%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP102^1 : 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 : n015.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 08:08:21 AM UTC 2026
% Result : Theorem 1.07s 0.55s
% Output : Refutation 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP102^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n015.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 19:57:04 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.28 Running higher-order theorem proving
% 0.25/0.33 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
% 1.07/0.53 % (4031688)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.07/0.53 % (4031695)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2053099456:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.07/0.53 % (4031695)Instruction limit reached!
% 1.07/0.53 % (4031695)------------------------------
% 1.07/0.53 % (4031695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.53 % (4031695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.53 % (4031695)CaDiCaL version: 2.1.3
% 1.07/0.53 % (4031695)Termination reason: Instruction limit
% 1.07/0.53 % (4031695)Termination phase: shuffling
% 1.07/0.53 % (4031695)Time elapsed: 0.002 s
% 1.07/0.53 % (4031695)Peak memory usage: 10 MB
% 1.07/0.53 % (4031695)Instructions burned: 5 (million)
% 1.07/0.53 % (4031699)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.07/0.53 % (4031699)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
% 1.07/0.53 % (4031694)lrs+10_16_si=on:nwc=1.5:random_seed=719168945:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.07/0.53 % (4031697)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2789180831:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.07/0.53 % (4031693)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4019291868:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.07/0.53 % (4031696)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=2860163456: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)
% 1.07/0.53 % (4031698)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2032401918:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.07/0.53 % (4031699)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=222959117:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.07/0.53 % (4031701)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1656986269:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.07/0.53 % (4031701)Instruction limit reached!
% 1.07/0.53 % (4031701)------------------------------
% 1.07/0.53 % (4031701)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.53 % (4031701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.53 % (4031701)CaDiCaL version: 2.1.3
% 1.07/0.53 % (4031701)Termination reason: Instruction limit
% 1.07/0.53 % (4031701)Termination phase: shuffling
% 1.07/0.53 % (4031701)Time elapsed: 0.002 s
% 1.07/0.53 % (4031701)Peak memory usage: 10 MB
% 1.07/0.53 % (4031701)Instructions burned: 3 (million)
% 1.07/0.53 % (4031694)Instruction limit reached!
% 1.07/0.53 % (4031694)------------------------------
% 1.07/0.53 % (4031694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.53 % (4031694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.53 % (4031694)CaDiCaL version: 2.1.3
% 1.07/0.53 % (4031694)Termination reason: Instruction limit
% 1.07/0.53 % (4031694)Termination phase: Property scanning
% 1.07/0.53 % (4031694)Time elapsed: 0.016 s
% 1.07/0.53 % (4031694)Peak memory usage: 10 MB
% 1.07/0.53 % (4031694)Instructions burned: 18 (million)
% 1.07/0.53 % (4031697)Instruction limit reached!
% 1.07/0.53 % (4031697)------------------------------
% 1.07/0.53 % (4031697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.53 % (4031697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.53 % (4031697)CaDiCaL version: 2.1.3
% 1.07/0.53 % (4031697)Termination reason: Instruction limit
% 1.07/0.53 % (4031697)Termination phase: Preprocessing 1
% 1.07/0.53 % (4031697)Time elapsed: 0.020 s
% 1.07/0.53 % (4031697)Peak memory usage: 10 MB
% 1.07/0.53 % (4031697)Instructions burned: 25 (million)
% 1.07/0.53 % (4031710)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.07/0.55 % (4031710)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=668553778:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.07/0.55 % (4031709)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1390198284:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.07/0.55 % (4031710)Instruction limit reached!
% 1.07/0.55 % (4031710)------------------------------
% 1.07/0.55 % (4031710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (4031710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (4031710)CaDiCaL version: 2.1.3
% 1.07/0.55 % (4031710)Termination reason: Instruction limit
% 1.07/0.55 % (4031710)Termination phase: shuffling
% 1.07/0.55 % (4031710)Time elapsed: 0.004 s
% 1.07/0.55 % (4031710)Peak memory usage: 10 MB
% 1.07/0.55 % (4031710)Instructions burned: 9 (million)
% 1.07/0.55 % (4031711)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1410976275:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.07/0.55 % (4031709)Instruction limit reached!
