0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.10/0.39 % Computer : n003.cluster.edu 0.10/0.39 % Model : x86_64 x86_64 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.39 % Memory : 8046.5625MB 0.10/0.39 % OS : Linux 6.8.0-71-generic 0.10/0.39 % CPULimit : 1440 0.10/0.39 % WCLimit : 180 0.10/0.39 % DateTime : Mon Jul 27 09:05:56 UTC 2026 0.10/0.39 % CPUTime : 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.10/0.43 Running higher-order theorem proving 0.10/0.44 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 0.16/0.55 % (3741632)Detected a higher-order problem, will run a greedy HOL sequence. 0.16/0.55 % (3741637)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1376921383:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi) 0.16/0.55 % (3741643)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 0.16/0.55 % (3741643)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 0.16/0.55 % (3741640)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=22802140: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) 0.16/0.55 % (3741638)lrs+10_16_si=on:nwc=1.5:random_seed=2188285187:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi) 0.16/0.55 % (3741639)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1052169958:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi) 0.16/0.55 % (3741643)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=650219829:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi) 0.16/0.55 % (3741641)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3077620257:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi) 0.16/0.55 % (3741642)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1699480886:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi) 0.16/0.55 % (3741639)Instruction limit reached! 0.16/0.55 % (3741639)------------------------------ 0.16/0.55 % (3741639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741639)CaDiCaL version: 2.1.3 0.16/0.55 % (3741639)Termination reason: Instruction limit 0.16/0.55 % (3741639)Termination phase: Saturation 0.16/0.55 % (3741639)Time elapsed: 0.003 s 0.16/0.55 % (3741639)Peak memory usage: 12 MB 0.16/0.55 % (3741639)Instructions burned: 4 (million) 0.16/0.55 % (3741643)Refutation not found, incomplete strategy 0.16/0.55 % (3741643)------------------------------ 0.16/0.55 % (3741643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741643)CaDiCaL version: 2.1.3 0.16/0.55 % (3741643)Termination reason: Refutation not found, incomplete strategy 0.16/0.55 % (3741643)Time elapsed: 0.007 s 0.16/0.55 % (3741643)Peak memory usage: 12 MB 0.16/0.55 % (3741643)Instructions burned: 11 (million) 0.16/0.55 % (3741643)------------------------------ 0.16/0.55 % (3741643)------------------------------ 0.16/0.55 % (3741638)Instruction limit reached! 0.16/0.55 % (3741638)------------------------------ 0.16/0.55 % (3741638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741638)CaDiCaL version: 2.1.3 0.16/0.55 % (3741638)Termination reason: Instruction limit 0.16/0.55 % (3741638)Termination phase: Saturation 0.16/0.55 % (3741638)Time elapsed: 0.012 s 0.16/0.55 % (3741638)Peak memory usage: 12 MB 0.16/0.55 % (3741638)Instructions burned: 20 (million) 0.16/0.55 % (3741641)Instruction limit reached! 0.16/0.55 % (3741641)------------------------------ 0.16/0.55 % (3741641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741641)CaDiCaL version: 2.1.3 0.16/0.55 % (3741641)Termination reason: Instruction limit 0.16/0.55 % (3741641)Termination phase: Saturation 0.16/0.55 % (3741641)Time elapsed: 0.014 s 0.16/0.55 % (3741641)Peak memory usage: 12 MB 0.16/0.55 % (3741641)Instructions burned: 24 (million) 0.16/0.55 % (3741637)Instruction limit reached! 