~spl37_116)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5548])). 70.10/10.68 thf(f5556,plain,( 70.10/10.68 ($false = $true) | ($false = ((mrel @ mactual @ sK5))) | (~spl37_30 | ~spl37_33 | ~spl37_116)), 70.10/10.68 inference(constrained_superposition,[],[f1482,f5549])). 70.10/10.68 thf(f5557,plain,( 70.10/10.68 ($false = ((mrel @ mactual @ sK5))) | (~spl37_30 | ~spl37_33 | ~spl37_116)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5556])). 70.10/10.68 thf(f5564,plain,( 70.10/10.68 ($false = $true) | (~spl37_30 | ~spl37_33 | ~spl37_116)), 70.10/10.68 inference(constrained_superposition,[],[f5557,f537])). 70.10/10.68 thf(f5570,plain,( 70.10/10.68 $false | (~spl37_30 | ~spl37_33 | ~spl37_116)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5564])). 70.10/10.68 thf(f5571,plain,( 70.10/10.68 ~spl37_30 | ~spl37_33 | ~spl37_116), 70.10/10.68 inference(avatar_contradiction_clause,[],[f5570])). 70.10/10.68 thf(f5583,plain,( 70.10/10.68 (((mrel @ sK5 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))) = $false) | ($false = $true) | (~spl37_44 | ~spl37_118)), 70.10/10.68 inference(constrained_superposition,[],[f3550,f1611])). 70.10/10.68 thf(f5587,plain,( 70.10/10.68 (((mrel @ sK5 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2)))) = $false) | (~spl37_44 | ~spl37_118)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5583])). 70.10/10.68 thf(f5674,plain,( 70.10/10.68 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = ((mrel @ X0 @ sK5))) | ($false = $true)) ) | (~spl37_44 | ~spl37_118)), 70.10/10.68 inference(constrained_superposition,[],[f441,f5587])). 70.10/10.68 thf(f5675,plain,( 70.10/10.68 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ (sK36 @ e3 @ mactual @ (op @ e2 @ e2))))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_44 | ~spl37_118)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5674])). 70.10/10.68 thf(f5758,plain,( 70.10/10.68 ($false = ((mrel @ mactual @ sK5))) | ($false = $true) | (~spl37_44 | ~spl37_47 | ~spl37_118)), 70.10/10.68 inference(constrained_superposition,[],[f1624,f5675])). 70.10/10.68 thf(f5759,plain,( 70.10/10.68 ($false = ((mrel @ mactual @ sK5))) | (~spl37_44 | ~spl37_47 | ~spl37_118)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5758])). 70.10/10.68 thf(f5768,plain,( 70.10/10.68 ($false = $true) | (~spl37_44 | ~spl37_47 | ~spl37_118)), 70.10/10.68 inference(constrained_superposition,[],[f537,f5759])). 70.10/10.68 thf(f5772,plain,( 70.10/10.68 $false | (~spl37_44 | ~spl37_47 | ~spl37_118)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5768])). 70.10/10.68 thf(f5773,plain,( 70.10/10.68 ~spl37_44 | ~spl37_47 | ~spl37_118), 70.10/10.68 inference(avatar_contradiction_clause,[],[f5772])). 70.10/10.68 thf(f5776,plain,( 70.10/10.68 ($false = $true) | ($false = ((mrel @ sK5 @ sK12))) | (~spl37_11 | ~spl37_105)), 70.10/10.68 inference(constrained_superposition,[],[f1201,f3132])). 70.10/10.68 thf(f5780,plain,( 70.10/10.68 ($false = ((mrel @ sK5 @ sK12))) | (~spl37_11 | ~spl37_105)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5776])). 70.10/10.68 thf(f5794,plain,( 70.10/10.68 ( ! [X0 : mworld] : (($false = $true) | ($false = ((mrel @ X0 @ sK12))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_11 | ~spl37_105)), 70.10/10.68 inference(constrained_superposition,[],[f441,f5780])). 70.10/10.68 thf(f5795,plain,( 70.10/10.68 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ sK12))) | ($false = ((mrel @ X0 @ sK5)))) ) | (~spl37_11 | ~spl37_105)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5794])). 70.10/10.68 thf(f5799,plain,( 70.10/10.68 ($false = $true) | ($false = ((mrel @ mactual @ sK5))) | (~spl37_5 | ~spl37_11 | ~spl37_105)), 70.10/10.68 inference(constrained_superposition,[],[f5795,f1179])). 70.10/10.68 thf(f5804,plain,( 70.10/10.68 ($false = ((mrel @ mactual @ sK5))) | (~spl37_5 | ~spl37_11 | ~spl37_105)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5799])). 70.10/10.68 thf(f5810,plain,( 70.10/10.68 ($false = $true) | (~spl37_5 | ~spl37_11 | ~spl37_105)), 70.10/10.68 inference(constrained_superposition,[],[f5804,f537])). 70.10/10.68 thf(f5815,plain,( 70.10/10.68 $false | (~spl37_5 | ~spl37_11 | ~spl37_105)), 70.10/10.68 inference(trivial_inequality_removal,[],[f5810])). 70.10/10.68 thf(f5816,plain,( 70.10/10.68 ~spl37_5 | ~spl37_11 | ~spl37_105), 70.10/10.68 inference(avatar_contradiction_clause,[],[f5815])). 70.10/10.68 cnf(s2, plain, spl37_5 | spl37_6 | spl37_7 | spl37_8, inference(sat_conversion,[],[f1189])). 70.10/10.68 cnf(s3, plain, spl37_5 | spl37_6 | spl37_7 | spl37_9, inference(sat_conversion,[],[f1193])). 70.10/10.68 cnf(s4, plain, spl37_5 | spl37_7 | spl37_9 | spl37_10, inference(sat_conversion,[],[f1197])). 70.10/10.68 cnf(s5, plain, spl37_5 | spl37_7 | spl37_8 | spl37_10, inference(sat_conversion,[],[f1198])). 70.10/10.68 cnf(s6, plain, spl37_6 | spl37_7 | spl37_8 | spl37_11, inference(sat_conversion,[],[f1202])). 70.10/10.68 cnf(s7, plain, spl37_6 | spl37_7 | spl37_9 | spl37_11, inference(sat_conversion,[],[f1203])). 70.10/10.68 cnf(s8, plain, spl37_7 | spl37_9 | spl37_10 | spl37_11, inference(sat_conversion,[],[f1204])). 70.10/10.68 cnf(s9, plain, spl37_7 | spl37_8 | spl37_10 | spl37_11, inference(sat_conversion,[],[f1205])). 70.10/10.68 cnf(s10, plain, spl37_5 | spl37_9 | spl37_10 | spl37_12, inference(sat_conversion,[],[f1209])). 70.10/10.68 cnf(s11, plain, spl37_5 | spl37_6 | spl37_9 | spl37_12, inference(sat_conversion,[],[f1210])). 70.10/10.68 cnf(s12, plain, spl37_5 | spl37_6 | spl37_8 | spl37_12, inference(sat_conversion,[],[f1211])). 70.10/10.68 cnf(s13, plain, spl37_5 | spl37_8 | spl37_10 | spl37_12, inference(sat_conversion,[],[f1212])). 70.10/10.68 cnf(s14, plain, spl37_8 | spl37_10 | spl37_11 | spl37_12, inference(sat_conversion,[],[f1213])). 70.10/10.68 cnf(s15, plain, spl37_6 | spl37_8 | spl37_11 | spl37_12, inference(sat_conversion,[],[f1214])). 70.10/10.68 cnf(s16, plain, spl37_6 | spl37_9 | spl37_11 | spl37_12, inference(sat_conversion,[],[f1215])). 70.10/10.68 cnf(s17, plain, spl37_9 | spl37_10 | spl37_11 | spl37_12, inference(sat_conversion,[],[f1216])). 70.10/10.68 cnf(s19, plain, spl37_17 | spl37_18 | spl37_19 | spl37_20, inference(sat_conversion,[],[f1334])). 70.10/10.68 cnf(s20, plain, spl37_17 | spl37_19 | spl37_20 | spl37_21, inference(sat_conversion,[],[f1338])). 70.10/10.68 cnf(s21, plain, spl37_17 | spl37_18 | spl37_20 | spl37_22, inference(sat_conversion,[],[f1342])). 70.10/10.68 cnf(s22, plain, spl37_17 | spl37_20 | spl37_21 | spl37_22, inference(sat_conversion,[],[f1343])). 70.10/10.68 cnf(s23, plain, spl37_17 | spl37_18 | spl37_19 | spl37_23, inference(sat_conversion,[],[f1347])). 70.10/10.68 cnf(s24, plain, spl37_17 | spl37_18 | spl37_22 | spl37_23, inference(sat_conversion,[],[f1348])). 70.10/10.68 cnf(s25, plain, spl37_17 | spl37_21 | spl37_22 | spl37_23, inference(sat_conversion,[],[f1349])). 70.10/10.68 cnf(s26, plain, spl37_17 | spl37_19 | spl37_21 | spl37_23, inference(sat_conversion,[],[f1350])). 70.10/10.68 cnf(s27, plain, spl37_19 | spl37_21 | spl37_23 | spl37_24, inference(sat_conversion,[],[f1354])). 70.10/10.68 cnf(s28, plain, spl37_21 | spl37_22 | spl37_23 | spl37_24, inference(sat_conversion,[],[f1355])). 70.10/10.68 cnf(s29, plain, spl37_18 | spl37_19 | spl37_23 | spl37_24, inference(sat_conversion,[],[f1356])). 70.10/10.68 cnf(s30, plain, spl37_18 | spl37_22 | spl37_23 | spl37_24, inference(sat_conversion,[],[f1357])). 70.10/10.68 cnf(s31, plain, spl37_19 | spl37_20 | spl37_21 | spl37_24, inference(sat_conversion,[],[f1358])). 