% 1.07/0.55 % (4031709)------------------------------
% 1.07/0.55 % (4031709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (4031709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (4031709)CaDiCaL version: 2.1.3
% 1.07/0.55 % (4031709)Termination reason: Instruction limit
% 1.07/0.55 % (4031709)Termination phase: shuffling
% 1.07/0.55 % (4031709)Time elapsed: 0.005 s
% 1.07/0.55 % (4031709)Peak memory usage: 10 MB
% 1.07/0.55 % (4031709)Instructions burned: 5 (million)
% 1.07/0.55 % (4031711)Instruction limit reached!
% 1.07/0.55 % (4031711)------------------------------
% 1.07/0.55 % (4031711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (4031711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (4031711)CaDiCaL version: 2.1.3
% 1.07/0.55 % (4031711)Termination reason: Instruction limit
% 1.07/0.55 % (4031711)Termination phase: shuffling
% 1.07/0.55 % (4031711)Time elapsed: 0.006 s
% 1.07/0.55 % (4031711)Peak memory usage: 10 MB
% 1.07/0.55 % (4031711)Instructions burned: 12 (million)
% 1.07/0.55 % (4031698)Instruction limit reached!
% 1.07/0.55 % (4031698)------------------------------
% 1.07/0.55 % (4031698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (4031698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (4031698)CaDiCaL version: 2.1.3
% 1.07/0.55 % (4031698)Termination reason: Instruction limit
% 1.07/0.55 % (4031698)Termination phase: Property scanning
% 1.07/0.55 % (4031698)Time elapsed: 0.062 s
% 1.07/0.55 % (4031698)Peak memory usage: 12 MB
% 1.07/0.55 % (4031698)Instructions burned: 76 (million)
% 1.07/0.55 % (4031714)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
% 1.07/0.55 % (4031714)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.07/0.55 % (4031693)Instruction limit reached!
% 1.07/0.55 % (4031693)------------------------------
% 1.07/0.55 % (4031693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (4031693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (4031693)CaDiCaL version: 2.1.3
% 1.07/0.55 % (4031693)Termination reason: Instruction limit
% 1.07/0.55 % (4031693)Termination phase: Property scanning
% 1.07/0.55 % (4031693)Time elapsed: 0.070 s
% 1.07/0.55 % (4031693)Peak memory usage: 12 MB
% 1.07/0.55 % (4031693)Instructions burned: 87 (million)
% 1.07/0.55 % (4031717)lrs+10_1_si=on:cs=on:random_seed=412982213:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.07/0.55 % (4031714)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=148562308:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.07/0.55 % (4031717)Instruction limit reached!
% 1.07/0.55 % (4031717)------------------------------
% 1.07/0.55 % (4031717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (4031717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (4031717)CaDiCaL version: 2.1.3
% 1.07/0.55 % (4031717)Termination reason: Instruction limit
% 1.07/0.55 % (4031717)Termination phase: shuffling
% 1.07/0.55 % (4031717)Time elapsed: 0.005 s
% 1.07/0.55 % (4031717)Peak memory usage: 10 MB
% 1.07/0.55 % (4031717)Instructions burned: 10 (million)
% 1.07/0.55 % (4031716)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=374152612:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.07/0.55 % (4031718)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.07/0.55 % (4031722)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1733753499:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.07/0.55 % (4031714)Instruction limit reached!
% 1.07/0.55 % (4031714)------------------------------
% 1.07/0.55 % (4031714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (4031714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (4031714)CaDiCaL version: 2.1.3
% 1.07/0.55 % (4031714)Termination reason: Instruction limit
% 1.07/0.55 % (4031714)Termination phase: Property scanning
% 1.07/0.55 % (4031714)Time elapsed: 0.024 s
% 1.07/0.55 % (4031714)Peak memory usage: 11 MB
% 1.07/0.55 % (4031714)Instructions burned: 29 (million)
% 1.07/0.55 % (4031718)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=1463194020:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.07/0.55 % (4031718)Instruction limit reached!
