0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.18/0.41 % Computer : n019.cluster.edu 0.18/0.41 % Model : x86_64 x86_64 0.18/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.18/0.41 % Memory : 8046.5625MB 0.18/0.41 % OS : Linux 6.8.0-71-generic 0.18/0.41 % CPULimit : 1440 0.18/0.41 % WCLimit : 180 0.18/0.41 % DateTime : Mon Jul 27 12:28:08 UTC 2026 0.18/0.42 % CPUTime : 0.18/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.18/0.47 Running higher-order theorem proving 0.26/0.58 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.37/0.81 % (2408879)Detected a higher-order problem, will run a greedy HOL sequence. 0.37/0.81 % (2408889)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3583212050:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi) 0.37/0.81 % (2408890)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 0.37/0.81 % (2408890)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 0.37/0.81 % (2408885)lrs+10_16_si=on:nwc=1.5:random_seed=3998241028:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi) 0.37/0.81 % (2408884)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1970009380:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi) 0.37/0.81 % (2408888)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=79556045:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi) 0.37/0.81 % (2408887)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=1796432331: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) 0.37/0.81 % (2408886)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4056154679:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi) 0.37/0.81 % (2408890)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=748849353:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi) 0.37/0.81 % (2408886)Instruction limit reached! 0.37/0.81 % (2408886)------------------------------ 0.37/0.81 % (2408886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.81 % (2408886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.81 % (2408886)CaDiCaL version: 2.1.3 0.37/0.81 % (2408886)Termination reason: Instruction limit 0.37/0.81 % (2408886)Termination phase: shuffling 0.37/0.81 % (2408886)Time elapsed: 0.003 s 0.37/0.81 % (2408886)Peak memory usage: 10 MB 0.37/0.81 % (2408886)Instructions burned: 3 (million) 0.37/0.81 % (2408885)Instruction limit reached! 0.37/0.81 % (2408885)------------------------------ 0.37/0.81 % (2408885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.81 % (2408885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.81 % (2408885)CaDiCaL version: 2.1.3 0.37/0.81 % (2408885)Termination reason: Instruction limit 0.37/0.81 % (2408885)Termination phase: shuffling 0.37/0.81 % (2408885)Time elapsed: 0.016 s 0.37/0.81 % (2408885)Peak memory usage: 10 MB 0.37/0.81 % (2408885)Instructions burned: 18 (million) 0.37/0.81 % (2408889)Instruction limit reached! 0.37/0.81 % (2408889)------------------------------ 0.37/0.81 % (2408889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.81 % (2408889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.81 % (2408889)CaDiCaL version: 2.1.3 0.37/0.81 % (2408889)Termination reason: Instruction limit 0.37/0.81 % (2408889)Termination phase: Preprocessing 3 0.37/0.81 % (2408889)Time elapsed: 0.033 s 0.37/0.81 % (2408889)Peak memory usage: 12 MB 0.37/0.81 % (2408889)Instructions burned: 76 (million) 0.37/0.81 % (2408888)Instruction limit reached! 0.37/0.81 % (2408888)------------------------------ 0.37/0.81 % (2408888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.81 % (2408888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.81 % (2408888)CaDiCaL version: 2.1.3 0.37/0.81 % (2408888)Termination reason: Instruction limit 0.37/0.81 % (2408888)Termination phase: shuffling 0.37/0.81 % (2408888)Time elapsed: 0.020 s 0.37/0.81 % (2408888)Peak memory usage: 10 MB 0.37/0.81 % (2408888)Instructions burned: 24 (million) 0.37/0.81 % (2408898)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2453197113:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 0.37/0.81 % (2408898)Instruction limit reached! 0.37/0.81 % (2408898)------------------------------ 0.37/0.81 % (2408898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.88 % (2408898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.88 % (2408898)CaDiCaL version: 2.1.3 0.37/0.88 % (2408898)Termination reason: Instruction limit 0.37/0.88 % (2408898)Termination phase: shuffling 0.37/0.88 % (2408898)Time elapsed: 0.003 s 0.37/0.88 % (2408898)Peak memory usage: 10 MB 0.37/0.88 % (2408898)Instructions burned: 2 (million) 0.37/0.88 % (2408900)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 0.37/0.88 % (2408899)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2997749808:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1799 on theBenchmark for (1799ds/5Mi) 0.37/0.88 % (2408901)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=94634515:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_1799 on theBenchmark for (1799ds/12Mi) 0.37/0.88 % (2408900)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=668485184:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1799 on theBenchmark for (1799ds/7Mi) 0.37/0.88 % (2408899)Instruction limit reached! 0.37/0.88 % (2408899)------------------------------ 0.37/0.88 % (2408899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.88 % (2408899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.88 % (2408899)CaDiCaL version: 2.1.3 0.37/0.88 % (2408899)Termination reason: Instruction limit 0.37/0.88 % (2408899)Termination phase: shuffling 0.37/0.88 % (2408899)Time elapsed: 0.005 s 0.37/0.88 % (2408899)Peak memory usage: 10 MB 0.37/0.88 % (2408899)Instructions burned: 5 (million) 0.37/0.88 % (2408900)Instruction limit reached! 0.37/0.88 % (2408900)------------------------------ 0.37/0.88 % (2408900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.88 % (2408900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.88 % (2408900)CaDiCaL version: 2.1.3 0.37/0.88 % (2408900)Termination reason: Instruction limit 0.37/0.88 % (2408900)Termination phase: shuffling 0.37/0.88 % (2408900)Time elapsed: 0.006 s 0.37/0.88 % (2408900)Peak memory usage: 10 MB 0.37/0.88 % (2408900)Instructions burned: 7 (million) 0.37/0.88 % (2408901)Instruction limit reached! 0.37/0.88 % (2408901)------------------------------ 0.37/0.88 % (2408901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.88 % (2408901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.88 % (2408901)CaDiCaL version: 2.1.3 0.37/0.88 % (2408901)Termination reason: Instruction limit 0.37/0.88 % (2408901)Termination phase: shuffling 0.37/0.88 % (2408901)Time elapsed: 0.011 s 0.37/0.88 % (2408901)Peak memory usage: 10 MB 0.37/0.88 % (2408901)Instructions burned: 12 (million) 0.37/0.88 % (2408903)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 0.37/0.88 % (2408903)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 0.37/0.88 % (2408884)Instruction limit reached! 0.37/0.88 % (2408884)------------------------------ 0.37/0.88 % (2408884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.88 % (2408884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.88 % (2408884)CaDiCaL version: 2.1.3 0.37/0.88 % (2408884)Termination reason: Instruction limit 0.37/0.88 % (2408884)Termination phase: Preprocessing 3 0.37/0.88 % (2408884)Time elapsed: 0.073 s 0.37/0.88 % (2408884)Peak memory usage: 12 MB 0.37/0.88 % (2408884)Instructions burned: 87 (million) 0.37/0.88 % (2408903)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3697195564:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1798 on theBenchmark for (1798ds/28Mi) 0.37/0.88 % (2408909)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on 0.37/0.88 % (2408907)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=608644266:i=86:piset=equals:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/86Mi) 0.37/0.94 % (2408908)lrs+10_1_si=on:cs=on:random_seed=925859396:i=8:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/8Mi) 0.37/0.94 % (2408909)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=3294691046:i=2:add=on:rtra=on_1798 on theBenchmark for (1798ds/2Mi) 0.37/0.94 % (2408909)Instruction limit reached! 0.37/0.94 % (2408909)------------------------------ 0.37/0.94 % (2408909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.94 % (2408909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.94 % (2408909)CaDiCaL version: 2.1.3 0.37/0.94 % (2408909)Termination reason: Instruction limit 0.37/0.94 % (2408909)Termination phase: shuffling 0.37/0.94 % (2408909)Time elapsed: 0.003 s 0.37/0.94 % (2408909)Peak memory usage: 10 MB 0.37/0.94 % (2408909)Instructions burned: 3 (million) 0.37/0.94 % (2408908)Instruction limit reached! 0.37/0.94 % (2408908)------------------------------ 0.37/0.94 % (2408908)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.94 % (2408908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.94 % (2408908)CaDiCaL version: 2.1.3 0.37/0.94 % (2408908)Termination reason: Instruction limit 0.37/0.94 % (2408908)Termination phase: shuffling 0.37/0.94 % (2408908)Time elapsed: 0.007 s 0.37/0.94 % (2408908)Peak memory usage: 10 MB 0.37/0.94 % (2408908)Instructions burned: 8 (million) 0.37/0.94 % (2408903)Instruction limit reached! 0.37/0.94 % (2408903)------------------------------ 0.37/0.94 % (2408903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.94 % (2408903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.94 % (2408903)CaDiCaL version: 2.1.3 0.37/0.94 % (2408903)Termination reason: Instruction limit 0.37/0.94 % (2408903)Termination phase: shuffling 0.37/0.94 % (2408903)Time elapsed: 0.024 s 0.37/0.94 % (2408903)Peak memory usage: 10 MB 0.37/0.94 % (2408903)Instructions burned: 29 (million) 0.37/0.94 % (2408910)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3417099659:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_1798 on theBenchmark for (1798ds/38Mi) 0.37/0.94 % (2408890)Instruction limit reached! 0.37/0.94 % (2408890)------------------------------ 0.37/0.94 % (2408890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.94 % (2408890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.94 % (2408890)CaDiCaL version: 2.1.3 0.37/0.94 % (2408890)Termination reason: Instruction limit 0.37/0.94 % (2408890)Termination phase: Saturation 0.37/0.94 % (2408890)Time elapsed: 0.125 s 0.37/0.94 % (2408890)Peak memory usage: 13 MB 0.37/0.94 % (2408890)Instructions burned: 159 (million) 0.37/0.94 % (2408915)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3443516538:st=2:i=249:sd=1:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/249Mi) 0.37/0.94 % (2408916)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2746719306:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1798 on theBenchmark for (1798ds/25Mi) 0.37/0.94 % (2408917)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4267284272:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_1798 on theBenchmark for (1798ds/14Mi) 0.37/0.94 % (2408910)Instruction limit reached! 0.37/0.94 % (2408910)------------------------------ 0.37/0.94 % (2408910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.94 % (2408910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.94 % (2408910)CaDiCaL version: 2.1.3 0.37/0.94 % (2408910)Termination reason: Instruction limit 0.37/0.94 % (2408910)Termination phase: Property scanning 0.37/0.94 % (2408910)Time elapsed: 0.032 s 0.37/0.94 % (2408910)Peak memory usage: 11 MB 0.37/0.94 % (2408910)Instructions burned: 39 (million) 0.37/0.94 % (2408917)Instruction limit reached! 0.37/0.94 % (2408917)------------------------------ 0.37/0.94 % (2408917)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/0.94 % (2408917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/0.94 % (2408917)CaDiCaL version: 2.1.3 0.37/0.94 % (2408917)Termination reason: Instruction limit 0.37/0.94 % (2408917)Termination phase: shuffling 0.37/0.94 % (2408917)Time elapsed: 0.013 s 0.37/1.07 % (2408917)Peak memory usage: 10 MB 0.37/1.07 % (2408917)Instructions burned: 14 (million) 0.37/1.07 % (2408916)Instruction limit reached! 0.37/1.07 % (2408916)------------------------------ 0.37/1.07 % (2408916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/1.07 % (2408916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/1.07 % (2408916)CaDiCaL version: 2.1.3 0.37/1.07 % (2408916)Termination reason: Instruction limit 0.37/1.07 % (2408916)Termination phase: shuffling 0.37/1.07 % (2408916)Time elapsed: 0.021 s 0.37/1.07 % (2408916)Peak memory usage: 10 MB 0.37/1.07 % (2408916)Instructions burned: 25 (million) 0.37/1.07 % (2408907)Instruction limit reached! 