70.10/10.68 cnf(s32, plain, spl37_18 | spl37_19 | spl37_20 | spl37_24, inference(sat_conversion,[],[f1359])). 70.10/10.68 cnf(s33, plain, spl37_20 | spl37_21 | spl37_22 | spl37_24, inference(sat_conversion,[],[f1360])). 70.10/10.68 cnf(s34, plain, spl37_18 | spl37_20 | spl37_22 | spl37_24, inference(sat_conversion,[],[f1361])). 70.10/10.68 cnf(s36, plain, spl37_29 | spl37_30 | spl37_31 | spl37_32, inference(sat_conversion,[],[f1479])). 70.10/10.68 cnf(s37, plain, spl37_29 | spl37_31 | spl37_32 | spl37_33, inference(sat_conversion,[],[f1483])). 70.10/10.68 cnf(s38, plain, spl37_29 | spl37_31 | spl37_33 | spl37_34, inference(sat_conversion,[],[f1487])). 70.10/10.68 cnf(s39, plain, spl37_29 | spl37_30 | spl37_31 | spl37_34, inference(sat_conversion,[],[f1488])). 70.10/10.68 cnf(s40, plain, spl37_29 | spl37_30 | spl37_32 | spl37_35, inference(sat_conversion,[],[f1492])). 70.10/10.68 cnf(s41, plain, spl37_29 | spl37_32 | spl37_33 | spl37_35, inference(sat_conversion,[],[f1493])). 70.10/10.68 cnf(s42, plain, spl37_29 | spl37_33 | spl37_34 | spl37_35, inference(sat_conversion,[],[f1494])). 70.10/10.68 cnf(s43, plain, spl37_29 | spl37_30 | spl37_34 | spl37_35, inference(sat_conversion,[],[f1495])). 70.10/10.68 cnf(s44, plain, spl37_33 | spl37_34 | spl37_35 | spl37_36, inference(sat_conversion,[],[f1499])). 70.10/10.68 cnf(s45, plain, spl37_30 | spl37_34 | spl37_35 | spl37_36, inference(sat_conversion,[],[f1500])). 70.10/10.68 cnf(s46, plain, spl37_30 | spl37_32 | spl37_35 | spl37_36, inference(sat_conversion,[],[f1501])). 70.10/10.68 cnf(s47, plain, spl37_32 | spl37_33 | spl37_35 | spl37_36, inference(sat_conversion,[],[f1502])). 70.10/10.68 cnf(s48, plain, spl37_31 | spl37_33 | spl37_34 | spl37_36, inference(sat_conversion,[],[f1503])). 70.10/10.68 cnf(s49, plain, spl37_30 | spl37_31 | spl37_34 | spl37_36, inference(sat_conversion,[],[f1504])). 70.10/10.68 cnf(s50, plain, spl37_30 | spl37_31 | spl37_32 | spl37_36, inference(sat_conversion,[],[f1505])). 70.10/10.68 cnf(s51, plain, spl37_31 | spl37_32 | spl37_33 | spl37_36, inference(sat_conversion,[],[f1506])). 70.10/10.68 cnf(s53, plain, spl37_41 | spl37_42 | spl37_43 | spl37_44, inference(sat_conversion,[],[f1612])). 70.10/10.68 cnf(s54, plain, spl37_42 | spl37_43 | spl37_44 | spl37_45, inference(sat_conversion,[],[f1616])). 70.10/10.68 cnf(s55, plain, spl37_41 | spl37_43 | spl37_44 | spl37_46, inference(sat_conversion,[],[f1620])). 70.10/10.68 cnf(s56, plain, spl37_43 | spl37_44 | spl37_45 | spl37_46, inference(sat_conversion,[],[f1621])). 70.10/10.68 cnf(s57, plain, spl37_41 | spl37_43 | spl37_46 | spl37_47, inference(sat_conversion,[],[f1625])). 70.10/10.68 cnf(s58, plain, spl37_41 | spl37_42 | spl37_43 | spl37_47, inference(sat_conversion,[],[f1626])). 70.10/10.68 cnf(s59, plain, spl37_42 | spl37_43 | spl37_45 | spl37_47, inference(sat_conversion,[],[f1627])). 70.10/10.68 cnf(s60, plain, spl37_43 | spl37_45 | spl37_46 | spl37_47, inference(sat_conversion,[],[f1628])). 70.10/10.68 cnf(s61, plain, spl37_41 | spl37_42 | spl37_47 | spl37_48, inference(sat_conversion,[],[f1632])). 70.10/10.68 cnf(s62, plain, spl37_41 | spl37_46 | spl37_47 | spl37_48, inference(sat_conversion,[],[f1633])). 70.10/10.68 cnf(s63, plain, spl37_41 | spl37_42 | spl37_44 | spl37_48, inference(sat_conversion,[],[f1634])). 70.10/10.68 cnf(s64, plain, spl37_41 | spl37_44 | spl37_46 | spl37_48, inference(sat_conversion,[],[f1635])). 70.10/10.68 cnf(s65, plain, spl37_42 | spl37_45 | spl37_47 | spl37_48, inference(sat_conversion,[],[f1636])). 70.10/10.68 cnf(s66, plain, spl37_45 | spl37_46 | spl37_47 | spl37_48, inference(sat_conversion,[],[f1637])). 70.10/10.68 cnf(s67, plain, spl37_42 | spl37_44 | spl37_45 | spl37_48, inference(sat_conversion,[],[f1638])). 70.10/10.68 cnf(s68, plain, spl37_44 | spl37_45 | spl37_46 | spl37_48, inference(sat_conversion,[],[f1639])). 70.10/10.68 cnf(s81, plain, spl37_97 | spl37_98 | spl37_99 | spl37_100, inference(sat_conversion,[],[f2903])). 70.10/10.68 cnf(s83, plain, spl37_97 | spl37_98 | spl37_99 | spl37_105, inference(sat_conversion,[],[f3133])). 70.10/10.68 cnf(s84, plain, spl37_97 | spl37_98 | spl37_100 | spl37_106, inference(sat_conversion,[],[f3190])). 70.10/10.68 cnf(s85, plain, spl37_97 | spl37_99 | spl37_100 | spl37_107, inference(sat_conversion,[],[f3204])). 70.10/10.68 cnf(s86, plain, spl37_98 | spl37_99 | spl37_100 | spl37_108, inference(sat_conversion,[],[f3244])). 70.10/10.68 cnf(s88, plain, spl37_97 | spl37_98 | spl37_99 | spl37_113, inference(sat_conversion,[],[f3310])). 70.10/10.68 cnf(s89, plain, spl37_97 | spl37_98 | spl37_99 | spl37_114, inference(sat_conversion,[],[f3438])). 70.10/10.68 cnf(s90, plain, spl37_97 | spl37_99 | spl37_105 | spl37_107, inference(sat_conversion,[],[f3456])). 70.10/10.68 cnf(s91, plain, spl37_97 | spl37_98 | spl37_105 | spl37_106, inference(sat_conversion,[],[f3469])). 70.10/10.68 cnf(s92, plain, spl37_98 | spl37_99 | spl37_105 | spl37_108, inference(sat_conversion,[],[f3509])). 70.10/10.68 cnf(s93, plain, spl37_97 | spl37_98 | spl37_100 | spl37_115, inference(sat_conversion,[],[f3526])). 70.10/10.68 cnf(s94, plain, spl37_97 | spl37_98 | spl37_100 | spl37_116, inference(sat_conversion,[],[f3530])). 70.10/10.68 cnf(s95, plain, spl37_97 | spl37_100 | spl37_106 | spl37_107, inference(sat_conversion,[],[f3531])). 70.10/10.68 cnf(s96, plain, spl37_97 | spl37_99 | spl37_100 | spl37_117, inference(sat_conversion,[],[f3547])). 70.10/10.68 cnf(s97, plain, spl37_97 | spl37_99 | spl37_100 | spl37_118, inference(sat_conversion,[],[f3551])). 70.10/10.68 cnf(s98, plain, spl37_98 | spl37_99 | spl37_100 | spl37_119, inference(sat_conversion,[],[f3555])). 70.10/10.68 cnf(s99, plain, spl37_98 | spl37_99 | spl37_100 | spl37_120, inference(sat_conversion,[],[f3592])). 70.10/10.68 cnf(s100, plain, spl37_98 | spl37_100 | spl37_106 | spl37_108, inference(sat_conversion,[],[f3600])). 70.10/10.68 cnf(s101, plain, spl37_99 | spl37_100 | spl37_107 | spl37_108, inference(sat_conversion,[],[f3603])). 70.10/10.68 cnf(s103, plain, spl37_97 | spl37_99 | spl37_107 | spl37_113, inference(sat_conversion,[],[f3645])). 70.10/10.68 cnf(s104, plain, spl37_97 | spl37_98 | spl37_106 | spl37_113, inference(sat_conversion,[],[f3664])). 70.10/10.68 cnf(s105, plain, spl37_98 | spl37_99 | spl37_108 | spl37_113, inference(sat_conversion,[],[f3665])). 70.10/10.68 cnf(s106, plain, spl37_98 | spl37_99 | spl37_108 | spl37_114, inference(sat_conversion,[],[f3785])). 70.10/10.68 cnf(s107, plain, spl37_97 | spl37_98 | spl37_106 | spl37_114, inference(sat_conversion,[],[f3788])). 70.10/10.68 cnf(s108, plain, spl37_97 | spl37_99 | spl37_107 | spl37_114, inference(sat_conversion,[],[f3789])). 70.10/10.68 cnf(s109, plain, spl37_97 | spl37_99 | spl37_105 | spl37_117, inference(sat_conversion,[],[f3802])). 70.10/10.68 cnf(s110, plain, spl37_97 | spl37_99 | spl37_105 | spl37_118, inference(sat_conversion,[],[f3803])). 70.10/10.68 cnf(s111, plain, spl37_97 | spl37_105 | spl37_106 | spl37_107, inference(sat_conversion,[],[f3814])). 70.10/10.68 cnf(s112, plain, spl37_97 | spl37_98 | spl37_105 | spl37_116, inference(sat_conversion,[],[f3815])). 70.10/10.68 cnf(s113, plain, spl37_97 | spl37_98 | spl37_105 | spl37_115, inference(sat_conversion,[],[f3816])). 70.10/10.68 cnf(s114, plain, spl37_98 | spl37_105 | spl37_106 | spl37_108, inference(sat_conversion,[],[f3833])). 70.10/10.68 cnf(s115, plain, spl37_99 | spl37_105 | spl37_107 | spl37_108, inference(sat_conversion,[],[f3863])). 70.10/10.68 cnf(s116, plain, spl37_98 | spl37_99 | spl37_105 | spl37_120, inference(sat_conversion,[],[f3868])). 