% 1.07/0.55 % (4031718)------------------------------
% 1.07/0.55 % (4031718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (4031718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (4031718)CaDiCaL version: 2.1.3
% 1.07/0.55 % (4031718)Termination reason: Instruction limit
% 1.07/0.55 % (4031718)Termination phase: shuffling
% 1.07/0.55 % (4031718)Time elapsed: 0.004 s
% 1.07/0.55 % (4031718)Peak memory usage: 10 MB
% 1.07/0.55 % (4031718)Instructions burned: 4 (million)
% 1.07/0.55 % (4031720)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1410221667:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.07/0.55 % (4031726)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2036435957:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.07/0.55 % (4031726)Instruction limit reached!
% 1.07/0.55 % (4031726)------------------------------
% 1.07/0.55 % (4031726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (4031726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (4031726)CaDiCaL version: 2.1.3
% 1.07/0.55 % (4031726)Termination reason: Instruction limit
% 1.07/0.55 % (4031726)Termination phase: SInE selection
% 1.07/0.55 % (4031726)Time elapsed: 0.012 s
% 1.07/0.55 % (4031726)Peak memory usage: 10 MB
% 1.07/0.55 % (4031726)Instructions burned: 26 (million)
% 1.07/0.55 % (4031699)Instruction limit reached!
% 1.07/0.55 % (4031699)------------------------------
% 1.07/0.55 % (4031699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (4031699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (4031699)CaDiCaL version: 2.1.3
% 1.07/0.55 % (4031699)Termination reason: Instruction limit
% 1.07/0.55 % (4031699)Termination phase: Saturation
% 1.07/0.55 % (4031699)Time elapsed: 0.131 s
% 1.07/0.55 % (4031699)Peak memory usage: 14 MB
% 1.07/0.55 % (4031699)Instructions burned: 157 (million)
% 1.07/0.55 % (4031728)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3490210906:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.07/0.55 % (4031720)Instruction limit reached!
% 1.07/0.55 % (4031720)------------------------------
% 1.07/0.55 % (4031720)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (4031720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (4031720)CaDiCaL version: 2.1.3
% 1.07/0.55 % (4031720)Termination reason: Instruction limit
% 1.07/0.55 % (4031720)Termination phase: Preprocessing 3
% 1.07/0.55 % (4031720)Time elapsed: 0.032 s
% 1.07/0.55 % (4031720)Peak memory usage: 11 MB
% 1.07/0.55 % (4031720)Instructions burned: 39 (million)
% 1.07/0.55 % (4031722) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4031688-4031722"...
% 1.07/0.55 % (4031722)...printing done.
% 1.07/0.55 % (4031716)Instruction limit reached!
% 1.07/0.55 % (4031716)------------------------------
% 1.07/0.55 % (4031716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (4031728)Instruction limit reached!
% 1.07/0.55 % (4031728)------------------------------
% 1.07/0.55 % (4031728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (4031728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (4031716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (4031728)CaDiCaL version: 2.1.3
% 1.07/0.55 % (4031728)Termination reason: Instruction limit
% 1.07/0.55 % (4031728)Termination phase: shuffling
% 1.07/0.55 % (4031728)Time elapsed: 0.013 s
% 1.07/0.55 % (4031716)CaDiCaL version: 2.1.3
% 1.07/0.55 % (4031728)Peak memory usage: 10 MB
% 1.07/0.55 % (4031716)Termination reason: Instruction limit
% 1.07/0.55 % (4031716)Termination phase: Function definition elimination
% 1.07/0.55 % (4031728)Instructions burned: 14 (million)
% 1.07/0.55 % (4031716)Time elapsed: 0.070 s
% 1.07/0.55 % (4031716)Peak memory usage: 11 MB
% 1.07/0.55 % (4031716)Instructions burned: 87 (million)
% 1.07/0.55 % (4031722)Refutation found. Thanks to Tanya!
