%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP177^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:08:41 AM UTC 2026
% Result : Theorem 0.28s 0.45s
% Output : Refutation 0.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP177^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 20:01:22 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.21/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.28/0.44 % (825496)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.28/0.44 % (825520)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2025028204:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.28/0.44 % (825527)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.28/0.44 % (825527)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
% 0.28/0.44 % (825521)lrs+10_16_si=on:nwc=1.5:random_seed=85879664:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.28/0.44 % (825522)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3152466683:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.28/0.44 % (825525)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1194184105:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.28/0.44 % (825524)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=783528285: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)
% 0.28/0.44 % (825526)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2014937367:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.28/0.44 % (825527)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=1642627892:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.28/0.44 % (825522)Instruction limit reached!
% 0.28/0.44 % (825522)------------------------------
% 0.28/0.44 % (825522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.44 % (825522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.44 % (825522)CaDiCaL version: 2.1.3
% 0.28/0.44 % (825522)Termination reason: Instruction limit
% 0.28/0.44 % (825522)Termination phase: shuffling
% 0.28/0.44 % (825522)Time elapsed: 0.002 s
% 0.28/0.44 % (825522)Peak memory usage: 10 MB
% 0.28/0.44 % (825522)Instructions burned: 3 (million)
% 0.28/0.44 % (825521)Instruction limit reached!
% 0.28/0.44 % (825521)------------------------------
% 0.28/0.44 % (825521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.44 % (825521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.44 % (825521)CaDiCaL version: 2.1.3
% 0.28/0.44 % (825521)Termination reason: Instruction limit
% 0.28/0.44 % (825521)Termination phase: shuffling
% 0.28/0.44 % (825521)Time elapsed: 0.010 s
% 0.28/0.44 % (825521)Peak memory usage: 10 MB
% 0.28/0.44 % (825521)Instructions burned: 20 (million)
% 0.28/0.44 % (825525)Instruction limit reached!
% 0.28/0.44 % (825525)------------------------------
% 0.28/0.44 % (825525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.44 % (825525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.44 % (825525)CaDiCaL version: 2.1.3
% 0.28/0.44 % (825525)Termination reason: Instruction limit
% 0.28/0.44 % (825525)Termination phase: shuffling
% 0.28/0.44 % (825525)Time elapsed: 0.012 s
% 0.28/0.44 % (825525)Peak memory usage: 10 MB
% 0.28/0.44 % (825525)Instructions burned: 24 (million)
% 0.28/0.44 % (825520)Instruction limit reached!
% 0.28/0.44 % (825520)------------------------------
% 0.28/0.44 % (825520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.44 % (825520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.44 % (825520)CaDiCaL version: 2.1.3
% 0.28/0.44 % (825520)Termination reason: Instruction limit
% 0.28/0.44 % (825520)Termination phase: Property scanning
% 0.28/0.44 % (825520)Time elapsed: 0.023 s
% 0.28/0.44 % (825520)Peak memory usage: 12 MB
% 0.28/0.44 % (825520)Instructions burned: 87 (million)
% 0.28/0.44 % (825545)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2433545804:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.28/0.44 % (825545)Instruction limit reached!
% 0.28/0.44 % (825545)------------------------------
% 0.28/0.44 % (825545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.44 % (825545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (825545)CaDiCaL version: 2.1.3
% 0.28/0.45 % (825545)Termination reason: Instruction limit
% 0.28/0.45 % (825545)Termination phase: shuffling
% 0.28/0.45 % (825545)Time elapsed: 0.002 s
% 0.28/0.45 % (825545)Peak memory usage: 10 MB
% 0.28/0.45 % (825545)Instructions burned: 3 (million)
% 0.28/0.45 % (825553)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1342984975:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.28/0.45 % (825550)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.28/0.45 % (825548)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1654372397:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.28/0.45 % (825553)Instruction limit reached!
% 0.28/0.45 % (825553)------------------------------
% 0.28/0.45 % (825553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (825553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (825553)CaDiCaL version: 2.1.3
% 0.28/0.45 % (825553)Termination reason: Instruction limit
% 0.28/0.45 % (825553)Termination phase: shuffling
% 0.28/0.45 % (825553)Time elapsed: 0.004 s
% 0.28/0.45 % (825553)Peak memory usage: 10 MB
% 0.28/0.45 % (825553)Instructions burned: 14 (million)
% 0.28/0.45 % (825550)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1882247868:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.28/0.45 % (825548)Instruction limit reached!