0.16/0.55 % (3741637)------------------------------ 0.16/0.55 % (3741637)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741637)CaDiCaL version: 2.1.3 0.16/0.55 % (3741637)Termination reason: Instruction limit 0.16/0.55 % (3741637)Termination phase: Saturation 0.16/0.55 % (3741637)Time elapsed: 0.026 s 0.16/0.55 % (3741637)Peak memory usage: 12 MB 0.16/0.55 % (3741637)Instructions burned: 87 (million) 0.16/0.55 % (3741651)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3881211365:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 0.16/0.55 % (3741651)Instruction limit reached! 0.16/0.55 % (3741651)------------------------------ 0.16/0.55 % (3741651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741651)CaDiCaL version: 2.1.3 0.16/0.55 % (3741651)Termination reason: Instruction limit 0.16/0.55 % (3741651)Termination phase: Saturation 0.16/0.55 % (3741651)Time elapsed: 0.002 s 0.16/0.55 % (3741651)Peak memory usage: 12 MB 0.16/0.55 % (3741651)Instructions burned: 2 (million) 0.16/0.55 % (3741655)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 0.16/0.55 % (3741655)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 0.16/0.55 % (3741652)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3434114732:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1799 on theBenchmark for (1799ds/5Mi) 0.16/0.55 % (3741653)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 0.16/0.55 % (3741655)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3447512145:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1799 on theBenchmark for (1799ds/28Mi) 0.16/0.55 % (3741653)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3183412883:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1799 on theBenchmark for (1799ds/7Mi) 0.16/0.55 % (3741652)Instruction limit reached! 0.16/0.55 % (3741652)------------------------------ 0.16/0.55 % (3741652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741652)CaDiCaL version: 2.1.3 0.16/0.55 % (3741652)Termination reason: Instruction limit 0.16/0.55 % (3741652)Termination phase: Saturation 0.16/0.55 % (3741652)Time elapsed: 0.004 s 0.16/0.55 % (3741652)Peak memory usage: 12 MB 0.16/0.55 % (3741652)Instructions burned: 6 (million) 0.16/0.55 % (3741654)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2715602363:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_1799 on theBenchmark for (1799ds/12Mi) 0.16/0.55 % (3741653)Instruction limit reached! 0.16/0.55 % (3741653)------------------------------ 0.16/0.55 % (3741653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741653)CaDiCaL version: 2.1.3 0.16/0.55 % (3741653)Termination reason: Instruction limit 0.16/0.55 % (3741653)Termination phase: Saturation 0.16/0.55 % (3741653)Time elapsed: 0.004 s 0.16/0.55 % (3741653)Peak memory usage: 12 MB 0.16/0.55 % (3741653)Instructions burned: 7 (million) 0.16/0.55 % (3741655)Instruction limit reached! 0.16/0.55 % (3741655)------------------------------ 0.16/0.55 % (3741655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741655)CaDiCaL version: 2.1.3 0.16/0.55 % (3741655)Termination reason: Instruction limit 0.16/0.55 % (3741655)Termination phase: Saturation 0.16/0.55 % (3741655)Time elapsed: 0.007 s 0.16/0.55 % (3741655)Peak memory usage: 12 MB 0.16/0.55 % (3741655)Instructions burned: 30 (million) 0.16/0.55 % (3741642)Instruction limit reached! 0.16/0.55 % (3741642)------------------------------ 0.16/0.55 % (3741642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741642)CaDiCaL version: 2.1.3 0.16/0.55 % (3741642)Termination reason: Instruction limit 0.16/0.55 % (3741642)Termination phase: Saturation 0.16/0.55 % (3741642)Time elapsed: 0.040 s 0.16/0.55 % (3741642)Peak memory usage: 13 MB 0.16/0.55 % (3741642)Instructions burned: 76 (million) 0.16/0.55 % (3741654)Instruction limit reached! 