%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP180^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:08:42 AM UTC 2026
% Result : Theorem 0.58s 0.43s
% Output : Refutation 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP180^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n007.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 20:05:42 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.26 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
% 0.58/0.42 % (3864967)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.58/0.42 % (3864976)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=311021222:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.58/0.42 % (3864978)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.58/0.42 % (3864978)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
% 0.58/0.42 % (3864973)lrs+10_16_si=on:nwc=1.5:random_seed=4204377700:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.58/0.42 % (3864972)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1291145416:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.58/0.42 % (3864974)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3728081071:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.58/0.42 % (3864977)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1250196533:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.58/0.42 % (3864976)Instruction limit reached!
% 0.58/0.42 % (3864976)------------------------------
% 0.58/0.42 % (3864976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3864975)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=2699087703: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)
% 0.58/0.42 % (3864976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3864976)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3864976)Termination reason: Instruction limit
% 0.58/0.42 % (3864976)Termination phase: Property scanning
% 0.58/0.42 % (3864976)Time elapsed: 0.007 s
% 0.58/0.42 % (3864976)Peak memory usage: 10 MB
% 0.58/0.42 % (3864976)Instructions burned: 25 (million)
% 0.58/0.42 % (3864978)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=4248705053:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.58/0.42 % (3864974)Instruction limit reached!
% 0.58/0.42 % (3864974)------------------------------
% 0.58/0.42 % (3864974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3864974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3864974)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3864974)Termination reason: Instruction limit
% 0.58/0.42 % (3864974)Termination phase: shuffling
% 0.58/0.42 % (3864974)Time elapsed: 0.003 s
% 0.58/0.42 % (3864974)Peak memory usage: 10 MB
% 0.58/0.42 % (3864974)Instructions burned: 6 (million)
% 0.58/0.42 % (3864986)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3437518004:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.58/0.42 % (3864973)Instruction limit reached!
% 0.58/0.42 % (3864973)------------------------------
% 0.58/0.42 % (3864973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3864973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3864973)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3864973)Termination reason: Instruction limit
% 0.58/0.42 % (3864973)Termination phase: shuffling
% 0.58/0.42 % (3864973)Time elapsed: 0.014 s
% 0.58/0.42 % (3864973)Peak memory usage: 10 MB
% 0.58/0.42 % (3864973)Instructions burned: 19 (million)
% 0.58/0.42 % (3864986)Instruction limit reached!
% 0.58/0.42 % (3864986)------------------------------
% 0.58/0.42 % (3864986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3864986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3864986)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3864986)Termination reason: Instruction limit
% 0.58/0.42 % (3864986)Termination phase: shuffling
% 0.58/0.42 % (3864986)Time elapsed: 0.003 s
% 0.58/0.42 % (3864986)Peak memory usage: 10 MB
% 0.58/0.42 % (3864986)Instructions burned: 11 (million)
% 0.58/0.42 % (3864987)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3499584016:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.58/0.43 % (3864989)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.58/0.43 % (3864989)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=341369350:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.58/0.43 % (3864987)Instruction limit reached!
% 0.58/0.43 % (3864987)------------------------------
% 0.58/0.43 % (3864987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.43 % (3864987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.43 % (3864987)CaDiCaL version: 2.1.3
% 0.58/0.43 % (3864987)Termination reason: Instruction limit
% 0.58/0.43 % (3864987)Termination phase: shuffling
% 0.58/0.43 % (3864987)Time elapsed: 0.004 s
% 0.58/0.43 % (3864987)Peak memory usage: 10 MB
% 0.58/0.43 % (3864987)Instructions burned: 7 (million)
% 0.58/0.43 % (3864989)Instruction limit reached!
% 0.58/0.43 % (3864989)------------------------------
% 0.58/0.43 % (3864989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.43 % (3864989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.43 % (3864989)CaDiCaL version: 2.1.3
% 0.58/0.43 % (3864989)Termination reason: Instruction limit
% 0.58/0.43 % (3864989)Termination phase: shuffling
% 0.58/0.43 % (3864989)Time elapsed: 0.003 s
% 0.58/0.43 % (3864989)Peak memory usage: 10 MB
% 0.58/0.43 % (3864989)Instructions burned: 10 (million)
% 0.58/0.43 % (3864977)Instruction limit reached!
% 0.58/0.43 % (3864977)------------------------------
% 0.58/0.43 % (3864977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.43 % (3864977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.43 % (3864977)CaDiCaL version: 2.1.3
% 0.58/0.43 % (3864977)Termination reason: Instruction limit
% 0.58/0.43 % (3864977)Termination phase: Property scanning
% 0.58/0.43 % (3864977)Time elapsed: 0.038 s
% 0.58/0.43 % (3864977)Peak memory usage: 12 MB
% 0.58/0.43 % (3864977)Instructions burned: 76 (million)
% 0.58/0.43 % (3864994)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=3528057428:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.58/0.43 % (3864972)Instruction limit reached!