% 0.28/0.45 % (825548)------------------------------
% 0.28/0.45 % (825548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (825548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (825548)CaDiCaL version: 2.1.3
% 0.28/0.45 % (825548)Termination reason: Instruction limit
% 0.28/0.45 % (825548)Termination phase: shuffling
% 0.28/0.45 % (825548)Time elapsed: 0.003 s
% 0.28/0.45 % (825548)Peak memory usage: 10 MB
% 0.28/0.45 % (825548)Instructions burned: 5 (million)
% 0.28/0.45 % (825550)Instruction limit reached!
% 0.28/0.45 % (825550)------------------------------
% 0.28/0.45 % (825550)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (825550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (825550)CaDiCaL version: 2.1.3
% 0.28/0.45 % (825550)Termination reason: Instruction limit
% 0.28/0.45 % (825550)Termination phase: shuffling
% 0.28/0.45 % (825550)Time elapsed: 0.004 s
% 0.28/0.45 % (825550)Peak memory usage: 10 MB
% 0.28/0.45 % (825550)Instructions burned: 8 (million)
% 0.28/0.45 % (825526)Instruction limit reached!
% 0.28/0.45 % (825526)------------------------------
% 0.28/0.45 % (825526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (825526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (825526)CaDiCaL version: 2.1.3
% 0.28/0.45 % (825526)Termination reason: Instruction limit
% 0.28/0.45 % (825526)Termination phase: Preprocessing 3
% 0.28/0.45 % (825526)Time elapsed: 0.038 s
% 0.28/0.45 % (825526)Peak memory usage: 12 MB
% 0.28/0.45 % (825526)Instructions burned: 77 (million)
% 0.28/0.45 % (825556)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
% 0.28/0.45 % (825556)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.28/0.45 % (825562)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=316259772:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.28/0.45 % (825556)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3291131219:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.28/0.45 % (825565)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.28/0.45 % (825564)lrs+10_1_si=on:cs=on:random_seed=1315697011:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.28/0.45 % (825565)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=70284859:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.28/0.45 % (825564)Instruction limit reached!
% 0.28/0.45 % (825564)------------------------------
% 0.28/0.45 % (825564)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (825564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (825564)CaDiCaL version: 2.1.3
% 0.28/0.45 % (825564)Termination reason: Instruction limit
% 0.28/0.45 % (825564)Termination phase: shuffling
% 0.28/0.45 % (825564)Time elapsed: 0.005 s
% 0.28/0.45 % (825564)Peak memory usage: 10 MB
% 0.28/0.45 % (825564)Instructions burned: 10 (million)
% 0.28/0.45 % (825556)Instruction limit reached!
% 0.28/0.45 % (825556)------------------------------
% 0.28/0.45 % (825556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (825556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (825556)CaDiCaL version: 2.1.3
% 0.28/0.45 % (825556)Termination reason: Instruction limit
% 0.28/0.45 % (825556)Termination phase: shuffling
% 0.28/0.45 % (825556)Time elapsed: 0.014 s
% 0.28/0.45 % (825556)Peak memory usage: 10 MB
% 0.28/0.45 % (825556)Instructions burned: 30 (million)
% 0.28/0.45 % (825565)Instruction limit reached!
% 0.28/0.45 % (825565)------------------------------
% 0.28/0.45 % (825565)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (825565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (825565)CaDiCaL version: 2.1.3
% 0.28/0.45 % (825565)Termination reason: Instruction limit
% 0.28/0.45 % (825565)Termination phase: shuffling
% 0.28/0.45 % (825565)Time elapsed: 0.002 s
% 0.28/0.45 % (825565)Peak memory usage: 10 MB
% 0.28/0.45 % (825565)Instructions burned: 3 (million)
% 0.28/0.45 % (825568)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=233857960:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.28/0.45 % (825562)Instruction limit reached!
% 0.28/0.45 % (825562)------------------------------
% 0.28/0.45 % (825562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (825562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (825562)CaDiCaL version: 2.1.3
% 0.28/0.45 % (825562)Termination reason: Instruction limit
% 0.28/0.45 % (825562)Termination phase: Preprocessing 1
% 0.28/0.45 % (825562)Time elapsed: 0.022 s
% 0.28/0.45 % (825562)Peak memory usage: 11 MB
% 0.28/0.45 % (825562)Instructions burned: 88 (million)
% 0.28/0.45 % (825587)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=938056851:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.28/0.45 % (825527)Instruction limit reached!