% 1.07/0.55 % SZS status Theorem for theBenchmark
% 1.07/0.55 % SZS output start Proof for theBenchmark
% 1.07/0.55 thf(type_def_5, type, list_nat: $tType).
% 1.07/0.55 thf(type_def_6, type, list_a: $tType).
% 1.07/0.55 thf(type_def_7, type, nat: $tType).
% 1.07/0.55 thf(type_def_8, type, a: $tType).
% 1.07/0.55 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 1.07/0.55 thf(func_def_0, type, minus_minus_nat: (nat > nat > nat)).
% 1.07/0.55 thf(func_def_1, type, list_asc_nat: (list_nat > $o)).
% 1.07/0.55 thf(func_def_2, type, list_desc_nat: (list_nat > $o)).
% 1.07/0.55 thf(func_def_3, type, list_strict_asc_nat: (list_nat > $o)).
% 1.07/0.55 thf(func_def_4, type, list_strict_desc_nat: (list_nat > $o)).
% 1.07/0.55 thf(func_def_5, type, listIn923761578nd_nat: (list_nat > (nat > nat) > nat > nat)).
% 1.07/0.55 thf(func_def_6, type, listIn1312259492pend_a: (list_a > (nat > a) > nat > a)).
% 1.07/0.55 thf(func_def_7, type, linorder_sorted_nat: (list_nat > $o)).
% 1.07/0.55 thf(func_def_8, type, list_ex_nat: ((nat > $o) > list_nat > $o)).
% 1.07/0.55 thf(func_def_9, type, list_ex_a: ((a > $o) > list_a > $o)).
% 1.07/0.55 thf(func_def_10, type, nth_nat: (list_nat > nat > nat)).
% 1.07/0.55 thf(func_def_11, type, nth_a: (list_a > nat > a)).
% 1.07/0.55 thf(func_def_12, type, rev_nat: (list_nat > list_nat)).
% 1.07/0.55 thf(func_def_13, type, rev_a: (list_a > list_a)).
% 1.07/0.55 thf(func_def_14, type, suc: (nat > nat)).
% 1.07/0.55 thf(func_def_15, type, size_size_list_nat: (list_nat > nat)).
% 1.07/0.55 thf(func_def_16, type, size_size_list_a: (list_a > nat)).
% 1.07/0.55 thf(func_def_17, type, ord_less_nat: (nat > nat > $o)).
% 1.07/0.55 thf(func_def_18, type, ord_less_eq_nat: (nat > nat > $o)).
% 1.07/0.55 thf(func_def_19, type, f: (nat > a)).
% 1.07/0.55 thf(func_def_20, type, g: (nat > a)).
% 1.07/0.55 thf(func_def_21, type, xs: list_a).
% 1.07/0.55 thf(func_def_22, type, ys: list_a).
% 1.07/0.55 thf(func_def_26, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.07/0.55 thf(func_def_27, type, vIMP: ($o > $o > $o)).
% 1.07/0.55 thf(func_def_28, type, db0: !>[X0: $tType]:(X0)).
% 1.07/0.55 thf(func_def_29, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.07/0.55 thf(func_def_30, type, db1: !>[X0: $tType]:(X0)).
% 1.07/0.55 thf(func_def_31, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.07/0.55 thf(func_def_32, type, vAND: ($o > $o > $o)).
% 1.07/0.55 thf(func_def_33, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.07/0.55 thf(func_def_34, type, vOR: ($o > $o > $o)).
% 1.07/0.55 thf(func_def_35, type, db2: !>[X0: $tType]:(X0)).
% 1.07/0.55 thf(func_def_36, type, vNOT: ($o > $o)).
% 1.07/0.55 thf(func_def_37, type, sP0: (nat > nat > nat > $o)).
% 1.07/0.55 thf(func_def_38, type, sP1: (nat > nat > nat > $o)).
% 1.07/0.55 thf(func_def_39, type, sP2: (nat > nat > nat > $o)).
% 1.07/0.55 thf(func_def_40, type, sK3: (nat > nat)).
% 1.07/0.55 thf(func_def_41, type, sK4: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_42, type, sK5: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_43, type, sK6: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_44, type, sK7: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_45, type, sK8: (nat > nat)).