% 0.58/0.43 % (3864972)------------------------------
% 0.58/0.43 % (3864972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.43 % (3864972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.43 % (3864972)CaDiCaL version: 2.1.3
% 0.58/0.43 % (3864972)Termination reason: Instruction limit
% 0.58/0.43 % (3864972)Termination phase: Function definition elimination
% 0.58/0.43 % (3864993)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
% 0.58/0.43 % (3864972)Time elapsed: 0.043 s
% 0.58/0.43 % (3864972)Peak memory usage: 12 MB
% 0.58/0.43 % (3864972)Instructions burned: 89 (million)
% 0.58/0.43 % (3864993)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.58/0.43 % (3864990)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1421649006:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.58/0.43 % (3864993)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1873679849:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.58/0.43 % (3864990)Instruction limit reached!
% 0.58/0.43 % (3864990)------------------------------
% 0.58/0.43 % (3864990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.43 % (3864990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.43 % (3864990)CaDiCaL version: 2.1.3
% 0.58/0.43 % (3864990)Termination reason: Instruction limit
% 0.58/0.43 % (3864990)Termination phase: shuffling
% 0.58/0.43 % (3864990)Time elapsed: 0.006 s
% 0.58/0.43 % (3864990)Peak memory usage: 10 MB
% 0.58/0.43 % (3864990)Instructions burned: 12 (million)
% 0.58/0.43 % (3864995)lrs+10_1_si=on:cs=on:random_seed=1171857545:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.58/0.43 % (3864998)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.58/0.43 % (3864993)Instruction limit reached!
% 0.58/0.43 % (3864993)------------------------------
% 0.58/0.43 % (3864993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.43 % (3864993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.43 % (3864993)CaDiCaL version: 2.1.3
% 0.58/0.43 % (3864993)Termination reason: Instruction limit
% 0.58/0.43 % (3864993)Termination phase: shuffling
% 0.58/0.43 % (3864993)Time elapsed: 0.014 s
% 0.58/0.43 % (3864993)Peak memory usage: 10 MB
% 0.58/0.43 % (3864993)Instructions burned: 29 (million)
% 0.58/0.43 % (3864995)Instruction limit reached!
% 0.58/0.43 % (3864995)------------------------------
% 0.58/0.43 % (3864995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.43 % (3864995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.43 % (3864995)CaDiCaL version: 2.1.3
% 0.58/0.43 % (3864995)Termination reason: Instruction limit
% 0.58/0.43 % (3864995)Termination phase: shuffling
% 0.58/0.43 % (3864995)Time elapsed: 0.004 s
% 0.58/0.43 % (3864995)Peak memory usage: 10 MB
% 0.58/0.43 % (3864995)Instructions burned: 8 (million)
% 0.58/0.43 % (3864994)Instruction limit reached!
% 0.58/0.43 % (3864994)------------------------------
% 0.58/0.43 % (3864994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.43 % (3864994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.43 % (3864994)CaDiCaL version: 2.1.3
% 0.58/0.43 % (3864994)Termination reason: Instruction limit
% 0.58/0.43 % (3864994)Termination phase: shuffling
% 0.58/0.43 % (3864994)Time elapsed: 0.021 s
% 0.58/0.43 % (3864994)Peak memory usage: 11 MB
% 0.58/0.43 % (3864994)Instructions burned: 89 (million)
% 0.58/0.43 % (3864998)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=1758259753:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.58/0.43 % (3864998)Instruction limit reached!
% 0.58/0.43 % (3864998)------------------------------
% 0.58/0.43 % (3864998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.43 % (3864998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.43 % (3864998)CaDiCaL version: 2.1.3
% 0.58/0.43 % (3864998)Termination reason: Instruction limit
% 0.58/0.43 % (3864998)Termination phase: shuffling
% 0.58/0.43 % (3864998)Time elapsed: 0.002 s
% 0.58/0.43 % (3864998)Peak memory usage: 10 MB
% 0.58/0.43 % (3864998)Instructions burned: 3 (million)
% 0.58/0.43 % (3865000)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2114052502:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.58/0.43 % (3865002)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2911616771:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.58/0.43 % (3865004)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3101023906:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.58/0.43 % (3865003)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2840750413:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.58/0.43 % (3865006)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2721868830:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.58/0.43 % (3865000)Instruction limit reached!
% 0.58/0.43 % (3865000)------------------------------
% 0.58/0.43 % (3865000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.43 % (3865000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.43 % (3865000)CaDiCaL version: 2.1.3
% 0.58/0.43 % (3865000)Termination reason: Instruction limit
% 0.58/0.43 % (3865000)Termination phase: SInE selection
% 0.58/0.43 % (3865000)Time elapsed: 0.018 s
% 0.58/0.43 % (3865000)Peak memory usage: 11 MB
% 0.58/0.43 % (3865000)Instructions burned: 38 (million)
% 0.58/0.43 % (3865004)Instruction limit reached!
% 0.58/0.43 % (3865004)------------------------------
% 0.58/0.43 % (3865004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.43 % (3865004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.43 % (3865004)CaDiCaL version: 2.1.3
% 0.58/0.43 % (3865004)Termination reason: Instruction limit
% 0.58/0.43 % (3865004)Termination phase: shuffling
% 0.58/0.43 % (3865004)Time elapsed: 0.007 s
% 0.58/0.43 % (3865004)Peak memory usage: 10 MB
% 0.58/0.43 % (3865004)Instructions burned: 14 (million)
% 0.58/0.43 % (3864975) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3864967-3864975"...
% 0.58/0.43 % (3865003)Instruction limit reached!