0.16/0.55 % (3741654)------------------------------ 0.16/0.55 % (3741654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741654)CaDiCaL version: 2.1.3 0.16/0.55 % (3741654)Termination reason: Instruction limit 0.16/0.55 % (3741654)Termination phase: Saturation 0.16/0.55 % (3741654)Time elapsed: 0.008 s 0.16/0.55 % (3741654)Peak memory usage: 12 MB 0.16/0.55 % (3741654)Instructions burned: 14 (million) 0.16/0.55 % (3741657)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=1844476033:i=86:piset=equals:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/86Mi) 0.16/0.55 % (3741664)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2013648831:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_1799 on theBenchmark for (1799ds/38Mi) 0.16/0.55 % (3741661)lrs+10_1_si=on:cs=on:random_seed=1946383154:i=8:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/8Mi) 0.16/0.55 % (3741663)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on 0.16/0.55 % (3741664)Refutation not found, incomplete strategy 0.16/0.55 % (3741664)------------------------------ 0.16/0.55 % (3741664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741664)CaDiCaL version: 2.1.3 0.16/0.55 % (3741664)Termination reason: Refutation not found, incomplete strategy 0.16/0.55 % (3741664)Time elapsed: 0.005 s 0.16/0.55 % (3741664)Peak memory usage: 12 MB 0.16/0.55 % (3741664)Instructions burned: 14 (million) 0.16/0.55 % (3741664)------------------------------ 0.16/0.55 % (3741664)------------------------------ 0.16/0.55 % (3741663)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=2302215169:i=2:add=on:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 0.16/0.55 % (3741661)Instruction limit reached! 0.16/0.55 % (3741661)------------------------------ 0.16/0.55 % (3741661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741661)CaDiCaL version: 2.1.3 0.16/0.55 % (3741661)Termination reason: Instruction limit 0.16/0.55 % (3741661)Termination phase: Saturation 0.16/0.55 % (3741661)Time elapsed: 0.005 s 0.16/0.55 % (3741661)Peak memory usage: 12 MB 0.16/0.55 % (3741661)Instructions burned: 9 (million) 0.16/0.55 % (3741663)Instruction limit reached! 0.16/0.55 % (3741663)------------------------------ 0.16/0.55 % (3741663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741663)CaDiCaL version: 2.1.3 0.16/0.55 % (3741663)Termination reason: Instruction limit 0.16/0.55 % (3741663)Termination phase: Saturation 0.16/0.55 % (3741663)Time elapsed: 0.003 s 0.16/0.55 % (3741663)Peak memory usage: 12 MB 0.16/0.55 % (3741663)Instructions burned: 4 (million) 0.16/0.55 % (3741665)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3261001411:st=2:i=249:sd=1:rtra=on:ss=axioms_1799 on theBenchmark for (1799ds/249Mi) 0.16/0.55 % (3741666)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4140019446:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1799 on theBenchmark for (1799ds/25Mi) 0.16/0.55 % (3741670)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3269620746:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_1799 on theBenchmark for (1799ds/14Mi) 0.16/0.55 % (3741657) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3741632-3741657"... 0.16/0.55 % (3741670)Instruction limit reached! 0.16/0.55 % (3741670)------------------------------ 0.16/0.55 % (3741670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.55 % (3741670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.55 % (3741670)CaDiCaL version: 2.1.3 0.16/0.55 % (3741670)Termination reason: Instruction limit 0.16/0.55 % (3741670)Termination phase: Saturation 0.16/0.55 % (3741670)Time elapsed: 0.005 s 0.16/0.55 % (3741670)Peak memory usage: 12 MB 0.16/0.55 % (3741670)Instructions burned: 14 (million) 0.16/0.55 % (3741657)...printing done. 0.16/0.55 % (3741657)Refutation found. Thanks to Tanya! 0.16/0.55 % SZS status Theorem for theBenchmark 0.16/0.55 % SZS output start Proof for theBenchmark 0.16/0.55 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType). 0.16/0.55 thf(func_def_1, type, vNOT: ($o > $o)). 0.16/0.55 thf(func_def_2, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))). 0.16/0.55 thf(func_def_3, type, vIMP: ($o > $o > $o)). 0.16/0.55 thf(func_def_4, type, db1: !>[X0: $tType]:(X0)). 0.16/0.55 thf(func_def_5, type, db0: !>[X0: $tType]:(X0)). 0.16/0.55 thf(func_def_6, type, db2: !>[X0: $tType]:(X0)). 0.16/0.55 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))). 0.16/0.55 thf(func_def_8, type, db3: !