% 1.07/0.55 thf(func_def_46, type, sK9: (nat > nat)).
% 1.07/0.55 thf(func_def_47, type, sK10: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_48, type, sK11: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_49, type, sK12: ((nat > $o) > nat)).
% 1.07/0.55 thf(func_def_50, type, sK13: nat).
% 1.07/0.55 thf(func_def_51, type, sK14: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_52, type, sK15: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_53, type, sK16: (nat > nat)).
% 1.07/0.55 thf(func_def_54, type, sK17: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_55, type, sK18: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_56, type, sK19: (nat > (nat > $o) > nat)).
% 1.07/0.55 thf(func_def_57, type, sK20: ((nat > $o) > nat)).
% 1.07/0.55 thf(func_def_58, type, sK21: ((list_a > $o) > list_a)).
% 1.07/0.55 thf(func_def_59, type, sK22: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_60, type, sK23: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_61, type, sK24: ((nat > $o) > nat)).
% 1.07/0.55 thf(func_def_62, type, sK25: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_63, type, sK26: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_64, type, sK27: (nat > nat)).
% 1.07/0.55 thf(func_def_65, type, sK28: (nat > nat)).
% 1.07/0.55 thf(func_def_66, type, sK29: (nat > list_a)).
% 1.07/0.55 thf(func_def_67, type, sK30: ((nat > nat > $o) > nat)).
% 1.07/0.55 thf(func_def_68, type, sK31: ((nat > nat > $o) > nat)).
% 1.07/0.55 thf(func_def_69, type, sK32: ((nat > nat > $o) > nat)).
% 1.07/0.55 thf(func_def_70, type, sK33: ((nat > nat > $o) > nat)).
% 1.07/0.55 thf(func_def_71, type, sK34: ((nat > nat > $o) > nat)).
% 1.07/0.55 thf(func_def_72, type, sK35: (nat > nat)).
% 1.07/0.55 thf(func_def_73, type, sK36: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_74, type, sK37: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_75, type, sK38: ((nat > nat > $o) > nat)).
% 1.07/0.55 thf(func_def_76, type, sK39: ((nat > nat > $o) > nat)).
% 1.07/0.55 thf(func_def_77, type, sK40: ((nat > nat > $o) > nat)).
% 1.07/0.55 thf(func_def_78, type, sK41: ((nat > nat > $o) > nat)).
% 1.07/0.55 thf(func_def_79, type, sK42: (nat > nat > (nat > $o) > nat)).
% 1.07/0.55 thf(func_def_80, type, sK43: (nat > nat > (nat > $o) > nat)).
% 1.07/0.55 thf(func_def_81, type, sK44: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_82, type, sK45: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_83, type, sK46: (nat > nat)).
% 1.07/0.55 thf(func_def_84, type, sK47: (nat > nat)).
% 1.07/0.55 thf(func_def_85, type, sK48: (nat > nat)).
% 1.07/0.55 thf(func_def_86, type, sK49: (nat > (nat > $o) > nat)).
% 1.07/0.55 thf(func_def_87, type, sK50: (nat > (nat > $o) > nat)).
% 1.07/0.55 thf(func_def_88, type, sK51: (nat > nat)).
% 1.07/0.55 thf(func_def_89, type, sK52: (list_a > list_a > nat)).
% 1.07/0.55 thf(func_def_90, type, sK53: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_91, type, sK54: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_92, type, sK55: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_93, type, sK56: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_94, type, sK57: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_95, type, sK58: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_96, type, sK59: (nat > nat)).
% 1.07/0.55 thf(func_def_97, type, sK60: ((nat > $o) > nat)).
% 1.07/0.55 thf(func_def_98, type, sK61: (nat > nat)).
% 1.07/0.55 thf(func_def_99, type, sK62: ((nat > nat) > nat)).
% 1.07/0.55 thf(func_def_100, type, sK63: ((nat > nat) > nat)).
