%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV488^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:38:44 AM UTC 2026
% Result : Theorem 0.82s 0.37s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV488^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.18 % Computer : n019.cluster.edu
% 0.13/0.18 % Model : x86_64 x86_64
% 0.13/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.18 % Memory : 8046.5625MB
% 0.13/0.18 % OS : Linux 6.8.0-71-generic
% 0.13/0.18 % CPULimit : 300
% 0.13/0.18 % WCLimit : 300
% 0.13/0.18 % DateTime : Tue Sep 29 15:53:03 UTC 2026
% 0.13/0.19 % CPUTime :
% 0.13/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.22 Running higher-order theorem proving
% 0.13/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.82/0.37 % (956500)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.82/0.37 % (956518)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1199862540:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.82/0.37 % (956525)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.82/0.37 % (956525)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
% 0.82/0.37 % (956521)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=23713260:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.82/0.37 % (956519)lrs+10_16_si=on:nwc=1.5:random_seed=726789701:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.82/0.37 % (956524)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1083473591:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.82/0.37 % (956522)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=2559895379: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_2999 on theBenchmark for (2999ds/634Mi)
% 0.82/0.37 % (956523)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3944263430:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.82/0.37 % (956525)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=4021301203:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.82/0.37 % (956521)Instruction limit reached!
% 0.82/0.37 % (956521)------------------------------
% 0.82/0.37 % (956521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956521)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956521)Termination reason: Instruction limit
% 0.82/0.37 % (956521)Termination phase: Saturation
% 0.82/0.37 % (956521)Time elapsed: 0.003 s
% 0.82/0.37 % (956521)Peak memory usage: 12 MB
% 0.82/0.37 % (956521)Instructions burned: 4 (million)
% 0.82/0.37 % (956519)Instruction limit reached!
% 0.82/0.37 % (956519)------------------------------
% 0.82/0.37 % (956519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956519)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956519)Termination reason: Instruction limit
% 0.82/0.37 % (956519)Termination phase: Saturation
% 0.82/0.37 % (956519)Time elapsed: 0.012 s
% 0.82/0.37 % (956519)Peak memory usage: 12 MB
% 0.82/0.37 % (956519)Instructions burned: 19 (million)
% 0.82/0.37 % (956523)Instruction limit reached!
% 0.82/0.37 % (956523)------------------------------
% 0.82/0.37 % (956523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956523)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956523)Termination reason: Instruction limit
% 0.82/0.37 % (956523)Termination phase: Saturation
% 0.82/0.37 % (956523)Time elapsed: 0.014 s
% 0.82/0.37 % (956523)Peak memory usage: 12 MB
% 0.82/0.37 % (956523)Instructions burned: 24 (million)
% 0.82/0.37 % (956518)Instruction limit reached!
% 0.82/0.37 % (956518)------------------------------
% 0.82/0.37 % (956518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956518)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956518)Termination reason: Instruction limit
% 0.82/0.37 % (956518)Termination phase: Saturation
% 0.82/0.37 % (956518)Time elapsed: 0.027 s
% 0.82/0.37 % (956518)Peak memory usage: 13 MB
% 0.82/0.37 % (956518)Instructions burned: 90 (million)
% 0.82/0.37 % (956539)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=724487336:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.82/0.37 % (956539)Instruction limit reached!
% 0.82/0.37 % (956539)------------------------------
% 0.82/0.37 % (956539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956539)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956539)Termination reason: Instruction limit
% 0.82/0.37 % (956539)Termination phase: Saturation
% 0.82/0.37 % (956539)Time elapsed: 0.002 s
% 0.82/0.37 % (956539)Peak memory usage: 12 MB
% 0.82/0.37 % (956539)Instructions burned: 3 (million)
% 0.82/0.37 % (956550)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=531267520:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.82/0.37 % (956547)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.82/0.37 % (956545)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3201124163:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.82/0.37 % (956550)Instruction limit reached!
% 0.82/0.37 % (956550)------------------------------
% 0.82/0.37 % (956550)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956547)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4257056542:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.82/0.37 % (956550)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956550)Termination reason: Instruction limit
% 0.82/0.37 % (956550)Termination phase: Saturation
% 0.82/0.37 % (956550)Time elapsed: 0.004 s
% 0.82/0.37 % (956550)Peak memory usage: 12 MB
% 0.82/0.37 % (956550)Instructions burned: 12 (million)
% 0.82/0.37 % (956545)Instruction limit reached!
% 0.82/0.37 % (956545)------------------------------
% 0.82/0.37 % (956545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956545)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956545)Termination reason: Instruction limit
% 0.82/0.37 % (956545)Termination phase: Saturation
% 0.82/0.37 % (956545)Time elapsed: 0.003 s
% 0.82/0.37 % (956545)Peak memory usage: 12 MB
% 0.82/0.37 % (956545)Instructions burned: 5 (million)
% 0.82/0.37 % (956547)Instruction limit reached!