70.10/10.68 cnf(s117, plain, spl37_98 | spl37_99 | spl37_105 | spl37_119, inference(sat_conversion,[],[f3874])). 70.10/10.68 cnf(s118, plain, spl37_97 | spl37_100 | spl37_107 | spl37_115, inference(sat_conversion,[],[f3875])). 70.10/10.68 cnf(s119, plain, spl37_97 | spl37_100 | spl37_107 | spl37_116, inference(sat_conversion,[],[f3876])). 70.10/10.68 cnf(s120, plain, spl37_97 | spl37_100 | spl37_106 | spl37_118, inference(sat_conversion,[],[f3881])). 70.10/10.68 cnf(s121, plain, spl37_97 | spl37_100 | spl37_106 | spl37_117, inference(sat_conversion,[],[f3882])). 70.10/10.68 cnf(s122, plain, spl37_98 | spl37_100 | spl37_106 | spl37_119, inference(sat_conversion,[],[f3883])). 70.10/10.68 cnf(s123, plain, spl37_99 | spl37_100 | spl37_107 | spl37_119, inference(sat_conversion,[],[f3886])). 70.10/10.68 cnf(s124, plain, spl37_99 | spl37_100 | spl37_107 | spl37_120, inference(sat_conversion,[],[f3907])). 70.10/10.68 cnf(s125, plain, spl37_98 | spl37_100 | spl37_106 | spl37_120, inference(sat_conversion,[],[f3918])). 70.10/10.68 cnf(s126, plain, spl37_98 | spl37_100 | spl37_108 | spl37_115, inference(sat_conversion,[],[f3921])). 70.10/10.68 cnf(s127, plain, spl37_98 | spl37_100 | spl37_108 | spl37_116, inference(sat_conversion,[],[f3922])). 70.10/10.68 cnf(s128, plain, spl37_99 | spl37_100 | spl37_108 | spl37_117, inference(sat_conversion,[],[f3923])). 70.10/10.68 cnf(s129, plain, spl37_99 | spl37_100 | spl37_108 | spl37_118, inference(sat_conversion,[],[f3924])). 70.10/10.68 cnf(s130, plain, spl37_100 | spl37_106 | spl37_107 | spl37_108, inference(sat_conversion,[],[f3927])). 70.10/10.68 cnf(s133, plain, spl37_97 | spl37_106 | spl37_107 | spl37_113, inference(sat_conversion,[],[f3979])). 70.10/10.68 cnf(s134, plain, spl37_97 | spl37_99 | spl37_113 | spl37_118, inference(sat_conversion,[],[f3985])). 70.10/10.68 cnf(s135, plain, spl37_97 | spl37_99 | spl37_113 | spl37_117, inference(sat_conversion,[],[f3986])). 70.10/10.68 cnf(s136, plain, spl37_97 | spl37_98 | spl37_113 | spl37_116, inference(sat_conversion,[],[f3991])). 70.10/10.68 cnf(s137, plain, spl37_97 | spl37_98 | spl37_113 | spl37_115, inference(sat_conversion,[],[f3992])). 70.10/10.68 cnf(s138, plain, spl37_98 | spl37_106 | spl37_108 | spl37_113, inference(sat_conversion,[],[f3995])). 70.10/10.68 cnf(s139, plain, spl37_99 | spl37_107 | spl37_108 | spl37_113, inference(sat_conversion,[],[f4005])). 70.10/10.68 cnf(s140, plain, spl37_98 | spl37_99 | spl37_113 | spl37_120, inference(sat_conversion,[],[f4043])). 70.10/10.68 cnf(s141, plain, spl37_98 | spl37_99 | spl37_113 | spl37_119, inference(sat_conversion,[],[f4044])). 70.10/10.68 cnf(s142, plain, spl37_98 | spl37_106 | spl37_108 | spl37_114, inference(sat_conversion,[],[f4089])). 70.10/10.68 cnf(s143, plain, spl37_98 | spl37_99 | spl37_114 | spl37_119, inference(sat_conversion,[],[f4110])). 70.10/10.68 cnf(s144, plain, spl37_98 | spl37_99 | spl37_114 | spl37_120, inference(sat_conversion,[],[f4111])). 70.10/10.68 cnf(s145, plain, spl37_99 | spl37_107 | spl37_108 | spl37_114, inference(sat_conversion,[],[f4114])). 70.10/10.68 cnf(s146, plain, spl37_97 | spl37_98 | spl37_114 | spl37_116, inference(sat_conversion,[],[f4115])). 70.10/10.68 cnf(s147, plain, spl37_97 | spl37_98 | spl37_114 | spl37_115, inference(sat_conversion,[],[f4116])). 70.10/10.68 cnf(s148, plain, spl37_97 | spl37_99 | spl37_114 | spl37_118, inference(sat_conversion,[],[f4117])). 70.10/10.68 cnf(s149, plain, spl37_97 | spl37_99 | spl37_114 | spl37_117, inference(sat_conversion,[],[f4118])). 70.10/10.68 cnf(s150, plain, spl37_97 | spl37_106 | spl37_107 | spl37_114, inference(sat_conversion,[],[f4131])). 70.10/10.68 cnf(s151, plain, spl37_97 | spl37_105 | spl37_107 | spl37_115, inference(sat_conversion,[],[f4136])). 70.10/10.68 cnf(s152, plain, spl37_97 | spl37_105 | spl37_107 | spl37_116, inference(sat_conversion,[],[f4137])). 70.10/10.68 cnf(s153, plain, spl37_97 | spl37_105 | spl37_106 | spl37_117, inference(sat_conversion,[],[f4138])). 70.10/10.68 cnf(s154, plain, spl37_97 | spl37_105 | spl37_106 | spl37_118, inference(sat_conversion,[],[f4139])). 70.10/10.68 cnf(s155, plain, spl37_98 | spl37_105 | spl37_106 | spl37_119, inference(sat_conversion,[],[f4147])). 70.10/10.68 cnf(s156, plain, spl37_98 | spl37_105 | spl37_106 | spl37_120, inference(sat_conversion,[],[f4148])). 70.10/10.68 cnf(s157, plain, spl37_105 | spl37_106 | spl37_107 | spl37_108, inference(sat_conversion,[],[f4149])). 70.10/10.68 cnf(s158, plain, spl37_98 | spl37_105 | spl37_108 | spl37_115, inference(sat_conversion,[],[f4152])). 70.10/10.68 cnf(s159, plain, spl37_98 | spl37_105 | spl37_108 | spl37_116, inference(sat_conversion,[],[f4153])). 70.10/10.68 cnf(s160, plain, spl37_99 | spl37_105 | spl37_108 | spl37_118, inference(sat_conversion,[],[f4183])). 70.10/10.68 cnf(s161, plain, spl37_99 | spl37_105 | spl37_108 | spl37_117, inference(sat_conversion,[],[f4184])). 70.10/10.68 cnf(s162, plain, spl37_99 | spl37_105 | spl37_107 | spl37_120, inference(sat_conversion,[],[f4187])). 70.10/10.68 cnf(s163, plain, spl37_99 | spl37_105 | spl37_107 | spl37_119, inference(sat_conversion,[],[f4188])). 70.10/10.68 cnf(s164, plain, spl37_97 | spl37_100 | spl37_115 | spl37_118, inference(sat_conversion,[],[f4191])). 70.10/10.68 cnf(s165, plain, spl37_97 | spl37_100 | spl37_115 | spl37_117, inference(sat_conversion,[],[f4192])). 70.10/10.68 cnf(s166, plain, spl37_97 | spl37_100 | spl37_116 | spl37_118, inference(sat_conversion,[],[f4193])). 70.10/10.68 cnf(s167, plain, spl37_97 | spl37_100 | spl37_116 | spl37_117, inference(sat_conversion,[],[f4194])). 70.10/10.68 cnf(s168, plain, spl37_98 | spl37_100 | spl37_116 | spl37_119, inference(sat_conversion,[],[f4195])). 70.10/10.68 cnf(s169, plain, spl37_98 | spl37_100 | spl37_115 | spl37_119, inference(sat_conversion,[],[f4196])). 70.10/10.68 cnf(s170, plain, spl37_100 | spl37_106 | spl37_107 | spl37_119, inference(sat_conversion,[],[f4197])). 70.10/10.68 cnf(s171, plain, spl37_99 | spl37_100 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4203])). 70.10/10.68 cnf(s172, plain, spl37_99 | spl37_100 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4209])). 70.10/10.68 cnf(s173, plain, spl37_100 | spl37_106 | spl37_107 | spl37_120, inference(sat_conversion,[],[f4212])). 70.10/10.68 cnf(s174, plain, spl37_99 | spl37_100 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4213])). 70.10/10.68 cnf(s175, plain, spl37_99 | spl37_100 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4214])). 70.10/10.68 cnf(s176, plain, spl37_98 | spl37_100 | spl37_115 | spl37_120, inference(sat_conversion,[],[f4225])). 70.10/10.68 cnf(s177, plain, spl37_98 | spl37_100 | spl37_116 | spl37_120, inference(sat_conversion,[],[f4226])). 70.10/10.68 cnf(s178, plain, spl37_100 | spl37_107 | spl37_108 | spl37_115, inference(sat_conversion,[],[f4227])). 70.10/10.68 cnf(s179, plain, spl37_100 | spl37_107 | spl37_108 | spl37_116, inference(sat_conversion,[],[f4228])). 70.10/10.68 cnf(s180, plain, spl37_100 | spl37_106 | spl37_108 | spl37_117, inference(sat_conversion,[],[f4231])). 70.10/10.68 cnf(s181, plain, spl37_100 | spl37_106 | spl37_108 | spl37_118, inference(sat_conversion,[],[f4232])). 70.10/10.68 cnf(s182, plain, spl37_97 | spl37_107 | spl37_113 | spl37_116, inference(sat_conversion,[],[f4250])). 70.10/10.68 cnf(s183, plain, spl37_97 | spl37_107 | spl37_113 | spl37_115, inference(sat_conversion,[],[f4251])). 70.10/10.68 cnf(s184, plain, spl37_97 | spl37_106 | spl37_113 | spl37_118, inference(sat_conversion,[],[f4254])). 