0.37/1.07 % (2408907)------------------------------ 0.37/1.07 % (2408907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/1.07 % (2408907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/1.07 % (2408907)CaDiCaL version: 2.1.3 0.37/1.07 % (2408907)Termination reason: Instruction limit 0.37/1.07 % (2408907)Termination phase: Property scanning 0.37/1.07 % (2408907)Time elapsed: 0.068 s 0.37/1.07 % (2408907)Peak memory usage: 11 MB 0.37/1.07 % (2408907)Instructions burned: 86 (million) 0.37/1.07 % (2408919)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2767476594:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/327Mi) 0.37/1.07 % (2408923)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3174418299:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_1797 on theBenchmark for (1797ds/14Mi) 0.37/1.07 % (2408924)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3151918497:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_1797 on theBenchmark for (1797ds/2Mi) 0.37/1.07 % (2408924)Instruction limit reached! 0.37/1.07 % (2408924)------------------------------ 0.37/1.07 % (2408924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/1.07 % (2408924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/1.07 % (2408924)CaDiCaL version: 2.1.3 0.37/1.07 % (2408924)Termination reason: Instruction limit 0.37/1.07 % (2408924)Termination phase: shuffling 0.37/1.07 % (2408924)Time elapsed: 0.003 s 0.37/1.07 % (2408924)Peak memory usage: 10 MB 0.37/1.07 % (2408924)Instructions burned: 2 (million) 0.37/1.07 % (2408923)Instruction limit reached! 0.37/1.07 % (2408923)------------------------------ 0.37/1.07 % (2408923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/1.07 % (2408923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/1.07 % (2408923)CaDiCaL version: 2.1.3 0.37/1.07 % (2408923)Termination reason: Instruction limit 0.37/1.07 % (2408923)Termination phase: shuffling 0.37/1.07 % (2408923)Time elapsed: 0.012 s 0.37/1.07 % (2408923)Peak memory usage: 10 MB 0.37/1.07 % (2408923)Instructions burned: 14 (million) 0.37/1.07 % (2408925)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=4225374227:i=26:ep=R:rtra=on:ntd=on_1797 on theBenchmark for (1797ds/26Mi) 0.37/1.07 % (2408926)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=286979067:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_1797 on theBenchmark for (1797ds/23Mi) 0.37/1.07 % (2408925)Instruction limit reached! 0.37/1.07 % (2408925)------------------------------ 0.37/1.07 % (2408925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.37/1.07 % (2408925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.37/1.07 % (2408925)CaDiCaL version: 2.1.3 0.37/1.07 % (2408925)Termination reason: Instruction limit 0.37/1.07 % (2408925)Termination phase: shuffling 0.37/1.07 % (2408925)Time elapsed: 0.022 s 0.37/1.07 % (2408925)Peak memory usage: 10 MB 0.37/1.07 % (2408925)Instructions burned: 26 (million) 0.37/1.07 % (2408931)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 0.37/1.07 % (2408931)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs 0.37/1.07 % (2408926)Instruction limit reached! 0.37/1.07 % (2408926)------------------------------ 0.37/1.07 % (2408926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.39/1.18 % (2408926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.39/1.18 % (2408926)CaDiCaL version: 2.1.3 3.39/1.18 % (2408926)Termination reason: Instruction limit 3.39/1.18 % (2408926)Termination phase: shuffling 3.39/1.18 % (2408926)Time elapsed: 0.020 s 3.39/1.18 % (2408926)Peak memory usage: 10 MB 3.39/1.18 % (2408926)Instructions burned: 23 (million) 3.39/1.18 % (2408930)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=712675684:cond=on:i=60:rtra=on:ntd=on_1797 on theBenchmark for (1797ds/60Mi) 3.39/1.18 % (2408931)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=2308486476:i=14:add=off:nm=40:rtra=on:rawr=on_1797 on theBenchmark for (1797ds/14Mi) 3.39/1.18 % (2408931)Instruction limit reached! 3.39/1.18 % (2408931)------------------------------ 3.39/1.18 % (2408931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.39/1.18 % (2408931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.39/1.18 % (2408931)CaDiCaL version: 2.1.3 3.39/1.18 % (2408931)Termination reason: Instruction limit 3.39/1.18 % (2408931)Termination phase: shuffling 3.39/1.18 % (2408931)Time elapsed: 0.013 s 3.39/1.18 % (2408931)Peak memory usage: 10 MB 3.39/1.18 % (2408931)Instructions burned: 15 (million) 3.39/1.18 % (2408934)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off 3.39/1.18 % (2408934)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=3417964782:i=8:nm=2:rtra=on:fe=abstraction:inj=on_1797 on theBenchmark for (1797ds/8Mi) 3.39/1.18 % (2408935)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=3789904121:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_1797 on theBenchmark for (1797ds/31Mi) 3.39/1.18 % (2408934)Instruction limit reached! 3.39/1.18 % (2408934)------------------------------ 3.39/1.18 % (2408934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.39/1.18 % (2408934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.39/1.18 % (2408934)CaDiCaL version: 2.1.3 3.39/1.18 % (2408934)Termination reason: Instruction limit 3.39/1.18 % (2408934)Termination phase: shuffling 3.39/1.18 % (2408934)Time elapsed: 0.007 s 3.39/1.18 % (2408934)Peak memory usage: 10 MB 3.39/1.18 % (2408934)Instructions burned: 8 (million) 3.39/1.18 % (2408938)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1115653091:i=7:hud=5:bd=preordered:rtra=on:bet=on_1796 on theBenchmark for (1796ds/7Mi) 3.39/1.18 % (2408930)Instruction limit reached! 3.39/1.18 % (2408930)------------------------------ 3.39/1.18 % (2408930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.39/1.18 % (2408930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.39/1.18 % (2408930)CaDiCaL version: 2.1.3 3.39/1.18 % (2408930)Termination reason: Instruction limit 3.39/1.18 % (2408930)Termination phase: Preprocessing 3 3.39/1.18 % (2408930)Time elapsed: 0.051 s 3.39/1.18 % (2408930)Peak memory usage: 11 MB 3.39/1.18 % (2408930)Instructions burned: 61 (million) 3.39/1.18 % (2408935)Instruction limit reached! 3.39/1.18 % (2408935)------------------------------ 3.39/1.18 % (2408935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.39/1.18 % (2408935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.39/1.18 % (2408935)CaDiCaL version: 2.1.3 3.39/1.18 % (2408935)Termination reason: Instruction limit 3.39/1.18 % (2408935)Termination phase: shuffling 3.39/1.18 % (2408935)Time elapsed: 0.025 s 3.39/1.18 % (2408935)Peak memory usage: 10 MB 3.39/1.18 % (2408935)Instructions burned: 31 (million) 3.39/1.18 % (2408938)Instruction limit reached! 3.39/1.18 % (2408938)------------------------------ 3.39/1.18 % (2408938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.39/1.18 % (2408938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.39/1.18 % (2408938)CaDiCaL version: 2.1.3 3.39/1.18 % (2408938)Termination reason: Instruction limit 3.39/1.18 % (2408938)Termination phase: shuffling 3.39/1.18 % (2408938)Time elapsed: 0.007 s 3.39/1.18 % (2408938)Peak memory usage: 10 MB 3.39/1.18 % (2408938)Instructions burned: 8 (million) 3.66/1.20 % (2408941)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=726654729:i=23:rtra=on:ntd=on_1796 on theBenchmark for (1796ds/23Mi) 3.66/1.20 % (2408943)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3922185462:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_1796 on theBenchmark for (1796ds/20Mi) 3.66/1.20 % (2408944)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3912394307:i=1240:rtra=on:ixr=off_1796 on theBenchmark for (1796ds/1240Mi) 3.66/1.20 % (2408945)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=875589572:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_1796 on theBenchmark for (1796ds/143Mi) 3.66/1.20 % (2408941)Instruction limit reached! 3.66/1.20 % (2408941)------------------------------ 3.66/1.20 % (2408941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.66/1.20 % (2408941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.66/1.20 % (2408941)CaDiCaL version: 2.1.3 3.66/1.20 % (2408941)Termination reason: Instruction limit 3.66/1.20 % (2408941)Termination phase: shuffling 3.66/1.20 % (2408941)Time elapsed: 0.020 s 3.66/1.20 % (2408941)Peak memory usage: 10 MB 3.66/1.20 % (2408941)Instructions burned: 23 (million) 3.66/1.20 % (2408943)Instruction limit reached! 3.66/1.20 % (2408943)------------------------------ 3.66/1.20 % (2408943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.66/1.20 % (2408943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.66/1.20 % (2408943)CaDiCaL version: 2.1.3 3.66/1.20 % (2408943)Termination reason: Instruction limit 3.66/1.20 % (2408943)Termination phase: shuffling 3.66/1.20 % (2408943)Time elapsed: 0.017 s 3.66/1.20 % (2408943)Peak memory usage: 10 MB 3.66/1.20 % (2408943)Instructions burned: 20 (million) 3.66/1.20 % (2408915)Instruction limit reached! 3.66/1.20 % (2408915)------------------------------ 3.66/1.20 % (2408915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.66/1.20 % (2408915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.66/1.20 % (2408915)CaDiCaL version: 2.1.3 3.66/1.20 % (2408915)Termination reason: Instruction limit 3.66/1.20 % (2408915)Termination phase: Saturation 3.66/1.20 % (2408915)Time elapsed: 0.198 s 3.66/1.20 % (2408915)Peak memory usage: 15 MB 3.66/1.20 % (2408915)Instructions burned: 249 (million) 3.66/1.20 % (2408951)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2692762777:i=42:hud=10:rtra=on_1796 on theBenchmark for (1796ds/42Mi) 3.66/1.20 % (2408950)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3078104010:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_1796 on theBenchmark for (1796ds/193Mi) 3.66/1.20 % (2408952)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 3.66/1.20 % (2408952)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1831480189:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1795 on theBenchmark for (1795ds/7Mi) 3.66/1.20 % (2408952)Instruction limit reached! 3.66/1.20 % (2408952)------------------------------ 3.66/1.20 % (2408952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.66/1.20 % (2408952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.66/1.20 % (2408952)CaDiCaL version: 2.1.3 3.66/1.20 % (2408952)Termination reason: Instruction limit 3.66/1.20 % (2408952)Termination phase: shuffling 3.66/1.20 % (2408952)Time elapsed: 0.006 s 3.66/1.20 % (2408952)Peak memory usage: 10 MB 3.66/1.20 % (2408952)Instructions burned: 7 (million) 3.66/1.20 % (2408951)Instruction limit reached! 3.66/1.20 % (2408951)------------------------------ 3.66/1.20 % (2408951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.66/1.20 % (2408951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.66/1.20 % (2408951)CaDiCaL version: 2.1.3 3.66/1.20 % (2408951)Termination reason: Instruction limit 3.66/1.20 % (2408951)Termination phase: Property scanning 3.66/1.20 % (2408951)Time elapsed: 0.036 s 3.66/1.20 % (2408951)Peak memory usage: 11 MB 3.66/1.20 % (2408951)Instructions burned: 43 (million) 3.66/1.20 % (2408956)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=671657808:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_1795 on theBenchmark for (1795ds/181Mi) 3.66/1.20 % (2408945)Instruction limit reached! 3.66/1.20 % (2408945)------------------------------ 3.66/1.20 % (2408945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.66/1.20 % (2408945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.66/1.20 % (2408945)CaDiCaL version: 2.1.3 3.66/1.20 % (2408945)Termination reason: Instruction limit 3.66/1.20 % (2408945)Termination phase: Property scanning 3.66/1.20 % (2408945)Time elapsed: 0.112 s 3.66/1.20 % (2408945)Peak memory usage: 12 MB 3.66/1.20 % (2408945)Instructions burned: 144 (million) 3.66/1.20 % (2408957)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=2335337954:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1795 on theBenchmark for (1795ds/169Mi) 3.66/1.20 % (2408919)Instruction limit reached! 