% 0.82/0.37 % (956547)------------------------------
% 0.82/0.37 % (956547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956547)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956547)Termination reason: Instruction limit
% 0.82/0.37 % (956547)Termination phase: Saturation
% 0.82/0.37 % (956547)Time elapsed: 0.005 s
% 0.82/0.37 % (956547)Peak memory usage: 12 MB
% 0.82/0.37 % (956547)Instructions burned: 9 (million)
% 0.82/0.37 % (956555)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
% 0.82/0.37 % (956555)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.82/0.37 % (956524)Instruction limit reached!
% 0.82/0.37 % (956524)------------------------------
% 0.82/0.37 % (956524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956524)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956524)Termination reason: Instruction limit
% 0.82/0.37 % (956524)Termination phase: Saturation
% 0.82/0.37 % (956524)Time elapsed: 0.042 s
% 0.82/0.37 % (956524)Peak memory usage: 13 MB
% 0.82/0.37 % (956524)Instructions burned: 76 (million)
% 0.82/0.37 % (956555)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1077209186:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.82/0.37 % (956564)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=3182502949:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.82/0.37 % (956566)lrs+10_1_si=on:cs=on:random_seed=3193425036:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.82/0.37 % (956570)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.82/0.37 % (956566)Instruction limit reached!
% 0.82/0.37 % (956566)------------------------------
% 0.82/0.37 % (956566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956566)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956566)Termination reason: Instruction limit
% 0.82/0.37 % (956566)Termination phase: Saturation
% 0.82/0.37 % (956566)Time elapsed: 0.004 s
% 0.82/0.37 % (956566)Peak memory usage: 12 MB
% 0.82/0.37 % (956566)Instructions burned: 9 (million)
% 0.82/0.37 % (956570)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=1619393130:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.82/0.37 % (956570)Instruction limit reached!
% 0.82/0.37 % (956570)------------------------------
% 0.82/0.37 % (956570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956570)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956570)Termination reason: Instruction limit
% 0.82/0.37 % (956570)Termination phase: Saturation
% 0.82/0.37 % (956570)Time elapsed: 0.002 s
% 0.82/0.37 % (956570)Peak memory usage: 12 MB
% 0.82/0.37 % (956570)Instructions burned: 3 (million)
% 0.82/0.37 % (956573)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2280247955:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.82/0.37 % (956555)Instruction limit reached!
% 0.82/0.37 % (956555)------------------------------
% 0.82/0.37 % (956555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956555)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956555)Termination reason: Instruction limit
% 0.82/0.37 % (956555)Termination phase: Saturation
% 0.82/0.37 % (956555)Time elapsed: 0.017 s
% 0.82/0.37 % (956555)Peak memory usage: 12 MB
% 0.82/0.37 % (956555)Instructions burned: 31 (million)
% 0.82/0.37 % (956564)Instruction limit reached!
% 0.82/0.37 % (956564)------------------------------
% 0.82/0.37 % (956564)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956564)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956564)Termination reason: Instruction limit
% 0.82/0.37 % (956564)Termination phase: Saturation
% 0.82/0.37 % (956564)Time elapsed: 0.022 s
% 0.82/0.37 % (956564)Peak memory usage: 12 MB
% 0.82/0.37 % (956564)Instructions burned: 88 (million)
% 0.82/0.37 % (956588)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4271375334:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.82/0.37 % (956582)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1901884512:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.82/0.37 % (956586)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=701829448:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.82/0.37 % (956587)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=38747767:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.82/0.37 % (956573) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-956500-956573"...
% 0.82/0.37 % (956525)Instruction limit reached!
% 0.82/0.37 % (956525)------------------------------
% 0.82/0.37 % (956525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956525)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956525)Termination reason: Instruction limit
% 0.82/0.37 % (956525)Termination phase: Saturation
% 0.82/0.37 % (956525)Time elapsed: 0.085 s
% 0.82/0.37 % (956525)Peak memory usage: 13 MB
% 0.82/0.37 % (956525)Instructions burned: 157 (million)
% 0.82/0.37 % (956573)...printing done.
% 0.82/0.37 % (956573)Refutation found. Thanks to Tanya!
% 0.82/0.37 % SZS status Theorem for theBenchmark
% 0.82/0.37 % SZS output start Proof for theBenchmark
% 0.82/0.37 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.82/0.37 thf(type_def_6, type, sK4: $tType).
% 0.82/0.37 thf(func_def_0, type, 'const/trivia/I': !>[X0: $tType]:((X0 > X0))).
% 0.82/0.37 thf(func_def_1, type, 'const/sets/UNIONS': !>[X0: $tType]:((((X0 > $o) > $o) > X0 > $o))).
% 0.82/0.37 thf(func_def_2, type, 'const/sets/SUBSET': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.82/0.37 thf(func_def_3, type, 'const/sets/pairwise': !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > $o) > $o))).