% 0.58/0.43 % (3865003)------------------------------
% 0.58/0.43 % (3865003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.43 % (3865003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.43 % (3865003)CaDiCaL version: 2.1.3
% 0.58/0.43 % (3865003)Termination reason: Instruction limit
% 0.58/0.43 % (3865003)Termination phase: Property scanning
% 0.58/0.43 % (3865003)Time elapsed: 0.012 s
% 0.58/0.43 % (3865003)Peak memory usage: 11 MB
% 0.58/0.43 % (3865003)Instructions burned: 26 (million)
% 0.58/0.43 % (3864975)...printing done.
% 0.58/0.43 % (3864975)Refutation found. Thanks to Tanya!
% 0.58/0.43 % SZS status Theorem for theBenchmark
% 0.58/0.43 % SZS output start Proof for theBenchmark
% 0.58/0.43 thf(type_def_5, type, standard_Constant: $tType > $tType).
% 0.58/0.43 thf(type_def_6, type, allegorical_term: $tType > $tType).
% 0.58/0.43 thf(type_def_7, type, labeled_graph: ($tType * $tType) > $tType).
% 0.58/0.43 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 0.58/0.43 thf(type_def_9, type, set: $tType > $tType).
% 0.58/0.43 thf(type_def_10, type, nat: $tType).
% 0.58/0.43 thf(type_def_11, type, itself: $tType > $tType).
% 0.58/0.43 thf(type_def_12, type, v: $tType).
% 0.58/0.43 thf(type_def_13, type, v2: $tType).
% 0.58/0.43 thf(type_def_14, type, sTfun: ($tType * $tType) > $tType).
% 0.58/0.43 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:($o)).
% 0.58/0.43 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.58/0.43 thf(func_def_2, type, bot: !>[X0: $tType]:($o)).
% 0.58/0.43 thf(func_def_3, type, lattice: !>[X0: $tType]:($o)).
% 0.58/0.43 thf(func_def_4, type, preorder: !>[X0: $tType]:($o)).
% 0.58/0.43 thf(func_def_5, type, semilattice_sup: !>[X0: $tType]:($o)).
% 0.58/0.43 thf(func_def_6, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 0.58/0.43 thf(func_def_7, type, bNF_Gr: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > set @ product_prod @ X0 @ X1))).
% 0.58/0.43 thf(func_def_8, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X0) > X2 > X1))).
% 0.58/0.43 thf(func_def_9, type, standard_S_Bot: !>[X0: $tType]:(standard_Constant @ X0)).
% 0.58/0.43 thf(func_def_10, type, standard_S_Const: !>[X0: $tType]:((X0 > standard_Constant @ X0))).
% 0.58/0.43 thf(func_def_11, type, standard_S_Top: !>[X0: $tType]:(standard_Constant @ X0)).
% 0.58/0.43 thf(func_def_12, type, getRel: !>[X0: $tType, X1: $tType]:((X0 > labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X1))).
% 0.58/0.43 thf(func_def_13, type, semantics: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > allegorical_term @ X0 > set @ product_prod @ X1 @ X1))).
% 0.58/0.43 thf(func_def_14, 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))).
% 0.58/0.43 thf(func_def_15, type, graph_homomorphism: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > set @ product_prod @ X1 @ X2 > $o))).
% 0.58/0.43 thf(func_def_16, type, graph_union: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1))).
% 0.58/0.43 thf(func_def_17, type, labeled_LG: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ product_prod @ X1 @ X1 > set @ X1 > labeled_graph @ X0 @ X1))).
% 0.58/0.43 thf(func_def_18, 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))).
% 0.58/0.43 thf(func_def_19, type, labeled_edges: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X0 @ product_prod @ X1 @ X1))).
% 0.58/0.43 thf(func_def_20, type, labeled_vertices: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > set @ X1))).
% 0.58/0.43 thf(func_def_21, type, map_graph: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ X1 > labeled_graph @ X2 @ X0 > labeled_graph @ X2 @ X1))).
% 0.58/0.43 thf(func_def_22, type, restrict: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1))).
% 0.58/0.43 thf(func_def_23, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.58/0.43 thf(func_def_24, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.58/0.43 thf(func_def_25, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.58/0.43 thf(func_def_26, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.58/0.43 thf(func_def_27, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.58/0.43 thf(func_def_28, type, field: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0))).
% 0.58/0.43 thf(func_def_29, type, id_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0))).
% 0.58/0.43 thf(func_def_30, type, total_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.58/0.43 thf(func_def_31, type, agree_on: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X1 @ X2 > $o))).
% 0.58/0.43 thf(func_def_32, 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))).
% 0.58/0.43 thf(func_def_33, 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))).
% 0.58/0.43 thf(func_def_34, 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))).
% 0.58/0.43 thf(func_def_35, 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))).
% 0.58/0.43 thf(func_def_36, type, maintained: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > $o))).
% 0.58/0.43 thf(func_def_37, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.58/0.43 thf(func_def_38, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.58/0.43 thf(func_def_39, type, is_singleton: !>[X0: $tType]:((set @ X0 > $o))).
% 0.58/0.43 thf(func_def_40, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 0.58/0.43 thf(func_def_41, type, standa1138209853_rules: !>[X0: $tType]:((set @ X0 > set @ product_prod @ labeled_graph @ standard_Constant @ X0 @ nat @ labeled_graph @ standard_Constant @ X0 @ nat))).