3.66/1.20 % (2408919)------------------------------ 3.66/1.20 % (2408919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.66/1.20 % (2408919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.66/1.20 % (2408919)CaDiCaL version: 2.1.3 3.66/1.20 % (2408919)Termination reason: Instruction limit 3.66/1.20 % (2408919)Termination phase: Saturation 3.66/1.20 % (2408919)Time elapsed: 0.271 s 3.66/1.20 % (2408919)Peak memory usage: 15 MB 3.66/1.20 % (2408919)Instructions burned: 328 (million) 3.66/1.20 % (2408959)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on 3.66/1.20 % (2408959)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=341973821:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_1795 on theBenchmark for (1795ds/6Mi) 3.66/1.20 % (2408950)Instruction limit reached! 3.66/1.20 % (2408950)------------------------------ 3.66/1.20 % (2408950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.66/1.20 % (2408950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.66/1.20 % (2408950)CaDiCaL version: 2.1.3 3.66/1.20 % (2408950)Termination reason: Instruction limit 3.66/1.20 % (2408950)Termination phase: Saturation 3.66/1.20 % (2408950)Time elapsed: 0.098 s 3.66/1.20 % (2408950)Peak memory usage: 14 MB 3.66/1.20 % (2408950)Instructions burned: 193 (million) 3.66/1.20 % (2408959)Instruction limit reached! 3.66/1.20 % (2408959)------------------------------ 3.66/1.20 % (2408959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.66/1.20 % (2408959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.66/1.20 % (2408959)CaDiCaL version: 2.1.3 3.66/1.20 % (2408959)Termination reason: Instruction limit 3.66/1.20 % (2408959)Termination phase: shuffling 3.66/1.20 % (2408959)Time elapsed: 0.006 s 3.66/1.20 % (2408959)Peak memory usage: 10 MB 3.66/1.20 % (2408959)Instructions burned: 7 (million) 3.66/1.20 % (2408961)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2555539336:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1794 on theBenchmark for (1794ds/22Mi) 3.66/1.20 % (2408964)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=1035289983:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_1794 on theBenchmark for (1794ds/316Mi) 3.66/1.20 % (2408961)Instruction limit reached! 3.66/1.20 % (2408961)------------------------------ 3.66/1.20 % (2408961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.66/1.20 % (2408961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.66/1.20 % (2408961)CaDiCaL version: 2.1.3 3.66/1.20 % (2408961)Termination reason: Instruction limit 3.66/1.20 % (2408961)Termination phase: shuffling 3.66/1.20 % (2408961)Time elapsed: 0.019 s 3.66/1.20 % (2408961)Peak memory usage: 10 MB 3.66/1.20 % (2408961)Instructions burned: 23 (million) 3.66/1.20 % (2408963)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3876629748:i=19:add=on:rtra=on_1794 on theBenchmark for (1794ds/19Mi) 3.66/1.20 % (2408963)Instruction limit reached! 3.66/1.20 % (2408963)------------------------------ 3.66/1.20 % (2408963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.66/1.20 % (2408963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.66/1.20 % (2408963)CaDiCaL version: 2.1.3 3.66/1.20 % (2408963)Termination reason: Instruction limit 3.66/1.20 % (2408963)Termination phase: shuffling 3.66/1.20 % (2408887) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2408879-2408887"... 3.66/1.20 % (2408963)Time elapsed: 0.017 s 3.66/1.20 % (2408963)Peak memory usage: 10 MB 3.66/1.20 % (2408963)Instructions burned: 19 (million) 3.66/1.20 % (2408967)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=2183809480:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_1794 on theBenchmark for (1794ds/853Mi) 3.66/1.20 % (2408887)...printing done. 3.66/1.20 % (2408887)Refutation found. Thanks to Tanya! 3.66/1.20 % SZS status Theorem for theBenchmark 3.66/1.20 % SZS output start Proof for theBenchmark 3.66/1.20 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType). 3.66/1.20 thf(func_def_0, type, in: ($i > $i > $o)). 3.66/1.20 thf(func_def_1, type, exu: (($i > $o) > $o)). 3.66/1.20 thf(func_def_3, type, setextAx: $o). 3.66/1.20 thf(func_def_5, type, emptysetAx: $o). 3.66/1.20 thf(func_def_6, type, setadjoin: ($i > $i > $i)). 3.66/1.20 thf(func_def_7, type, setadjoinAx: $o). 3.66/1.20 thf(func_def_8, type, powerset: ($i > $i)). 3.66/1.20 thf(func_def_9, type, powersetAx: $o). 3.66/1.20 thf(func_def_10, type, setunion: ($i > $i)). 3.66/1.20 thf(func_def_11, type, setunionAx: $o). 3.66/1.20 thf(func_def_13, type, omega0Ax: $o). 3.66/1.20 thf(func_def_14, type, omegaSAx: $o). 3.66/1.20 thf(func_def_15, type, omegaIndAx: $o). 3.66/1.20 thf(func_def_16, type, replAx: $o). 3.66/1.20 thf(func_def_17, type, foundationAx: $o). 3.66/1.20 thf(func_def_18, type, wellorderingAx: $o). 3.66/1.20 thf(func_def_19, type, descr: (($i > $o) > $i)). 3.66/1.20 thf(func_def_20, type, descrp: $o). 3.66/1.20 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)). 3.66/1.20 thf(func_def_22, type, dsetconstrI: $o). 3.66/1.20 thf(func_def_23, type, dsetconstrEL: $o). 3.66/1.20 thf(func_def_24, type, dsetconstrER: $o). 3.66/1.20 thf(func_def_25, type, exuE1: $o). 3.66/1.20 thf(func_def_26, type, prop2set: ($o > $i)). 3.66/1.20 thf(func_def_27, type, prop2setE: $o). 3.66/1.20 thf(func_def_28, type, emptysetE: $o). 3.66/1.20 thf(func_def_29, type, emptysetimpfalse: $o). 3.66/1.20 thf(func_def_30, type, notinemptyset: $o). 3.66/1.20 thf(func_def_31, type, exuE3e: $o). 3.66/1.20 thf(func_def_32, type, setext: $o). 3.66/1.20 thf(func_def_33, type, emptyI: $o). 3.66/1.20 thf(func_def_34, type, noeltsimpempty: $o). 3.66/1.20 thf(func_def_35, type, setbeta: $o). 3.66/1.20 thf(func_def_36, type, nonempty: ($i > $o)). 3.66/1.20 thf(func_def_37, type, nonemptyE1: $o). 3.66/1.20 thf(func_def_38, type, nonemptyI: $o). 3.66/1.20 thf(func_def_39, type, nonemptyI1: $o). 3.66/1.20 thf(func_def_40, type, setadjoinIL: $o). 3.66/1.20 thf(func_def_41, type, emptyinunitempty: $o). 3.66/1.20 thf(func_def_42, type, setadjoinIR: $o). 3.66/1.20 thf(func_def_43, type, setadjoinE: $o). 3.66/1.20 thf(func_def_44, type, setadjoinOr: $o). 3.66/1.20 thf(func_def_45, type, setoftrueEq: $o). 3.66/1.20 thf(func_def_46, type, powersetI: $o). 3.66/1.20 thf(func_def_47, type, emptyinPowerset: $o). 3.66/1.20 thf(func_def_48, type, emptyInPowerset: $o). 3.66/1.20 thf(func_def_49, type, powersetE: $o). 3.66/1.20 thf(func_def_50, type, setunionI: $o). 3.66/1.20 thf(func_def_51, type, setunionE: $o). 3.66/1.20 thf(func_def_52, type, subPowSU: $o). 3.66/1.20 thf(func_def_53, type, exuE2: $o). 3.66/1.20 thf(func_def_54, type, nonemptyImpWitness: $o). 3.66/1.20 thf(func_def_55, type, uniqinunit: $o). 3.66/1.20 thf(func_def_56, type, notinsingleton: $o). 3.66/1.20 thf(func_def_57, type, eqinunit: $o). 3.66/1.20 thf(func_def_58, type, singletonsswitch: $o). 3.66/1.20 thf(func_def_59, type, upairsetE: $o). 3.66/1.20 thf(func_def_60, type, upairsetIL: $o). 3.66/1.20 thf(func_def_61, type, upairsetIR: $o). 3.66/1.20 thf(func_def_62, type, emptyE1: $o). 3.66/1.20 thf(func_def_63, type, vacuousDall: $o). 3.66/1.20 thf(func_def_64, type, quantDeMorgan1: $o). 3.66/1.20 thf(func_def_65, type, quantDeMorgan2: $o). 3.66/1.20 thf(func_def_66, type, quantDeMorgan3: $o). 3.66/1.20 thf(func_def_67, type, quantDeMorgan4: $o). 3.66/1.20 thf(func_def_68, type, prop2setI: $o). 3.66/1.20 thf(func_def_69, type, set2prop: ($i > $o)). 3.66/1.20 thf(func_def_70, type, prop2set2propI: $o). 3.66/1.20 thf(func_def_71, type, notdexE: $o). 3.66/1.20 thf(func_def_72, type, notdallE: $o). 3.66/1.20 thf(func_def_73, type, exuI1: $o). 3.66/1.20 thf(func_def_74, type, exuI3: $o). 3.66/1.20 thf(func_def_75, type, exuI2: $o). 3.66/1.20 thf(func_def_76, type, inCongP: $o). 3.66/1.20 thf(func_def_77, type, in__Cong: $o). 3.66/1.20 thf(func_def_78, type, exuE3u: $o). 3.66/1.20 thf(func_def_79, type, exu__Cong: $o). 3.66/1.20 thf(func_def_80, type, emptyset__Cong: $o). 3.66/1.20 thf(func_def_81, type, setadjoin__Cong: $o). 3.66/1.20 thf(func_def_82, type, powerset__Cong: $o). 3.66/1.20 thf(func_def_83, type, setunion__Cong: $o). 3.66/1.20 thf(func_def_84, type, omega__Cong: $o). 3.66/1.20 thf(func_def_85, type, exuEu: $o). 3.66/1.20 thf(func_def_86, type, descr__Cong: $o). 3.66/1.20 thf(func_def_87, type, dsetconstr__Cong: $o). 3.66/1.20 thf(func_def_88, type, subset: ($i > $i > $o)). 3.66/1.20 thf(func_def_89, type, disjoint: ($i > $i > $o)). 3.66/1.20 thf(func_def_90, type, setsmeet: ($i > $i > $o)). 3.66/1.20 thf(func_def_91, type, subsetI1: $o). 3.66/1.20 thf(func_def_92, type, eqimpsubset2: $o). 3.66/1.20 thf(func_def_93, type, eqimpsubset1: $o). 3.66/1.20 thf(func_def_94, type, subsetI2: $o). 3.66/1.20 thf(func_def_95, type, emptysetsubset: $o). 3.66/1.20 thf(func_def_96, type, subsetE: $o). 3.66/1.20 thf(func_def_97, type, subsetE2: $o). 3.66/1.20 thf(func_def_98, type, notsubsetI: $o). 3.66/1.20 thf(func_def_99, type, notequalI1: $o). 3.66/1.20 thf(func_def_100, type, notequalI2: $o). 3.66/1.20 thf(func_def_101, type, subsetRefl: $o). 3.66/1.20 thf(func_def_102, type, subsetTrans: $o). 3.66/1.20 thf(func_def_103, type, setadjoinSub: $o). 3.66/1.20 thf(func_def_104, type, setadjoinSub2: $o). 3.66/1.20 thf(func_def_105, type, subset2powerset: $o). 3.66/1.20 thf(func_def_106, type, setextsub: $o). 3.66/1.20 thf(func_def_107, type, subsetemptysetimpeq: $o). 3.66/1.20 thf(func_def_108, type, powersetI1: $o). 3.66/1.20 thf(func_def_109, type, powersetE1: $o). 3.66/1.20 thf(func_def_110, type, inPowerset: $o). 3.66/1.20 thf(func_def_111, type, powersetsubset: $o). 3.66/1.20 thf(func_def_112, type, sepInPowerset: $o). 3.66/1.20 thf(func_def_113, type, sepSubset: $o). 3.66/1.20 thf(func_def_114, type, binunion: ($i > $i > $i)). 3.66/1.20 thf(func_def_115, type, binunionIL: $o). 3.66/1.20 thf(func_def_116, type, upairset2IR: $o). 3.66/1.20 thf(func_def_117, type, binunionIR: $o). 3.66/1.20 thf(func_def_118, type, binunionEcases: $o). 3.66/1.20 thf(func_def_119, type, binunionE: $o). 3.66/1.20 thf(func_def_120, type, binunionLsub: $o). 3.66/1.20 thf(func_def_121, type, binunionRsub: $o). 3.66/1.20 thf(func_def_122, type, binintersect: ($i > $i > $i)). 3.66/1.20 thf(func_def_123, type, binintersectI: $o). 3.66/1.20 thf(func_def_124, type, binintersectSubset5: $o). 3.66/1.20 thf(func_def_125, type, binintersectEL: $o). 3.66/1.20 thf(func_def_126, type, binintersectLsub: $o). 3.66/1.20 thf(func_def_127, type, binintersectSubset2: $o). 3.66/1.20 thf(func_def_128, type, binintersectSubset3: $o). 3.66/1.20 thf(func_def_129, type, binintersectER: $o). 3.66/1.20 thf(func_def_130, type, disjointsetsI1: $o). 3.66/1.20 thf(func_def_131, type, binintersectRsub: $o). 3.66/1.20 thf(func_def_132, type, binintersectSubset4: $o). 3.66/1.20 thf(func_def_133, type, binintersectSubset1: $o). 3.66/1.20 thf(func_def_134, type, bs114d: $o). 3.66/1.20 thf(func_def_135, type, regular: ($i > $o)). 3.66/1.20 thf(func_def_136, type, setminus: ($i > $i > $i)). 3.66/1.20 thf(func_def_137, type, setminusI: $o). 3.66/1.20 thf(func_def_138, type, setminusEL: $o). 3.66/1.20 thf(func_def_139, type, setminusER: $o). 3.66/1.20 thf(func_def_140, type, setminusSubset2: $o). 3.66/1.20 thf(func_def_141, type, setminusERneg: $o). 3.66/1.20 thf(func_def_142, type, setminusELneg: $o). 3.66/1.20 thf(func_def_143, type, setminusILneg: $o). 3.66/1.20 thf(func_def_144, type, setminusIRneg: $o). 3.66/1.20 thf(func_def_145, type, setminusLsub: $o). 3.66/1.20 thf(func_def_146, type, setminusSubset1: $o). 3.66/1.20 thf(func_def_147, type, symdiff: ($i > $i > $i)). 3.66/1.20 thf(func_def_148, type, symdiffE: $o). 3.66/1.20 thf(func_def_149, type, symdiffI1: $o). 3.66/1.20 thf(func_def_150, type, symdiffI2: $o). 3.66/1.20 thf(func_def_151, type, symdiffIneg1: $o). 3.66/1.20 thf(func_def_152, type, symdiffIneg2: $o). 3.66/1.20 thf(func_def_153, type, iskpair: ($i > $o)). 3.66/1.20 thf(func_def_154, type, secondinupair: $o). 3.66/1.20 thf(func_def_155, type, setukpairIL: $o). 3.66/1.20 thf(func_def_156, type, setukpairIR: $o). 3.66/1.20 thf(func_def_157, type, kpairiskpair: $o). 3.66/1.20 thf(func_def_158, type, kpair: ($i > $i > $i)). 3.66/1.20 thf(func_def_159, type, kpairp: $o). 3.66/1.20 thf(func_def_160, type, cartprod: ($i > $i > $i)). 3.66/1.20 thf(func_def_161, type, singletonsubset: $o). 3.66/1.20 thf(func_def_162, type, singletoninpowerset: $o). 3.66/1.20 thf(func_def_163, type, singletoninpowunion: $o). 3.66/1.20 thf(func_def_164, type, upairset2E: $o). 3.66/1.20 thf(func_def_165, type, upairsubunion: $o). 3.66/1.20 thf(func_def_166, type, upairinpowunion: $o). 3.66/1.20 thf(func_def_167, type, ubforcartprodlem1: $o). 3.66/1.20 thf(func_def_168, type, ubforcartprodlem2: $o). 3.66/1.20 thf(func_def_169, type, ubforcartprodlem3: $o). 3.66/1.20 thf(func_def_170, type, cartprodpairin: $o). 3.66/1.20 thf(func_def_171, type, cartprodmempair1: $o). 