>[X0: $tType]:(X0)). 0.16/0.55 thf(func_def_9, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))). 0.16/0.55 thf(func_def_10, type, vAND: ($o > $o > $o)). 0.16/0.55 thf(func_def_11, type, db4: !>[X0: $tType]:(X0)). 0.16/0.55 thf(func_def_14, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))). 0.16/0.55 thf(func_def_15, type, sK0: (($i > $o) > $i > $o)). 0.16/0.55 thf(func_def_18, type, sK3: (($i > $o) > $i)). 0.16/0.55 thf(func_def_20, type, sK5: ($i > $o)). 0.16/0.55 thf(func_def_21, type, sK6: (($i > $o) > $i)). 0.16/0.55 thf(f1,conjecture,( 0.16/0.55 ! [X0 : (($i > $o) > $i > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : (! [X3 : $i] : ((X1 @ X3) => (X2 @ X3)) => ! [X3 : $i] : ((X0 @ X1 @ X3) => (X0 @ X2 @ X3))) => ! [X1 : $i] : ((X0 @ (^[X3 : $i] : (? [X4 : ($i > $o)] : (! [X5 : $i] : ((X4 @ X5) => (X0 @ X4 @ X5)) & (X4 @ X3)))) @ X1) => ? [X4 : ($i > $o)] : (! [X3 : $i] : ((X4 @ X3) => (X0 @ X4 @ X3)) & (X4 @ X1))))), 0.16/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM2A_ONE_pme)). 0.16/0.55 thf(f2,negated_conjecture,( 0.16/0.55 ~ ! [X0 : (($i > $o) > $i > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : (! [X3 : $i] : ((X1 @ X3) => (X2 @ X3)) => ! [X3 : $i] : ((X0 @ X1 @ X3) => (X0 @ X2 @ X3))) => ! [X1 : $i] : ((X0 @ (^[X3 : $i] : (? [X4 : ($i > $o)] : (! [X5 : $i] : ((X4 @ X5) => (X0 @ X4 @ X5)) & (X4 @ X3)))) @ X1) => ? [X4 : ($i > $o)] : (! [X3 : $i] : ((X4 @ X3) => (X0 @ X4 @ X3)) & (X4 @ X1))))), 0.16/0.55 inference(negated_conjecture,[status(cth)],[f1])). 0.16/0.55 thf(f3,plain,( 0.16/0.55 ~ ! [X0 : (($i > $o) > $i > $o)] : (! [X1 : ($i > $o),X2 : ($i > $o)] : (! [X3 : $i] : ((X1 @ X3) => (X2 @ X3)) => ! [X4 : $i] : ((X0 @ X1 @ X4) => (X0 @ X2 @ X4))) => ! [X5 : $i] : ((X0 @ (^[X6 : $i] : (? [X7 : ($i > $o)] : (! [X8 : $i] : ((X7 @ X8) => (X0 @ X7 @ X8)) & (X7 @ X6)))) @ X5) => ? [X9 : ($i > $o)] : (! [X10 : $i] : ((X9 @ X10) => (X0 @ X9 @ X10)) & (X9 @ X5))))), 0.16/0.55 inference(rectify,[],[f2])). 0.16/0.55 thf(f4,plain,( 0.16/0.55 ($true = ((~ (!! @ (($i > $o) > $i > $o) @ (^[Y0 : ($i > $o) > $i > $o]: ((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y1 @ Y3)))) => (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y1 @ Y3))))))))) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))))))) @ Y1) => (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y0 @ Y2 @ Y3))))))))))))))))), 0.16/0.55 inference(fool_elimination,[],[f3])). 0.16/0.55 thf(f5,plain,( 0.16/0.55 ($true = ((~ (!! @ (($i > $o) > $i > $o) @ (^[Y0 : ($i > $o) > $i > $o]: ((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y1 @ Y3)))) => (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y1 @ Y3))))))))) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))))))) @ Y1) => (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y0 @ Y2 @ Y3))))))))))))))))), 0.16/0.55 inference(cnf_transformation,[],[f4])). 0.16/0.55 thf(f8,plain,( 0.16/0.55 (((!! @ (($i > $o) > $i > $o) @ (^[Y0 : ($i > $o) > $i > $o]: ((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y1 @ Y3)))) => (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y1 @ Y3))))))))) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))))))) @ Y1) => (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y0 @ Y2 @ Y3)))))))))))))) = $false)), 0.16/0.55 inference(not_proxy_clausification,[],[f5])). 0.16/0.55 thf(f9,plain,( 0.16/0.55 ($false = (((^[Y0 : ($i > $o) > $i > $o]: ((!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y1 @ Y3)))) => (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y0 @ Y1 @ Y3))))))))) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))))))) @ Y1) => (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y0 @ Y2 @ Y3)))))))))))) @ sK0)))), 0.16/0.55 inference(sigma_proxy_clausification,[],[f8])). 0.16/0.55 thf(f12,plain,( 0.16/0.55 ($false = (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y1 @ Y2) => (sK0 @ Y0 @ Y2))))))))) => (!! @ $i @ (^[Y0 : $i]: ((sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))) @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))))))))), 0.16/0.55 inference(beta-eta_normalization,[],[f9])). 