% 0.58/0.43 thf(func_def_42, type, standa2002409347_rules: !>[X0: $tType]:((set @ standard_Constant @ X0 > set @ product_prod @ labeled_graph @ standard_Constant @ X0 @ nat @ labeled_graph @ standard_Constant @ X0 @ nat))).
% 0.58/0.43 thf(func_def_43, type, standa244753842y_rule: !>[X0: $tType]:(product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat)).
% 0.58/0.43 thf(func_def_44, type, standa438229444_rules: !>[X0: $tType]:((set @ X0 > set @ standard_Constant @ X0 > set @ product_prod @ labeled_graph @ standard_Constant @ X0 @ nat @ labeled_graph @ standard_Constant @ X0 @ nat))).
% 0.58/0.43 thf(func_def_45, type, standa400804411p_rule: !>[X0: $tType]:((X0 > product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat))).
% 0.58/0.43 thf(func_def_46, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.58/0.43 thf(func_def_47, type, c: set @ v2).
% 0.58/0.43 thf(func_def_48, type, g: labeled_graph @ standard_Constant @ v2 @ v).
% 0.58/0.43 thf(func_def_49, type, l: set @ standard_Constant @ v2).
% 0.58/0.43 thf(func_def_50, type, h: (v > v)).
% 0.58/0.43 thf(func_def_51, type, m: (v2 > v)).
% 0.58/0.43 thf(func_def_52, type, x: v).
% 0.58/0.43 thf(func_def_53, type, xa: v2).
% 0.58/0.43 thf(func_def_54, type, y: v2).
% 0.58/0.43 thf(func_def_58, type, db1: !>[X0: $tType]:(X0)).
% 0.58/0.43 thf(func_def_59, type, db0: !>[X0: $tType]:(X0)).
% 0.58/0.43 thf(func_def_60, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.58/0.43 thf(func_def_61, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.58/0.43 thf(func_def_62, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.58/0.43 thf(func_def_63, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.58/0.43 thf(func_def_64, type, vIMP: ($o > $o > $o)).
% 0.58/0.43 thf(func_def_65, type, db2: !>[X0: $tType]:(X0)).
% 0.58/0.43 thf(func_def_66, type, db3: !>[X0: $tType]:(X0)).
% 0.58/0.43 thf(func_def_67, type, vNOT: ($o > $o)).
% 0.58/0.43 thf(func_def_68, type, vOR: ($o > $o > $o)).
% 0.58/0.43 thf(func_def_69, type, vAND: ($o > $o > $o)).
% 0.58/0.43 thf(func_def_70, type, sK0: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.58/0.43 thf(func_def_71, type, sK1: (v2 > v)).
% 0.58/0.43 thf(func_def_72, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X1 @ product_prod @ X0 @ X0 > (X2 > X0) > labeled_graph @ X1 @ X2 > X1))).
% 0.58/0.43 thf(func_def_73, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X1 @ product_prod @ X0 @ X0 > (X2 > X0) > labeled_graph @ X1 @ X2 > X2))).
% 0.58/0.43 thf(func_def_74, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X1 @ product_prod @ X0 @ X0 > (X2 > X0) > labeled_graph @ X1 @ X2 > X2))).
% 0.58/0.43 thf(func_def_75, type, sK5: !>[X0: $tType]:((set @ X0 > X0))).
% 0.58/0.43 thf(func_def_76, type, sK6: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.58/0.43 thf(func_def_77, type, sK7: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.58/0.43 thf(func_def_78, type, sK8: !>[X0: $tType]:((set @ X0 > X0))).
% 0.58/0.43 thf(func_def_79, type, sK9: !>[X0: $tType]:((set @ X0 > X0))).
% 0.58/0.43 thf(func_def_80, type, sK10: (v2 > v)).
% 0.58/0.43 thf(func_def_81, type, sK11: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.58/0.43 thf(func_def_82, type, sK12: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.58/0.43 thf(func_def_83, type, sK13: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.58/0.43 thf(func_def_84, type, sK14: v).
% 0.58/0.43 thf(func_def_85, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X2 > labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X2))).
% 0.58/0.43 thf(func_def_86, type, sK16: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 0.58/0.43 thf(func_def_87, type, sK17: !>[X0: $tType]:((set @ X0 > product_prod @ X0 @ X0 > X0))).
% 0.58/0.43 thf(func_def_88, type, sK18: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.58/0.43 thf(func_def_89, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ X2 > $o) > X1))).
% 0.58/0.43 thf(func_def_90, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ X2 > $o) > X2))).
% 0.58/0.43 thf(func_def_91, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ X2 > $o) > X0))).
% 0.58/0.43 thf(func_def_92, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((labeled_graph @ X1 @ X2 > set @ product_prod @ labeled_graph @ X1 @ X3 @ labeled_graph @ X1 @ X3 > labeled_graph @ X1 @ X2 > labeled_graph @ X1 @ X0))).
% 0.58/0.43 thf(func_def_93, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X1))).
% 0.58/0.43 thf(func_def_94, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X3))).
% 0.58/0.43 thf(func_def_95, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X2))).
% 0.58/0.43 thf(func_def_96, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X0))).
% 0.58/0.43 thf(func_def_97, type, sK27: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.58/0.43 thf(func_def_98, type, sK28: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.58/0.43 thf(func_def_99, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X0) > labeled_graph @ X2 @ X0 > (X0 > X1) > X0))).