3.66/1.20 thf(func_def_172, type, cartprodmempair: $o). 3.66/1.20 thf(func_def_173, type, setunionE2: $o). 3.66/1.20 thf(func_def_174, type, setunionsingleton1: $o). 3.66/1.20 thf(func_def_175, type, setunionsingleton2: $o). 3.66/1.20 thf(func_def_176, type, setunionsingleton: $o). 3.66/1.20 thf(func_def_177, type, singleton: ($i > $o)). 3.66/1.20 thf(func_def_178, type, singletonprop: $o). 3.66/1.20 thf(func_def_179, type, ex1: ($i > ($i > $o) > $o)). 3.66/1.20 thf(func_def_180, type, ex1E1: $o). 3.66/1.20 thf(func_def_181, type, ex1I: $o). 3.66/1.20 thf(func_def_182, type, ex1I2: $o). 3.66/1.20 thf(func_def_183, type, singletonsuniq: $o). 3.66/1.20 thf(func_def_184, type, atmost1p: ($i > $o)). 3.66/1.20 thf(func_def_185, type, atleast2p: ($i > $o)). 3.66/1.20 thf(func_def_186, type, atmost2p: ($i > $o)). 3.66/1.20 thf(func_def_187, type, upairsetp: ($i > $o)). 3.66/1.20 thf(func_def_188, type, setukpairinjL1: $o). 3.66/1.20 thf(func_def_189, type, kfstsingleton: $o). 3.66/1.20 thf(func_def_190, type, theprop: $o). 3.66/1.20 thf(func_def_191, type, kfst: ($i > $i)). 3.66/1.20 thf(func_def_192, type, kfstpairEq: $o). 3.66/1.20 thf(func_def_193, type, cartprodfstin: $o). 3.66/1.20 thf(func_def_194, type, setukpairinjL2: $o). 3.66/1.20 thf(func_def_195, type, setukpairinjL: $o). 3.66/1.20 thf(func_def_196, type, setukpairinjR11: $o). 3.66/1.20 thf(func_def_197, type, setukpairinjR12: $o). 3.66/1.20 thf(func_def_198, type, setukpairinjR1: $o). 3.66/1.20 thf(func_def_199, type, upairequniteq: $o). 3.66/1.20 thf(func_def_200, type, setukpairinjR2: $o). 3.66/1.20 thf(func_def_201, type, setukpairinjR: $o). 3.66/1.20 thf(func_def_202, type, ksndsingleton: $o). 3.66/1.20 thf(func_def_203, type, ksnd: ($i > $i)). 3.66/1.20 thf(func_def_204, type, ksndpairEq: $o). 3.66/1.20 thf(func_def_205, type, kpairsurjEq: $o). 3.66/1.20 thf(func_def_206, type, cartprodsndin: $o). 3.66/1.20 thf(func_def_207, type, cartprodpairmemEL: $o). 3.66/1.20 thf(func_def_208, type, cartprodpairmemER: $o). 3.66/1.20 thf(func_def_209, type, cartprodmempaircEq: $o). 3.66/1.20 thf(func_def_210, type, cartprodfstpairEq: $o). 3.66/1.20 thf(func_def_211, type, cartprodsndpairEq: $o). 3.66/1.20 thf(func_def_212, type, cartprodpairsurjEq: $o). 3.66/1.20 thf(func_def_213, type, breln: ($i > $i > $i > $o)). 3.66/1.20 thf(func_def_214, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)). 3.66/1.20 thf(func_def_215, type, dpsetconstrI: $o). 3.66/1.20 thf(func_def_216, type, dpsetconstrSub: $o). 3.66/1.20 thf(func_def_217, type, setOfPairsIsBReln: $o). 3.66/1.20 thf(func_def_218, type, dpsetconstrERa: $o). 3.66/1.20 thf(func_def_219, type, dpsetconstrEL1: $o). 3.66/1.20 thf(func_def_220, type, dpsetconstrEL2: $o). 3.66/1.20 thf(func_def_221, type, dpsetconstrER: $o). 3.66/1.20 thf(func_def_222, type, func: ($i > $i > $i > $o)). 3.66/1.20 thf(func_def_223, type, funcSet: ($i > $i > $i)). 3.66/1.20 thf(func_def_224, type, funcImageSingleton: $o). 3.66/1.20 thf(func_def_225, type, apProp: $o). 3.66/1.20 thf(func_def_226, type, ap: ($i > $i > $i > $i > $i)). 3.66/1.20 thf(func_def_227, type, app: $o). 3.66/1.20 thf(func_def_228, type, infuncsetfunc: $o). 3.66/1.20 thf(func_def_229, type, ap2p: $o). 3.66/1.20 thf(func_def_230, type, funcinfuncset: $o). 3.66/1.20 thf(func_def_231, type, lamProp: $o). 3.66/1.20 thf(func_def_232, type, lam: ($i > $i > ($i > $i) > $i)). 3.66/1.20 thf(func_def_233, type, lamp: $o). 3.66/1.20 thf(func_def_234, type, lam2p: $o). 3.66/1.20 thf(func_def_235, type, brelnall1: $o). 3.66/1.20 thf(func_def_236, type, brelnall2: $o). 3.66/1.20 thf(func_def_237, type, ex1E2: $o). 3.66/1.20 thf(func_def_238, type, funcGraphProp1: $o). 3.66/1.20 thf(func_def_239, type, funcGraphProp3: $o). 3.66/1.20 thf(func_def_240, type, funcGraphProp2: $o). 3.66/1.20 thf(func_def_241, type, funcextLem: $o). 3.66/1.20 thf(func_def_242, type, funcGraphProp4: $o). 3.66/1.20 thf(func_def_243, type, subbreln: $o). 3.66/1.20 thf(func_def_244, type, eqbreln: $o). 3.66/1.20 thf(func_def_245, type, funcext: $o). 3.66/1.20 thf(func_def_246, type, funcext2: $o). 3.66/1.20 thf(func_def_247, type, ap2apEq1: $o). 3.66/1.20 thf(func_def_248, type, ap2apEq2: $o). 3.66/1.20 thf(func_def_249, type, beta1: $o). 3.66/1.20 thf(func_def_250, type, eta1: $o). 3.66/1.20 thf(func_def_251, type, lam2lamEq: $o). 3.66/1.20 thf(func_def_252, type, beta2: $o). 3.66/1.20 thf(func_def_253, type, eta2: $o). 3.66/1.20 thf(func_def_254, type, iffalseProp1: $o). 3.66/1.20 thf(func_def_255, type, iffalseProp2: $o). 3.66/1.20 thf(func_def_256, type, iftrueProp1: $o). 3.66/1.20 thf(func_def_257, type, iftrueProp2: $o). 3.66/1.20 thf(func_def_258, type, ifSingleton: $o). 3.66/1.20 thf(func_def_259, type, if: ($i > $o > $i > $i > $i)). 3.66/1.20 thf(func_def_260, type, ifp: $o). 3.66/1.20 thf(func_def_261, type, theeq: $o). 3.66/1.20 thf(func_def_262, type, iftrue: $o). 3.66/1.20 thf(func_def_263, type, iffalse: $o). 3.66/1.20 thf(func_def_264, type, iftrueorfalse: $o). 3.66/1.20 thf(func_def_265, type, binintersectT_lem: $o). 3.66/1.20 thf(func_def_266, type, binunionT_lem: $o). 3.66/1.20 thf(func_def_267, type, powersetT_lem: $o). 3.66/1.20 thf(func_def_268, type, setminusT_lem: $o). 3.66/1.20 thf(func_def_269, type, complementT_lem: $o). 3.66/1.20 thf(func_def_270, type, setextT: $o). 3.66/1.20 thf(func_def_271, type, subsetTI: $o). 3.66/1.20 thf(func_def_272, type, powersetTI1: $o). 3.66/1.20 thf(func_def_273, type, powersetTE1: $o). 3.66/1.20 thf(func_def_274, type, complementTI1: $o). 3.66/1.20 thf(func_def_275, type, complementTE1: $o). 3.66/1.20 thf(func_def_276, type, binintersectTELcontra: $o). 3.66/1.20 thf(func_def_277, type, binintersectTERcontra: $o). 3.66/1.20 thf(func_def_278, type, contrasubsetT: $o). 3.66/1.20 thf(func_def_279, type, contrasubsetT1: $o). 3.66/1.20 thf(func_def_280, type, contrasubsetT2: $o). 3.66/1.20 thf(func_def_281, type, contrasubsetT3: $o). 3.66/1.20 thf(func_def_282, type, doubleComplementI1: $o). 3.66/1.20 thf(func_def_283, type, doubleComplementE1: $o). 3.66/1.20 thf(func_def_284, type, doubleComplementSub1: $o). 3.66/1.20 thf(func_def_285, type, doubleComplementSub2: $o). 3.66/1.20 thf(func_def_286, type, doubleComplementEq: $o). 3.66/1.20 thf(func_def_287, type, complementTnotintersectT: $o). 3.66/1.20 thf(func_def_288, type, complementImpComplementIntersect: $o). 3.66/1.20 thf(func_def_289, type, complementSubsetComplementIntersect: $o). 3.66/1.20 thf(func_def_290, type, complementInPowersetComplementIntersect: $o). 3.66/1.20 thf(func_def_291, type, contraSubsetComplement: $o). 3.66/1.20 thf(func_def_292, type, complementTcontraSubset: $o). 3.66/1.20 thf(func_def_293, type, binunionTILcontra: $o). 3.66/1.20 thf(func_def_294, type, binunionTIRcontra: $o). 3.66/1.20 thf(func_def_295, type, inIntersectImpInUnion: $o). 3.66/1.20 thf(func_def_296, type, inIntersectImpInUnion2: $o). 3.66/1.20 thf(func_def_299, type, db0: !>[X0: $tType]:(X0)). 3.66/1.20 thf(func_def_300, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))). 3.66/1.20 thf(func_def_301, type, db1: !>[X0: $tType]:(X0)). 3.66/1.20 thf(func_def_302, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))). 3.66/1.20 thf(func_def_303, type, vNOT: ($o > $o)). 3.66/1.20 thf(func_def_304, type, vOR: ($o > $o > $o)). 3.66/1.20 thf(func_def_305, type, vAND: ($o > $o > $o)). 3.66/1.20 thf(func_def_306, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))). 3.66/1.20 thf(func_def_307, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))). 3.66/1.20 thf(func_def_308, type, vIMP: ($o > $o > $o)). 3.66/1.20 thf(func_def_309, type, db2: !>[X0: $tType]:(X0)). 3.66/1.20 thf(func_def_310, type, sP0: ($i > $i > $o)). 3.66/1.20 thf(func_def_311, type, sP1: ($i > $o)). 3.66/1.20 thf(func_def_312, type, sP2: $o). 3.66/1.20 thf(func_def_313, type, sP3: $o). 3.66/1.20 thf(func_def_321, type, sK11: ($i > $i)). 3.66/1.20 thf(func_def_324, type, sK14: ($i > $i > $o)). 3.66/1.20 thf(func_def_328, type, sK18: ($i > $o)). 3.66/1.20 thf(func_def_350, type, sK40: ($i > $o)). 3.66/1.20 thf(func_def_352, type, sK42: (($i > $o) > $i > $i > $i > $i)). 3.66/1.20 thf(func_def_353, type, sK43: (($i > $o) > $i > $i > $i > $i)). 3.66/1.20 thf(func_def_372, type, sK62: ($i > $i)). 3.66/1.20 thf(func_def_373, type, sK63: (($i > $i) > $i > $i > $i)). 3.66/1.20 thf(func_def_383, type, sK73: $o). 3.66/1.20 thf(func_def_388, type, sK78: ($i > $i > $i)). 3.66/1.20 thf(func_def_393, type, sK83: ($i > $i > $i)). 3.66/1.20 thf(func_def_404, type, sK94: ($i > $i > $o)). 3.66/1.20 thf(func_def_410, type, sK100: $o). 3.66/1.20 thf(func_def_430, type, sK120: ($i > $o)). 3.66/1.20 thf(func_def_440, type, sK130: ($i > $i > $i > $i)). 3.66/1.20 thf(func_def_441, type, sK131: ($i > $i > $i > $i)). 3.66/1.20 thf(func_def_442, type, sK132: (($i > $o) > $i > $i > $i)). 3.66/1.20 thf(func_def_445, type, sK135: ($i > $o)). 3.66/1.20 thf(func_def_455, type, sK145: ($i > $o)). 3.66/1.20 thf(func_def_459, type, sK149: ($i > $o)). 3.66/1.20 thf(func_def_462, type, sK152: ($i > ($i > $o) > $i)). 3.66/1.20 thf(func_def_481, type, sK171: ($i > $o)). 3.66/1.20 thf(func_def_486, type, sK176: $o). 3.66/1.20 thf(func_def_487, type, sK177: ($i > $i)). 3.66/1.20 thf(func_def_516, type, sK206: (($i > $o) > $i > $i)). 3.66/1.20 thf(func_def_518, type, sK208: ($i > $o)). 3.66/1.20 thf(func_def_520, type, sK210: $o). 3.66/1.20 thf(func_def_537, type, sK227: $o). 3.66/1.20 thf(func_def_542, type, sK232: ($i > $i > $i)). 3.66/1.20 thf(func_def_547, type, sK237: ($i > $o)). 3.66/1.20 thf(func_def_551, type, sK241: $o). 3.66/1.20 thf(func_def_555, type, sK245: (($i > $o) > ($i > $o) > $i > $i > $i)). 3.66/1.20 thf(func_def_556, type, sK246: (($i > $o) > ($i > $o) > $i > $i > $i)). 3.66/1.20 thf(func_def_559, type, sK249: ($i > $o)). 3.66/1.20 thf(func_def_560, type, sK250: ($i > $o)). 3.66/1.20 thf(func_def_567, type, sK257: ($i > $i > $i > $i > $i)). 3.66/1.20 thf(func_def_574, type, sK264: (($i > $o) > $i > $i)). 3.66/1.20 thf(func_def_576, type, sK266: ($i > $o)). 3.66/1.20 thf(func_def_580, type, sK270: ($i > $o)). 3.66/1.20 thf(func_def_586, type, sK276: $o). 3.66/1.20 thf(func_def_595, type, sK285: ($i > $i > $i)). 3.66/1.20 thf(func_def_596, type, sK286: ($i > $i > $i)). 3.66/1.20 thf(func_def_606, type, sK296: ($i > $i)). 3.66/1.20 thf(func_def_608, type, sK298: ($i > $i)). 3.66/1.20 thf(func_def_609, type, sK299: (($i > $i) > $i > $i > $i)). 3.66/1.20 thf(func_def_612, type, sK302: ($i > $i)). 3.66/1.20 thf(func_def_617, type, sK307: ($i > $o)). 3.66/1.20 thf(func_def_619, type, sK309: (($i > $o) > $i > $i > $i > $i)). 3.66/1.20 thf(func_def_620, type, sK310: (($i > $o) > $i > $i > $i > $i)). 3.66/1.20 thf(func_def_621, type, sK311: ($i > $i)). 3.66/1.20 thf(func_def_625, type, sK315: $o). 3.66/1.20 thf(func_def_641, type, sK331: ($i > $i > $o)). 3.66/1.20 thf(func_def_642, type, sK332: ($i > ($i > $o) > $i)). 3.66/1.20 thf(func_def_643, type, sK333: ($i > $o)). 3.66/1.20 thf(func_def_645, type, sK335: ($i > $i > ($i > $i) > $i)). 3.66/1.20 thf(func_def_646, type, sK336: ($i > $i)). 3.66/1.20 thf(func_def_654, type, sK344: ($i > $o)). 3.66/1.20 thf(func_def_660, type, sK350: ($i > $i > $i)). 3.66/1.20 thf(func_def_662, type, sK352: ($i > $i > $o)). 3.66/1.20 thf(func_def_663, type, sK353: ($i > $i)). 3.66/1.20 thf(func_def_664, type, sK354: ($i > $i)). 3.66/1.20 thf(func_def_665, type, sK355: (($i > $i > $o) > $i > $i)). 3.66/1.20 thf(func_def_666, type, sK356: ($i > ($i > $i > $o) > $i > $i)). 3.66/1.20 thf(func_def_667, type, sK357: (($i > $i > $o) > $i > $i)). 3.66/1.20 thf(func_def_677, type, sK367: ($i > ($i > $o) > $i)). 3.66/1.20 thf(func_def_678, type, sK368: ($i > $o)). 3.66/1.20 thf(func_def_680, type, sK370: ($i > $i > ($i > $i) > $i)). 3.66/1.20 thf(func_def_681, type, sK371: ($i > $i)). 3.66/1.20 thf(func_def_694, type, sK384: ($i > ($i > $o) > $i)). 3.66/1.20 thf(func_def_695, type, sK385: ($i > $o)). 3.66/1.20 thf(func_def_703, type, sK393: $o). 3.66/1.20 thf(func_def_708, type, sK398: ($i > $o)). 3.66/1.20 thf(func_def_718, type, sK408: ($i > $i > $i)). 3.66/1.20 thf(func_def_735, type, sK425: ($i > $o)). 3.66/1.20 thf(func_def_738, type, sK428: ($i > ($i > $o) > $i)). 3.66/1.20 thf(func_def_742, type, sK432: ($i > $i > $i)). 3.66/1.20 thf(func_def_748, type, sK438: ($i > $i > $o)). 3.66/1.20 thf(func_def_757, type, sK447: (($i > $o) > $i)). 3.66/1.20 thf(func_def_758, type, sK448: ($i > $o)). 3.66/1.20 thf(func_def_765, type, sK455: ($i > $o)). 3.66/1.20 thf(func_def_767, type, sK457: (($i > $o) > $i > $i)). 