% 0.82/0.37 thf(func_def_4, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.82/0.37 thf(func_def_8, type, sK0: !>[X0: $tType]:((X0 > ((X0 > $o) > $o) > X0 > $o))).
% 0.82/0.37 thf(func_def_9, type, sK1: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.82/0.37 thf(func_def_10, type, sK2: !>[X0: $tType]:(((X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.37 thf(func_def_11, type, sK3: !>[X0: $tType]:(((X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.82/0.37 thf(func_def_12, type, sK5: ((sK4 > $o) > $o)).
% 0.82/0.37 thf(func_def_13, type, sK6: (sK4 > sK4 > $o)).
% 0.82/0.37 thf(func_def_14, type, vNOT: ($o > $o)).
% 0.82/0.37 thf(func_def_15, type, db0: !>[X0: $tType]:(X0)).
% 0.82/0.37 thf(func_def_16, type, db1: !>[X0: $tType]:(X0)).
% 0.82/0.37 thf(func_def_17, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.82/0.37 thf(func_def_18, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.82/0.37 thf(func_def_19, type, db2: !>[X0: $tType]:(X0)).
% 0.82/0.37 thf(f3,axiom,(
% 0.82/0.37 ! [X0 : $tType,X2 : X0,X1 : ((X0 > $o) > $o)] : (? [X3 : (X0 > $o)] : (('const/sets/IN' @ X0 @ X2 @ X3) & ('const/sets/IN' @ (X0 > $o) @ X3 @ X1)) = (('const/sets/IN' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))))),
% 0.82/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_UNIONS_')).
% 0.82/0.37 thf(f4,axiom,(
% 0.82/0.37 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)) = (('const/sets/SUBSET' @ X0 @ X1 @ X2)))),
% 0.82/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_')).
% 0.82/0.37 thf(f5,axiom,(
% 0.82/0.37 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > X0 > $o)] : (! [X3 : X0,X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1) & ('const/sets/IN' @ X0 @ X3 @ X1) & (X3 != X4)) => (X2 @ X3 @ X4)) = (('const/sets/pairwise' @ X0 @ X2 @ X1)))),
% 0.82/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/pairwise_')).
% 0.82/0.37 thf(f6,conjecture,(
% 0.82/0.37 ! [X0 : $tType,X2 : ((X0 > $o) > $o),X1 : (X0 > X0 > $o)] : ((! [X3 : (X0 > $o)] : (('const/sets/IN' @ (X0 > $o) @ X3 @ X2) => ('const/sets/pairwise' @ X0 @ X1 @ X3)) & ! [X4 : (X0 > $o),X3 : (X0 > $o)] : ((('const/sets/IN' @ (X0 > $o) @ X3 @ X2) & ('const/sets/IN' @ (X0 > $o) @ X4 @ X2)) => (('const/sets/SUBSET' @ X0 @ X3 @ X4) | ('const/sets/SUBSET' @ X0 @ X4 @ X3)))) => ('const/sets/pairwise' @ X0 @ X1 @ ('const/sets/UNIONS' @ X0 @ X2)))),
% 0.82/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/PAIRWISE_CHAIN_UNIONS_')).
% 0.82/0.37 thf(f7,negated_conjecture,(
% 0.82/0.37 ~ ! [X0 : $tType,X2 : ((X0 > $o) > $o),X1 : (X0 > X0 > $o)] : ((! [X3 : (X0 > $o)] : (('const/sets/IN' @ (X0 > $o) @ X3 @ X2) => ('const/sets/pairwise' @ X0 @ X1 @ X3)) & ! [X4 : (X0 > $o),X3 : (X0 > $o)] : ((('const/sets/IN' @ (X0 > $o) @ X3 @ X2) & ('const/sets/IN' @ (X0 > $o) @ X4 @ X2)) => (('const/sets/SUBSET' @ X0 @ X3 @ X4) | ('const/sets/SUBSET' @ X0 @ X4 @ X3)))) => ('const/sets/pairwise' @ X0 @ X1 @ ('const/sets/UNIONS' @ X0 @ X2)))),
% 0.82/0.37 inference(negated_conjecture,[status(cth)],[f6])).
% 0.82/0.37 thf(f8,plain,(
% 0.82/0.37 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)) = (('const/sets/SUBSET' @ X0 @ X1 @ X2)))),
% 0.82/0.37 inference(rectify,[],[f4])).
% 0.82/0.37 thf(f9,plain,(
% 0.82/0.37 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) <=> ! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X1)) = $true) => ((('const/sets/IN' @ X0 @ X3 @ X2)) = $true)))),
% 0.82/0.37 inference(fool_elimination,[],[f8])).