0.16/0.55 thf(f13,plain,( 0.16/0.55 ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))) @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))))))), 0.16/0.55 inference(imp_proxy_clausification,[],[f12])). 0.16/0.55 thf(f14,plain,( 0.16/0.55 ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y1 @ Y2) => (sK0 @ Y0 @ Y2)))))))))))), 0.16/0.55 inference(imp_proxy_clausification,[],[f12])). 0.16/0.55 thf(f15,plain,( 0.16/0.55 ( ! [X1 : ($i > $o)] : (((((^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y0 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y1 @ Y2) => (sK0 @ Y0 @ Y2)))))))) @ X1)) = $true)) )), 0.16/0.55 inference(pi_proxy_clausification,[],[f14])). 0.16/0.55 thf(f16,plain,( 0.16/0.55 ( ! [X1 : ($i > $o)] : (($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (X1 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK0 @ X1 @ Y1)))))))))) )), 0.16/0.55 inference(beta-eta_normalization,[],[f15])). 0.16/0.55 thf(f17,plain,( 0.16/0.55 ( ! [X2 : ($i > $o),X1 : ($i > $o)] : (($true = (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (X1 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK0 @ X1 @ Y1)))))) @ X2)))) )), 0.16/0.55 inference(pi_proxy_clausification,[],[f16])). 0.16/0.55 thf(f18,plain,( 0.16/0.55 ( ! [X2 : ($i > $o),X1 : ($i > $o)] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) => (X1 @ Y0)))) => (!! @ $i @ (^[Y0 : $i]: ((sK0 @ X2 @ Y0) => (sK0 @ X1 @ Y0)))))))) )), 0.16/0.55 inference(beta-eta_normalization,[],[f17])). 0.16/0.55 thf(f19,plain,( 0.16/0.55 ( ! [X2 : ($i > $o),X1 : ($i > $o)] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ X2 @ Y0) => (sK0 @ X1 @ Y0)))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) => (X1 @ Y0))))))) )), 0.16/0.55 inference(imp_proxy_clausification,[],[f18])). 0.16/0.55 thf(f20,plain,( 0.16/0.55 ((((^[Y0 : $i]: ((sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))) @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))) @ sK1)) = $false)), 0.16/0.55 inference(sigma_proxy_clausification,[],[f13])). 0.16/0.55 thf(f21,plain,( 0.16/0.55 ($false = (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK1) => (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK0 @ Y0 @ Y1))))))))))), 0.16/0.55 inference(beta-eta_normalization,[],[f20])). 0.16/0.55 thf(f22,plain,( 0.16/0.55 ($false = ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK0 @ Y0 @ Y1)))))))))), 0.16/0.55 inference(imp_proxy_clausification,[],[f21])). 0.16/0.55 thf(f23,plain,( 0.16/0.55 ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK1)))), 0.16/0.55 inference(imp_proxy_clausification,[],[f21])). 0.16/0.55 thf(f24,plain,( 0.16/0.55 ( ! [X1 : ($i > $o)] : (($false = (((^[Y0 : $i > $o]: ((Y0 @ sK1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK0 @ Y0 @ Y1)))))) @ X1)))) )), 0.16/0.55 inference(pi_proxy_clausification,[],[f22])). 0.16/0.55 thf(f25,plain,( 0.16/0.55 ( ! [X1 : ($i > $o)] : (((((X1 @ sK1) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (sK0 @ X1 @ Y0)))))) = $false)) )), 0.16/0.55 inference(beta-eta_normalization,[],[f24])). 0.16/0.55 thf(f28,plain,( 0.16/0.55 ((($true & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))) @ Y0) => (sK0 @ (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3))))))))) @ Y0)))))) = $false)), 0.16/0.55 inference(constrained_superposition,[],[f25,f23])). 0.16/0.55 thf(f29,plain,( 0.16/0.55 ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))) @ Y0) => (sK0 @ (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3))))))))) @ Y0))))))), 0.16/0.55 inference(boolean_simplification,[],[f28])). 0.16/0.55 thf(f31,plain,( 0.16/0.55 ((((^[Y0 : $i]: ((sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))) @ Y0) => (sK0 @ (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3))))))))) @ Y0))) @ sK2)) = $false)), 0.16/0.55 inference(sigma_proxy_clausification,[],[f29])). 