70.10/10.68 cnf(s185, plain, spl37_97 | spl37_106 | spl37_113 | spl37_117, inference(sat_conversion,[],[f4255])). 70.10/10.68 cnf(s186, plain, spl37_98 | spl37_108 | spl37_113 | spl37_116, inference(sat_conversion,[],[f4258])). 70.10/10.68 cnf(s187, plain, spl37_98 | spl37_108 | spl37_113 | spl37_115, inference(sat_conversion,[],[f4259])). 70.10/10.68 cnf(s188, plain, spl37_99 | spl37_108 | spl37_113 | spl37_118, inference(sat_conversion,[],[f4260])). 70.10/10.68 cnf(s189, plain, spl37_99 | spl37_108 | spl37_113 | spl37_117, inference(sat_conversion,[],[f4261])). 70.10/10.68 cnf(s190, plain, spl37_106 | spl37_107 | spl37_108 | spl37_113, inference(sat_conversion,[],[f4274])). 70.10/10.68 cnf(s191, plain, spl37_98 | spl37_106 | spl37_113 | spl37_119, inference(sat_conversion,[],[f4277])). 70.10/10.68 cnf(s192, plain, spl37_98 | spl37_106 | spl37_113 | spl37_120, inference(sat_conversion,[],[f4291])). 70.10/10.68 cnf(s193, plain, spl37_99 | spl37_107 | spl37_113 | spl37_120, inference(sat_conversion,[],[f4308])). 70.10/10.68 cnf(s194, plain, spl37_99 | spl37_107 | spl37_113 | spl37_119, inference(sat_conversion,[],[f4309])). 70.10/10.68 cnf(s195, plain, spl37_98 | spl37_108 | spl37_114 | spl37_115, inference(sat_conversion,[],[f4343])). 70.10/10.68 cnf(s196, plain, spl37_98 | spl37_108 | spl37_114 | spl37_116, inference(sat_conversion,[],[f4344])). 70.10/10.68 cnf(s197, plain, spl37_106 | spl37_107 | spl37_108 | spl37_114, inference(sat_conversion,[],[f4345])). 70.10/10.68 cnf(s198, plain, spl37_98 | spl37_106 | spl37_114 | spl37_119, inference(sat_conversion,[],[f4348])). 70.10/10.68 cnf(s199, plain, spl37_98 | spl37_106 | spl37_114 | spl37_120, inference(sat_conversion,[],[f4352])). 70.10/10.68 cnf(s200, plain, spl37_99 | spl37_107 | spl37_114 | spl37_120, inference(sat_conversion,[],[f4360])). 70.10/10.68 cnf(s201, plain, spl37_99 | spl37_107 | spl37_114 | spl37_119, inference(sat_conversion,[],[f4363])). 70.10/10.68 cnf(s202, plain, spl37_99 | spl37_108 | spl37_114 | spl37_117, inference(sat_conversion,[],[f4364])). 70.10/10.68 cnf(s203, plain, spl37_99 | spl37_108 | spl37_114 | spl37_118, inference(sat_conversion,[],[f4365])). 70.10/10.68 cnf(s204, plain, spl37_97 | spl37_107 | spl37_114 | spl37_116, inference(sat_conversion,[],[f4366])). 70.10/10.68 cnf(s205, plain, spl37_97 | spl37_107 | spl37_114 | spl37_115, inference(sat_conversion,[],[f4369])). 70.10/10.68 cnf(s206, plain, spl37_97 | spl37_106 | spl37_114 | spl37_117, inference(sat_conversion,[],[f4372])). 70.10/10.68 cnf(s207, plain, spl37_97 | spl37_106 | spl37_114 | spl37_118, inference(sat_conversion,[],[f4373])). 70.10/10.68 cnf(s208, plain, spl37_97 | spl37_105 | spl37_116 | spl37_118, inference(sat_conversion,[],[f4374])). 70.10/10.68 cnf(s209, plain, spl37_97 | spl37_105 | spl37_115 | spl37_118, inference(sat_conversion,[],[f4375])). 70.10/10.68 cnf(s210, plain, spl37_97 | spl37_105 | spl37_116 | spl37_117, inference(sat_conversion,[],[f4376])). 70.10/10.68 cnf(s211, plain, spl37_97 | spl37_105 | spl37_115 | spl37_117, inference(sat_conversion,[],[f4377])). 70.10/10.68 cnf(s212, plain, spl37_105 | spl37_106 | spl37_107 | spl37_119, inference(sat_conversion,[],[f4380])). 70.10/10.68 cnf(s213, plain, spl37_105 | spl37_106 | spl37_107 | spl37_120, inference(sat_conversion,[],[f4381])). 70.10/10.68 cnf(s214, plain, spl37_105 | spl37_106 | spl37_108 | spl37_118, inference(sat_conversion,[],[f4384])). 70.10/10.68 cnf(s215, plain, spl37_105 | spl37_106 | spl37_108 | spl37_117, inference(sat_conversion,[],[f4385])). 70.10/10.68 cnf(s216, plain, spl37_105 | spl37_107 | spl37_108 | spl37_115, inference(sat_conversion,[],[f4386])). 70.10/10.68 cnf(s217, plain, spl37_105 | spl37_107 | spl37_108 | spl37_116, inference(sat_conversion,[],[f4389])). 70.10/10.68 cnf(s218, plain, spl37_98 | spl37_105 | spl37_116 | spl37_119, inference(sat_conversion,[],[f4401])). 70.10/10.68 cnf(s219, plain, spl37_98 | spl37_105 | spl37_115 | spl37_119, inference(sat_conversion,[],[f4402])). 70.10/10.68 cnf(s220, plain, spl37_98 | spl37_105 | spl37_116 | spl37_120, inference(sat_conversion,[],[f4403])). 70.10/10.68 cnf(s221, plain, spl37_98 | spl37_105 | spl37_115 | spl37_120, inference(sat_conversion,[],[f4409])). 70.10/10.68 cnf(s222, plain, spl37_99 | spl37_105 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4415])). 70.10/10.68 cnf(s223, plain, spl37_99 | spl37_105 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4416])). 70.10/10.68 cnf(s224, plain, spl37_99 | spl37_105 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4417])). 70.10/10.68 cnf(s225, plain, spl37_99 | spl37_105 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4418])). 70.10/10.68 cnf(s226, plain, spl37_100 | spl37_107 | spl37_116 | spl37_119, inference(sat_conversion,[],[f4419])). 70.10/10.68 cnf(s227, plain, spl37_100 | spl37_107 | spl37_115 | spl37_119, inference(sat_conversion,[],[f4420])). 70.10/10.68 cnf(s228, plain, spl37_100 | spl37_106 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4423])). 70.10/10.68 cnf(s229, plain, spl37_100 | spl37_106 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4426])). 70.10/10.68 cnf(s230, plain, spl37_100 | spl37_107 | spl37_116 | spl37_120, inference(sat_conversion,[],[f4427])). 70.10/10.68 cnf(s231, plain, spl37_100 | spl37_107 | spl37_115 | spl37_120, inference(sat_conversion,[],[f4428])). 70.10/10.68 cnf(s232, plain, spl37_100 | spl37_106 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4429])). 70.10/10.68 cnf(s233, plain, spl37_100 | spl37_106 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4432])). 70.10/10.68 cnf(s234, plain, spl37_100 | spl37_108 | spl37_115 | spl37_117, inference(sat_conversion,[],[f4435])). 70.10/10.68 cnf(s235, plain, spl37_100 | spl37_108 | spl37_116 | spl37_117, inference(sat_conversion,[],[f4436])). 70.10/10.68 cnf(s236, plain, spl37_100 | spl37_108 | spl37_116 | spl37_118, inference(sat_conversion,[],[f4437])). 70.10/10.68 cnf(s237, plain, spl37_100 | spl37_108 | spl37_115 | spl37_118, inference(sat_conversion,[],[f4438])). 70.10/10.68 cnf(s238, plain, spl37_97 | spl37_113 | spl37_115 | spl37_118, inference(sat_conversion,[],[f4454])). 70.10/10.68 cnf(s239, plain, spl37_97 | spl37_113 | spl37_116 | spl37_118, inference(sat_conversion,[],[f4455])). 70.10/10.68 cnf(s240, plain, spl37_97 | spl37_113 | spl37_115 | spl37_117, inference(sat_conversion,[],[f4456])). 70.10/10.68 cnf(s241, plain, spl37_97 | spl37_113 | spl37_116 | spl37_117, inference(sat_conversion,[],[f4457])). 70.10/10.68 cnf(s242, plain, spl37_106 | spl37_108 | spl37_113 | spl37_118, inference(sat_conversion,[],[f4458])). 70.10/10.68 cnf(s243, plain, spl37_106 | spl37_108 | spl37_113 | spl37_117, inference(sat_conversion,[],[f4459])). 70.10/10.68 cnf(s244, plain, spl37_107 | spl37_108 | spl37_113 | spl37_115, inference(sat_conversion,[],[f4464])). 70.10/10.68 cnf(s245, plain, spl37_107 | spl37_108 | spl37_113 | spl37_116, inference(sat_conversion,[],[f4465])). 70.10/10.68 cnf(s246, plain, spl37_98 | spl37_113 | spl37_116 | spl37_119, inference(sat_conversion,[],[f4466])). 70.10/10.68 cnf(s247, plain, spl37_98 | spl37_113 | spl37_115 | spl37_119, inference(sat_conversion,[],[f4467])). 70.10/10.68 cnf(s248, plain, spl37_106 | spl37_107 | spl37_113 | spl37_119, inference(sat_conversion,[],[f4468])). 70.10/10.68 cnf(s249, plain, spl37_98 | spl37_113 | spl37_115 | spl37_120, inference(sat_conversion,[],[f4480])). 70.10/10.68 cnf(s250, plain, spl37_98 | spl37_113 | spl37_116 | spl37_120, inference(sat_conversion,[],[f4481])). 