% 0.28/0.45 % (825527)------------------------------
% 0.28/0.45 % (825527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (825527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (825527)CaDiCaL version: 2.1.3
% 0.28/0.45 % (825527)Termination reason: Instruction limit
% 0.28/0.45 % (825527)Termination phase: Saturation
% 0.28/0.45 % (825527)Time elapsed: 0.073 s
% 0.28/0.45 % (825527)Peak memory usage: 14 MB
% 0.28/0.45 % (825527)Instructions burned: 157 (million)
% 0.28/0.45 % (825582)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=734475998:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.28/0.45 % (825583)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2555393933:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.28/0.45 % (825568)Instruction limit reached!
% 0.28/0.45 % (825568)------------------------------
% 0.28/0.45 % (825568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (825568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (825568)CaDiCaL version: 2.1.3
% 0.28/0.45 % (825568)Termination reason: Instruction limit
% 0.28/0.45 % (825568)Termination phase: Property scanning
% 0.28/0.45 % (825568)Time elapsed: 0.018 s
% 0.28/0.45 % (825568)Peak memory usage: 11 MB
% 0.28/0.45 % (825568)Instructions burned: 39 (million)
% 0.28/0.45 % (825581)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2483739831:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.28/0.45 % (825524) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-825496-825524"...
% 0.28/0.45 % (825583)Instruction limit reached!
% 0.28/0.45 % (825583)------------------------------
% 0.28/0.45 % (825583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (825583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (825583)CaDiCaL version: 2.1.3
% 0.28/0.45 % (825583)Termination reason: Instruction limit
% 0.28/0.45 % (825583)Termination phase: shuffling
% 0.28/0.45 % (825583)Time elapsed: 0.009 s
% 0.28/0.45 % (825583)Peak memory usage: 10 MB
% 0.28/0.45 % (825583)Instructions burned: 14 (million)
% 0.28/0.45 % (825524)...printing done.
% 0.28/0.45 % (825524)Refutation found. Thanks to Tanya!
% 0.28/0.45 % SZS status Theorem for theBenchmark
% 0.28/0.45 % SZS output start Proof for theBenchmark
% 0.28/0.45 thf(type_def_5, type, standard_Constant: $tType > $tType).
% 0.28/0.45 thf(type_def_6, type, allegorical_term: $tType > $tType).
% 0.28/0.45 thf(type_def_7, type, labeled_graph: ($tType * $tType) > $tType).
% 0.28/0.45 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 0.28/0.45 thf(type_def_9, type, set: $tType > $tType).
% 0.28/0.45 thf(type_def_10, type, nat: $tType).
% 0.28/0.45 thf(type_def_11, type, itself: $tType > $tType).
% 0.28/0.45 thf(type_def_12, type, b: $tType).
% 0.28/0.45 thf(type_def_13, type, a: $tType).
% 0.28/0.45 thf(type_def_14, type, sTfun: ($tType * $tType) > $tType).
% 0.28/0.45 thf(func_def_0, type, bNF_Gr: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > set @ product_prod @ X0 @ X1))).
% 0.28/0.45 thf(func_def_1, type, equiv_congruent: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 0.28/0.45 thf(func_def_2, type, equiv_equiv: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.28/0.45 thf(func_def_3, type, equiv_proj: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > X0 > set @ X1))).
% 0.28/0.45 thf(func_def_4, type, hilbert_Eps: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.28/0.45 thf(func_def_5, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.28/0.45 thf(func_def_6, type, standard_S_Idt: !>[X0: $tType]:(standard_Constant @ X0)).
% 0.28/0.45 thf(func_def_7, type, getRel: !>[X0: $tType, X1: $tType]:((X0 > labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X1))).
% 0.28/0.45 thf(func_def_8, type, semantics: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > allegorical_term @ X0 > set @ product_prod @ X1 @ X1))).
% 0.28/0.45 thf(func_def_9, type, edge_preserving: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X2 @ product_prod @ X0 @ X0 > set @ product_prod @ X2 @ product_prod @ X1 @ X1 > $o))).
% 0.28/0.45 thf(func_def_10, type, graph_homomorphism: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > set @ product_prod @ X1 @ X2 > $o))).
% 0.28/0.45 thf(func_def_11, type, graph_union: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1))).