% 0.58/0.43 thf(func_def_100, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((labeled_graph @ X1 @ X2 > labeled_graph @ X1 @ X2 > set @ product_prod @ labeled_graph @ X1 @ X3 @ labeled_graph @ X1 @ X3 > labeled_graph @ X1 @ X0))).
% 0.58/0.43 thf(func_def_101, type, sK31: !>[X0: $tType]:((set @ X0 > X0))).
% 0.58/0.43 thf(func_def_102, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X2 @ X5 > X6))).
% 0.58/0.43 thf(func_def_103, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X2 @ X5 > X5))).
% 0.58/0.43 thf(func_def_104, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X2 @ X5 > X0))).
% 0.58/0.43 thf(func_def_105, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X2 @ X5 > X1))).
% 0.58/0.43 thf(func_def_106, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X2 @ X5 > X3))).
% 0.58/0.43 thf(func_def_107, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X2 @ X5 > X2))).
% 0.58/0.43 thf(func_def_108, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X2 @ X5 > X4))).
% 0.58/0.43 thf(func_def_109, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X0) > labeled_graph @ X1 @ X2 > (X2 > X0) > X2))).
% 0.58/0.43 thf(func_def_110, type, sK40: (v2 > v)).
% 0.58/0.43 thf(func_def_111, type, sK41: !>[X0: $tType]:((X0 > set @ X0 > X0 > set @ X0 > set @ X0))).
% 0.58/0.43 thf(func_def_112, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ X2 > $o) > X3))).
% 0.58/0.43 thf(func_def_113, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ X2 > $o) > X4))).
% 0.58/0.43 thf(func_def_114, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ X2 > $o) > X1))).
% 0.58/0.43 thf(func_def_115, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ X2 > $o) > X0))).
% 0.58/0.43 thf(func_def_116, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ X2 > $o) > X2))).
% 0.58/0.43 thf(func_def_117, type, sK47: !>[X0: $tType]:((set @ X0 > X0))).
% 0.58/0.43 thf(func_def_118, type, sK48: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > set @ X1))).
% 0.58/0.43 thf(func_def_119, type, sK49: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X0 @ product_prod @ X1 @ X1))).
% 0.58/0.43 thf(func_def_120, type, sK50: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.58/0.43 thf(func_def_121, type, sK51: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.58/0.43 thf(func_def_122, type, sK52: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.58/0.43 thf(func_def_123, type, sK53: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.58/0.43 thf(func_def_124, type, sK54: !>[X0: $tType]:(((X0 > $o) > set @ X0 > set @ X0 > X0))).
% 0.58/0.43 thf(func_def_125, type, sK55: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.58/0.43 thf(func_def_126, type, sK56: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.58/0.43 thf(func_def_127, type, sK57: !>[X0: $tType]:((set @ X0 > X0))).
% 0.58/0.43 thf(func_def_128, type, sK58: !>[X0: $tType, X1: $tType]:(((labeled_graph @ X1 @ X0 > $o) > set @ product_prod @ X1 @ product_prod @ X0 @ X0))).
% 0.58/0.43 thf(func_def_129, type, sK59: !>[X0: $tType, X1: $tType]:(((labeled_graph @ X1 @ X0 > $o) > set @ X0))).
% 0.58/0.43 thf(func_def_130, type, sK60: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.58/0.43 thf(func_def_131, type, sK61: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.58/0.43 thf(func_def_132, type, sK62: !>[X0: $tType, X1: $tType]:(((X1 > X1) > labeled_graph @ X0 @ X1 > X1))).
% 0.58/0.43 thf(func_def_133, type, sK63: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.58/0.43 thf(func_def_134, type, sK64: (v2 > v)).
% 0.58/0.43 thf(func_def_135, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X5 @ X4 > $o) > X0))).
% 0.58/0.43 thf(func_def_136, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X5 @ X4 > $o) > X4))).
% 0.58/0.43 thf(func_def_137, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X5 @ X4 > $o) > X5))).
% 0.58/0.43 thf(func_def_138, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X5 @ X4 > $o) > X3))).
% 0.58/0.43 thf(func_def_139, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X5 @ X4 > $o) > X2))).
% 0.58/0.43 thf(func_def_140, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X5 @ X4 > $o) > X1))).
% 0.58/0.43 thf(func_def_141, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X3 @ product_prod @ X5 @ X4 > $o) > X6))).
% 0.58/0.43 thf(func_def_142, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X5 @ X4 > $o) > X1))).
% 0.58/0.43 thf(func_def_143, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X5 @ X4 > $o) > X4))).
% 0.58/0.43 thf(func_def_144, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X5 @ X4 > $o) > X3))).
% 0.58/0.43 thf(func_def_145, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X5 @ X4 > $o) > X5))).
% 0.58/0.43 thf(func_def_146, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X5 @ X4 > $o) > X2))).
% 0.58/0.43 thf(func_def_147, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X5 @ X4 > $o) > X0))).
% 0.58/0.43 thf(func_def_148, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X1 > X4))).
% 0.58/0.43 thf(func_def_149, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X1 > X1))).
% 0.58/0.43 thf(func_def_150, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X1 > X5))).
% 0.58/0.43 thf(func_def_151, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X1 > X3))).
% 0.58/0.43 thf(func_def_152, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X1 > X0))).
% 0.58/0.43 thf(func_def_153, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X5 @ X1 > X2))).