% 0.82/0.37 thf(f10,plain,(
% 0.82/0.37 ~ ! [X0 : $tType,X1 : ((X0 > $o) > $o),X2 : (X0 > X0 > $o)] : ((! [X3 : (X0 > $o)] : (('const/sets/IN' @ (X0 > $o) @ X3 @ X1) => ('const/sets/pairwise' @ X0 @ X2 @ X3)) & ! [X4 : (X0 > $o),X5 : (X0 > $o)] : ((('const/sets/IN' @ (X0 > $o) @ X5 @ X1) & ('const/sets/IN' @ (X0 > $o) @ X4 @ X1)) => (('const/sets/SUBSET' @ X0 @ X5 @ X4) | ('const/sets/SUBSET' @ X0 @ X4 @ X5)))) => ('const/sets/pairwise' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1)))),
% 0.82/0.37 inference(rectify,[],[f7])).
% 0.82/0.37 thf(f11,plain,(
% 0.82/0.37 ~ ! [X0 : $tType,X1 : ((X0 > $o) > $o),X2 : (X0 > X0 > $o)] : ((! [X3 : (X0 > $o)] : (((('const/sets/IN' @ (X0 > $o) @ X3 @ X1)) = $true) => ($true = (('const/sets/pairwise' @ X0 @ X2 @ X3)))) & ! [X4 : (X0 > $o),X5 : (X0 > $o)] : ((((('const/sets/IN' @ (X0 > $o) @ X5 @ X1)) = $true) & ($true = (('const/sets/IN' @ (X0 > $o) @ X4 @ X1)))) => (((('const/sets/SUBSET' @ X0 @ X4 @ X5)) = $true) | ((('const/sets/SUBSET' @ X0 @ X5 @ X4)) = $true)))) => ((('const/sets/pairwise' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))) = $true))),
% 0.82/0.37 inference(fool_elimination,[],[f10])).
% 0.82/0.37 thf(f12,plain,(
% 0.82/0.37 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > X0 > $o)] : (! [X3 : X0,X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1) & ('const/sets/IN' @ X0 @ X3 @ X1) & (X3 != X4)) => (X2 @ X3 @ X4)) = (('const/sets/pairwise' @ X0 @ X2 @ X1)))),
% 0.82/0.37 inference(rectify,[],[f5])).
% 0.82/0.37 thf(f13,plain,(
% 0.82/0.37 ! [X0 : $tType,X2 : (X0 > X0 > $o),X1 : (X0 > $o)] : (! [X3 : X0,X4 : X0] : ((((('const/sets/IN' @ X0 @ X3 @ X1)) = $true) & (X3 != X4) & ((('const/sets/IN' @ X0 @ X4 @ X1)) = $true)) => (((X2 @ X3 @ X4)) = $true)) <=> ((('const/sets/pairwise' @ X0 @ X2 @ X1)) = $true))),
% 0.82/0.37 inference(fool_elimination,[],[f12])).
% 0.82/0.37 thf(f14,plain,(
% 0.82/0.37 ! [X0 : $tType,X1 : X0,X2 : ((X0 > $o) > $o)] : (? [X3 : (X0 > $o)] : (('const/sets/IN' @ X0 @ X1 @ X3) & ('const/sets/IN' @ (X0 > $o) @ X3 @ X2)) = (('const/sets/IN' @ X0 @ X1 @ ('const/sets/UNIONS' @ X0 @ X2))))),
% 0.82/0.37 inference(rectify,[],[f3])).
% 0.82/0.37 thf(f15,plain,(
% 0.82/0.37 ! [X0 : $tType,X2 : ((X0 > $o) > $o),X1 : X0] : (($true = (('const/sets/IN' @ X0 @ X1 @ ('const/sets/UNIONS' @ X0 @ X2)))) <=> ? [X3 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X1 @ X3)) = $true) & ((('const/sets/IN' @ (X0 > $o) @ X3 @ X2)) = $true)))),
% 0.82/0.37 inference(fool_elimination,[],[f14])).
% 0.82/0.37 thf(f16,plain,(
% 0.82/0.37 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true)) <=> ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true))),
% 0.82/0.37 inference(ennf_transformation,[],[f9])).
% 0.82/0.37 thf(f17,plain,(
% 0.82/0.37 ? [X0 : $tType,X1 : ((X0 > $o) > $o),X2 : (X0 > X0 > $o)] : (((('const/sets/pairwise' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))) != $true) & (! [X3 : (X0 > $o)] : (((('const/sets/IN' @ (X0 > $o) @ X3 @ X1)) != $true) | ($true = (('const/sets/pairwise' @ X0 @ X2 @ X3)))) & ! [X4 : (X0 > $o),X5 : (X0 > $o)] : ((((('const/sets/SUBSET' @ X0 @ X4 @ X5)) = $true) | ((('const/sets/SUBSET' @ X0 @ X5 @ X4)) = $true)) | (((('const/sets/IN' @ (X0 > $o) @ X5 @ X1)) != $true) | ($true != (('const/sets/IN' @ (X0 > $o) @ X4 @ X1)))))))),
% 0.82/0.37 inference(ennf_transformation,[],[f11])).