% 0.28/0.45 thf(func_def_12, type, labeled_LG: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ product_prod @ X1 @ X1 > set @ X1 > labeled_graph @ X0 @ X1))).
% 0.28/0.45 thf(func_def_13, type, labele1974067554_graph: !>[X0: $tType, X1: $tType, X2: $tType]:(((set @ product_prod @ X0 @ product_prod @ X1 @ X1 > set @ X1 > X2) > labeled_graph @ X0 @ X1 > X2))).
% 0.28/0.45 thf(func_def_14, type, labeled_edges: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X0 @ product_prod @ X1 @ X1))).
% 0.28/0.45 thf(func_def_15, type, labeled_vertices: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > set @ X1))).
% 0.28/0.45 thf(func_def_16, type, map_graph: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ X1 > labeled_graph @ X2 @ X0 > labeled_graph @ X2 @ X1))).
% 0.28/0.45 thf(func_def_17, type, restrict: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1))).
% 0.28/0.45 thf(func_def_18, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.28/0.45 thf(func_def_19, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.28/0.45 thf(func_def_20, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.28/0.45 thf(func_def_21, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.28/0.45 thf(func_def_22, type, id_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0))).
% 0.28/0.45 thf(func_def_23, type, image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X0 > set @ X1))).
% 0.28/0.45 thf(func_def_24, type, refl_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.28/0.45 thf(func_def_25, type, relcomp: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X0 @ X2))).
% 0.28/0.45 thf(func_def_26, type, agree_on: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X1 @ X2 > $o))).
% 0.28/0.45 thf(func_def_27, type, consequence_graph: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > $o))).
% 0.28/0.45 thf(func_def_28, type, extensible: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > set @ product_prod @ X1 @ X2 > $o))).
% 0.28/0.45 thf(func_def_29, type, least: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((itself @ X0 > set @ product_prod @ labeled_graph @ X1 @ X2 @ labeled_graph @ X1 @ X2 > labeled_graph @ X1 @ X3 > labeled_graph @ X1 @ X3 > $o))).
% 0.28/0.45 thf(func_def_30, type, least_559130134_graph: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((itself @ X0 > set @ product_prod @ labeled_graph @ X1 @ X2 @ labeled_graph @ X1 @ X2 > labeled_graph @ X1 @ X3 > labeled_graph @ X1 @ X3 > $o))).
% 0.28/0.45 thf(func_def_31, type, maintained: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > $o))).
% 0.28/0.45 thf(func_def_32, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.28/0.45 thf(func_def_33, type, image2: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.28/0.45 thf(func_def_34, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.28/0.45 thf(func_def_35, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 0.28/0.45 thf(func_def_36, type, standa2002409347_rules: !>[X0: $tType]:((set @ standard_Constant @ X0 > set @ product_prod @ labeled_graph @ standard_Constant @ X0 @ nat @ labeled_graph @ standard_Constant @ X0 @ nat))).
% 0.28/0.45 thf(func_def_37, type, standa244753842y_rule: !>[X0: $tType]:(product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat)).
% 0.28/0.45 thf(func_def_38, type, standa245363227y_rule: !>[X0: $tType]:((X0 > product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat))).
% 0.28/0.45 thf(func_def_39, type, standa1805702094y_rule: !>[X0: $tType]:((X0 > product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat))).
% 0.28/0.45 thf(func_def_40, type, standa2114124375e_rule: !>[X0: $tType]:((X0 > product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat))).
% 0.28/0.45 thf(func_def_41, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.28/0.45 thf(func_def_42, type, g: labeled_graph @ standard_Constant @ a @ b).
% 0.28/0.45 thf(func_def_43, type, l: set @ standard_Constant @ a).
% 0.28/0.45 thf(func_def_44, type, p: (b > b > $o)).
% 0.28/0.45 thf(func_def_45, type, f: (b > b)).
% 0.28/0.45 thf(func_def_46, type, l2: standard_Constant @ a).
% 0.28/0.45 thf(func_def_47, type, x: b).
% 0.28/0.45 thf(func_def_48, type, y: b).
% 0.28/0.45 thf(func_def_52, type, vAND: ($o > $o > $o)).
% 0.28/0.45 thf(func_def_53, type, db0: !>[X0: $tType]:(X0)).
% 0.28/0.45 thf(func_def_54, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.28/0.45 thf(func_def_55, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.28/0.45 thf(func_def_56, type, db1: !>[X0: $tType]:(X0)).
% 0.28/0.45 thf(func_def_57, type, vIMP: ($o > $o > $o)).