% 1.07/0.55 thf(f4,axiom,(
% 1.07/0.55 ! [X0 : nat,X2 : (nat > a),X1 : list_a] : ((ord_less_nat @ X0 @ (size_size_list_a @ X1)) => (((listIn1312259492pend_a @ X1 @ X2 @ X0)) = ((nth_a @ X1 @ X0))))),
% 1.07/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_i__append__nth1)).
% 1.07/0.55 thf(f65,axiom,(
% 1.07/0.55 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X0 @ X1) => ~(ord_less_nat @ X1 @ X0))),
% 1.07/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__asym_H)).
% 1.07/0.55 thf(f76,axiom,(
% 1.07/0.55 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(ord_less_nat @ X0 @ X1) => (ord_less_nat @ X1 @ X0)))),
% 1.07/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_linorder__neqE__nat)).
% 1.07/0.55 thf(f113,axiom,(
% 1.07/0.55 ! [X1 : nat,X0 : nat,X2 : nat] : ((ord_less_eq_nat @ X0 @ X1) => ((ord_less_nat @ X1 @ X2) => (ord_less_nat @ X0 @ X2)))),
% 1.07/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_le__less__trans)).
% 1.07/0.55 thf(f127,axiom,(
% 1.07/0.55 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X0 @ X1) => ~(ord_less_nat @ X1 @ X0))),
% 1.07/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_leD)).
% 1.07/0.55 thf(f253,axiom,(
% 1.07/0.55 ! [X0 : nat] : (((listIn1312259492pend_a @ xs @ f @ X0)) = ((listIn1312259492pend_a @ ys @ g @ X0)))),
% 1.07/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 1.07/0.55 thf(f254,axiom,(
% 1.07/0.55 (ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys))),
% 1.07/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 1.07/0.55 thf(f255,conjecture,(
% 1.07/0.55 ! [X0 : nat] : ((((nth_a @ xs @ X0)) = ((nth_a @ ys @ X0))) | ~(ord_less_nat @ X0 @ (size_size_list_a @ xs)))),
% 1.07/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)).
% 1.07/0.55 thf(f256,negated_conjecture,(
% 1.07/0.55 ~ ! [X0 : nat] : ((((nth_a @ xs @ X0)) = ((nth_a @ ys @ X0))) | ~(ord_less_nat @ X0 @ (size_size_list_a @ xs)))),
% 1.07/0.55 inference(negated_conjecture,[status(cth)],[f255])).
% 1.07/0.55 thf(f259,plain,(
% 1.07/0.55 ~ ! [X0 : nat] : ((((nth_a @ xs @ X0)) = ((nth_a @ ys @ X0))) | ~(ord_less_nat @ X0 @ (size_size_list_a @ xs)))),
% 1.07/0.55 inference(rectify,[],[f256])).
% 1.07/0.55 thf(f260,plain,(
% 1.07/0.55 ~ ! [X0 : nat] : ((((nth_a @ xs @ X0)) = ((nth_a @ ys @ X0))) | ~ (((ord_less_nat @ X0 @ (size_size_list_a @ xs))) = $true))),
% 1.07/0.55 inference(fool_elimination,[],[f259])).
% 1.07/0.55 thf(f325,plain,(
% 1.07/0.55 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X0 @ X1) => ~(ord_less_nat @ X1 @ X0))),
% 1.07/0.55 inference(rectify,[],[f65])).
% 1.07/0.55 thf(f326,plain,(
% 1.07/0.55 ! [X0 : nat,X1 : nat] : ((((ord_less_nat @ X0 @ X1)) = $true) => ~ (((ord_less_nat @ X1 @ X0)) = $true))),
% 1.07/0.55 inference(fool_elimination,[],[f325])).
% 1.07/0.55 thf(f462,plain,(
% 1.07/0.55 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(ord_less_nat @ X0 @ X1) => (ord_less_nat @ X1 @ X0)))),
% 1.07/0.55 inference(rectify,[],[f76])).