% 0.82/0.37 thf(f18,plain,(
% 0.82/0.37 ? [X0 : $tType,X1 : ((X0 > $o) > $o),X2 : (X0 > X0 > $o)] : (! [X4 : (X0 > $o),X5 : (X0 > $o)] : (((('const/sets/IN' @ (X0 > $o) @ X5 @ X1)) != $true) | ($true != (('const/sets/IN' @ (X0 > $o) @ X4 @ X1))) | ((('const/sets/SUBSET' @ X0 @ X5 @ X4)) = $true) | ((('const/sets/SUBSET' @ X0 @ X4 @ X5)) = $true)) & ! [X3 : (X0 > $o)] : (((('const/sets/IN' @ (X0 > $o) @ X3 @ X1)) != $true) | ($true = (('const/sets/pairwise' @ X0 @ X2 @ X3)))) & ((('const/sets/pairwise' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))) != $true))),
% 0.82/0.37 inference(flattening,[],[f17])).
% 0.82/0.37 thf(f19,plain,(
% 0.82/0.37 ! [X0 : $tType,X2 : (X0 > X0 > $o),X1 : (X0 > $o)] : (! [X3 : X0,X4 : X0] : ((((X2 @ X3 @ X4)) = $true) | (((('const/sets/IN' @ X0 @ X3 @ X1)) != $true) | (X3 = X4) | ((('const/sets/IN' @ X0 @ X4 @ X1)) != $true))) <=> ((('const/sets/pairwise' @ X0 @ X2 @ X1)) = $true))),
% 0.82/0.37 inference(ennf_transformation,[],[f13])).
% 0.82/0.37 thf(f20,plain,(
% 0.82/0.37 ! [X0 : $tType,X2 : (X0 > X0 > $o),X1 : (X0 > $o)] : (((('const/sets/pairwise' @ X0 @ X2 @ X1)) = $true) <=> ! [X4 : X0,X3 : X0] : (((('const/sets/IN' @ X0 @ X4 @ X1)) != $true) | (X3 = X4) | (((X2 @ X3 @ X4)) = $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true)))),
% 0.82/0.37 inference(flattening,[],[f19])).
% 0.82/0.37 thf(f21,plain,(
% 0.82/0.37 ! [X0 : $tType,X2 : ((X0 > $o) > $o),X1 : X0] : ((($true = (('const/sets/IN' @ X0 @ X1 @ ('const/sets/UNIONS' @ X0 @ X2)))) | ! [X3 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X1 @ X3)) != $true) | ((('const/sets/IN' @ (X0 > $o) @ X3 @ X2)) != $true))) & (? [X3 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X1 @ X3)) = $true) & ((('const/sets/IN' @ (X0 > $o) @ X3 @ X2)) = $true)) | ($true != (('const/sets/IN' @ X0 @ X1 @ ('const/sets/UNIONS' @ X0 @ X2))))))),
% 0.82/0.37 inference(nnf_transformation,[],[f15])).
% 0.82/0.37 thf(f22,plain,(
% 0.82/0.37 ! [X0 : $tType,X1 : ((X0 > $o) > $o),X2 : X0] : ((((('const/sets/IN' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))) = $true) | ! [X3 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X2 @ X3)) != $true) | ((('const/sets/IN' @ (X0 > $o) @ X3 @ X1)) != $true))) & (? [X4 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X2 @ X4)) = $true) & ($true = (('const/sets/IN' @ (X0 > $o) @ X4 @ X1)))) | ((('const/sets/IN' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))) != $true)))),
% 0.82/0.37 inference(rectify,[],[f21])).
% 0.82/0.37 thf(f23,plain,(
% 0.82/0.37 ! [X0 : $tType,X1 : ((X0 > $o) > $o),X2 : X0] : ((((('const/sets/IN' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))) = $true) | ! [X3 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X2 @ X3)) != $true) | ((('const/sets/IN' @ (X0 > $o) @ X3 @ X1)) != $true))) & ((((('const/sets/IN' @ X0 @ X2 @ (sK0 @ X0 @ X2 @ X1))) = $true) & ($true = (('const/sets/IN' @ (X0 > $o) @ (sK0 @ X0 @ X2 @ X1) @ X1)))) | ((('const/sets/IN' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))) != $true)))),
% 0.82/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK0 @ X0 @ X2 @ X1)],[f22])).
% 0.82/0.37 thf(f24,plain,(
% 0.82/0.37 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true)) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true)) & (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) | ? [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) & ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true))))),
% 0.82/0.37 inference(nnf_transformation,[],[f16])).
% 0.82/0.37 thf(f25,plain,(
% 0.82/0.37 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true)) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true)) & (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) | ? [X4 : X0] : (((('const/sets/IN' @ X0 @ X4 @ X2)) != $true) & ((('const/sets/IN' @ X0 @ X4 @ X1)) = $true))))),
% 0.82/0.37 inference(rectify,[],[f24])).