% 0.28/0.45 thf(func_def_58, type, vNOT: ($o > $o)).
% 0.28/0.45 thf(func_def_59, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.28/0.45 thf(func_def_60, type, db3: !>[X0: $tType]:(X0)).
% 0.28/0.45 thf(func_def_61, type, db2: !>[X0: $tType]:(X0)).
% 0.28/0.45 thf(func_def_62, type, vOR: ($o > $o > $o)).
% 0.28/0.45 thf(func_def_63, type, sK0: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X0 @ X1 > X1))).
% 0.28/0.45 thf(func_def_64, type, sK1: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X0 @ X1 > X0))).
% 0.28/0.45 thf(func_def_65, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X0 @ X1 > X2))).
% 0.28/0.45 thf(func_def_66, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > set @ product_prod @ X2 @ X1 > X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.28/0.45 thf(func_def_67, type, sK4: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.28/0.45 thf(func_def_68, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X2 @ X0 > set @ product_prod @ X1 @ X2 > (X1 > X0 > $o) > X0))).
% 0.28/0.45 thf(func_def_69, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X2 @ X0 > set @ product_prod @ X1 @ X2 > (X1 > X0 > $o) > X1))).
% 0.28/0.45 thf(func_def_70, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X2 @ X0 > set @ product_prod @ X1 @ X2 > (X1 > X0 > $o) > X2))).
% 0.28/0.45 thf(func_def_71, type, sK8: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 0.28/0.45 thf(func_def_72, type, sK9: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.28/0.45 thf(func_def_73, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > X2))).
% 0.28/0.45 thf(func_def_74, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > X1))).
% 0.28/0.45 thf(func_def_75, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > X0))).
% 0.28/0.45 thf(func_def_76, type, sK13: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.28/0.45 thf(func_def_77, type, sK14: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.28/0.45 thf(func_def_78, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X0))).
% 0.28/0.45 thf(func_def_79, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X1))).
% 0.28/0.45 thf(func_def_80, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X2))).
% 0.28/0.45 thf(func_def_81, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > X2))).
% 0.28/0.45 thf(func_def_82, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > X0))).
% 0.28/0.45 thf(func_def_83, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > X1))).
% 0.28/0.45 thf(func_def_84, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > X3))).
% 0.28/0.45 thf(func_def_85, type, sK22: !>[X0: $tType]:((product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.28/0.45 thf(func_def_86, type, sK23: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.28/0.45 thf(func_def_87, type, sK24: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ product_prod @ X1 @ X0 > X0 > X1))).
% 0.28/0.45 thf(func_def_88, type, sK25: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.28/0.45 thf(func_def_89, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > set @ product_prod @ X0 @ X1 > set @ product_prod @ X2 @ X0 > X1 > X0))).
% 0.28/0.45 thf(func_def_90, type, sK27: !>[X0: $tType, X1: $tType]:((X1 > labeled_graph @ X1 @ X0 > product_prod @ labeled_graph @ X1 @ nat @ labeled_graph @ X1 @ nat))).
% 0.28/0.45 thf(func_def_91, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2) > (X0 > X2) > labeled_graph @ X1 @ X0 > X0))).
% 0.28/0.45 thf(func_def_92, type, sK29: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.28/0.45 thf(func_def_93, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X0))).
% 0.28/0.45 thf(func_def_94, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X3))).
% 0.28/0.45 thf(func_def_95, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X2))).
% 0.28/0.45 thf(func_def_96, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X1))).
% 0.28/0.45 thf(func_def_97, type, sK34: !>[X0: $tType, X1: $tType]:((labeled_graph @ X1 @ X0 > set @ product_prod @ X1 @ product_prod @ X0 @ X0))).
% 0.28/0.45 thf(func_def_98, type, sK35: !>[X0: $tType, X1: $tType]:((labeled_graph @ X1 @ X0 > set @ X0))).
% 0.28/0.45 thf(func_def_99, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ X2 > $o) > X0))).
% 0.28/0.45 thf(func_def_100, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ X2 > $o) > X1))).
% 0.28/0.45 thf(func_def_101, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ X2 > $o) > X4))).
% 0.28/0.45 thf(func_def_102, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ X2 > $o) > X3))).
% 0.28/0.45 thf(func_def_103, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X3 @ X2 > $o) > X2))).