70.10/10.68 cnf(s251, plain, spl37_106 | spl37_107 | spl37_113 | spl37_120, inference(sat_conversion,[],[f4482])). 70.10/10.68 cnf(s252, plain, spl37_99 | spl37_113 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4493])). 70.10/10.68 cnf(s253, plain, spl37_99 | spl37_113 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4494])). 70.10/10.68 cnf(s254, plain, spl37_99 | spl37_113 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4495])). 70.10/10.68 cnf(s255, plain, spl37_99 | spl37_113 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4496])). 70.10/10.68 cnf(s256, plain, spl37_98 | spl37_114 | spl37_115 | spl37_120, inference(sat_conversion,[],[f4497])). 70.10/10.68 cnf(s257, plain, spl37_98 | spl37_114 | spl37_115 | spl37_119, inference(sat_conversion,[],[f4502])). 70.10/10.68 cnf(s258, plain, spl37_98 | spl37_114 | spl37_116 | spl37_119, inference(sat_conversion,[],[f4515])). 70.10/10.68 cnf(s259, plain, spl37_98 | spl37_114 | spl37_116 | spl37_120, inference(sat_conversion,[],[f4516])). 70.10/10.68 cnf(s260, plain, spl37_107 | spl37_108 | spl37_114 | spl37_115, inference(sat_conversion,[],[f4517])). 70.10/10.68 cnf(s261, plain, spl37_107 | spl37_108 | spl37_114 | spl37_116, inference(sat_conversion,[],[f4518])). 70.10/10.68 cnf(s262, plain, spl37_106 | spl37_108 | spl37_114 | spl37_118, inference(sat_conversion,[],[f4523])). 70.10/10.68 cnf(s263, plain, spl37_106 | spl37_108 | spl37_114 | spl37_117, inference(sat_conversion,[],[f4524])). 70.10/10.68 cnf(s264, plain, spl37_106 | spl37_107 | spl37_114 | spl37_119, inference(sat_conversion,[],[f4525])). 70.10/10.68 cnf(s265, plain, spl37_106 | spl37_107 | spl37_114 | spl37_120, inference(sat_conversion,[],[f4530])). 70.10/10.68 cnf(s266, plain, spl37_99 | spl37_114 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4531])). 70.10/10.68 cnf(s267, plain, spl37_99 | spl37_114 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4532])). 70.10/10.68 cnf(s268, plain, spl37_99 | spl37_114 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4533])). 70.10/10.68 cnf(s269, plain, spl37_99 | spl37_114 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4534])). 70.10/10.68 cnf(s270, plain, spl37_97 | spl37_114 | spl37_116 | spl37_117, inference(sat_conversion,[],[f4535])). 70.10/10.68 cnf(s271, plain, spl37_97 | spl37_114 | spl37_116 | spl37_118, inference(sat_conversion,[],[f4536])). 70.10/10.68 cnf(s272, plain, spl37_97 | spl37_114 | spl37_115 | spl37_117, inference(sat_conversion,[],[f4537])). 70.10/10.68 cnf(s273, plain, spl37_97 | spl37_114 | spl37_115 | spl37_118, inference(sat_conversion,[],[f4538])). 70.10/10.68 cnf(s274, plain, spl37_105 | spl37_106 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4539])). 70.10/10.68 cnf(s275, plain, spl37_105 | spl37_106 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4540])). 70.10/10.68 cnf(s276, plain, spl37_105 | spl37_106 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4541])). 70.10/10.68 cnf(s277, plain, spl37_105 | spl37_106 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4542])). 70.10/10.68 cnf(s278, plain, spl37_105 | spl37_108 | spl37_115 | spl37_117, inference(sat_conversion,[],[f4543])). 70.10/10.68 cnf(s279, plain, spl37_105 | spl37_108 | spl37_115 | spl37_118, inference(sat_conversion,[],[f4544])). 70.10/10.68 cnf(s280, plain, spl37_105 | spl37_108 | spl37_116 | spl37_117, inference(sat_conversion,[],[f4545])). 70.10/10.68 cnf(s281, plain, spl37_105 | spl37_108 | spl37_116 | spl37_118, inference(sat_conversion,[],[f4546])). 70.10/10.68 cnf(s282, plain, spl37_105 | spl37_107 | spl37_116 | spl37_119, inference(sat_conversion,[],[f4547])). 70.10/10.68 cnf(s283, plain, spl37_105 | spl37_107 | spl37_115 | spl37_119, inference(sat_conversion,[],[f4548])). 70.10/10.68 cnf(s284, plain, spl37_105 | spl37_107 | spl37_116 | spl37_120, inference(sat_conversion,[],[f4555])). 70.10/10.68 cnf(s285, plain, spl37_105 | spl37_107 | spl37_115 | spl37_120, inference(sat_conversion,[],[f4558])). 70.10/10.68 cnf(s286, plain, spl37_100 | spl37_115 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4559])). 70.10/10.68 cnf(s287, plain, spl37_100 | spl37_116 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4560])). 70.10/10.68 cnf(s288, plain, spl37_100 | spl37_115 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4561])). 70.10/10.68 cnf(s289, plain, spl37_100 | spl37_116 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4562])). 70.10/10.68 cnf(s290, plain, spl37_100 | spl37_116 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4563])). 70.10/10.68 cnf(s291, plain, spl37_100 | spl37_115 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4564])). 70.10/10.68 cnf(s292, plain, spl37_100 | spl37_115 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4565])). 70.10/10.68 cnf(s293, plain, spl37_100 | spl37_116 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4566])). 70.10/10.68 cnf(s294, plain, spl37_108 | spl37_113 | spl37_115 | spl37_117, inference(sat_conversion,[],[f4582])). 70.10/10.68 cnf(s295, plain, spl37_108 | spl37_113 | spl37_116 | spl37_117, inference(sat_conversion,[],[f4583])). 70.10/10.68 cnf(s296, plain, spl37_108 | spl37_113 | spl37_115 | spl37_118, inference(sat_conversion,[],[f4584])). 70.10/10.68 cnf(s297, plain, spl37_108 | spl37_113 | spl37_116 | spl37_118, inference(sat_conversion,[],[f4585])). 70.10/10.68 cnf(s298, plain, spl37_107 | spl37_113 | spl37_115 | spl37_119, inference(sat_conversion,[],[f4586])). 70.10/10.68 cnf(s299, plain, spl37_107 | spl37_113 | spl37_116 | spl37_119, inference(sat_conversion,[],[f4587])). 70.10/10.68 cnf(s300, plain, spl37_106 | spl37_113 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4592])). 70.10/10.68 cnf(s301, plain, spl37_106 | spl37_113 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4593])). 70.10/10.68 cnf(s302, plain, spl37_106 | spl37_113 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4594])). 70.10/10.68 cnf(s303, plain, spl37_106 | spl37_113 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4595])). 70.10/10.68 cnf(s304, plain, spl37_107 | spl37_113 | spl37_115 | spl37_120, inference(sat_conversion,[],[f4596])). 70.10/10.68 cnf(s305, plain, spl37_107 | spl37_113 | spl37_116 | spl37_120, inference(sat_conversion,[],[f4599])). 70.10/10.68 cnf(s306, plain, spl37_107 | spl37_114 | spl37_115 | spl37_120, inference(sat_conversion,[],[f4602])). 70.10/10.68 cnf(s307, plain, spl37_107 | spl37_114 | spl37_115 | spl37_119, inference(sat_conversion,[],[f4607])). 70.10/10.68 cnf(s308, plain, spl37_107 | spl37_114 | spl37_116 | spl37_119, inference(sat_conversion,[],[f4608])). 70.10/10.68 cnf(s309, plain, spl37_107 | spl37_114 | spl37_116 | spl37_120, inference(sat_conversion,[],[f4611])). 70.10/10.68 cnf(s310, plain, spl37_108 | spl37_114 | spl37_116 | spl37_117, inference(sat_conversion,[],[f4614])). 70.10/10.68 cnf(s311, plain, spl37_108 | spl37_114 | spl37_115 | spl37_117, inference(sat_conversion,[],[f4615])). 70.10/10.68 cnf(s312, plain, spl37_108 | spl37_114 | spl37_116 | spl37_118, inference(sat_conversion,[],[f4616])). 70.10/10.68 cnf(s313, plain, spl37_108 | spl37_114 | spl37_115 | spl37_118, inference(sat_conversion,[],[f4617])). 70.10/10.68 cnf(s314, plain, spl37_106 | spl37_114 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4618])). 70.10/10.68 cnf(s315, plain, spl37_106 | spl37_114 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4619])). 70.10/10.68 cnf(s316, plain, spl37_106 | spl37_114 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4620])). 70.10/10.68 cnf(s317, plain, spl37_106 | spl37_114 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4621])). 