% 0.82/0.37 thf(f26,plain,(
% 0.82/0.37 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true)) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true)) & (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) | (($true != (('const/sets/IN' @ X0 @ (sK1 @ X0 @ X2 @ X1) @ X2))) & ((('const/sets/IN' @ X0 @ (sK1 @ X0 @ X2 @ X1) @ X1)) = $true))))),
% 0.82/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK0 @ X0 @ X2 @ X1)],[f25])).
% 0.82/0.37 thf(f28,plain,(
% 0.82/0.37 ! [X0 : $tType,X2 : (X0 > X0 > $o),X1 : (X0 > $o)] : ((((('const/sets/pairwise' @ X0 @ X2 @ X1)) = $true) | ? [X4 : X0,X3 : X0] : (((('const/sets/IN' @ X0 @ X4 @ X1)) = $true) & (X3 != X4) & (((X2 @ X3 @ X4)) != $true) & ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true))) & (! [X4 : X0,X3 : X0] : (((('const/sets/IN' @ X0 @ X4 @ X1)) != $true) | (X3 = X4) | (((X2 @ X3 @ X4)) = $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true)) | ((('const/sets/pairwise' @ X0 @ X2 @ X1)) != $true)))),
% 0.82/0.37 inference(nnf_transformation,[],[f20])).
% 0.82/0.37 thf(f29,plain,(
% 0.82/0.37 ! [X0 : $tType,X1 : (X0 > X0 > $o),X2 : (X0 > $o)] : ((((('const/sets/pairwise' @ X0 @ X1 @ X2)) = $true) | ? [X3 : X0,X4 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) & (X3 != X4) & (((X1 @ X4 @ X3)) != $true) & ((('const/sets/IN' @ X0 @ X4 @ X2)) = $true))) & (! [X5 : X0,X6 : X0] : (((('const/sets/IN' @ X0 @ X5 @ X2)) != $true) | (X5 = X6) | (((X1 @ X6 @ X5)) = $true) | ((('const/sets/IN' @ X0 @ X6 @ X2)) != $true)) | ((('const/sets/pairwise' @ X0 @ X1 @ X2)) != $true)))),
% 0.82/0.37 inference(rectify,[],[f28])).
% 0.82/0.37 thf(f30,plain,(
% 0.82/0.37 ! [X0 : $tType,X1 : (X0 > X0 > $o),X2 : (X0 > $o)] : ((((('const/sets/pairwise' @ X0 @ X1 @ X2)) = $true) | (((('const/sets/IN' @ X0 @ (sK2 @ X0 @ X2 @ X1) @ X2)) = $true) & (((sK2 @ X0 @ X2 @ X1)) != ((sK3 @ X0 @ X2 @ X1))) & (((X1 @ (sK3 @ X0 @ X2 @ X1) @ (sK2 @ X0 @ X2 @ X1))) != $true) & ((('const/sets/IN' @ X0 @ (sK3 @ X0 @ X2 @ X1) @ X2)) = $true))) & (! [X5 : X0,X6 : X0] : (((('const/sets/IN' @ X0 @ X5 @ X2)) != $true) | (X5 = X6) | (((X1 @ X6 @ X5)) = $true) | ((('const/sets/IN' @ X0 @ X6 @ X2)) != $true)) | ((('const/sets/pairwise' @ X0 @ X1 @ X2)) != $true)))),
% 0.82/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK0 @ X0 @ X2 @ X1),skolemize(X4,sK0 @ X0 @ X2 @ X1)],[f29])).
% 0.82/0.37 thf(f31,plain,(
% 0.82/0.37 ? [X0 : $tType,X1 : ((X0 > $o) > $o),X2 : (X0 > X0 > $o)] : (! [X3 : (X0 > $o),X4 : (X0 > $o)] : (($true != (('const/sets/IN' @ (X0 > $o) @ X4 @ X1))) | ((('const/sets/IN' @ (X0 > $o) @ X3 @ X1)) != $true) | ((('const/sets/SUBSET' @ X0 @ X4 @ X3)) = $true) | ((('const/sets/SUBSET' @ X0 @ X3 @ X4)) = $true)) & ! [X5 : (X0 > $o)] : (((('const/sets/IN' @ (X0 > $o) @ X5 @ X1)) != $true) | ($true = (('const/sets/pairwise' @ X0 @ X2 @ X5)))) & ((('const/sets/pairwise' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))) != $true))),
% 0.82/0.37 inference(rectify,[],[f18])).