% 0.58/0.43 thf(func_def_154, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ X0 > X0))).
% 0.58/0.43 thf(func_def_155, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ X0 > X1))).
% 0.58/0.43 thf(func_def_156, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ X0 > X2))).
% 0.58/0.43 thf(func_def_157, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ X0 > X4))).
% 0.58/0.43 thf(func_def_158, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ X0 > X3))).
% 0.58/0.43 thf(func_def_159, type, sK89: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.58/0.43 thf(func_def_160, type, sK90: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.58/0.43 thf(func_def_161, type, sK91: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.58/0.43 thf(func_def_162, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > X2))).
% 0.58/0.43 thf(func_def_163, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > X0))).
% 0.58/0.43 thf(func_def_164, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > X1))).
% 0.58/0.43 thf(func_def_165, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X0))).
% 0.58/0.43 thf(func_def_166, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X1))).
% 0.58/0.43 thf(func_def_167, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X2))).
% 0.58/0.43 thf(func_def_168, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ X3 > X3))).
% 0.58/0.43 thf(func_def_170, type, inv_standard_S_Const_100: !>[X0: $tType]:((standard_Constant @ X0 > X0))).
% 0.58/0.43 thf(f7,axiom,(
% 0.58/0.43 (member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g)))),
% 0.58/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062)).
% 0.58/0.43 thf(f9,axiom,(
% 0.58/0.43 (graph_homomorphism @ standard_Constant @ v2 @ v @ v @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g) @ g @ (id_on @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g))))),
% 0.58/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_h_I3_J)).
% 0.58/0.43 thf(f30,axiom,(
% 0.58/0.43 ! [X1 : $tType,X0 : $tType,X6 : labeled_graph @ X1 @ X0,X2 : X0,X5 : labeled_graph @ X1 @ X0,X4 : X1,X3 : X0] : ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X2 @ X3) @ (getRel @ X1 @ X0 @ X4 @ X5)) => ((graph_homomorphism @ X1 @ X0 @ X0 @ X5 @ X6 @ (id_on @ X0 @ (labeled_vertices @ X1 @ X0 @ X5))) => (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X2 @ X3) @ (getRel @ X1 @ X0 @ X4 @ X6))))),
% 0.58/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_getRel__subgraph)).
% 0.58/0.43 thf(f279,conjecture,(
% 0.58/0.43 (member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ g))),
% 0.58/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.58/0.43 thf(f280,negated_conjecture,(
% 0.58/0.43 ~(member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ g))),
% 0.58/0.43 inference(negated_conjecture,[status(cth)],[f279])).
% 0.58/0.43 thf(f306,plain,(
% 0.58/0.43 (member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g)))),
% 0.58/0.43 inference(rectify,[],[f7])).
% 0.58/0.43 thf(f307,plain,(
% 0.58/0.43 (((member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g)))) = $true)),
% 0.58/0.43 inference(fool_elimination,[],[f306])).
% 0.58/0.43 thf(f370,plain,(
% 0.58/0.43 (graph_homomorphism @ standard_Constant @ v2 @ v @ v @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g) @ g @ (id_on @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g))))),
% 0.58/0.43 inference(rectify,[],[f9])).
% 0.58/0.43 thf(f371,plain,(
% 0.58/0.43 (((graph_homomorphism @ standard_Constant @ v2 @ v @ v @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g) @ g @ (id_on @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g))))) = $true)),
% 0.58/0.43 inference(fool_elimination,[],[f370])).
% 0.58/0.43 thf(f372,plain,(
% 0.58/0.43 ! [X0 : $tType,X1 : $tType,X2 : labeled_graph @ X0 @ X1,X3 : X1,X4 : labeled_graph @ X0 @ X1,X5 : X0,X6 : X1] : ((member @ product_prod @ X1 @ X1 @ (product_Pair @ X1 @ X1 @ X3 @ X6) @ (getRel @ X0 @ X1 @ X5 @ X4)) => ((graph_homomorphism @ X0 @ X1 @ X1 @ X4 @ X2 @ (id_on @ X1 @ (labeled_vertices @ X0 @ X1 @ X4))) => (member @ product_prod @ X1 @ X1 @ (product_Pair @ X1 @ X1 @ X3 @ X6) @ (getRel @ X0 @ X1 @ X5 @ X2))))),
% 0.58/0.43 inference(rectify,[],[f30])).
% 0.58/0.43 thf(f373,plain,(
% 0.58/0.43 ! [X0 : $tType,X1 : $tType,X2 : labeled_graph @ X0 @ X1,X3 : X1,X4 : labeled_graph @ X0 @ X1,X6 : X1,X5 : X0] : ((((member @ product_prod @ X1 @ X1 @ (product_Pair @ X1 @ X1 @ X3 @ X6) @ (getRel @ X0 @ X1 @ X5 @ X4))) = $true) => (($true = ((graph_homomorphism @ X0 @ X1 @ X1 @ X4 @ X2 @ (id_on @ X1 @ (labeled_vertices @ X0 @ X1 @ X4))))) => ($true = ((member @ product_prod @ X1 @ X1 @ (product_Pair @ X1 @ X1 @ X3 @ X6) @ (getRel @ X0 @ X1 @ X5 @ X2))))))),
% 0.58/0.43 inference(fool_elimination,[],[f372])).