0.16/0.55 thf(f32,plain,( 0.16/0.55 ((((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK2) => (sK0 @ (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))) @ sK2))) = $false)), 0.16/0.55 inference(beta-eta_normalization,[],[f31])). 0.16/0.55 thf(f43,plain,( 0.16/0.55 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o)] : (($true = (((^[Y0 : $i]: ((sK0 @ X2 @ Y0) => (sK0 @ X1 @ Y0))) @ X3))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) => (X1 @ Y0))))))) )), 0.16/0.55 inference(pi_proxy_clausification,[],[f19])). 0.16/0.55 thf(f44,plain,( 0.16/0.55 ( ! [X2 : ($i > $o),X3 : $i,X1 : ($i > $o)] : (($true = (((sK0 @ X2 @ X3) => (sK0 @ X1 @ X3)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) => (X1 @ Y0))))))) )), 0.16/0.55 inference(beta-eta_normalization,[],[f43])). 0.16/0.55 thf(f93,plain,( 0.16/0.55 ($true = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))) @ Y0) => (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))) @ Y0))))))), 0.16/0.55 inference(constrained_superposition,[],[f44,f32])). 0.16/0.55 thf(f106,plain,( 0.16/0.55 ($false = ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))) @ Y0) => (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))) @ Y0))))))), 0.16/0.55 inference(trivial_inequality_removal,[],[f93])). 0.16/0.55 thf(f107,plain,( 0.16/0.55 ($false = ((!! @ $i @ (^[Y0 : $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))) => (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))) @ Y0))))))), 0.16/0.56 inference(beta-eta_normalization,[],[f106])). 0.16/0.56 thf(f119,plain,( 0.16/0.56 ($false = (((^[Y0 : $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))) => (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))) @ Y0))) @ sK4)))), 0.16/0.56 inference(sigma_proxy_clausification,[],[f107])). 0.16/0.56 thf(f120,plain,( 0.16/0.56 ($false = (((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK4) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK0 @ Y0 @ Y1))))))) => (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK4))))), 0.16/0.56 inference(beta-eta_normalization,[],[f119])). 0.16/0.56 thf(f121,plain,( 0.16/0.56 (((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK4)) = $false)), 0.16/0.56 inference(imp_proxy_clausification,[],[f120])). 0.16/0.56 thf(f122,plain,( 0.16/0.56 ($true = ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK4) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK0 @ Y0 @ Y1)))))))))), 0.16/0.56 inference(imp_proxy_clausification,[],[f120])). 0.16/0.56 thf(f123,plain,( 0.16/0.56 ($true = (((^[Y0 : $i > $o]: ((Y0 @ sK4) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK0 @ Y0 @ Y1)))))) @ sK5)))), 0.16/0.56 inference(sigma_proxy_clausification,[],[f122])). 0.16/0.56 thf(f124,plain,( 0.16/0.56 ($true = (((sK5 @ sK4) & (!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) => (sK0 @ sK5 @ Y0)))))))), 0.16/0.56 inference(beta-eta_normalization,[],[f123])). 0.16/0.56 thf(f125,plain,( 0.16/0.56 ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) => (sK0 @ sK5 @ Y0))))))), 0.16/0.56 inference(and_proxy_clausification,[],[f124])). 0.16/0.56 thf(f126,plain,( 0.16/0.56 ($true = ((sK5 @ sK4)))), 0.16/0.56 inference(and_proxy_clausification,[],[f124])). 0.16/0.56 thf(f129,plain,( 0.16/0.56 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((sK5 @ Y0) => (sK0 @ sK5 @ Y0))) @ X1)))) )), 0.16/0.56 inference(pi_proxy_clausification,[],[f125])). 0.16/0.56 thf(f130,plain,( 0.16/0.56 ( ! [X1 : $i] : (($true = (((sK5 @ X1) => (sK0 @ sK5 @ X1))))) )), 0.16/0.56 inference(beta-eta_normalization,[],[f129])). 0.16/0.56 thf(f131,plain,( 0.16/0.56 ( ! [X1 : $i] : (($true = ((sK0 @ sK5 @ X1))) | ($false = ((sK5 @ X1)))) )), 0.16/0.56 inference(imp_proxy_clausification,[],[f130])). 0.16/0.56 thf(f134,plain,( 0.16/0.56 ($true = (($true => (sK0 @ sK5 @ sK4))))), 0.16/0.56 inference(constrained_superposition,[],[f130,f126])). 0.16/0.56 thf(f140,plain,( 0.16/0.56 ($true = ((sK0 @ sK5 @ sK4)))), 0.16/0.56 inference(boolean_simplification,[],[f134])). 