3.66/1.20 thf(func_def_769, type, sK459: ($i > $o)). 3.66/1.20 thf(func_def_771, type, sK461: (($i > $o) > $i > $i)). 3.66/1.20 thf(func_def_772, type, sK462: (($i > $o) > $i > $i)). 3.66/1.20 thf(func_def_777, type, sK467: ($i > $o)). 3.66/1.20 thf(func_def_778, type, sK468: ($i > $o)). 3.66/1.20 thf(func_def_779, type, sK469: (($i > $o) > ($i > $o) > $i)). 3.66/1.20 thf(func_def_780, type, sK470: (($i > $o) > ($i > $o) > $i)). 3.66/1.20 thf(func_def_784, type, sK474: $o). 3.66/1.20 thf(func_def_793, type, sK483: $o). 3.66/1.20 thf(func_def_795, type, sK485: ($i > $i)). 3.66/1.20 thf(func_def_805, type, sK495: ($i > $o)). 3.66/1.20 thf(func_def_815, type, sK505: ($i > $i)). 3.66/1.20 thf(func_def_816, type, sK506: ($i > $i)). 3.66/1.20 thf(func_def_817, type, sK507: ($i > $i)). 3.66/1.20 thf(func_def_818, type, sK508: ($i > $i)). 3.66/1.20 thf(func_def_819, type, sK509: ($i > $i)). 3.66/1.20 thf(func_def_820, type, sK510: ($i > $i > $i > $i)). 3.66/1.20 thf(func_def_821, type, sK511: ($i > $i)). 3.66/1.20 thf(func_def_822, type, sK512: ($i > $i)). 3.66/1.20 thf(func_def_823, type, sK513: ($i > $i)). 3.66/1.20 thf(func_def_824, type, sK514: ($i > $i)). 3.66/1.20 thf(func_def_825, type, sK515: ($i > $i > $i)). 3.66/1.20 thf(func_def_826, type, sK516: ($i > $i > $i)). 3.66/1.20 thf(func_def_827, type, sK517: ($i > $i > $i > $i)). 3.66/1.20 thf(func_def_828, type, sK518: ($i > $i > $i > $i)). 3.66/1.20 thf(func_def_829, type, sK519: ($i > $i > $i > $i)). 3.66/1.20 thf(func_def_830, type, sK520: ($i > $i > $i)). 3.66/1.20 thf(func_def_831, type, sK521: ($i > $i > $i)). 3.66/1.20 thf(func_def_832, type, sK522: ($i > $i > $i)). 3.66/1.20 thf(func_def_842, type, sK532: ($i > $o)). 3.66/1.20 thf(func_def_863, type, sK553: (($i > $o) > $i > $i)). 3.66/1.20 thf(func_def_864, type, sK554: (($i > $o) > $i > $i)). 3.66/1.20 thf(func_def_866, type, sK556: ($i > $o)). 3.66/1.20 thf(func_def_870, type, sK560: $o). 3.66/1.20 thf(func_def_885, type, sK575: ($i > $i > $o)). 3.66/1.20 thf(func_def_890, type, sK580: $o). 3.66/1.20 thf(func_def_893, type, sK583: ($i > $i > $i)). 3.66/1.20 thf(func_def_894, type, sK584: ($i > $o)). 3.66/1.20 thf(func_def_905, type, sK595: $o). 3.66/1.20 thf(func_def_910, type, sK600: (($i > $o) > $i)). 3.66/1.20 thf(func_def_911, type, sK601: ($i > $o)). 3.66/1.20 thf(func_def_912, type, sK602: ($i > $i)). 3.66/1.20 thf(func_def_916, type, sK606: ($i > $i > $i > $i > $i)). 3.66/1.20 thf(func_def_917, type, sK607: ($i > $i > $i > $i > $i)). 3.66/1.20 thf(func_def_931, type, sK621: ($i > $i > $i > $i > $i)). 3.66/1.20 thf(func_def_940, type, sK630: ($i > $i > $i > $i)). 3.66/1.20 thf(func_def_948, type, sK638: $o). 3.66/1.20 thf(func_def_954, type, sK644: ($i > $o)). 3.66/1.20 thf(func_def_955, type, sK645: ($i > $i > $o)). 3.66/1.20 thf(func_def_974, type, sK664: $o). 3.66/1.20 thf(func_def_981, type, sK671: ($i > $i > $i > $i > $i)). 3.66/1.20 thf(func_def_982, type, sK672: ($i > $i > $i > $i > $i)). 3.66/1.20 thf(func_def_983, type, sK673: ($i > $i > $i > $i > $i)). 3.66/1.20 thf(func_def_984, type, sK674: ($i > $i > $i > $i > $i)). 3.66/1.20 thf(func_def_985, type, sK675: ($i > $i > $i > $i)). 3.66/1.20 thf(func_def_989, type, sK679: ($i > $i > $i > $i)). 3.66/1.20 thf(func_def_990, type, sK680: ($i > $i > $i > $i)). 3.66/1.20 thf(func_def_1003, type, sK693: ($i > $i > $i > $i > $i)). 3.66/1.20 thf(func_def_1018, type, sK708: ($i > $i)). 3.66/1.20 thf(func_def_1022, type, sK712: ($i > $i > $i)). 3.66/1.20 thf(func_def_1035, type, sK725: ($i > ($i > $i) > $i > $i)). 3.66/1.20 thf(func_def_1037, type, sK727: ($i > $i)). 3.66/1.20 thf(func_def_1048, type, sK738: ($i > $i > $o)). 3.66/1.20 thf(func_def_1054, type, sK744: ($i > $o)). 3.66/1.20 thf(func_def_1056, type, sK746: (($i > $o) > $i)). 3.66/1.20 thf(func_def_1057, type, sK747: (($i > $o) > $i)). 3.66/1.20 thf(func_def_1062, type, sK752: ($i > $o)). 3.66/1.20 thf(func_def_1064, type, sK754: (($i > $o) > $i > $i)). 3.66/1.20 thf(func_def_1075, type, sK765: ($i > $i)). 3.66/1.20 thf(func_def_1079, type, sK769: ($i > $i > ($i > $i) > $i)). 3.66/1.20 thf(func_def_1101, type, sK791: (($i > $o) > $i)). 3.66/1.20 thf(func_def_1102, type, sK792: ($i > $o)). 3.66/1.20 thf(func_def_1103, type, sK793: ($i > $i)). 3.66/1.20 thf(func_def_1106, type, sK796: ($i > $o)). 3.66/1.20 thf(func_def_1111, type, sK801: (($i > $o) > ($i > $o) > $i)). 3.66/1.20 thf(func_def_1112, type, sK802: (($i > $o) > ($i > $o) > $i)). 3.66/1.20 thf(func_def_1113, type, sK803: ($i > $o)). 3.66/1.20 thf(func_def_1114, type, sK804: ($i > $o)). 3.66/1.20 thf(func_def_1120, type, sK810: ($o > $i > $i > $i)). 3.66/1.20 thf(func_def_1123, type, sK813: $o). 3.66/1.20 thf(f101,axiom,( 3.66/1.20 (binunionIL = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => (in @ X2 @ (binunion @ X0 @ X1))))), 3.66/1.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL)). 3.66/1.20 thf(f108,axiom,( 3.66/1.20 (binintersectI = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))))), 3.66/1.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI)). 3.66/1.20 thf(f110,axiom,( 3.66/1.20 (binintersectEL = ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))), 3.66/1.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL)). 3.66/1.20 thf(f114,axiom,( 3.66/1.20 (binintersectER = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))), 3.66/1.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER)). 3.66/1.20 thf(f263,conjecture,( 3.66/1.20 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 3.66/1.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions)). 3.66/1.20 thf(f264,negated_conjecture,( 3.66/1.20 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 3.66/1.20 inference(negated_conjecture,[status(cth)],[f263])). 3.66/1.20 thf(f314,plain,( 3.66/1.20 (binunionIL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => (in @ X1 @ (binunion @ X2 @ X0))))), 3.66/1.20 inference(rectify,[],[f101])). 3.66/1.20 thf(f315,plain,( 3.66/1.20 (binunionIL = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X1 @ X2)) = $true) => (((in @ X1 @ (binunion @ X2 @ X0))) = $true))), 3.66/1.20 inference(fool_elimination,[],[f314])). 3.66/1.20 thf(f501,plain,( 3.66/1.20 (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (binintersect @ X2 @ X0)) => (in @ X1 @ X0)))), 3.66/1.20 inference(rectify,[],[f114])). 3.66/1.20 thf(f502,plain,( 3.66/1.20 (binintersectER = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X1 @ (binintersect @ X2 @ X0)))) => (((in @ X1 @ X0)) = $true))), 3.66/1.20 inference(fool_elimination,[],[f501])). 3.66/1.20 thf(f531,plain,( 3.66/1.20 (binintersectI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ (binintersect @ X2 @ X0)))))), 3.66/1.20 inference(rectify,[],[f108])). 3.66/1.20 thf(f532,plain,( 3.66/1.20 (binintersectI = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X1 @ X2)) = $true) => ((((in @ X1 @ X0)) = $true) => ($true = ((in @ X1 @ (binintersect @ X2 @ X0))))))), 3.66/1.20 inference(fool_elimination,[],[f531])). 3.66/1.20 thf(f611,plain,( 3.66/1.20 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 3.66/1.20 inference(rectify,[],[f264])). 3.66/1.20 thf(f612,plain,( 3.66/1.20 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ((contrasubsetT = $true) => ((contrasubsetT1 = $true) => ((contrasubsetT2 = $true) => ((contrasubsetT3 = $true) => ((doubleComplementI1 = $true) => ((doubleComplementE1 = $true) => ((doubleComplementSub1 = $true) => ((doubleComplementSub2 = $true) => ((doubleComplementEq = $true) => ((complementTnotintersectT = $true) => ((complementImpComplementIntersect = $true) => ((complementSubsetComplementIntersect = $true) => ((complementInPowersetComplementIntersect = $true) => ((contraSubsetComplement = $true) => ((complementTcontraSubset = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => ! [X3 : $i] : ((((in @ X3 @ (powerset @ X0))) = $true) => ! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => ((((in @ X4 @ (binintersect @ X1 @ X2))) = $true) => (((in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 3.66/1.20 inference(fool_elimination,[],[f611])). 3.66/1.20 thf(f679,plain,( 3.66/1.20 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (binintersect @ X0 @ X2)) => (in @ X1 @ X0)))), 3.66/1.20 inference(rectify,[],[f110])). 3.66/1.20 thf(f680,plain,( 3.66/1.20 (binintersectEL = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (($true = ((in @ X1 @ (binintersect @ X0 @ X2)))) => (((in @ X1 @ X0)) = $true))), 3.66/1.20 inference(fool_elimination,[],[f679])). 3.66/1.20 thf(f900,plain,( 3.66/1.20 (binunionIL = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (binunion @ X2 @ X0))) = $true) | (((in @ X1 @ X2)) != $true))), 3.66/1.20 inference(ennf_transformation,[],[f315])). 3.66/1.20 thf(f904,plain,( 3.66/1.20 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((((in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) != $true) & (((in @ X4 @ (binintersect @ X1 @ X2))) = $true)) & (((in @ X4 @ X0)) = $true)) & (((in @ X3 @ (powerset @ X0))) = $true)) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTcontraSubset = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)), 3.66/1.20 inference(ennf_transformation,[],[f612])). 3.66/1.20 thf(f905,plain,( 3.66/1.20 (lam2lamEq = $true) & (binunionTILcontra = $true) & (iffalseProp2 = $true) & (setminusSubset1 = $true) & (setukpairinjR = $true) & (complementInPowersetComplementIntersect = $true) & (ksndsingleton = $true) & (setukpairinjR12 = $true) & (exuI1 = $true) & (kpairiskpair = $true) & (symdiffIneg1 = $true) & (setadjoinSub = $true) & (setextsub = $true) & (eqinunit = $true) & (beta1 = $true) & (binunionLsub = $true) & (iftrueorfalse = $true) & (setunion__Cong = $true) & (singletonprop = $true) & (dsetconstrEL = $true) & (eta1 = $true) & (ex1I = $true) & (subsetI2 = $true) & (powersetT_lem = $true) & (contrasubsetT = $true) & (complementSubsetComplementIntersect = $true) & (binintersectTERcontra = $true) & (setminusELneg = $true) & (setminusIRneg = $true) & (binunionRsub = $true) & (exuE1 = $true) & (symdiffIneg2 = $true) & (upairinpowunion = $true) & (subsetI1 = $true) & (binintersectRsub = $true) & (powersetsubset = $true) & (binintersectT_lem = $true) & (symdiffE = $true) & (notdexE = $true) & (upairset2IR = $true) & (ap2apEq2 = $true) & (ex1E2 = $true) & (subsetTrans = $true) & (setunionsingleton = $true) & (descr__Cong = $true) & (setunionE = $true) & (notsubsetI = $true) & (subsetE = $true) & (contraSubsetComplement = $true) & (setminusER = $true) & (omegaSAx = $true) & (doubleComplementEq = $true) & (quantDeMorgan1 = $true) & (contrasubsetT2 = $true) & (disjointsetsI1 = $true) & (setminusILneg = $true) & (cartprodpairin = $true) & (upairsetIR = $true) & (prop2setE = $true) & (quantDeMorgan3 = $true) & (upairset2E = $true) & (setadjoinOr = $true) & (dpsetconstrER = $true) & (cartprodpairmemEL = $true) & (ifSingleton = $true) & (emptyI = $true) & (cartprodmempair1 = $true) & (cartprodpairsurjEq = $true) & (subsetemptysetimpeq = $true) & (setext = $true) & (dpsetconstrSub = $true) & (setukpairinjR1 = $true) & (iffalse = $true) & (binintersectSubset4 = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (upairsetE = $true) & (subPowSU = $true) & (setminusLsub = $true) & (theprop = $true) & (cartprodmempair = $true) & (complementTnotintersectT = $true) & (iffalseProp1 = $true) & (singletoninpowunion = $true) & (upairsubunion = $true) & (powersetE = $true) & (setoftrueEq = $true) & (notequalI2 = $true) & (setunionsingleton1 = $true) & (binintersectER = $true) & (upairsetIL = $true) & (cartprodfstpairEq = $true) & (inCongP = $true) & (doubleComplementI1 = $true) & (singletoninpowerset = $true) & (doubleComplementSub2 = $true) & (ex1E1 = $true) & (notequalI1 = $true) & (prop2set2propI = $true) & (binintersectEL = $true) & (apProp = $true) & (quantDeMorgan4 = $true) & (exuE3u = $true) & (complementTE1 = $true) & (binintersectSubset1 = $true) & (singletonsubset = $true) & (sepInPowerset = $true) & (foundationAx = $true) & (sepSubset = $true) & (binunionT_lem = $true) & (iftrue = $true) & (binunionE = $true) & (symdiffI2 = $true) & (exuI2 = $true) & (cartprodsndpairEq = $true) & (powersetE1 = $true) & (descrp = $true) & (cartprodmempaircEq = $true) & (dsetconstr__Cong = $true) & (complementTI1 = $true) & (powersetTE1 = $true) & (setminusSubset2 = $true) & (kpairsurjEq = $true) & (beta2 = $true) & (doubleComplementSub1 = $true) & (emptyinPowerset = $true) & (emptysetE = $true) & (funcGraphProp2 = $true) & (setunionE2 = $true) & (eta2 = $true) & (doubleComplementE1 = $true) & (ap2p = $true) & (eqimpsubset1 = $true) & (complementTcontraSubset = $true) & (setadjoin__Cong = $true) & (in__Cong = $true) & (funcextLem = $true) & (powersetAx = $true) & (setukpairinjR11 = $true) & (setminusEL = $true) & ? [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((((in @ X4 @ (binintersect @ X1 @ X2))) = $true) & (((in @ X4 @ X0)) = $true) & (((in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) != $true)) & (((in @ X3 @ (powerset @ X0))) = $true)) & (((in @ X2 @ (powerset @ X0))) = $true))) & (exuE3e = $true) & (setukpairIR = $true) & (brelnall2 = $true) & (emptyInPowerset = $true) & (omega__Cong = $true) & (infuncsetfunc = $true) & (quantDeMorgan2 = $true) & (setminusERneg = $true) & (dpsetconstrI = $true) & (exu__Cong = $true) & (dsetconstrER = $true) & (funcext2 = $true) & (dpsetconstrEL2 = $true) & (emptyE1 = $true) & (ubforcartprodlem3 = $true) & (lam2p = $true) & (brelnall1 = $true) & (complementImpComplementIntersect = $true) & (binintersectSubset5 = $true) & (kfstsingleton = $true) & (upairequniteq = $true) & (eqbreln = $true) & (ubforcartprodlem2 = $true) & (notinemptyset = $true) & (noeltsimpempty = $true) & (setadjoinSub2 = $true) & (binunionEcases = $true) & (exuEu = $true) & (binintersectLsub = $true) & (kpairp = $true) & (setadjoinIL = $true) & (setukpairIL = $true) & (ap2apEq1 = $true) & (inPowerset = $true) & (nonemptyE1 = $true) & (exuI3 = $true) & (contrasubsetT3 = $true) & (iftrueProp1 = $true) & (setukpairinjL2 = $true) & (setminusT_lem = $true) & (setukpairinjL = $true) & (subbreln = $true) & (binintersectI = $true) & (powersetI1 = $true) & (funcinfuncset = $true) & (subset2powerset = $true) & (omegaIndAx = $true) & (ex1I2 = $true) & (dpsetconstrERa = $true) & (funcImageSingleton = $true) & (dsetconstrI = $true) & (contrasubsetT1 = $true) & (cartprodsndin = $true) & (emptyinunitempty = $true) & (complementT_lem = $true) & (subsetTI = $true) & (theeq = $true) & (binintersectSubset3 = $true) & (secondinupair = $true) & (setminusI = $true) & (funcext = $true) & (subsetRefl = $true) & (funcGraphProp1 = $true) & (inIntersectImpInUnion = $true) & (powersetTI1 = $true) & (setOfPairsIsBReln = $true) & (vacuousDall = $true) & (setadjoinIR = $true) & (funcGraphProp3 = $true) & (kfstpairEq = $true) & (binunionIR = $true) & (app = $true) & (emptysetAx = $true) & (setextAx = $true) & (emptysetsubset = $true) & (singletonsswitch = $true) & (setunionI = $true) & (cartprodpairmemER = $true) & (binunionTIRcontra = $true) & (notdallE = $true) & (ksndpairEq = $true) & (setadjoinAx = $true) & (ifp = $true) & (cartprodfstin = $true) & (prop2setI = $true) & (iftrueProp2 = $true) & (notinsingleton = $true) & (omega0Ax = $true) & (powerset__Cong = $true) & (setextT = $true) & (wellorderingAx = $true) & (nonemptyI1 = $true) & (binunionIL = $true) & (subsetE2 = $true) & (powersetI = $true) & (lamProp = $true) & (setadjoinE = $true) & (setukpairinjR2 = $true) & (uniqinunit = $true) & (binintersectTELcontra = $true) & (bs114d = $true) & (eqimpsubset2 = $true) & (exuE2 = $true) & (binintersectSubset2 = $true) & (lamp = $true) & (inIntersectImpInUnion2 = $true) & (replAx = $true) & (funcGraphProp4 = $true) & (emptyset__Cong = $true) & (symdiffI1 = $true) & (emptysetimpfalse = $true) & (ubforcartprodlem1 = $true) & (dpsetconstrEL1 = $true) & (nonemptyI = $true) & (setunionsingleton2 = $true) & (nonemptyImpWitness = $true) & (setbeta = $true) & (setunionAx = $true)), 3.66/1.20 inference(flattening,[],[f904])). 3.66/1.20 thf(f984,plain,( 3.66/1.20 (binintersectER = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (($true != ((in @ X1 @ (binintersect @ X2 @ X0)))) | (((in @ X1 @ X0)) = $true))), 3.66/1.20 inference(ennf_transformation,[],[f502])). 3.66/1.20 thf(f1082,plain,( 3.66/1.20 (binintersectI = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : ((($true = ((in @ X1 @ (binintersect @ X2 @ X0)))) | (((in @ X1 @ X0)) != $true)) | (((in @ X1 @ X2)) != $true))), 3.66/1.20 inference(ennf_transformation,[],[f532])). 3.66/1.20 thf(f1083,plain,( 3.66/1.20 (binintersectI = $true) <=> ! [X1 : $i,X0 : $i,X2 : $i] : (($true = ((in @ X1 @ (binintersect @ X2 @ X0)))) | (((in @ X1 @ X0)) != $true) | (((in @ X1 @ X2)) != $true))), 3.66/1.21 inference(flattening,[],[f1082])). 3.66/1.21 thf(f1099,plain,( 3.66/1.21 ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X0)) = $true) | ($true != ((in @ X1 @ (binintersect @ X0 @ X2))))) <=> (binintersectEL = $true)), 3.66/1.21 inference(ennf_transformation,[],[f680])). 3.66/1.21 thf(f1286,plain,( 3.66/1.21 (lam2lamEq = $true) & (binunionTILcontra = $true) & (iffalseProp2 = $true) & (setminusSubset1 = $true) & (setukpairinjR = $true) & (complementInPowersetComplementIntersect = $true) & (ksndsingleton = $true) & (setukpairinjR12 = $true) & (exuI1 = $true) & (kpairiskpair = $true) & (symdiffIneg1 = $true) & (setadjoinSub = $true) & (setextsub = $true) & (eqinunit = $true) & (beta1 = $true) & (binunionLsub = $true) & (iftrueorfalse = $true) & (setunion__Cong = $true) & (singletonprop = $true) & (dsetconstrEL = $true) & (eta1 = $true) & (ex1I = $true) & (subsetI2 = $true) & (powersetT_lem = $true) & (contrasubsetT = $true) & (complementSubsetComplementIntersect = $true) & (binintersectTERcontra = $true) & (setminusELneg = $true) & (setminusIRneg = $true) & (binunionRsub = $true) & (exuE1 = $true) & (symdiffIneg2 = $true) & (upairinpowunion = $true) & (subsetI1 = $true) & (binintersectRsub = $true) & (powersetsubset = $true) & (binintersectT_lem = $true) & (symdiffE = $true) & (notdexE = $true) & (upairset2IR = $true) & (ap2apEq2 = $true) & (ex1E2 = $true) & (subsetTrans = $true) & (setunionsingleton = $true) & (descr__Cong = $true) & (setunionE = $true) & (notsubsetI = $true) & (subsetE = $true) & (contraSubsetComplement = $true) & (setminusER = $true) & (omegaSAx = $true) & (doubleComplementEq = $true) & (quantDeMorgan1 = $true) & (contrasubsetT2 = $true) & (disjointsetsI1 = $true) & (setminusILneg = $true) & (cartprodpairin = $true) & (upairsetIR = $true) & (prop2setE = $true) & (quantDeMorgan3 = $true) & (upairset2E = $true) & (setadjoinOr = $true) & (dpsetconstrER = $true) & (cartprodpairmemEL = $true) & (ifSingleton = $true) & (emptyI = $true) & (cartprodmempair1 = $true) & (cartprodpairsurjEq = $true) & (subsetemptysetimpeq = $true) & (setext = $true) & (dpsetconstrSub = $true) & (setukpairinjR1 = $true) & (iffalse = $true) & (binintersectSubset4 = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (upairsetE = $true) & (subPowSU = $true) & (setminusLsub = $true) & (theprop = $true) & (cartprodmempair = $true) & (complementTnotintersectT = $true) & (iffalseProp1 = $true) & (singletoninpowunion = $true) & (upairsubunion = $true) & (powersetE = $true) & (setoftrueEq = $true) & (notequalI2 = $true) & (setunionsingleton1 = $true) & (binintersectER = $true) & (upairsetIL = $true) & (cartprodfstpairEq = $true) & (inCongP = $true) & (doubleComplementI1 = $true) & (singletoninpowerset = $true) & (doubleComplementSub2 = $true) & (ex1E1 = $true) & (notequalI1 = $true) & (prop2set2propI = $true) & (binintersectEL = $true) & (apProp = $true) & (quantDeMorgan4 = $true) & (exuE3u = $true) & (complementTE1 = $true) & (binintersectSubset1 = $true) & (singletonsubset = $true) & (sepInPowerset = $true) & (foundationAx = $true) & (sepSubset = $true) & (binunionT_lem = $true) & (iftrue = $true) & (binunionE = $true) & (symdiffI2 = $true) & (exuI2 = $true) & (cartprodsndpairEq = $true) & (powersetE1 = $true) & (descrp = $true) & (cartprodmempaircEq = $true) & (dsetconstr__Cong = $true) & (complementTI1 = $true) & (powersetTE1 = $true) & (setminusSubset2 = $true) & (kpairsurjEq = $true) & (beta2 = $true) & (doubleComplementSub1 = $true) & (emptyinPowerset = $true) & (emptysetE = $true) & (funcGraphProp2 = $true) & (setunionE2 = $true) & (eta2 = $true) & (doubleComplementE1 = $true) & (ap2p = $true) & (eqimpsubset1 = $true) & (complementTcontraSubset = $true) & (setadjoin__Cong = $true) & (in__Cong = $true) & (funcextLem = $true) & (powersetAx = $true) & (setukpairinjR11 = $true) & (setminusEL = $true) & ? [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = ((in @ X4 @ (binintersect @ X0 @ X2)))) & (((in @ X4 @ X1)) = $true) & (((in @ X4 @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3)))) != $true)) & ($true = ((in @ X3 @ (powerset @ X1))))) & (((in @ X2 @ (powerset @ X1))) = $true))) & (exuE3e = $true) & (setukpairIR = $true) & (brelnall2 = $true) & (emptyInPowerset = $true) & (omega__Cong = $true) & (infuncsetfunc = $true) & (quantDeMorgan2 = $true) & (setminusERneg = $true) & (dpsetconstrI = $true) & (exu__Cong = $true) & (dsetconstrER = $true) & (funcext2 = $true) & (dpsetconstrEL2 = $true) & (emptyE1 = $true) & (ubforcartprodlem3 = $true) & (lam2p = $true) & (brelnall1 = $true) & (complementImpComplementIntersect = $true) & (binintersectSubset5 = $true) & (kfstsingleton = $true) & (upairequniteq = $true) & (eqbreln = $true) & (ubforcartprodlem2 = $true) & (notinemptyset = $true) & (noeltsimpempty = $true) & (setadjoinSub2 = $true) & (binunionEcases = $true) & (exuEu = $true) & (binintersectLsub = $true) & (kpairp = $true) & (setadjoinIL = $true) & (setukpairIL = $true) & (ap2apEq1 = $true) & (inPowerset = $true) & (nonemptyE1 = $true) & (exuI3 = $true) & (contrasubsetT3 = $true) & (iftrueProp1 = $true) & (setukpairinjL2 = $true) & (setminusT_lem = $true) & (setukpairinjL = $true) & (subbreln = $true) & (binintersectI = $true) & (powersetI1 = $true) & (funcinfuncset = $true) & (subset2powerset = $true) & (omegaIndAx = $true) & (ex1I2 = $true) & (dpsetconstrERa = $true) & (funcImageSingleton = $true) & (dsetconstrI = $true) & (contrasubsetT1 = $true) & (cartprodsndin = $true) & (emptyinunitempty = $true) & (complementT_lem = $true) & (subsetTI = $true) & (theeq = $true) & (binintersectSubset3 = $true) & (secondinupair = $true) & (setminusI = $true) & (funcext = $true) & (subsetRefl = $true) & (funcGraphProp1 = $true) & (inIntersectImpInUnion = $true) & (powersetTI1 = $true) & (setOfPairsIsBReln = $true) & (vacuousDall = $true) & (setadjoinIR = $true) & (funcGraphProp3 = $true) & (kfstpairEq = $true) & (binunionIR = $true) & (app = $true) & (emptysetAx = $true) & (setextAx = $true) & (emptysetsubset = $true) & (singletonsswitch = $true) & (setunionI = $true) & (cartprodpairmemER = $true) & (binunionTIRcontra = $true) & (notdallE = $true) & (ksndpairEq = $true) & (setadjoinAx = $true) & (ifp = $true) & (cartprodfstin = $true) & (prop2setI = $true) & (iftrueProp2 = $true) & (notinsingleton = $true) & (omega0Ax = $true) & (powerset__Cong = $true) & (setextT = $true) & (wellorderingAx = $true) & (nonemptyI1 = $true) & (binunionIL = $true) & (subsetE2 = $true) & (powersetI = $true) & (lamProp = $true) & (setadjoinE = $true) & (setukpairinjR2 = $true) & (uniqinunit = $true) & (binintersectTELcontra = $true) & (bs114d = $true) & (eqimpsubset2 = $true) & (exuE2 = $true) & (binintersectSubset2 = $true) & (lamp = $true) & (inIntersectImpInUnion2 = $true) & (replAx = $true) & (funcGraphProp4 = $true) & (emptyset__Cong = $true) & (symdiffI1 = $true) & (emptysetimpfalse = $true) & (ubforcartprodlem1 = $true) & (dpsetconstrEL1 = $true) & (nonemptyI = $true) & (setunionsingleton2 = $true) & (nonemptyImpWitness = $true) & (setbeta = $true) & (setunionAx = $true)), 3.66/1.21 inference(rectify,[],[f905])). 