% 0.58/0.43 thf(f420,plain,(
% 0.58/0.43 ~(member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ g))),
% 0.58/0.43 inference(rectify,[],[f280])).
% 0.58/0.43 thf(f421,plain,(
% 0.58/0.43 ~ (((member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ g))) = $true)),
% 0.58/0.43 inference(fool_elimination,[],[f420])).
% 0.58/0.43 thf(f704,plain,(
% 0.58/0.43 (((member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ g))) != $true)),
% 0.58/0.43 inference(flattening,[],[f421])).
% 0.58/0.43 thf(f792,plain,(
% 0.58/0.43 ! [X0 : $tType,X1 : $tType,X2 : labeled_graph @ X0 @ X1,X3 : X1,X4 : labeled_graph @ X0 @ X1,X6 : X1,X5 : X0] : ((($true = ((member @ product_prod @ X1 @ X1 @ (product_Pair @ X1 @ X1 @ X3 @ X6) @ (getRel @ X0 @ X1 @ X5 @ X2)))) | ($true != ((graph_homomorphism @ X0 @ X1 @ X1 @ X4 @ X2 @ (id_on @ X1 @ (labeled_vertices @ X0 @ X1 @ X4)))))) | (((member @ product_prod @ X1 @ X1 @ (product_Pair @ X1 @ X1 @ X3 @ X6) @ (getRel @ X0 @ X1 @ X5 @ X4))) != $true))),
% 0.58/0.43 inference(ennf_transformation,[],[f373])).
% 0.58/0.43 thf(f793,plain,(
% 0.58/0.43 ! [X0 : $tType,X1 : $tType,X2 : labeled_graph @ X0 @ X1,X6 : X1,X4 : labeled_graph @ X0 @ X1,X3 : X1,X5 : X0] : ((((member @ product_prod @ X1 @ X1 @ (product_Pair @ X1 @ X1 @ X3 @ X6) @ (getRel @ X0 @ X1 @ X5 @ X4))) != $true) | ($true != ((graph_homomorphism @ X0 @ X1 @ X1 @ X4 @ X2 @ (id_on @ X1 @ (labeled_vertices @ X0 @ X1 @ X4))))) | ($true = ((member @ product_prod @ X1 @ X1 @ (product_Pair @ X1 @ X1 @ X3 @ X6) @ (getRel @ X0 @ X1 @ X5 @ X2)))))),
% 0.58/0.43 inference(flattening,[],[f792])).
% 0.58/0.43 thf(f1202,plain,(
% 0.58/0.43 ! [X0 : $tType,X1 : $tType,X2 : labeled_graph @ X0 @ X1,X3 : X1,X4 : labeled_graph @ X0 @ X1,X5 : X1,X6 : X0] : (($true != ((member @ product_prod @ X1 @ X1 @ (product_Pair @ X1 @ X1 @ X5 @ X3) @ (getRel @ X0 @ X1 @ X6 @ X4)))) | ($true != ((graph_homomorphism @ X0 @ X1 @ X1 @ X4 @ X2 @ (id_on @ X1 @ (labeled_vertices @ X0 @ X1 @ X4))))) | (((member @ product_prod @ X1 @ X1 @ (product_Pair @ X1 @ X1 @ X5 @ X3) @ (getRel @ X0 @ X1 @ X6 @ X2))) = $true))),
% 0.58/0.43 inference(rectify,[],[f793])).
% 0.58/0.43 thf(f1237,plain,(
% 0.58/0.43 (((graph_homomorphism @ standard_Constant @ v2 @ v @ v @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g) @ g @ (id_on @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g))))) = $true)),
% 0.58/0.43 inference(cnf_transformation,[],[f371])).
% 0.58/0.43 thf(f1298,plain,(
% 0.58/0.43 (((member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g)))) = $true)),
% 0.58/0.43 inference(cnf_transformation,[],[f307])).
% 0.58/0.43 thf(f1321,plain,(
% 0.58/0.43 (((member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ g))) != $true)),
% 0.58/0.43 inference(cnf_transformation,[],[f704])).
% 0.58/0.43 thf(f1609,plain,(
% 0.58/0.43 ( ! [X1 : $tType,X0 : $tType,X2 : labeled_graph @ X0 @ X1,X3 : X1,X6 : X0,X4 : labeled_graph @ X0 @ X1,X5 : X1] : ((((member @ product_prod @ X1 @ X1 @ (product_Pair @ X1 @ X1 @ X5 @ X3) @ (getRel @ X0 @ X1 @ X6 @ X2))) = $true) | ($true != ((graph_homomorphism @ X0 @ X1 @ X1 @ X4 @ X2 @ (id_on @ X1 @ (labeled_vertices @ X0 @ X1 @ X4))))) | ($true != ((member @ product_prod @ X1 @ X1 @ (product_Pair @ X1 @ X1 @ X5 @ X3) @ (getRel @ X0 @ X1 @ X6 @ X4))))) )),
% 0.58/0.43 inference(cnf_transformation,[],[f1202])).
% 0.58/0.43 thf(f1726,definition,(
% 0.58/0.43 spl99_7 <=> (((graph_homomorphism @ standard_Constant @ v2 @ v @ v @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g) @ g @ (id_on @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g))))) = $true)),
% 0.58/0.43 introduced(definition,[new_symbols(definition,[spl99_7])],[avatar_definition])).