% 1.07/0.55 thf(f463,plain,(
% 1.07/0.55 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~ (((ord_less_nat @ X0 @ X1)) = $true) => (((ord_less_nat @ X1 @ X0)) = $true)))),
% 1.07/0.55 inference(fool_elimination,[],[f462])).
% 1.07/0.55 thf(f579,plain,(
% 1.07/0.55 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X0 @ X1) => ~(ord_less_nat @ X1 @ X0))),
% 1.07/0.55 inference(rectify,[],[f127])).
% 1.07/0.55 thf(f580,plain,(
% 1.07/0.55 ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X0 @ X1)) = $true) => ~ (((ord_less_nat @ X1 @ X0)) = $true))),
% 1.07/0.55 inference(fool_elimination,[],[f579])).
% 1.07/0.55 thf(f585,plain,(
% 1.07/0.55 ! [X0 : nat,X1 : (nat > a),X2 : list_a] : ((ord_less_nat @ X0 @ (size_size_list_a @ X2)) => (((nth_a @ X2 @ X0)) = ((listIn1312259492pend_a @ X2 @ X1 @ X0))))),
% 1.07/0.55 inference(rectify,[],[f4])).
% 1.07/0.55 thf(f586,plain,(
% 1.07/0.55 ! [X1 : (nat > a),X0 : nat,X2 : list_a] : ((((ord_less_nat @ X0 @ (size_size_list_a @ X2))) = $true) => (((nth_a @ X2 @ X0)) = ((listIn1312259492pend_a @ X2 @ X1 @ X0))))),
% 1.07/0.55 inference(fool_elimination,[],[f585])).
% 1.07/0.55 thf(f625,plain,(
% 1.07/0.55 ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less_eq_nat @ X1 @ X0) => ((ord_less_nat @ X0 @ X2) => (ord_less_nat @ X1 @ X2)))),
% 1.07/0.55 inference(rectify,[],[f113])).
% 1.07/0.55 thf(f626,plain,(
% 1.07/0.55 ! [X1 : nat,X0 : nat,X2 : nat] : ((((ord_less_eq_nat @ X1 @ X0)) = $true) => ((((ord_less_nat @ X0 @ X2)) = $true) => (((ord_less_nat @ X1 @ X2)) = $true)))),
% 1.07/0.55 inference(fool_elimination,[],[f625])).
% 1.07/0.55 thf(f703,plain,(
% 1.07/0.55 (ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys))),
% 1.07/0.55 inference(rectify,[],[f254])).
% 1.07/0.55 thf(f704,plain,(
% 1.07/0.55 (((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys))) = $true)),
% 1.07/0.55 inference(fool_elimination,[],[f703])).
% 1.07/0.55 thf(f716,plain,(
% 1.07/0.55 ~ ! [X0 : nat] : ((((ord_less_nat @ X0 @ (size_size_list_a @ xs))) != $true) | (((nth_a @ xs @ X0)) = ((nth_a @ ys @ X0))))),
% 1.07/0.55 inference(flattening,[],[f260])).
% 1.07/0.55 thf(f725,plain,(
% 1.07/0.55 ! [X0 : nat,X1 : nat] : ((X0 != X1) => ((((ord_less_nat @ X0 @ X1)) != $true) => (((ord_less_nat @ X1 @ X0)) = $true)))),
% 1.07/0.55 inference(flattening,[],[f463])).
% 1.07/0.55 thf(f731,plain,(
% 1.07/0.55 ! [X1 : nat,X0 : nat] : ((((ord_less_nat @ X0 @ X1)) = $true) => (((ord_less_nat @ X1 @ X0)) != $true))),
% 1.07/0.55 inference(flattening,[],[f326])).
% 1.07/0.55 thf(f737,plain,(
% 1.07/0.55 ! [X1 : nat,X0 : nat] : ((((ord_less_eq_nat @ X0 @ X1)) = $true) => (((ord_less_nat @ X1 @ X0)) != $true))),
% 1.07/0.55 inference(flattening,[],[f580])).