3.66/1.21 thf(f1287,plain,( 3.66/1.21 (lam2lamEq = $true) & (binunionTILcontra = $true) & (iffalseProp2 = $true) & (setminusSubset1 = $true) & (setukpairinjR = $true) & (complementInPowersetComplementIntersect = $true) & (ksndsingleton = $true) & (setukpairinjR12 = $true) & (exuI1 = $true) & (kpairiskpair = $true) & (symdiffIneg1 = $true) & (setadjoinSub = $true) & (setextsub = $true) & (eqinunit = $true) & (beta1 = $true) & (binunionLsub = $true) & (iftrueorfalse = $true) & (setunion__Cong = $true) & (singletonprop = $true) & (dsetconstrEL = $true) & (eta1 = $true) & (ex1I = $true) & (subsetI2 = $true) & (powersetT_lem = $true) & (contrasubsetT = $true) & (complementSubsetComplementIntersect = $true) & (binintersectTERcontra = $true) & (setminusELneg = $true) & (setminusIRneg = $true) & (binunionRsub = $true) & (exuE1 = $true) & (symdiffIneg2 = $true) & (upairinpowunion = $true) & (subsetI1 = $true) & (binintersectRsub = $true) & (powersetsubset = $true) & (binintersectT_lem = $true) & (symdiffE = $true) & (notdexE = $true) & (upairset2IR = $true) & (ap2apEq2 = $true) & (ex1E2 = $true) & (subsetTrans = $true) & (setunionsingleton = $true) & (descr__Cong = $true) & (setunionE = $true) & (notsubsetI = $true) & (subsetE = $true) & (contraSubsetComplement = $true) & (setminusER = $true) & (omegaSAx = $true) & (doubleComplementEq = $true) & (quantDeMorgan1 = $true) & (contrasubsetT2 = $true) & (disjointsetsI1 = $true) & (setminusILneg = $true) & (cartprodpairin = $true) & (upairsetIR = $true) & (prop2setE = $true) & (quantDeMorgan3 = $true) & (upairset2E = $true) & (setadjoinOr = $true) & (dpsetconstrER = $true) & (cartprodpairmemEL = $true) & (ifSingleton = $true) & (emptyI = $true) & (cartprodmempair1 = $true) & (cartprodpairsurjEq = $true) & (subsetemptysetimpeq = $true) & (setext = $true) & (dpsetconstrSub = $true) & (setukpairinjR1 = $true) & (iffalse = $true) & (binintersectSubset4 = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (upairsetE = $true) & (subPowSU = $true) & (setminusLsub = $true) & (theprop = $true) & (cartprodmempair = $true) & (complementTnotintersectT = $true) & (iffalseProp1 = $true) & (singletoninpowunion = $true) & (upairsubunion = $true) & (powersetE = $true) & (setoftrueEq = $true) & (notequalI2 = $true) & (setunionsingleton1 = $true) & (binintersectER = $true) & (upairsetIL = $true) & (cartprodfstpairEq = $true) & (inCongP = $true) & (doubleComplementI1 = $true) & (singletoninpowerset = $true) & (doubleComplementSub2 = $true) & (ex1E1 = $true) & (notequalI1 = $true) & (prop2set2propI = $true) & (binintersectEL = $true) & (apProp = $true) & (quantDeMorgan4 = $true) & (exuE3u = $true) & (complementTE1 = $true) & (binintersectSubset1 = $true) & (singletonsubset = $true) & (sepInPowerset = $true) & (foundationAx = $true) & (sepSubset = $true) & (binunionT_lem = $true) & (iftrue = $true) & (binunionE = $true) & (symdiffI2 = $true) & (exuI2 = $true) & (cartprodsndpairEq = $true) & (powersetE1 = $true) & (descrp = $true) & (cartprodmempaircEq = $true) & (dsetconstr__Cong = $true) & (complementTI1 = $true) & (powersetTE1 = $true) & (setminusSubset2 = $true) & (kpairsurjEq = $true) & (beta2 = $true) & (doubleComplementSub1 = $true) & (emptyinPowerset = $true) & (emptysetE = $true) & (funcGraphProp2 = $true) & (setunionE2 = $true) & (eta2 = $true) & (doubleComplementE1 = $true) & (ap2p = $true) & (eqimpsubset1 = $true) & (complementTcontraSubset = $true) & (setadjoin__Cong = $true) & (in__Cong = $true) & (funcextLem = $true) & (powersetAx = $true) & (setukpairinjR11 = $true) & (setminusEL = $true) & (($true = ((in @ sK155 @ (powerset @ sK156)))) & ((((((in @ sK159 @ (binintersect @ sK155 @ sK157))) = $true) & (((in @ sK159 @ sK156)) = $true) & (((in @ sK159 @ (binintersect @ (binunion @ sK155 @ sK158) @ (binunion @ sK157 @ sK158)))) != $true)) & ($true = ((in @ sK158 @ (powerset @ sK156))))) & ($true = ((in @ sK157 @ (powerset @ sK156)))))) & (exuE3e = $true) & (setukpairIR = $true) & (brelnall2 = $true) & (emptyInPowerset = $true) & (omega__Cong = $true) & (infuncsetfunc = $true) & (quantDeMorgan2 = $true) & (setminusERneg = $true) & (dpsetconstrI = $true) & (exu__Cong = $true) & (dsetconstrER = $true) & (funcext2 = $true) & (dpsetconstrEL2 = $true) & (emptyE1 = $true) & (ubforcartprodlem3 = $true) & (lam2p = $true) & (brelnall1 = $true) & (complementImpComplementIntersect = $true) & (binintersectSubset5 = $true) & (kfstsingleton = $true) & (upairequniteq = $true) & (eqbreln = $true) & (ubforcartprodlem2 = $true) & (notinemptyset = $true) & (noeltsimpempty = $true) & (setadjoinSub2 = $true) & (binunionEcases = $true) & (exuEu = $true) & (binintersectLsub = $true) & (kpairp = $true) & (setadjoinIL = $true) & (setukpairIL = $true) & (ap2apEq1 = $true) & (inPowerset = $true) & (nonemptyE1 = $true) & (exuI3 = $true) & (contrasubsetT3 = $true) & (iftrueProp1 = $true) & (setukpairinjL2 = $true) & (setminusT_lem = $true) & (setukpairinjL = $true) & (subbreln = $true) & (binintersectI = $true) & (powersetI1 = $true) & (funcinfuncset = $true) & (subset2powerset = $true) & (omegaIndAx = $true) & (ex1I2 = $true) & (dpsetconstrERa = $true) & (funcImageSingleton = $true) & (dsetconstrI = $true) & (contrasubsetT1 = $true) & (cartprodsndin = $true) & (emptyinunitempty = $true) & (complementT_lem = $true) & (subsetTI = $true) & (theeq = $true) & (binintersectSubset3 = $true) & (secondinupair = $true) & (setminusI = $true) & (funcext = $true) & (subsetRefl = $true) & (funcGraphProp1 = $true) & (inIntersectImpInUnion = $true) & (powersetTI1 = $true) & (setOfPairsIsBReln = $true) & (vacuousDall = $true) & (setadjoinIR = $true) & (funcGraphProp3 = $true) & (kfstpairEq = $true) & (binunionIR = $true) & (app = $true) & (emptysetAx = $true) & (setextAx = $true) & (emptysetsubset = $true) & (singletonsswitch = $true) & (setunionI = $true) & (cartprodpairmemER = $true) & (binunionTIRcontra = $true) & (notdallE = $true) & (ksndpairEq = $true) & (setadjoinAx = $true) & (ifp = $true) & (cartprodfstin = $true) & (prop2setI = $true) & (iftrueProp2 = $true) & (notinsingleton = $true) & (omega0Ax = $true) & (powerset__Cong = $true) & (setextT = $true) & (wellorderingAx = $true) & (nonemptyI1 = $true) & (binunionIL = $true) & (subsetE2 = $true) & (powersetI = $true) & (lamProp = $true) & (setadjoinE = $true) & (setukpairinjR2 = $true) & (uniqinunit = $true) & (binintersectTELcontra = $true) & (bs114d = $true) & (eqimpsubset2 = $true) & (exuE2 = $true) & (binintersectSubset2 = $true) & (lamp = $true) & (inIntersectImpInUnion2 = $true) & (replAx = $true) & (funcGraphProp4 = $true) & (emptyset__Cong = $true) & (symdiffI1 = $true) & (emptysetimpfalse = $true) & (ubforcartprodlem1 = $true) & (dpsetconstrEL1 = $true) & (nonemptyI = $true) & (setunionsingleton2 = $true) & (nonemptyImpWitness = $true) & (setbeta = $true) & (setunionAx = $true)), 3.66/1.21 inference(skolemize,[status(esa),new_symbols(skolem,[sK155,sK156,sK157,sK158,sK159]),skolemize(X0,sK155),skolemize(X1,sK156),skolemize(X2,sK157),skolemize(X3,sK158),skolemize(X4,sK159)],[f1286])). 3.66/1.21 thf(f1291,plain,( 3.66/1.21 ((binintersectER = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (($true = ((in @ X1 @ (binintersect @ X2 @ X0)))) & (((in @ X1 @ X0)) != $true))) & (! [X1 : $i,X0 : $i,X2 : $i] : (($true != ((in @ X1 @ (binintersect @ X2 @ X0)))) | (((in @ X1 @ X0)) = $true)) | (binintersectER != $true))), 3.66/1.21 inference(nnf_transformation,[],[f984])). 3.66/1.21 thf(f1292,plain,( 3.66/1.21 ((binintersectER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ (binintersect @ X2 @ X1)))) & ($true != ((in @ X0 @ X1))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X3 @ (binintersect @ X5 @ X4)))) | (((in @ X3 @ X4)) = $true)) | (binintersectER != $true))), 3.66/1.21 inference(rectify,[],[f1291])). 3.66/1.21 thf(f1293,plain,( 3.66/1.21 ((binintersectER = $true) | ((((in @ sK162 @ (binintersect @ sK164 @ sK163))) = $true) & ($true != ((in @ sK162 @ sK163))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X3 @ (binintersect @ X5 @ X4)))) | (((in @ X3 @ X4)) = $true)) | (binintersectER != $true))), 3.66/1.21 inference(skolemize,[status(esa),new_symbols(skolem,[sK162,sK163,sK164]),skolemize(X0,sK162),skolemize(X1,sK163),skolemize(X2,sK164)],[f1292])). 3.66/1.21 thf(f1312,plain,( 3.66/1.21 ((binintersectI = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (($true != ((in @ X1 @ (binintersect @ X2 @ X0)))) & (((in @ X1 @ X0)) = $true) & (((in @ X1 @ X2)) = $true))) & (! [X1 : $i,X0 : $i,X2 : $i] : (($true = ((in @ X1 @ (binintersect @ X2 @ X0)))) | (((in @ X1 @ X0)) != $true) | (((in @ X1 @ X2)) != $true)) | (binintersectI != $true))), 3.66/1.21 inference(nnf_transformation,[],[f1083])). 3.66/1.21 thf(f1313,plain,( 3.66/1.21 ((binintersectI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ (binintersect @ X2 @ X1)))) & ($true = ((in @ X0 @ X1))) & ($true = ((in @ X0 @ X2))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X3 @ (binintersect @ X5 @ X4)))) | (((in @ X3 @ X4)) != $true) | (((in @ X3 @ X5)) != $true)) | (binintersectI != $true))), 3.66/1.21 inference(rectify,[],[f1312])). 3.66/1.21 thf(f1314,plain,( 3.66/1.21 ((binintersectI = $true) | (($true != ((in @ sK179 @ (binintersect @ sK181 @ sK180)))) & ($true = ((in @ sK179 @ sK180))) & ($true = ((in @ sK179 @ sK181))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X3 @ (binintersect @ X5 @ X4)))) | (((in @ X3 @ X4)) != $true) | (((in @ X3 @ X5)) != $true)) | (binintersectI != $true))), 3.66/1.21 inference(skolemize,[status(esa),new_symbols(skolem,[sK179,sK180,sK181]),skolemize(X0,sK179),skolemize(X1,sK180),skolemize(X2,sK181)],[f1313])). 3.66/1.21 thf(f1652,plain,( 3.66/1.21 (! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X0)) = $true) | ($true != ((in @ X1 @ (binintersect @ X0 @ X2))))) | (binintersectEL != $true)) & ((binintersectEL = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X0)) != $true) & ($true = ((in @ X1 @ (binintersect @ X0 @ X2))))))), 3.66/1.21 inference(nnf_transformation,[],[f1099])). 3.66/1.21 thf(f1653,plain,( 3.66/1.21 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) = $true) | ($true != ((in @ X2 @ (binintersect @ X1 @ X0))))) | (binintersectEL != $true)) & ((binintersectEL = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ X4))) & ($true = ((in @ X5 @ (binintersect @ X4 @ X3))))))), 3.66/1.21 inference(rectify,[],[f1652])). 3.66/1.21 thf(f1654,plain,( 3.66/1.21 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) = $true) | ($true != ((in @ X2 @ (binintersect @ X1 @ X0))))) | (binintersectEL != $true)) & ((binintersectEL = $true) | (($true != ((in @ sK548 @ sK547))) & ($true = ((in @ sK548 @ (binintersect @ sK547 @ sK546))))))), 3.66/1.21 inference(skolemize,[status(esa),new_symbols(skolem,[sK546,sK547,sK548]),skolemize(X3,sK546),skolemize(X4,sK547),skolemize(X5,sK548)],[f1653])). 3.66/1.21 thf(f1671,plain,( 3.66/1.21 ((binunionIL = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (binunion @ X2 @ X0))) != $true) & (((in @ X1 @ X2)) = $true))) & (! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (binunion @ X2 @ X0))) = $true) | (((in @ X1 @ X2)) != $true)) | (binunionIL != $true))), 3.66/1.21 inference(nnf_transformation,[],[f900])). 3.66/1.21 thf(f1672,plain,( 3.66/1.21 ((binunionIL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (binunion @ X0 @ X1))) != $true) & (((in @ X2 @ X0)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X5 @ (binunion @ X3 @ X4)))) | (((in @ X5 @ X3)) != $true)) | (binunionIL != $true))), 3.66/1.21 inference(rectify,[],[f1671])). 3.66/1.21 thf(f1673,plain,( 3.66/1.21 ((binunionIL = $true) | ((((in @ sK569 @ (binunion @ sK567 @ sK568))) != $true) & ($true = ((in @ sK569 @ sK567))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X5 @ (binunion @ X3 @ X4)))) | (((in @ X5 @ X3)) != $true)) | (binunionIL != $true))), 3.66/1.21 inference(skolemize,[status(esa),new_symbols(skolem,[sK567,sK568,sK569]),skolemize(X0,sK567),skolemize(X1,sK568),skolemize(X2,sK569)],[f1672])). 3.66/1.21 thf(f2133,plain,( 3.66/1.21 (binunionIL = $true)), 3.66/1.21 inference(cnf_transformation,[],[f1287])). 3.66/1.21 thf(f2183,plain,( 3.66/1.21 (binintersectI = $true)), 3.66/1.21 inference(cnf_transformation,[],[f1287])). 3.66/1.21 thf(f2228,plain,( 3.66/1.21 (((in @ sK159 @ (binintersect @ (binunion @ sK155 @ sK158) @ (binunion @ sK157 @ sK158)))) != $true)), 3.66/1.21 inference(cnf_transformation,[],[f1287])). 3.66/1.21 thf(f2230,plain,( 3.66/1.21 (((in @ sK159 @ (binintersect @ sK155 @ sK157))) = $true)), 3.66/1.21 inference(cnf_transformation,[],[f1287])). 3.66/1.21 thf(f2272,plain,( 3.66/1.21 (binintersectEL = $true)), 3.66/1.21 inference(cnf_transformation,[],[f1287])). 3.66/1.21 thf(f2282,plain,( 3.66/1.21 (binintersectER = $true)), 3.66/1.21 inference(cnf_transformation,[],[f1287])). 3.66/1.21 thf(f2374,plain,( 3.66/1.21 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((binintersectER != $true) | (((in @ X3 @ X4)) = $true) | ($true != ((in @ X3 @ (binintersect @ X5 @ X4))))) )), 3.66/1.21 inference(cnf_transformation,[],[f1293])). 3.66/1.21 thf(f2402,plain,( 3.66/1.21 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X3 @ (binintersect @ X5 @ X4)))) | (((in @ X3 @ X4)) != $true) | (binintersectI != $true) | (((in @ X3 @ X5)) != $true)) )), 3.66/1.21 inference(cnf_transformation,[],[f1314])). 3.66/1.21 thf(f2897,plain,( 3.66/1.21 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X1)) = $true) | (binintersectEL != $true) | ($true != ((in @ X2 @ (binintersect @ X1 @ X0))))) )), 3.66/1.21 inference(cnf_transformation,[],[f1654])). 