% 0.58/0.43 thf(f1729,plain,(
% 0.58/0.43 spl99_7),
% 0.58/0.43 inference(avatar_split_clause,[],[f1237,f1726])).
% 0.58/0.43 thf(f1791,definition,(
% 0.58/0.43 spl99_20 <=> (((member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g)))) = $true)),
% 0.58/0.43 introduced(definition,[new_symbols(definition,[spl99_20])],[avatar_definition])).
% 0.58/0.43 thf(f1793,plain,(
% 0.58/0.43 (((member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g)))) = $true) | ~spl99_20),
% 0.58/0.43 inference(avatar_component_clause,[],[f1791])).
% 0.58/0.43 thf(f1794,plain,(
% 0.58/0.43 spl99_20),
% 0.58/0.43 inference(avatar_split_clause,[],[f1298,f1791])).
% 0.58/0.43 thf(f1822,definition,(
% 0.58/0.43 spl99_26 <=> (((member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ g))) = $true)),
% 0.58/0.43 introduced(definition,[new_symbols(definition,[spl99_26])],[avatar_definition])).
% 0.58/0.43 thf(f1824,plain,(
% 0.58/0.43 (((member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ g))) != $true) | spl99_26),
% 0.58/0.43 inference(avatar_component_clause,[],[f1822])).
% 0.58/0.43 thf(f1825,plain,(
% 0.58/0.43 ~spl99_26),
% 0.58/0.43 inference(avatar_split_clause,[],[f1321,f1822])).
% 0.58/0.43 thf(f1940,plain,(
% 0.58/0.43 ( ! [X0 : labeled_graph @ standard_Constant @ v2 @ v] : (($true != ((member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ X0)))) | ($true != $true) | ($true != ((graph_homomorphism @ standard_Constant @ v2 @ v @ v @ X0 @ g @ (id_on @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ X0)))))) ) | spl99_26),
% 0.58/0.43 inference(superposition,[],[f1824,f1609])).
% 0.58/0.43 thf(f1944,plain,(
% 0.58/0.43 ( ! [X0 : labeled_graph @ standard_Constant @ v2 @ v] : (($true != ((member @ product_prod @ v @ v @ (product_Pair @ v @ v @ (m @ xa) @ (m @ xa)) @ (getRel @ standard_Constant @ v2 @ v @ (standard_S_Const @ v2 @ y) @ X0)))) | ($true != ((graph_homomorphism @ standard_Constant @ v2 @ v @ v @ X0 @ g @ (id_on @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ X0)))))) ) | spl99_26),
% 0.58/0.43 inference(trivial_inequality_removal,[],[f1940])).
% 0.58/0.43 thf(f1947,plain,(
% 0.58/0.43 ($true != $true) | (((graph_homomorphism @ standard_Constant @ v2 @ v @ v @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g) @ g @ (id_on @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g))))) != $true) | (~spl99_20 | spl99_26)),
% 0.58/0.43 inference(superposition,[],[f1944,f1793])).
% 0.58/0.43 thf(f1949,plain,(
% 0.58/0.43 (((graph_homomorphism @ standard_Constant @ v2 @ v @ v @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g) @ g @ (id_on @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ (map_graph @ v @ v @ standard_Constant @ v2 @ (bNF_Gr @ v @ v @ (labeled_vertices @ standard_Constant @ v2 @ v @ g) @ h) @ g))))) != $true) | (~spl99_20 | spl99_26)),
% 0.58/0.43 inference(trivial_inequality_removal,[],[f1947])).
% 0.58/0.43 thf(f1951,plain,(
% 0.58/0.43 ~spl99_7 | ~spl99_20 | spl99_26),
% 0.58/0.43 inference(avatar_split_clause,[],[f1949,f1822,f1791,f1726])).
% 0.58/0.43 cnf(s7, plain, spl99_7, inference(sat_conversion,[],[f1729])).
% 0.58/0.43 cnf(s20, plain, spl99_20, inference(sat_conversion,[],[f1794])).
% 0.58/0.43 cnf(s27, plain, ~spl99_26, inference(sat_conversion,[],[f1825])).
% 0.58/0.43 cnf(s32, plain, ~spl99_7 | ~spl99_20 | spl99_26, inference(sat_conversion,[],[f1951])).
% 0.58/0.43 cnf(s33, plain, ~spl99_7, inference(rat,[],[s32,s27,s20])).
% 0.58/0.43 cnf(s34, plain, $false, inference(rat,[],[s7,s33])).
% 0.58/0.43 thf(f1952,plain,(
% 0.58/0.43 $false),
% 0.58/0.43 inference(avatar_sat_refutation,[],[s34])).
% 0.58/0.43 % SZS output end Proof for theBenchmark
% 0.58/0.43 % (3864975)------------------------------
% 0.58/0.43 % (3864975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.43 % (3864975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.43 % (3864975)CaDiCaL version: 2.1.3
% 0.58/0.43 % (3864975)Termination reason: Refutation
% 0.58/0.43 % (3864975)Time elapsed: 0.095 s
% 0.58/0.43 % (3864975)Peak memory usage: 15 MB
% 0.58/0.43 % (3864975)Instructions burned: 180 (million)
% 0.58/0.43 % (3864967)Success in time 0.158 s
% 0.58/0.43 % Vampire exiting
%------------------------------------------------------------------------------