% 0.28/0.45 thf(func_def_104, type, sK41: !>[X0: $tType]:(((X0 > $o) > set @ X0 > (X0 > $o) > X0))).
% 0.28/0.45 thf(func_def_105, type, sK42: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ X1 > X0 > X1))).
% 0.28/0.45 thf(func_def_106, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X3 > X2))).
% 0.28/0.45 thf(func_def_107, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X3 > X0))).
% 0.28/0.45 thf(func_def_108, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X3 > X3))).
% 0.28/0.45 thf(func_def_109, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X3 > X4))).
% 0.28/0.45 thf(func_def_110, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X3 > X1))).
% 0.28/0.45 thf(func_def_111, type, sK48: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.28/0.45 thf(func_def_112, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X5 > $o) > X4))).
% 0.28/0.45 thf(func_def_113, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X5 > $o) > X5))).
% 0.28/0.45 thf(func_def_114, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X5 > $o) > X3))).
% 0.28/0.45 thf(func_def_115, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X5 > $o) > X0))).
% 0.28/0.45 thf(func_def_116, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X5 > $o) > X1))).
% 0.28/0.45 thf(func_def_117, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X5 > $o) > X2))).
% 0.28/0.45 thf(func_def_118, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ labeled_graph @ X3 @ X1 @ labeled_graph @ X3 @ X1 > labeled_graph @ X3 @ X2 > labeled_graph @ X3 @ X2 > labeled_graph @ X3 @ X0))).
% 0.28/0.45 thf(func_def_119, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ X3 > X3))).
% 0.28/0.45 thf(func_def_120, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ X3 > X0))).
% 0.28/0.45 thf(func_def_121, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ X3 > X5))).
% 0.28/0.45 thf(func_def_122, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ X3 > X4))).
% 0.28/0.45 thf(func_def_123, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ X3 > X1))).
% 0.28/0.45 thf(func_def_124, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ X3 > X2))).
% 0.28/0.45 thf(func_def_125, type, sK62: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 0.28/0.45 thf(func_def_126, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X3 > $o) > X6))).
% 0.28/0.45 thf(func_def_127, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X3 > $o) > X1))).
% 0.28/0.45 thf(func_def_128, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X3 > $o) > X5))).
% 0.28/0.45 thf(func_def_129, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X3 > $o) > X2))).
% 0.28/0.45 thf(func_def_130, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X3 > $o) > X3))).
% 0.28/0.45 thf(func_def_131, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X3 > $o) > X4))).
% 0.28/0.45 thf(func_def_132, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X3 > $o) > X0))).
% 0.28/0.45 thf(func_def_133, type, sK70: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.28/0.45 thf(func_def_134, type, sK71: !>[X0: $tType]:((set @ X0 > X0))).
% 0.28/0.45 thf(func_def_135, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > set @ product_prod @ X0 @ X2 > X1 > set @ product_prod @ X2 @ X1 > X1))).
% 0.28/0.45 thf(func_def_136, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > set @ product_prod @ X0 @ X2 > X1 > set @ product_prod @ X2 @ X1 > X2))).
% 0.28/0.45 thf(func_def_137, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > set @ product_prod @ X0 @ X2 > X1 > set @ product_prod @ X2 @ X1 > X0))).
% 0.28/0.45 thf(func_def_138, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ X5 > X6))).
% 0.28/0.45 thf(func_def_139, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ X5 > X1))).
% 0.28/0.45 thf(func_def_140, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ X5 > X5))).
% 0.28/0.45 thf(func_def_141, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ X5 > X4))).
% 0.28/0.45 thf(func_def_142, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ X5 > X3))).
% 0.28/0.45 thf(func_def_143, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ X5 > X0))).
% 0.28/0.45 thf(func_def_144, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ X5 > X2))).
% 0.28/0.45 thf(func_def_145, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X2 > labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X2))).
% 0.28/0.45 thf(func_def_146, type, sK83: !>[X0: $tType]:((set @ X0 > X0))).
% 0.28/0.45 thf(func_def_147, type, sK84: !>[X0: $tType]:((set @ X0 > X0))).
% 0.28/0.45 thf(func_def_148, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((labeled_graph @ X3 @ X1 > set @ product_prod @ labeled_graph @ X3 @ X2 @ labeled_graph @ X3 @ X2 > labeled_graph @ X3 @ X1 > labeled_graph @ X3 @ X0))).