% 0.82/0.37 thf(f32,plain,(
% 0.82/0.37 ! [X3 : (sK4 > $o),X4 : (sK4 > $o)] : (((('const/sets/IN' @ (sK4 > $o) @ X4 @ sK5)) != $true) | ($true != (('const/sets/IN' @ (sK4 > $o) @ X3 @ sK5))) | ($true = (('const/sets/SUBSET' @ sK4 @ X4 @ X3))) | ((('const/sets/SUBSET' @ sK4 @ X3 @ X4)) = $true)) & ! [X5 : (sK4 > $o)] : (($true != (('const/sets/IN' @ (sK4 > $o) @ X5 @ sK5))) | ((('const/sets/pairwise' @ sK4 @ sK6 @ X5)) = $true)) & ($true != (('const/sets/pairwise' @ sK4 @ sK6 @ ('const/sets/UNIONS' @ sK4 @ sK5))))),
% 0.82/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f31])).
% 0.82/0.37 thf(f33,plain,(
% 0.82/0.37 ( ! [X0 : $tType,X2 : X0,X1 : ((X0 > $o) > $o)] : (($true = (('const/sets/IN' @ (X0 > $o) @ (sK0 @ X0 @ X2 @ X1) @ X1))) | ((('const/sets/IN' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))) != $true)) )),
% 0.82/0.37 inference(cnf_transformation,[],[f23])).
% 0.82/0.37 thf(f34,plain,(
% 0.82/0.37 ( ! [X0 : $tType,X2 : X0,X1 : ((X0 > $o) > $o)] : (((('const/sets/IN' @ X0 @ X2 @ (sK0 @ X0 @ X2 @ X1))) = $true) | ((('const/sets/IN' @ X0 @ X2 @ ('const/sets/UNIONS' @ X0 @ X1))) != $true)) )),
% 0.82/0.37 inference(cnf_transformation,[],[f23])).
% 0.82/0.37 thf(f38,plain,(
% 0.82/0.37 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X2)) = $true)) )),
% 0.82/0.37 inference(cnf_transformation,[],[f26])).
% 0.82/0.37 thf(f40,plain,(
% 0.82/0.37 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > X0 > $o),X6 : X0,X5 : X0] : (((('const/sets/pairwise' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X5 @ X2)) != $true) | (X5 = X6) | (((X1 @ X6 @ X5)) = $true) | ((('const/sets/IN' @ X0 @ X6 @ X2)) != $true)) )),
% 0.82/0.37 inference(cnf_transformation,[],[f30])).
% 0.82/0.37 thf(f41,plain,(
% 0.82/0.37 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > X0 > $o)] : (((('const/sets/IN' @ X0 @ (sK3 @ X0 @ X2 @ X1) @ X2)) = $true) | ((('const/sets/pairwise' @ X0 @ X1 @ X2)) = $true)) )),
% 0.82/0.37 inference(cnf_transformation,[],[f30])).
% 0.82/0.37 thf(f42,plain,(
% 0.82/0.37 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > X0 > $o)] : ((((X1 @ (sK3 @ X0 @ X2 @ X1) @ (sK2 @ X0 @ X2 @ X1))) != $true) | ((('const/sets/pairwise' @ X0 @ X1 @ X2)) = $true)) )),
% 0.82/0.37 inference(cnf_transformation,[],[f30])).
% 0.82/0.37 thf(f43,plain,(
% 0.82/0.37 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > X0 > $o)] : ((((sK2 @ X0 @ X2 @ X1)) != ((sK3 @ X0 @ X2 @ X1))) | ((('const/sets/pairwise' @ X0 @ X1 @ X2)) = $true)) )),
% 0.82/0.37 inference(cnf_transformation,[],[f30])).
% 0.82/0.37 thf(f44,plain,(
% 0.82/0.37 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > X0 > $o)] : (((('const/sets/IN' @ X0 @ (sK2 @ X0 @ X2 @ X1) @ X2)) = $true) | ((('const/sets/pairwise' @ X0 @ X1 @ X2)) = $true)) )),
% 0.82/0.37 inference(cnf_transformation,[],[f30])).
% 0.82/0.37 thf(f45,plain,(
% 0.82/0.37 ($true != (('const/sets/pairwise' @ sK4 @ sK6 @ ('const/sets/UNIONS' @ sK4 @ sK5))))),
% 0.82/0.37 inference(cnf_transformation,[],[f32])).
% 0.82/0.37 thf(f46,plain,(
% 0.82/0.37 ( ! [X5 : (sK4 > $o)] : (($true != (('const/sets/IN' @ (sK4 > $o) @ X5 @ sK5))) | ((('const/sets/pairwise' @ sK4 @ sK6 @ X5)) = $true)) )),
% 0.82/0.37 inference(cnf_transformation,[],[f32])).
% 0.82/0.37 thf(f47,plain,(
% 0.82/0.37 ( ! [X3 : (sK4 > $o),X4 : (sK4 > $o)] : (($true != (('const/sets/IN' @ (sK4 > $o) @ X3 @ sK5))) | ((('const/sets/SUBSET' @ sK4 @ X3 @ X4)) = $true) | ($true = (('const/sets/SUBSET' @ sK4 @ X4 @ X3))) | ((('const/sets/IN' @ (sK4 > $o) @ X4 @ sK5)) != $true)) )),
% 0.82/0.37 inference(cnf_transformation,[],[f32])).