70.10/10.68 cnf(s318, plain, spl37_105 | spl37_115 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4622])). 70.10/10.68 cnf(s319, plain, spl37_105 | spl37_116 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4623])). 70.10/10.68 cnf(s320, plain, spl37_105 | spl37_115 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4624])). 70.10/10.68 cnf(s321, plain, spl37_105 | spl37_116 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4625])). 70.10/10.68 cnf(s322, plain, spl37_105 | spl37_116 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4626])). 70.10/10.68 cnf(s323, plain, spl37_105 | spl37_116 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4627])). 70.10/10.68 cnf(s324, plain, spl37_105 | spl37_115 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4628])). 70.10/10.68 cnf(s325, plain, spl37_105 | spl37_115 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4629])). 70.10/10.68 cnf(s326, plain, spl37_113 | spl37_115 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4645])). 70.10/10.68 cnf(s327, plain, spl37_113 | spl37_115 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4646])). 70.10/10.68 cnf(s328, plain, spl37_113 | spl37_116 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4647])). 70.10/10.68 cnf(s329, plain, spl37_113 | spl37_116 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4648])). 70.10/10.68 cnf(s330, plain, spl37_113 | spl37_115 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4649])). 70.10/10.68 cnf(s331, plain, spl37_113 | spl37_115 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4650])). 70.10/10.68 cnf(s332, plain, spl37_113 | spl37_116 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4651])). 70.10/10.68 cnf(s333, plain, spl37_113 | spl37_116 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4652])). 70.10/10.68 cnf(s334, plain, spl37_114 | spl37_115 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4653])). 70.10/10.68 cnf(s335, plain, spl37_114 | spl37_115 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4654])). 70.10/10.68 cnf(s336, plain, spl37_114 | spl37_115 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4655])). 70.10/10.68 cnf(s337, plain, spl37_114 | spl37_115 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4656])). 70.10/10.68 cnf(s338, plain, spl37_114 | spl37_116 | spl37_117 | spl37_119, inference(sat_conversion,[],[f4657])). 70.10/10.68 cnf(s339, plain, spl37_114 | spl37_116 | spl37_118 | spl37_119, inference(sat_conversion,[],[f4658])). 70.10/10.68 cnf(s340, plain, spl37_114 | spl37_116 | spl37_118 | spl37_120, inference(sat_conversion,[],[f4659])). 70.10/10.68 cnf(s341, plain, spl37_114 | spl37_116 | spl37_117 | spl37_120, inference(sat_conversion,[],[f4660])). 70.10/10.68 cnf(s346, plain, ~spl37_8 | ~spl37_9 | ~spl37_113, inference(sat_conversion,[],[f5074])). 70.10/10.68 cnf(s348, plain, ~spl37_7 | ~spl37_12 | ~spl37_100, inference(sat_conversion,[],[f5102])). 70.10/10.68 cnf(s350, plain, ~spl37_32 | ~spl37_34 | ~spl37_115, inference(sat_conversion,[],[f5133])). 70.10/10.68 cnf(s352, plain, ~spl37_41 | ~spl37_45 | ~spl37_117, inference(sat_conversion,[],[f5163])). 70.10/10.68 cnf(s354, plain, ~spl37_43 | ~spl37_48 | ~spl37_107, inference(sat_conversion,[],[f5194])). 70.10/10.68 cnf(s356, plain, ~spl37_18 | ~spl37_21 | ~spl37_120, inference(sat_conversion,[],[f5223])). 70.10/10.68 cnf(s358, plain, ~spl37_19 | ~spl37_22 | ~spl37_119, inference(sat_conversion,[],[f5258])). 70.10/10.68 cnf(s360, plain, ~spl37_29 | ~spl37_36 | ~spl37_99, inference(sat_conversion,[],[f5287])). 70.10/10.68 cnf(s366, plain, ~spl37_31 | ~spl37_35 | ~spl37_106, inference(sat_conversion,[],[f5350])). 70.10/10.68 cnf(s368, plain, ~spl37_6 | ~spl37_10 | ~spl37_114, inference(sat_conversion,[],[f5394])). 70.10/10.68 cnf(s372, plain, ~spl37_42 | ~spl37_46 | ~spl37_98, inference(sat_conversion,[],[f5438])). 70.10/10.68 cnf(s374, plain, ~spl37_20 | ~spl37_23 | ~spl37_108, inference(sat_conversion,[],[f5488])). 70.10/10.68 cnf(s376, plain, ~spl37_17 | ~spl37_24 | ~spl37_97, inference(sat_conversion,[],[f5527])). 70.10/10.68 cnf(s380, plain, ~spl37_30 | ~spl37_33 | ~spl37_116, inference(sat_conversion,[],[f5571])). 70.10/10.68 cnf(s390, plain, ~spl37_44 | ~spl37_47 | ~spl37_118, inference(sat_conversion,[],[f5773])). 70.10/10.68 cnf(s394, plain, ~spl37_5 | ~spl37_11 | ~spl37_105, inference(sat_conversion,[],[f5816])). 70.10/10.68 cnf(s395, plain, spl37_43 | spl37_42 | spl37_41 | ~spl37_118, inference(rat,[],[s390,s58,s53])). 70.10/10.68 cnf(s396, plain, spl37_42 | spl37_41 | ~spl37_107 | ~spl37_118, inference(rat,[],[s390,s61,s63,s354,s395])). 70.10/10.68 cnf(s397, plain, spl37_43 | spl37_46 | spl37_41 | ~spl37_118, inference(rat,[],[s390,s55,s57])). 70.10/10.68 cnf(s398, plain, spl37_41 | ~spl37_98 | ~spl37_107 | ~spl37_118, inference(rat,[],[s390,s64,s62,s354,s397,s372,s396])). 70.10/10.68 cnf(s399, plain, spl37_43 | spl37_46 | spl37_45 | ~spl37_118, inference(rat,[],[s390,s56,s60])). 70.10/10.68 cnf(s400, plain, spl37_46 | spl37_45 | ~spl37_107 | ~spl37_118, inference(rat,[],[s390,s66,s68,s354,s399])). 70.10/10.68 cnf(s401, plain, spl37_43 | spl37_42 | spl37_45 | ~spl37_118, inference(rat,[],[s390,s54,s59])). 70.10/10.68 cnf(s402, plain, spl37_115 | spl37_108 | spl37_113, inference(rat,[],[s390,s65,s67,s354,s401,s372,s400,s352,s398,s187,s244,s296,s294])). 70.10/10.68 cnf(s403, plain, spl37_34 | ~spl37_106 | spl37_30 | spl37_29, inference(rat,[],[s366,s39,s43])). 70.10/10.68 cnf(s404, plain, ~spl37_106 | spl37_30 | spl37_29 | ~spl37_115, inference(rat,[],[s366,s36,s40,s350,s403])). 70.10/10.68 cnf(s405, plain, spl37_45 | ~spl37_98 | ~spl37_107 | ~spl37_118, inference(rat,[],[s390,s65,s67,s354,s401,s372,s400])). 70.10/10.68 cnf(s406, plain, spl37_106 | spl37_108 | spl37_113, inference(rat,[],[s352,s398,s405,s138,s190,s242,s243])). 70.10/10.68 cnf(s407, plain, spl37_34 | spl37_33 | spl37_29 | ~spl37_106, inference(rat,[],[s366,s38,s42])). 70.10/10.68 cnf(s408, plain, spl37_33 | spl37_29 | ~spl37_106 | ~spl37_115, inference(rat,[],[s366,s37,s41,s350,s407])). 70.10/10.68 cnf(s409, plain, ~spl37_118 | ~spl37_98 | ~spl37_107 | ~spl37_117, inference(rat,[],[s352,s405,s398])). 70.10/10.68 cnf(s410, plain, spl37_116 | spl37_108 | spl37_113, inference(rat,[],[s297,s409,s186,s245,s295])). 70.10/10.68 cnf(s411, plain, spl37_30 | spl37_34 | ~spl37_99 | ~spl37_106 | ~spl37_115, inference(rat,[],[s366,s49,s45,s360,s404])). 70.10/10.68 cnf(s412, plain, spl37_34 | ~spl37_99 | ~spl37_116 | ~spl37_106 | ~spl37_115, inference(rat,[],[s366,s44,s48,s360,s407,s380,s411])). 70.10/10.68 cnf(s413, plain, spl37_30 | spl37_32 | ~spl37_99 | ~spl37_106 | ~spl37_115, inference(rat,[],[s366,s50,s46,s360,s404])). 70.10/10.68 cnf(s414, plain, ~spl37_99 | ~spl37_115 | ~spl37_116 | ~spl37_106, inference(rat,[],[s366,s47,s51,s360,s408,s380,s413,s350,s412])). 70.10/10.68 cnf(s415, plain, spl37_99 | spl37_108 | spl37_113, inference(rat,[],[s188,s409,s105,s139,s189])). 70.10/10.68 cnf(s416, plain, spl37_108 | spl37_113, inference(rat,[],[s415,s414,s410,s406,s402])). 70.10/10.68 cnf(s417, plain, spl37_23 | ~spl37_119 | spl37_18 | spl37_17, inference(rat,[],[s358,s23,s24])). 70.10/10.68 cnf(s418, plain, ~spl37_119 | spl37_18 | spl37_17 | ~spl37_108, inference(rat,[],[s358,s19,s21,s374,s417])). 70.10/10.68 cnf(s419, plain, spl37_115 | ~spl37_118 | spl37_119 | spl37_113, inference(rat,[],[s409,s247,s298,s326])). 70.10/10.68 cnf(s420, plain, spl37_98 | ~spl37_115 | spl37_119 | spl37_113, inference(rat,[],[s414,s141,s191,s246])). 