% 0.28/0.45 thf(func_def_149, type, sK86: !>[X0: $tType, X1: $tType]:(((labeled_graph @ X1 @ X0 > $o) > set @ product_prod @ X1 @ product_prod @ X0 @ X0))).
% 0.28/0.45 thf(func_def_150, type, sK87: !>[X0: $tType, X1: $tType]:(((labeled_graph @ X1 @ X0 > $o) > set @ X0))).
% 0.28/0.45 thf(func_def_151, type, sK88: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.28/0.45 thf(func_def_152, type, sK89: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.28/0.45 thf(func_def_153, type, sK90: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.28/0.45 thf(func_def_154, type, sK91: !>[X0: $tType]:((set @ X0 > X0 > set @ X0 > X0 > set @ X0))).
% 0.28/0.45 thf(func_def_155, type, sK92: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.28/0.45 thf(func_def_156, type, sK93: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.28/0.45 thf(func_def_157, type, sK94: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.28/0.45 thf(func_def_158, type, sK95: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.28/0.45 thf(func_def_159, type, sK96: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.28/0.45 thf(func_def_160, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ product_prod @ X1 @ X1 > (X2 > X1) > labeled_graph @ X0 @ X2 > X2))).
% 0.28/0.45 thf(func_def_161, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ product_prod @ X1 @ X1 > (X2 > X1) > labeled_graph @ X0 @ X2 > X2))).
% 0.28/0.45 thf(func_def_162, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ product_prod @ X1 @ X1 > (X2 > X1) > labeled_graph @ X0 @ X2 > X0))).
% 0.28/0.45 thf(func_def_163, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X2 > labeled_graph @ X0 @ X1 > set @ product_prod @ X2 @ X1 > set @ product_prod @ X2 @ X1))).
% 0.28/0.45 thf(f1,axiom,(
% 0.28/0.45 ! [X7 : b] : ((member @ b @ (f @ X7) @ (labeled_vertices @ standard_Constant @ a @ b @ g)) => (member @ b @ X7 @ (labeled_vertices @ standard_Constant @ a @ b @ g)))),
% 0.28/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062)).
% 0.28/0.45 thf(f3,axiom,(
% 0.28/0.45 (member @ b @ (f @ x) @ (labeled_vertices @ standard_Constant @ a @ b @ g))),
% 0.28/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_fv_I1_J)).
% 0.28/0.45 thf(f260,conjecture,(
% 0.28/0.45 (member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))),
% 0.28/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.28/0.45 thf(f261,negated_conjecture,(
% 0.28/0.45 ~(member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))),
% 0.28/0.45 inference(negated_conjecture,[status(cth)],[f260])).
% 0.28/0.45 thf(f508,plain,(
% 0.28/0.45 ~(member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))),
% 0.28/0.45 inference(rectify,[],[f261])).
% 0.28/0.45 thf(f509,plain,(
% 0.28/0.45 ~ (((member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true)),
% 0.28/0.45 inference(fool_elimination,[],[f508])).
% 0.28/0.45 thf(f546,plain,(
% 0.28/0.45 ! [X0 : b] : ((member @ b @ (f @ X0) @ (labeled_vertices @ standard_Constant @ a @ b @ g)) => (member @ b @ X0 @ (labeled_vertices @ standard_Constant @ a @ b @ g)))),
% 0.28/0.45 inference(rectify,[],[f1])).
% 0.28/0.45 thf(f547,plain,(
% 0.28/0.45 ! [X0 : b] : ((((member @ b @ (f @ X0) @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true) => (((member @ b @ X0 @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true))),
% 0.28/0.45 inference(fool_elimination,[],[f546])).
% 0.28/0.45 thf(f576,plain,(
% 0.28/0.45 (member @ b @ (f @ x) @ (labeled_vertices @ standard_Constant @ a @ b @ g))),
% 0.28/0.45 inference(rectify,[],[f3])).
% 0.28/0.45 thf(f577,plain,(
% 0.28/0.45 (((member @ b @ (f @ x) @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true)),
% 0.28/0.45 inference(fool_elimination,[],[f576])).
% 0.28/0.45 thf(f714,plain,(
% 0.28/0.45 (((member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))) != $true)),
% 0.28/0.45 inference(flattening,[],[f509])).
% 0.28/0.45 thf(f785,plain,(
% 0.28/0.45 ! [X0 : b] : ((((member @ b @ X0 @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true) | (((member @ b @ (f @ X0) @ (labeled_vertices @ standard_Constant @ a @ b @ g))) != $true))),
% 0.28/0.45 inference(ennf_transformation,[],[f547])).