0.16/0.56 thf(f149,plain,( 0.16/0.56 ( ! [X0 : ($i > $o)] : (($true = (($true => (sK0 @ X0 @ sK4)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) => (X0 @ Y0))))))) )), 0.16/0.56 inference(constrained_superposition,[],[f44,f140])). 0.16/0.56 thf(f152,plain,( 0.16/0.56 ( ! [X0 : ($i > $o)] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) => (X0 @ Y0)))))) | ($true = ((sK0 @ X0 @ sK4)))) )), 0.16/0.56 inference(boolean_simplification,[],[f149])). 0.16/0.56 thf(f183,plain,( 0.16/0.56 ( ! [X0 : ($i > $o)] : (($true = ((sK0 @ X0 @ sK4))) | ($false = (((^[Y0 : $i]: ((sK5 @ Y0) => (X0 @ Y0))) @ (sK6 @ X0))))) )), 0.16/0.56 inference(sigma_proxy_clausification,[],[f152])). 0.16/0.56 thf(f184,plain,( 0.16/0.56 ( ! [X0 : ($i > $o)] : (((((sK5 @ (sK6 @ X0)) => (X0 @ (sK6 @ X0)))) = $false) | ($true = ((sK0 @ X0 @ sK4)))) )), 0.16/0.56 inference(beta-eta_normalization,[],[f183])). 0.16/0.56 thf(f185,plain,( 0.16/0.56 ( ! [X0 : ($i > $o)] : (($true = ((sK0 @ X0 @ sK4))) | (((X0 @ (sK6 @ X0))) = $false)) )), 0.16/0.56 inference(imp_proxy_clausification,[],[f184])). 0.16/0.56 thf(f199,plain,( 0.16/0.56 ($true = $false) | ((((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ (sK6 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))))) = $false)), 0.16/0.56 inference(constrained_superposition,[],[f121,f185])). 0.16/0.56 thf(f205,plain,( 0.16/0.56 ((((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ (sK6 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))))) = $false)), 0.16/0.56 inference(trivial_inequality_removal,[],[f199])). 0.16/0.56 thf(f206,plain,( 0.16/0.56 ($false = ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ (sK6 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))))) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK0 @ Y0 @ Y1)))))))))), 0.16/0.56 inference(beta-eta_normalization,[],[f205])). 0.16/0.56 thf(f214,plain,( 0.16/0.56 ( ! [X1 : ($i > $o)] : (((((^[Y0 : $i > $o]: ((Y0 @ (sK6 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))))) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK0 @ Y0 @ Y1)))))) @ X1)) = $false)) )), 0.16/0.56 inference(pi_proxy_clausification,[],[f206])). 0.16/0.56 thf(f215,plain,( 0.16/0.56 ( ! [X1 : ($i > $o)] : (($false = (((X1 @ (sK6 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))))) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (sK0 @ X1 @ Y0)))))))) )), 0.16/0.56 inference(beta-eta_normalization,[],[f214])). 0.16/0.56 thf(f217,plain,( 0.16/0.56 ($false = ((sK5 @ (sK6 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))))))) | ((($true & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK5 @ Y0) => (sK0 @ (sK0 @ sK5) @ Y0)))))) = $false)), 0.16/0.56 inference(constrained_superposition,[],[f215,f131])). 0.16/0.56 thf(f218,plain,( 0.16/0.56 ($false = ((sK5 @ (sK6 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))))))) | (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK5 @ Y0) => (sK0 @ (sK0 @ sK5) @ Y0))))) = $false)), 0.16/0.56 inference(boolean_simplification,[],[f217])). 0.16/0.56 thf(f220,definition,( 0.16/0.56 spl7_1 <=> ($false = ((sK5 @ (sK6 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2))))))))))))), 0.16/0.56 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])). 0.16/0.56 thf(f222,plain,( 0.16/0.56 ($false = ((sK5 @ (sK6 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))))))) | ~spl7_1), 0.16/0.56 inference(avatar_component_clause,[],[f220])). 0.16/0.56 thf(f224,definition,( 0.16/0.56 spl7_2 <=> (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK5 @ Y0) => (sK0 @ (sK0 @ sK5) @ Y0))))) = $false)), 0.16/0.56 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])). 0.16/0.56 thf(f226,plain,( 0.16/0.56 (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK5 @ Y0) => (sK0 @ (sK0 @ sK5) @ Y0))))) = $false) | ~spl7_2), 0.16/0.56 inference(avatar_component_clause,[],[f224])). 