3.66/1.21 thf(f2923,plain,( 3.66/1.21 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((binunionIL != $true) | ($true = ((in @ X5 @ (binunion @ X3 @ X4)))) | (((in @ X5 @ X3)) != $true)) )), 3.66/1.21 inference(cnf_transformation,[],[f1673])). 3.66/1.21 thf(f3979,definition,( 3.66/1.21 spl817_113 <=> (binintersectEL = $true)), 3.66/1.21 introduced(definition,[new_symbols(definition,[spl817_113])],[avatar_definition])). 3.66/1.21 thf(f3983,definition,( 3.66/1.21 spl817_114 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X1)) = $true) | ($true != ((in @ X2 @ (binintersect @ X1 @ X0)))))), 3.66/1.21 introduced(definition,[new_symbols(definition,[spl817_114])],[avatar_definition])). 3.66/1.21 thf(f3984,plain,( 3.66/1.21 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X2 @ (binintersect @ X1 @ X0)))) | (((in @ X2 @ X1)) = $true)) ) | ~spl817_114), 3.66/1.21 inference(avatar_component_clause,[],[f3983])). 3.66/1.21 thf(f3985,plain,( 3.66/1.21 ~spl817_113 | spl817_114), 3.66/1.21 inference(avatar_split_clause,[],[f2897,f3983,f3979])). 3.66/1.21 thf(f4272,definition,( 3.66/1.21 spl817_181 <=> (binunionIL = $true)), 3.66/1.21 introduced(definition,[new_symbols(definition,[spl817_181])],[avatar_definition])). 3.66/1.21 thf(f5086,definition,( 3.66/1.21 spl817_361 <=> (binintersectER = $true)), 3.66/1.21 introduced(definition,[new_symbols(definition,[spl817_361])],[avatar_definition])). 3.66/1.21 thf(f5799,definition,( 3.66/1.21 spl817_514 <=> (((in @ sK159 @ (binintersect @ sK155 @ sK157))) = $true)), 3.66/1.21 introduced(definition,[new_symbols(definition,[spl817_514])],[avatar_definition])). 3.66/1.21 thf(f5801,plain,( 3.66/1.21 (((in @ sK159 @ (binintersect @ sK155 @ sK157))) = $true) | ~spl817_514), 3.66/1.21 inference(avatar_component_clause,[],[f5799])). 3.66/1.21 thf(f5802,plain,( 3.66/1.21 spl817_514), 3.66/1.21 inference(avatar_split_clause,[],[f2230,f5799])). 3.66/1.21 thf(f5872,definition,( 3.66/1.21 spl817_530 <=> (binintersectI = $true)), 3.66/1.21 introduced(definition,[new_symbols(definition,[spl817_530])],[avatar_definition])). 3.66/1.21 thf(f6018,definition,( 3.66/1.21 spl817_561 <=> (((in @ sK159 @ (binintersect @ (binunion @ sK155 @ sK158) @ (binunion @ sK157 @ sK158)))) = $true)), 3.66/1.21 introduced(definition,[new_symbols(definition,[spl817_561])],[avatar_definition])). 3.66/1.21 thf(f6020,plain,( 3.66/1.21 (((in @ sK159 @ (binintersect @ (binunion @ sK155 @ sK158) @ (binunion @ sK157 @ sK158)))) != $true) | spl817_561), 3.66/1.21 inference(avatar_component_clause,[],[f6018])). 3.66/1.21 thf(f6021,plain,( 3.66/1.21 ~spl817_561), 3.66/1.21 inference(avatar_split_clause,[],[f2228,f6018])). 3.66/1.21 thf(f6107,definition,( 3.66/1.21 spl817_580 <=> ! [X4 : $i,X5 : $i,X3 : $i] : (($true = ((in @ X3 @ (binintersect @ X5 @ X4)))) | (((in @ X3 @ X5)) != $true) | (((in @ X3 @ X4)) != $true))), 3.66/1.21 introduced(definition,[new_symbols(definition,[spl817_580])],[avatar_definition])). 3.66/1.21 thf(f6108,plain,( 3.66/1.21 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X3 @ (binintersect @ X5 @ X4)))) | (((in @ X3 @ X4)) != $true) | (((in @ X3 @ X5)) != $true)) ) | ~spl817_580), 3.66/1.21 inference(avatar_component_clause,[],[f6107])). 3.66/1.21 thf(f6109,plain,( 3.66/1.21 ~spl817_530 | spl817_580), 3.66/1.21 inference(avatar_split_clause,[],[f2402,f6107,f5872])). 3.66/1.21 thf(f6344,definition,( 3.66/1.21 spl817_629 <=> ! [X4 : $i,X5 : $i,X3 : $i] : ((((in @ X3 @ X4)) = $true) | ($true != ((in @ X3 @ (binintersect @ X5 @ X4)))))), 3.66/1.21 introduced(definition,[new_symbols(definition,[spl817_629])],[avatar_definition])). 3.66/1.21 thf(f6345,plain,( 3.66/1.21 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X3 @ (binintersect @ X5 @ X4)))) | (((in @ X3 @ X4)) = $true)) ) | ~spl817_629), 3.66/1.21 inference(avatar_component_clause,[],[f6344])). 3.66/1.21 thf(f6346,plain,( 3.66/1.21 ~spl817_361 | spl817_629), 3.66/1.21 inference(avatar_split_clause,[],[f2374,f6344,f5086])). 3.66/1.21 thf(f7617,plain,( 3.66/1.21 spl817_181), 3.66/1.21 inference(avatar_split_clause,[],[f2133,f4272])). 3.66/1.21 thf(f7747,plain,( 3.66/1.21 spl817_530), 3.66/1.21 inference(avatar_split_clause,[],[f2183,f5872])). 3.66/1.21 thf(f8345,plain,( 3.66/1.21 spl817_113), 3.66/1.21 inference(avatar_split_clause,[],[f2272,f3979])). 3.66/1.21 thf(f8827,plain,( 3.66/1.21 spl817_361), 3.66/1.21 inference(avatar_split_clause,[],[f2282,f5086])). 3.66/1.21 thf(f9182,definition,( 3.66/1.21 spl817_1213 <=> ! [X4 : $i,X5 : $i,X3 : $i] : (($true = ((in @ X5 @ (binunion @ X3 @ X4)))) | (((in @ X5 @ X3)) != $true))), 3.66/1.21 introduced(definition,[new_symbols(definition,[spl817_1213])],[avatar_definition])). 3.66/1.21 thf(f9183,plain,( 3.66/1.21 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X5 @ (binunion @ X3 @ X4)))) | (((in @ X5 @ X3)) != $true)) ) | ~spl817_1213), 3.66/1.21 inference(avatar_component_clause,[],[f9182])). 3.66/1.21 thf(f9184,plain,( 3.66/1.21 spl817_1213 | ~spl817_181), 3.66/1.21 inference(avatar_split_clause,[],[f2923,f4272,f9182])). 3.66/1.21 thf(f10098,definition,( 3.66/1.21 spl817_1317 <=> (((in @ sK159 @ sK157)) = $true)), 3.66/1.21 introduced(definition,[new_symbols(definition,[spl817_1317])],[avatar_definition])). 3.66/1.21 thf(f10100,plain,( 3.66/1.21 (((in @ sK159 @ sK157)) = $true) | ~spl817_1317), 3.66/1.21 inference(avatar_component_clause,[],[f10098])). 3.66/1.21 thf(f10111,definition,( 3.66/1.21 spl817_1320 <=> ($true = ((in @ sK159 @ (binunion @ sK157 @ sK158))))), 3.66/1.21 introduced(definition,[new_symbols(definition,[spl817_1320])],[avatar_definition])). 3.66/1.21 thf(f10112,plain,( 3.66/1.21 ($true = ((in @ sK159 @ (binunion @ sK157 @ sK158)))) | ~spl817_1320), 3.66/1.21 inference(avatar_component_clause,[],[f10111])). 3.66/1.21 thf(f10113,plain,( 3.66/1.21 ($true != ((in @ sK159 @ (binunion @ sK157 @ sK158)))) | spl817_1320), 3.66/1.21 inference(avatar_component_clause,[],[f10111])). 3.66/1.21 thf(f10206,definition,( 3.66/1.21 spl817_1328 <=> ($true = ((in @ sK159 @ (binunion @ sK155 @ sK158))))), 3.66/1.21 introduced(definition,[new_symbols(definition,[spl817_1328])],[avatar_definition])). 3.66/1.21 thf(f10208,plain,( 3.66/1.21 ($true != ((in @ sK159 @ (binunion @ sK155 @ sK158)))) | spl817_1328), 3.66/1.21 inference(avatar_component_clause,[],[f10206])). 3.66/1.21 thf(f10216,definition,( 3.66/1.21 spl817_1330 <=> ($true = ((in @ sK159 @ sK155)))), 3.66/1.21 introduced(definition,[new_symbols(definition,[spl817_1330])],[avatar_definition])). 3.66/1.21 thf(f10218,plain,( 3.66/1.21 ($true = ((in @ sK159 @ sK155))) | ~spl817_1330), 3.66/1.21 inference(avatar_component_clause,[],[f10216])). 3.66/1.21 thf(f10538,plain,( 3.66/1.21 ($true = ((in @ sK159 @ sK155))) | ($true != $true) | (~spl817_114 | ~spl817_514)), 3.66/1.21 inference(superposition,[],[f3984,f5801])). 3.66/1.21 thf(f10543,plain,( 3.66/1.21 ($true = ((in @ sK159 @ sK155))) | (~spl817_114 | ~spl817_514)), 3.66/1.21 inference(trivial_inequality_removal,[],[f10538])). 3.66/1.21 thf(f10546,plain,( 3.66/1.21 spl817_1330 | ~spl817_114 | ~spl817_514), 3.66/1.21 inference(avatar_split_clause,[],[f10543,f5799,f3983,f10216])). 3.66/1.21 thf(f10600,plain,( 3.66/1.21 ($true != $true) | (((in @ sK159 @ sK157)) = $true) | (~spl817_514 | ~spl817_629)), 3.66/1.21 inference(superposition,[],[f6345,f5801])). 3.66/1.21 thf(f10607,plain,( 3.66/1.21 (((in @ sK159 @ sK157)) = $true) | (~spl817_514 | ~spl817_629)), 3.66/1.21 inference(trivial_inequality_removal,[],[f10600])). 3.66/1.21 thf(f10610,plain,( 3.66/1.21 spl817_1317 | ~spl817_514 | ~spl817_629), 3.66/1.21 inference(avatar_split_clause,[],[f10607,f6344,f5799,f10098])). 3.66/1.21 thf(f10793,plain,( 3.66/1.21 ($true != $true) | (((in @ sK159 @ sK157)) != $true) | (~spl817_1213 | spl817_1320)), 3.66/1.21 inference(superposition,[],[f10113,f9183])). 3.66/1.21 thf(f10799,plain,( 3.66/1.21 (((in @ sK159 @ sK157)) != $true) | (~spl817_1213 | spl817_1320)), 3.66/1.21 inference(trivial_inequality_removal,[],[f10793])). 3.66/1.21 thf(f10802,plain,( 3.66/1.21 $false | (~spl817_1213 | ~spl817_1317 | spl817_1320)), 3.66/1.21 inference(forward_subsumption_resolution,[],[f10799,f10100])). 3.66/1.21 thf(f10803,plain,( 3.66/1.21 ~spl817_1213 | ~spl817_1317 | spl817_1320), 3.66/1.21 inference(avatar_contradiction_clause,[],[f10802])). 3.66/1.21 thf(f11998,plain,( 3.66/1.21 ($true != ((in @ sK159 @ (binunion @ sK155 @ sK158)))) | ($true != ((in @ sK159 @ (binunion @ sK157 @ sK158)))) | ($true != $true) | (spl817_561 | ~spl817_580)), 3.66/1.21 inference(superposition,[],[f6020,f6108])). 3.66/1.21 thf(f12005,plain,( 3.66/1.21 ($true != ((in @ sK159 @ (binunion @ sK155 @ sK158)))) | ($true != ((in @ sK159 @ (binunion @ sK157 @ sK158)))) | (spl817_561 | ~spl817_580)), 3.66/1.21 inference(trivial_inequality_removal,[],[f11998])). 3.66/1.21 thf(f12015,plain,( 3.66/1.21 ($true != ((in @ sK159 @ (binunion @ sK155 @ sK158)))) | (spl817_561 | ~spl817_580 | ~spl817_1320)), 3.66/1.21 inference(forward_subsumption_resolution,[],[f12005,f10112])). 3.66/1.21 thf(f12016,plain,( 3.66/1.21 ~spl817_1328 | spl817_561 | ~spl817_580 | ~spl817_1320), 3.66/1.21 inference(avatar_split_clause,[],[f12015,f10111,f6107,f6018,f10206])). 3.66/1.21 thf(f12304,plain,( 3.66/1.21 ($true != $true) | ($true != ((in @ sK159 @ sK155))) | (~spl817_1213 | spl817_1328)), 3.66/1.21 inference(superposition,[],[f10208,f9183])). 3.66/1.21 thf(f12309,plain,( 3.66/1.21 ($true != ((in @ sK159 @ sK155))) | (~spl817_1213 | spl817_1328)), 3.66/1.21 inference(trivial_inequality_removal,[],[f12304])). 3.66/1.21 thf(f12311,plain,( 3.66/1.21 $false | (~spl817_1213 | spl817_1328 | ~spl817_1330)), 3.66/1.21 inference(forward_subsumption_resolution,[],[f12309,f10218])). 3.66/1.21 thf(f12312,plain,( 3.66/1.21 ~spl817_1213 | spl817_1328 | ~spl817_1330), 3.66/1.21 inference(avatar_contradiction_clause,[],[f12311])). 3.66/1.21 cnf(s64, plain, ~spl817_113 | spl817_114, inference(sat_conversion,[],[f3985])). 3.66/1.21 cnf(s380, plain, spl817_514, inference(sat_conversion,[],[f5802])). 3.66/1.21 cnf(s419, plain, ~spl817_561, inference(sat_conversion,[],[f6021])). 3.66/1.21 cnf(s443, plain, ~spl817_530 | spl817_580, inference(sat_conversion,[],[f6109])). 3.66/1.21 cnf(s495, plain, ~spl817_361 | spl817_629, inference(sat_conversion,[],[f6346])). 3.66/1.21 cnf(s798, plain, spl817_181, inference(sat_conversion,[],[f7617])). 3.66/1.21 cnf(s832, plain, spl817_530, inference(sat_conversion,[],[f7747])). 3.66/1.21 cnf(s988, plain, spl817_113, inference(sat_conversion,[],[f8345])). 3.66/1.21 cnf(s1118, plain, spl817_361, inference(sat_conversion,[],[f8827])). 3.66/1.21 cnf(s1210, plain, ~spl817_181 | spl817_1213, inference(sat_conversion,[],[f9184])). 3.66/1.21 cnf(s1375, plain, ~spl817_114 | ~spl817_514 | spl817_1330, inference(sat_conversion,[],[f10546])). 3.66/1.21 cnf(s1378, plain, ~spl817_514 | ~spl817_629 | spl817_1317, inference(sat_conversion,[],[f10610])). 3.66/1.21 cnf(s1383, plain, ~spl817_1213 | ~spl817_1317 | spl817_1320, inference(sat_conversion,[],[f10803])). 3.66/1.21 cnf(s1408, plain, spl817_561 | ~spl817_580 | ~spl817_1320 | ~spl817_1328, inference(sat_conversion,[],[f12016])). 3.66/1.21 cnf(s1413, plain, ~spl817_1213 | spl817_1328 | ~spl817_1330, inference(sat_conversion,[],[f12312])). 3.66/1.21 cnf(s1488, plain, spl817_1213, inference(rat,[],[s1210,s798])). 3.66/1.21 cnf(s1555, plain, spl817_629, inference(rat,[],[s495,s1118])). 3.66/1.21 cnf(s1574, plain, spl817_580, inference(rat,[],[s443,s832])). 3.66/1.21 cnf(s1604, plain, spl817_1317, inference(rat,[],[s1378,s1555,s380])). 3.66/1.21 cnf(s1605, plain, spl817_1320, inference(rat,[],[s1383,s1488,s1604])). 3.66/1.21 cnf(s1606, plain, ~spl817_1328, inference(rat,[],[s1408,s419,s1574,s1605])). 3.66/1.21 cnf(s1607, plain, ~spl817_1330, inference(rat,[],[s1413,s1488,s1606])). 3.66/1.21 cnf(s1609, plain, ~spl817_114, inference(rat,[],[s1375,s380,s1607])). 3.66/1.21 cnf(s1744, plain, $false, inference(rat,[],[s64,s1609,s988])). 3.66/1.21 thf(f12313,plain,( 3.66/1.21 $false), 3.66/1.21 inference(avatar_sat_refutation,[],[s1744])). 3.66/1.21 % SZS output end Proof for theBenchmark 3.66/1.21 % (2408887)------------------------------ 3.66/1.21 % (2408887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.66/1.21 % (2408887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.66/1.21 % (2408887)CaDiCaL version: 2.1.3 3.66/1.21 % (2408887)Termination reason: Refutation 3.66/1.21 % (2408887)Time elapsed: 0.526 s 3.66/1.21 % (2408887)Peak memory usage: 21 MB 3.66/1.21 % (2408887)Instructions burned: 587 (million) 3.66/1.21 % (2408879)Success in time 0.607 s 3.66/1.21 % Vampire exiting 3.66/1.21 EOF