% 0.28/0.45 thf(f1237,plain,(
% 0.28/0.45 (((member @ b @ (f @ x) @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true)),
% 0.28/0.45 inference(cnf_transformation,[],[f577])).
% 0.28/0.45 thf(f1318,plain,(
% 0.28/0.45 (((member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))) != $true)),
% 0.28/0.45 inference(cnf_transformation,[],[f714])).
% 0.28/0.45 thf(f1401,plain,(
% 0.28/0.45 ( ! [X0 : b] : ((((member @ b @ (f @ X0) @ (labeled_vertices @ standard_Constant @ a @ b @ g))) != $true) | (((member @ b @ X0 @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true)) )),
% 0.28/0.45 inference(cnf_transformation,[],[f785])).
% 0.28/0.45 thf(f1660,definition,(
% 0.28/0.45 spl101_2 <=> (((member @ b @ (f @ x) @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true)),
% 0.28/0.45 introduced(definition,[new_symbols(definition,[spl101_2])],[avatar_definition])).
% 0.28/0.45 thf(f1662,plain,(
% 0.28/0.45 (((member @ b @ (f @ x) @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true) | ~spl101_2),
% 0.28/0.45 inference(avatar_component_clause,[],[f1660])).
% 0.28/0.45 thf(f1663,plain,(
% 0.28/0.45 spl101_2),
% 0.28/0.45 inference(avatar_split_clause,[],[f1237,f1660])).
% 0.28/0.45 thf(f1665,definition,(
% 0.28/0.45 spl101_3 <=> (((member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true)),
% 0.28/0.45 introduced(definition,[new_symbols(definition,[spl101_3])],[avatar_definition])).
% 0.28/0.45 thf(f1667,plain,(
% 0.28/0.45 (((member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))) != $true) | spl101_3),
% 0.28/0.45 inference(avatar_component_clause,[],[f1665])).
% 0.28/0.45 thf(f1668,plain,(
% 0.28/0.45 ~spl101_3),
% 0.28/0.45 inference(avatar_split_clause,[],[f1318,f1665])).
% 0.28/0.45 thf(f1719,plain,(
% 0.28/0.45 (((member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true) | ($true != $true) | ~spl101_2),
% 0.28/0.45 inference(superposition,[],[f1401,f1662])).
% 0.28/0.45 thf(f1722,plain,(
% 0.28/0.45 (((member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true) | ~spl101_2),
% 0.28/0.45 inference(trivial_inequality_removal,[],[f1719])).
% 0.28/0.45 thf(f1728,plain,(
% 0.28/0.45 $false | (~spl101_2 | spl101_3)),
% 0.28/0.45 inference(forward_subsumption_resolution,[],[f1722,f1667])).
% 0.28/0.45 thf(f1729,plain,(
% 0.28/0.45 ~spl101_2 | spl101_3),
% 0.28/0.45 inference(avatar_contradiction_clause,[],[f1728])).
% 0.28/0.45 cnf(s2, plain, spl101_2, inference(sat_conversion,[],[f1663])).
% 0.28/0.45 cnf(s3, plain, ~spl101_3, inference(sat_conversion,[],[f1668])).
% 0.28/0.45 cnf(s16, plain, ~spl101_2 | spl101_3, inference(sat_conversion,[],[f1729])).
% 0.28/0.45 cnf(s18, plain, ~spl101_2, inference(rat,[],[s16,s3])).
% 0.28/0.45 cnf(s19, plain, $false, inference(rat,[],[s2,s18])).
% 0.28/0.45 thf(f1730,plain,(
% 0.28/0.45 $false),
% 0.28/0.45 inference(avatar_sat_refutation,[],[s19])).
% 0.28/0.45 % SZS output end Proof for theBenchmark
% 0.28/0.45 % (825524)------------------------------
% 0.28/0.45 % (825524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.28/0.45 % (825524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.28/0.45 % (825524)CaDiCaL version: 2.1.3
% 0.28/0.45 % (825524)Termination reason: Refutation
% 0.28/0.45 % (825524)Time elapsed: 0.083 s
% 0.28/0.45 % (825524)Peak memory usage: 15 MB
% 0.28/0.45 % (825524)Instructions burned: 169 (million)
% 0.28/0.45 % (825496)Success in time 0.149 s
% 0.28/0.45 % Vampire exiting
%------------------------------------------------------------------------------