0.16/0.56 thf(f227,plain,( 0.16/0.56 spl7_1 | spl7_2), 0.16/0.56 inference(avatar_split_clause,[],[f218,f224,f220])). 0.16/0.56 thf(f228,plain,( 0.16/0.56 ($false = (((^[Y0 : $i]: ((sK0 @ sK5 @ Y0) => (sK0 @ (sK0 @ sK5) @ Y0))) @ (sK3 @ (sK0 @ sK5))))) | ~spl7_2), 0.16/0.56 inference(sigma_proxy_clausification,[],[f226])). 0.16/0.56 thf(f229,plain,( 0.16/0.56 ((((sK0 @ sK5 @ (sK3 @ (sK0 @ sK5))) => (sK0 @ (sK0 @ sK5) @ (sK3 @ (sK0 @ sK5))))) = $false) | ~spl7_2), 0.16/0.56 inference(beta-eta_normalization,[],[f228])). 0.16/0.56 thf(f236,plain,( 0.16/0.56 ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) => (sK0 @ sK5 @ Y0)))))) | ($true = $false) | ~spl7_2), 0.16/0.56 inference(constrained_superposition,[],[f44,f229])). 0.16/0.56 thf(f237,plain,( 0.16/0.56 ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) => (sK0 @ sK5 @ Y0)))))) | ~spl7_2), 0.16/0.56 inference(trivial_inequality_removal,[],[f236])). 0.16/0.56 thf(f274,plain,( 0.16/0.56 ($false = (((^[Y0 : $i]: ((sK5 @ Y0) => (sK0 @ sK5 @ Y0))) @ (sK3 @ sK5)))) | ~spl7_2), 0.16/0.56 inference(sigma_proxy_clausification,[],[f237])). 0.16/0.56 thf(f275,plain,( 0.16/0.56 ($false = (((sK5 @ (sK3 @ sK5)) => (sK0 @ sK5 @ (sK3 @ sK5))))) | ~spl7_2), 0.16/0.56 inference(beta-eta_normalization,[],[f274])). 0.16/0.56 thf(f276,plain,( 0.16/0.56 ($true = $false) | ~spl7_2), 0.16/0.56 inference(forward_demodulation,[],[f275,f130])). 0.16/0.56 thf(f277,plain,( 0.16/0.56 $false | ~spl7_2), 0.16/0.56 inference(trivial_inequality_removal,[],[f276])). 0.16/0.56 thf(f278,plain,( 0.16/0.56 ~spl7_2), 0.16/0.56 inference(avatar_contradiction_clause,[],[f277])). 0.16/0.56 thf(f363,plain,( 0.16/0.56 ((($false => ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ (sK6 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))))))) = $false) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK4))) | ~spl7_1), 0.16/0.56 inference(constrained_superposition,[],[f184,f222])). 0.16/0.56 thf(f365,plain,( 0.16/0.56 ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK4))) | ((($false => (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ (sK6 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK0 @ Y2 @ Y3)))))))))) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK0 @ Y0 @ Y1))))))))) = $false) | ~spl7_1), 0.16/0.56 inference(beta-eta_normalization,[],[f363])). 0.16/0.56 thf(f366,plain,( 0.16/0.56 ($true = $false) | ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK4))) | ~spl7_1), 0.16/0.56 inference(boolean_simplification,[],[f365])). 0.16/0.56 thf(f367,plain,( 0.16/0.56 ($true = ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK0 @ Y1 @ Y2)))))))) @ sK4))) | ~spl7_1), 0.16/0.56 inference(trivial_inequality_removal,[],[f366])). 0.16/0.56 thf(f370,plain,( 0.16/0.56 ($true = $false) | ~spl7_1), 0.16/0.56 inference(forward_demodulation,[],[f367,f121])). 0.16/0.56 thf(f371,plain,( 0.16/0.56 $false | ~spl7_1), 0.16/0.56 inference(trivial_inequality_removal,[],[f370])). 0.16/0.56 thf(f372,plain,( 0.16/0.56 ~spl7_1), 0.16/0.56 inference(avatar_contradiction_clause,[],[f371])). 0.16/0.56 cnf(s1, plain, spl7_1 | spl7_2, inference(sat_conversion,[],[f227])). 0.16/0.56 cnf(s4, plain, ~spl7_2, inference(sat_conversion,[],[f278])). 0.16/0.56 cnf(s6, plain, ~spl7_1, inference(sat_conversion,[],[f372])). 0.16/0.56 cnf(s7, plain, $false, inference(rat,[],[s1,s4,s6])). 0.16/0.56 thf(f373,plain,( 0.16/0.56 $false), 0.16/0.56 inference(avatar_sat_refutation,[],[s7])). 0.16/0.56 % SZS output end Proof for theBenchmark 0.16/0.56 % (3741657)------------------------------ 0.16/0.56 % (3741657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.16/0.56 % (3741657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.16/0.56 % (3741657)CaDiCaL version: 2.1.3 0.16/0.56 % (3741657)Termination reason: Refutation 0.16/0.56 % (3741657)Time elapsed: 0.023 s 0.16/0.56 % (3741657)Peak memory usage: 13 MB 0.16/0.56 % (3741657)Instructions burned: 37 (million) 0.16/0.56 % (3741632)Success in time 0.105 s 0.16/0.56 % Vampire exiting 0.82/0.56 EOF