70.10/10.68 cnf(s421, plain, spl37_107 | ~spl37_115 | spl37_119 | spl37_113, inference(rat,[],[s414,s194,s248,s299])). 70.10/10.68 cnf(s422, plain, ~spl37_118 | spl37_119 | spl37_113, inference(rat,[],[s414,s255,s329,s301,s409,s421,s420,s419])). 70.10/10.68 cnf(s423, plain, spl37_119 | spl37_118 | spl37_113, inference(rat,[],[s414,s300,s327,s252,s328])). 70.10/10.68 cnf(s424, plain, spl37_119 | spl37_113, inference(rat,[],[s423,s422])). 70.10/10.68 cnf(s425, plain, spl37_23 | spl37_21 | spl37_17 | ~spl37_119, inference(rat,[],[s358,s26,s25])). 70.10/10.68 cnf(s426, plain, spl37_21 | spl37_17 | spl37_113, inference(rat,[],[s358,s20,s22,s374,s425,s416,s424])). 70.10/10.68 cnf(s427, plain, spl37_115 | ~spl37_118 | spl37_120 | spl37_113, inference(rat,[],[s409,s249,s304,s330])). 70.10/10.68 cnf(s428, plain, spl37_107 | ~spl37_115 | spl37_120 | spl37_113, inference(rat,[],[s414,s305,s251,s193])). 70.10/10.68 cnf(s429, plain, spl37_117 | ~spl37_115 | spl37_120 | spl37_113, inference(rat,[],[s414,s303,s332,s254])). 70.10/10.68 cnf(s430, plain, ~spl37_118 | spl37_120 | spl37_113, inference(rat,[],[s414,s250,s192,s140,s409,s429,s428,s427])). 70.10/10.68 cnf(s431, plain, spl37_120 | spl37_118 | spl37_113, inference(rat,[],[s414,s253,s302,s333,s331])). 70.10/10.68 cnf(s432, plain, spl37_120 | spl37_113, inference(rat,[],[s431,s430])). 70.10/10.68 cnf(s433, plain, spl37_17 | spl37_113, inference(rat,[],[s356,s418,s426,s416,s424,s432])). 70.10/10.68 cnf(s434, plain, spl37_23 | spl37_18 | spl37_24 | ~spl37_119, inference(rat,[],[s358,s29,s30])). 70.10/10.68 cnf(s435, plain, spl37_18 | spl37_24 | spl37_113, inference(rat,[],[s358,s32,s34,s374,s434,s416,s424])). 70.10/10.68 cnf(s436, plain, spl37_23 | spl37_21 | spl37_24 | ~spl37_119, inference(rat,[],[s358,s27,s28])). 70.10/10.68 cnf(s437, plain, spl37_24 | spl37_113, inference(rat,[],[s358,s31,s33,s374,s436,s356,s435,s416,s424,s432])). 70.10/10.68 cnf(s438, plain, spl37_115 | spl37_97 | spl37_113, inference(rat,[],[s409,s137,s183,s240,s238])). 70.10/10.68 cnf(s439, plain, spl37_117 | spl37_113, inference(rat,[],[s414,s135,s185,s241,s438,s376,s437,s433])). 70.10/10.68 cnf(s440, plain, spl37_98 | spl37_113, inference(rat,[],[s414,s88,s104,s136,s438,s376,s437,s433])). 70.10/10.68 cnf(s441, plain, spl37_118 | spl37_113, inference(rat,[],[s414,s134,s184,s239,s438,s376,s437,s433])). 70.10/10.68 cnf(s442, plain, spl37_97 | spl37_113, inference(rat,[],[s414,s103,s133,s182,s409,s441,s440,s439,s438])). 70.10/10.68 cnf(s443, plain, spl37_113, inference(rat,[],[s442,s376,s437,s433])). 70.10/10.68 cnf(s446, plain, spl37_108 | ~spl37_118 | ~spl37_107 | spl37_114 | spl37_115, inference(rat,[],[s409,s311,s195])). 70.10/10.68 cnf(s447, plain, spl37_17 | ~spl37_120 | ~spl37_119 | ~spl37_108, inference(rat,[],[s358,s20,s22,s374,s425,s356,s418])). 70.10/10.68 cnf(s448, plain, spl37_18 | spl37_24 | ~spl37_119 | ~spl37_108, inference(rat,[],[s358,s32,s34,s374,s434])). 70.10/10.68 cnf(s449, plain, spl37_117 | ~spl37_108 | spl37_114 | spl37_115, inference(rat,[],[s358,s31,s33,s374,s436,s356,s448,s376,s447,s272,s334,s337])). 70.10/10.68 cnf(s450, plain, ~spl37_118 | ~spl37_107 | spl37_115 | spl37_114, inference(rat,[],[s358,s31,s33,s374,s436,s356,s448,s376,s447,s147,s256,s257,s409,s449,s446])). 70.10/10.68 cnf(s451, plain, spl37_118 | spl37_114 | spl37_115, inference(rat,[],[s358,s31,s33,s374,s436,s356,s448,s376,s447,s273,s313,s335,s336])). 70.10/10.68 cnf(s452, plain, spl37_107 | spl37_114 | spl37_115, inference(rat,[],[s358,s31,s33,s374,s436,s356,s448,s376,s447,s205,s260,s306,s307])). 70.10/10.68 cnf(s453, plain, ~spl37_118 | spl37_114 | spl37_115, inference(rat,[],[s452,s450])). 70.10/10.68 cnf(s454, plain, spl37_114 | spl37_115, inference(rat,[],[s453,s451])). 70.10/10.68 cnf(s456, plain, spl37_98 | spl37_108 | spl37_114, inference(rat,[],[s414,s106,s142,s196,s454])). 70.10/10.68 cnf(s457, plain, spl37_119 | spl37_117 | spl37_114, inference(rat,[],[s414,s269,s314,s338,s454])). 70.10/10.68 cnf(s458, plain, spl37_108 | ~spl37_107 | ~spl37_118 | spl37_114, inference(rat,[],[s414,s202,s263,s310,s409,s456,s454])). 70.10/10.68 cnf(s459, plain, spl37_119 | spl37_98 | spl37_114, inference(rat,[],[s414,s143,s258,s198,s454])). 70.10/10.68 cnf(s460, plain, spl37_120 | spl37_98 | spl37_114, inference(rat,[],[s414,s144,s259,s199,s454])). 70.10/10.68 cnf(s461, plain, spl37_24 | ~spl37_120 | ~spl37_119 | ~spl37_108, inference(rat,[],[s358,s31,s33,s374,s436,s356,s448])). 70.10/10.68 cnf(s462, plain, spl37_98 | ~spl37_108 | spl37_114, inference(rat,[],[s414,s89,s107,s146,s376,s461,s447,s460,s459,s454])). 70.10/10.68 cnf(s463, plain, spl37_120 | spl37_117 | spl37_114, inference(rat,[],[s414,s266,s317,s341,s454])). 70.10/10.68 cnf(s464, plain, ~spl37_107 | ~spl37_118 | spl37_114, inference(rat,[],[s414,s149,s270,s206,s376,s461,s447,s463,s457,s409,s462,s458,s454])). 70.10/10.68 cnf(s465, plain, spl37_108 | spl37_107 | spl37_114, inference(rat,[],[s414,s145,s197,s261,s454])). 70.10/10.68 cnf(s466, plain, spl37_119 | spl37_107 | spl37_114, inference(rat,[],[s414,s201,s308,s264,s454])). 70.10/10.68 cnf(s467, plain, spl37_106 | spl37_107 | spl37_114, inference(rat,[],[s376,s461,s447,s150,s265,s465,s466])). 70.10/10.68 cnf(s468, plain, spl37_120 | spl37_107 | spl37_114, inference(rat,[],[s414,s200,s309,s454,s467])). 70.10/10.68 cnf(s469, plain, spl37_107 | spl37_114, inference(rat,[],[s414,s204,s108,s376,s461,s447,s468,s467,s466,s465,s454])). 70.10/10.68 cnf(s470, plain, spl37_108 | spl37_114, inference(rat,[],[s414,s203,s262,s312,s454,s464,s469])). 70.10/10.68 cnf(s471, plain, spl37_106 | spl37_114, inference(rat,[],[s376,s461,s447,s207,s315,s316,s464,s469,s470])). 70.10/10.68 cnf(s472, plain, spl37_119 | spl37_114, inference(rat,[],[s414,s268,s339,s454,s464,s469,s471])). 70.10/10.68 cnf(s473, plain, spl37_116 | spl37_114, inference(rat,[],[s376,s461,s447,s271,s340,s464,s469,s470,s472])). 70.10/10.68 cnf(s474, plain, spl37_114, inference(rat,[],[s376,s461,s447,s148,s267,s414,s473,s472,s471,s470,s464,s469,s454])). 70.10/10.68 cnf(s478, plain, spl37_108 | spl37_115 | ~spl37_118 | spl37_105, inference(rat,[],[s409,s158,s278,s216])). 70.10/10.68 cnf(s479, plain, spl37_119 | ~spl37_107 | spl37_115 | ~spl37_118 | spl37_105, inference(rat,[],[s409,s219,s318])). 70.10/10.68 cnf(s482, plain, spl37_98 | ~spl37_119 | ~spl37_108 | spl37_115 | spl37_105, inference(rat,[],[s376,s461,s447,s113,s221])). 70.10/10.68 cnf(s483, plain, ~spl37_107 | spl37_115 | ~spl37_118 | spl37_105, inference(rat,[],[s376,s461,s447,s211,s325,s409,s482,s479,s478])). 70.10/10.68 cnf(s484, plain, spl37_115 | ~spl37_118 | spl37_105, inference(rat,[],[s376,s461,s447,s151,s285,s283,s483,s478])). 70.10/10.68 cnf(s486, plain, spl37_117 | spl37_108 | ~spl37_115 | spl37_105, inference(rat,[],[s414,s161,s280,s215])). 70.10/10.68 cnf(s487, plain, spl37_98 | spl37_108 | ~spl37_115 | spl37_105, inference(rat,[],[s414,s92,s159,s114])). 70.10/10.68 cnf(s488, plain, spl37_108 | ~spl37_118 | spl37_105, inference(rat,[],[s414,s115,s157,s217,s409,s487,s486,s484])). 70.10/10.68 cnf(s489, plain, spl37_98 | spl37_119 | ~spl37_115 | spl37_105, inference(rat,[],[s414,s218,s117,s155])). 70.10/10.68 cnf(s490, plain, spl37_119 | ~spl37_107 | ~spl37_118 | spl37_105, inference(rat,[],[s414,s225,s319,s275,s409,s489,s484])). 70.10/10.68 cnf(s491, plain, spl37_106 | spl37_98 | ~spl37_119 | ~spl37_108 | spl37_105, inference(rat,[],[s376,s461,s447,s91,s156])). 70.10/10.68 cnf(s492, plain, spl37_116 | spl37_98 | ~spl37_119 | ~spl37_108 | spl37_105, inference(rat,[],[s376,s461,s447,s220,s112])). 