% 0.82/0.37 thf(f55,plain,(
% 0.82/0.37 ((('const/sets/IN' @ sK4 @ (sK3 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ ('const/sets/UNIONS' @ sK4 @ sK5))) = $true)),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f41,f45])).
% 0.82/0.37 thf(f56,plain,(
% 0.82/0.37 ((('const/sets/IN' @ sK4 @ (sK2 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ ('const/sets/UNIONS' @ sK4 @ sK5))) = $true)),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f44,f45])).
% 0.82/0.37 thf(f58,plain,(
% 0.82/0.37 (((sK2 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6)) != ((sK3 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6)))),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f43,f45])).
% 0.82/0.37 thf(f64,plain,(
% 0.82/0.37 (((sK6 @ (sK3 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ (sK2 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6))) != $true)),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f42,f45])).
% 0.82/0.37 thf(f79,plain,(
% 0.82/0.37 ((('const/sets/IN' @ (sK4 > $o) @ (sK0 @ sK4 @ (sK3 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ sK5) @ sK5)) = $true)),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f33,f55])).
% 0.82/0.37 thf(f80,plain,(
% 0.82/0.37 ((('const/sets/IN' @ sK4 @ (sK3 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ (sK0 @ sK4 @ (sK3 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ sK5))) = $true)),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f34,f55])).
% 0.82/0.37 thf(f81,plain,(
% 0.82/0.37 ((('const/sets/IN' @ (sK4 > $o) @ (sK0 @ sK4 @ (sK2 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ sK5) @ sK5)) = $true)),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f33,f56])).
% 0.82/0.37 thf(f82,plain,(
% 0.82/0.37 ((('const/sets/IN' @ sK4 @ (sK2 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ (sK0 @ sK4 @ (sK2 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ sK5))) = $true)),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f34,f56])).
% 0.82/0.37 thf(f121,plain,(
% 0.82/0.37 ((('const/sets/pairwise' @ sK4 @ sK6 @ (sK0 @ sK4 @ (sK3 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ sK5))) = $true)),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f46,f79])).
% 0.82/0.37 thf(f122,plain,(
% 0.82/0.37 ($true = (('const/sets/pairwise' @ sK4 @ sK6 @ (sK0 @ sK4 @ (sK2 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ sK5))))),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f46,f81])).
% 0.82/0.37 thf(f123,plain,(
% 0.82/0.37 ((('const/sets/IN' @ sK4 @ (sK2 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ (sK0 @ sK4 @ (sK3 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ sK5))) != $true)),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f40,f58,f64,f121,f80])).
% 0.82/0.37 thf(f126,plain,(
% 0.82/0.37 ($true != (('const/sets/IN' @ sK4 @ (sK3 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ (sK0 @ sK4 @ (sK2 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ sK5))))),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f40,f58,f64,f82,f122])).
% 0.82/0.37 thf(f147,plain,(
% 0.82/0.37 ((('const/sets/SUBSET' @ sK4 @ (sK0 @ sK4 @ (sK2 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ sK5) @ (sK0 @ sK4 @ (sK3 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ sK5))) != $true)),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f38,f82,f123])).
% 0.82/0.37 thf(f153,plain,(
% 0.82/0.37 ((('const/sets/SUBSET' @ sK4 @ (sK0 @ sK4 @ (sK3 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ sK5) @ (sK0 @ sK4 @ (sK2 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ sK5))) != $true)),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f38,f80,f126])).
% 0.82/0.37 thf(f159,plain,(
% 0.82/0.37 ((('const/sets/SUBSET' @ sK4 @ (sK0 @ sK4 @ (sK3 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ sK5) @ (sK0 @ sK4 @ (sK2 @ sK4 @ ('const/sets/UNIONS' @ sK4 @ sK5) @ sK6) @ sK5))) = $true)),
% 0.82/0.37 inference(unit_resulting_resolution,[],[f47,f79,f81,f147])).
% 0.82/0.37 thf(f163,plain,(
% 0.82/0.37 $false),
% 0.82/0.37 inference(forward_subsumption_resolution,[],[f159,f153])).
% 0.82/0.37 % SZS output end Proof for theBenchmark
% 0.82/0.37 % (956573)------------------------------
% 0.82/0.37 % (956573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.37 % (956573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.37 % (956573)CaDiCaL version: 2.1.3
% 0.82/0.37 % (956573)Termination reason: Refutation
% 0.82/0.37 % (956573)Time elapsed: 0.023 s
% 0.82/0.37 % (956573)Peak memory usage: 13 MB
% 0.82/0.37 % (956573)Instructions burned: 39 (million)
% 0.82/0.37 % (956500)Success in time 0.123 s
% 0.82/0.37 % Vampire exiting
%------------------------------------------------------------------------------