70.10/10.68 cnf(s493, plain, spl37_98 | ~spl37_119 | ~spl37_118 | spl37_105, inference(rat,[],[s376,s461,s447,s116,s83,s414,s492,s491,s484,s488])). 70.10/10.68 cnf(s494, plain, spl37_106 | spl37_117 | ~spl37_119 | ~spl37_108 | spl37_105, inference(rat,[],[s376,s461,s447,s153,s277])). 70.10/10.68 cnf(s495, plain, spl37_116 | spl37_117 | ~spl37_119 | ~spl37_108 | spl37_105, inference(rat,[],[s376,s461,s447,s210,s323])). 70.10/10.68 cnf(s496, plain, ~spl37_107 | ~spl37_118 | spl37_105, inference(rat,[],[s376,s461,s447,s109,s223,s414,s495,s494,s409,s493,s490,s484,s488])). 70.10/10.68 cnf(s497, plain, spl37_119 | ~spl37_118 | spl37_105, inference(rat,[],[s414,s282,s163,s212,s484,s496])). 70.10/10.68 cnf(s498, plain, spl37_106 | ~spl37_118 | spl37_105, inference(rat,[],[s376,s461,s447,s213,s111,s488,s496,s497])). 70.10/10.68 cnf(s499, plain, spl37_116 | ~spl37_118 | spl37_105, inference(rat,[],[s376,s461,s447,s284,s152,s488,s496,s497])). 70.10/10.68 cnf(s500, plain, ~spl37_118 | spl37_105, inference(rat,[],[s376,s461,s447,s162,s90,s414,s499,s498,s497,s496,s488,s484])). 70.10/10.68 cnf(s501, plain, spl37_119 | spl37_118 | spl37_105, inference(rat,[],[s414,s224,s274,s321,s320])). 70.10/10.68 cnf(s502, plain, spl37_108 | spl37_105 | spl37_118, inference(rat,[],[s414,s160,s214,s281,s279])). 70.10/10.68 cnf(s503, plain, spl37_115 | spl37_105, inference(rat,[],[s376,s461,s447,s209,s324,s501,s502,s500])). 70.10/10.68 cnf(s504, plain, spl37_106 | spl37_105, inference(rat,[],[s376,s461,s447,s154,s276,s501,s502,s500])). 70.10/10.68 cnf(s505, plain, spl37_116 | spl37_105, inference(rat,[],[s376,s461,s447,s208,s322,s501,s502,s500])). 70.10/10.68 cnf(s506, plain, spl37_118 | spl37_105, inference(rat,[],[s376,s461,s447,s110,s222,s414,s505,s504,s503,s502,s501])). 70.10/10.68 cnf(s507, plain, spl37_105, inference(rat,[],[s506,s500])). 70.10/10.68 cnf(s512, plain, spl37_115 | spl37_119 | spl37_100 | ~spl37_118, inference(rat,[],[s409,s169,s227,s286])). 70.10/10.68 cnf(s516, plain, spl37_107 | ~spl37_115 | spl37_119 | spl37_100, inference(rat,[],[s414,s123,s170,s226])). 70.10/10.68 cnf(s517, plain, spl37_106 | spl37_119 | spl37_100 | ~spl37_118, inference(rat,[],[s409,s122,s228,s516,s512])). 70.10/10.68 cnf(s518, plain, spl37_116 | spl37_119 | spl37_100 | ~spl37_118, inference(rat,[],[s409,s287,s168,s516,s512])). 70.10/10.68 cnf(s519, plain, spl37_119 | spl37_100 | ~spl37_118, inference(rat,[],[s409,s171,s98,s414,s518,s517,s516,s512])). 70.10/10.68 cnf(s520, plain, spl37_116 | spl37_108 | ~spl37_107 | spl37_100 | ~spl37_118, inference(rat,[],[s409,s235,s127])). 70.10/10.68 cnf(s521, plain, spl37_98 | ~spl37_116 | spl37_108 | spl37_100, inference(rat,[],[s414,s86,s100,s126])). 70.10/10.68 cnf(s522, plain, spl37_108 | ~spl37_107 | ~spl37_118 | spl37_100, inference(rat,[],[s414,s128,s180,s234,s409,s521,s520])). 70.10/10.68 cnf(s523, plain, spl37_98 | spl37_116 | ~spl37_108 | ~spl37_119 | spl37_100, inference(rat,[],[s376,s461,s447,s177,s94])). 70.10/10.68 cnf(s524, plain, spl37_116 | ~spl37_107 | spl37_100 | ~spl37_118, inference(rat,[],[s376,s461,s447,s290,s167,s409,s523,s519,s522])). 70.10/10.68 cnf(s525, plain, spl37_106 | spl37_98 | ~spl37_108 | ~spl37_119 | spl37_100, inference(rat,[],[s376,s461,s447,s84,s125])). 70.10/10.68 cnf(s526, plain, spl37_115 | spl37_98 | ~spl37_108 | ~spl37_119 | spl37_100, inference(rat,[],[s376,s461,s447,s93,s176])). 70.10/10.68 cnf(s527, plain, spl37_98 | ~spl37_116 | ~spl37_108 | ~spl37_119 | spl37_100, inference(rat,[],[s376,s461,s447,s99,s81,s414,s526,s525])). 70.10/10.68 cnf(s528, plain, spl37_106 | spl37_117 | ~spl37_108 | ~spl37_119 | spl37_100, inference(rat,[],[s376,s461,s447,s121,s232])). 70.10/10.68 cnf(s529, plain, spl37_115 | spl37_117 | ~spl37_108 | ~spl37_119 | spl37_100, inference(rat,[],[s376,s461,s447,s165,s291])). 70.10/10.68 cnf(s530, plain, ~spl37_107 | spl37_100 | ~spl37_118, inference(rat,[],[s376,s461,s447,s96,s175,s414,s529,s528,s409,s527,s524,s522,s519])). 70.10/10.68 cnf(s531, plain, spl37_108 | spl37_100 | spl37_107, inference(rat,[],[s414,s101,s130,s179,s178])). 70.10/10.68 cnf(s532, plain, spl37_116 | spl37_107 | ~spl37_119 | spl37_100, inference(rat,[],[s376,s461,s447,s230,s119,s531])). 70.10/10.68 cnf(s533, plain, spl37_106 | spl37_107 | ~spl37_119 | spl37_100, inference(rat,[],[s376,s461,s447,s95,s173,s531])). 70.10/10.68 cnf(s534, plain, spl37_120 | ~spl37_106 | ~spl37_116 | spl37_107 | spl37_100, inference(rat,[],[s414,s124,s231])). 70.10/10.68 cnf(s535, plain, spl37_100 | ~spl37_118, inference(rat,[],[s414,s85,s118,s376,s461,s447,s534,s533,s532,s531,s530,s519])). 70.10/10.68 cnf(s536, plain, spl37_8 | spl37_11 | ~spl37_100 | spl37_6, inference(rat,[],[s348,s6,s15])). 70.10/10.68 cnf(s538, plain, spl37_8 | ~spl37_100 | spl37_5 | spl37_6, inference(rat,[],[s348,s2,s12])). 70.10/10.68 cnf(s539, plain, ~spl37_100 | spl37_5 | spl37_6, inference(rat,[],[s348,s11,s3,s346,s538,s443])). 70.10/10.68 cnf(s540, plain, spl37_108 | spl37_100 | spl37_118, inference(rat,[],[s414,s129,s181,s236,s237])). 70.10/10.68 cnf(s541, plain, spl37_119 | spl37_118 | spl37_100, inference(rat,[],[s414,s172,s229,s289,s288])). 70.10/10.68 cnf(s542, plain, spl37_116 | spl37_100, inference(rat,[],[s376,s461,s447,s166,s293,s540,s541,s535])). 70.10/10.68 cnf(s543, plain, spl37_106 | spl37_100, inference(rat,[],[s376,s461,s447,s120,s233,s540,s541,s535])). 70.10/10.68 cnf(s544, plain, spl37_120 | spl37_100, inference(rat,[],[s414,s174,s292,s535,s542,s543])). 70.10/10.68 cnf(s545, plain, spl37_100 | spl37_118, inference(rat,[],[s414,s97,s164,s376,s461,s447,s544,s543,s542,s541,s540])). 70.10/10.68 cnf(s546, plain, spl37_100, inference(rat,[],[s545,s535])). 70.10/10.68 cnf(s547, plain, spl37_9 | spl37_11 | spl37_6, inference(rat,[],[s348,s7,s16,s546])). 70.10/10.68 cnf(s548, plain, spl37_11 | spl37_6, inference(rat,[],[s547,s346,s536,s546,s443])). 70.10/10.68 cnf(s549, plain, spl37_6, inference(rat,[],[s548,s394,s539,s507,s546])). 70.10/10.68 cnf(s550, plain, ~spl37_10, inference(rat,[],[s368,s474,s549])). 70.10/10.68 cnf(s552, plain, spl37_9 | spl37_11, inference(rat,[],[s348,s17,s8,s550,s546])). 70.10/10.68 cnf(s554, plain, spl37_8 | spl37_5, inference(rat,[],[s348,s13,s5,s550,s546])). 70.10/10.68 cnf(s555, plain, spl37_9 | spl37_5, inference(rat,[],[s348,s10,s4,s550,s546])). 70.10/10.68 cnf(s556, plain, spl37_5, inference(rat,[],[s555,s346,s554,s443])). 70.10/10.68 cnf(s557, plain, ~spl37_11, inference(rat,[],[s394,s507,s556])). 70.10/10.68 cnf(s558, plain, spl37_9, inference(rat,[],[s552,s557])). 70.10/10.68 cnf(s559, plain, ~spl37_8, inference(rat,[],[s346,s443,s558])). 70.10/10.68 cnf(s560, plain, spl37_12, inference(rat,[],[s14,s550,s557,s559])). 70.10/10.68 cnf(s561, plain, spl37_7, inference(rat,[],[s9,s557,s550,s559])). 70.10/10.68 cnf(s562, plain, $false, inference(rat,[],[s348,s546,s561,s560])). 70.10/10.68 thf(f5819,plain,( 70.10/10.68 $false), 70.10/10.68 inference(avatar_sat_refutation,[],[s562])). 70.10/10.68 % SZS output end Proof for theBenchmark 70.10/10.68 % (3201545)------------------------------ 70.10/10.68 % (3201545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 70.10/10.68 % (3201545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 70.10/10.68 % (3201545)CaDiCaL version: 2.1.3 70.10/10.68 % (3201545)Termination reason: Refutation 70.10/10.68 % (3201545)Time elapsed: 0.607 s 70.10/10.68 % (3201545)Peak memory usage: 16 MB 70.10/10.68 % (3201545)Instructions burned: 1497 (million) 70.10/10.68 % (3200883)Success in time 10.19 s 70.10/10.68 % Vampire exiting 70.10/10.68 EOF