% 1.07/0.55 thf(f756,plain,(
% 1.07/0.55 ! [X1 : nat,X0 : nat,X2 : nat] : (((((ord_less_nat @ X1 @ X2)) = $true) | (((ord_less_nat @ X0 @ X2)) != $true)) | (((ord_less_eq_nat @ X1 @ X0)) != $true))),
% 1.07/0.55 inference(ennf_transformation,[],[f626])).
% 1.07/0.55 thf(f757,plain,(
% 1.07/0.55 ! [X2 : nat,X0 : nat,X1 : nat] : ((((ord_less_nat @ X1 @ X2)) = $true) | (((ord_less_nat @ X0 @ X2)) != $true) | (((ord_less_eq_nat @ X1 @ X0)) != $true))),
% 1.07/0.55 inference(flattening,[],[f756])).
% 1.07/0.55 thf(f764,plain,(
% 1.07/0.55 ? [X0 : nat] : ((((nth_a @ xs @ X0)) != ((nth_a @ ys @ X0))) & (((ord_less_nat @ X0 @ (size_size_list_a @ xs))) = $true))),
% 1.07/0.55 inference(ennf_transformation,[],[f716])).
% 1.07/0.55 thf(f791,plain,(
% 1.07/0.55 ! [X2 : list_a,X0 : nat,X1 : (nat > a)] : ((((nth_a @ X2 @ X0)) = ((listIn1312259492pend_a @ X2 @ X1 @ X0))) | (((ord_less_nat @ X0 @ (size_size_list_a @ X2))) != $true))),
% 1.07/0.55 inference(ennf_transformation,[],[f586])).
% 1.07/0.55 thf(f821,plain,(
% 1.07/0.55 ! [X0 : nat,X1 : nat] : (((((ord_less_nat @ X1 @ X0)) = $true) | (((ord_less_nat @ X0 @ X1)) = $true)) | (X0 = X1))),
% 1.07/0.55 inference(ennf_transformation,[],[f725])).
% 1.07/0.55 thf(f822,plain,(
% 1.07/0.55 ! [X0 : nat,X1 : nat] : ((X0 = X1) | (((ord_less_nat @ X0 @ X1)) = $true) | (((ord_less_nat @ X1 @ X0)) = $true))),
% 1.07/0.55 inference(flattening,[],[f821])).
% 1.07/0.55 thf(f835,plain,(
% 1.07/0.55 ! [X1 : nat,X0 : nat] : ((((ord_less_nat @ X1 @ X0)) != $true) | (((ord_less_nat @ X0 @ X1)) != $true))),
% 1.07/0.55 inference(ennf_transformation,[],[f731])).
% 1.07/0.55 thf(f843,plain,(
% 1.07/0.55 ! [X1 : nat,X0 : nat] : ((((ord_less_nat @ X1 @ X0)) != $true) | (((ord_less_eq_nat @ X0 @ X1)) != $true))),
% 1.07/0.55 inference(ennf_transformation,[],[f737])).
% 1.07/0.55 thf(f892,plain,(
% 1.07/0.55 ! [X0 : nat,X1 : nat] : ((((ord_less_nat @ X0 @ X1)) != $true) | (((ord_less_nat @ X1 @ X0)) != $true))),
% 1.07/0.55 inference(rectify,[],[f835])).
% 1.07/0.55 thf(f893,plain,(
% 1.07/0.55 ! [X0 : nat,X1 : nat] : ((((ord_less_nat @ X0 @ X1)) != $true) | (((ord_less_eq_nat @ X1 @ X0)) != $true))),
% 1.07/0.55 inference(rectify,[],[f843])).
% 1.07/0.55 thf(f905,plain,(
% 1.07/0.55 ! [X0 : list_a,X1 : nat,X2 : (nat > a)] : ((((listIn1312259492pend_a @ X0 @ X2 @ X1)) = ((nth_a @ X0 @ X1))) | (((ord_less_nat @ X1 @ (size_size_list_a @ X0))) != $true))),
% 1.07/0.55 inference(rectify,[],[f791])).
% 1.07/0.55 thf(f909,plain,(
% 1.07/0.55 (((nth_a @ xs @ sK13)) != ((nth_a @ ys @ sK13))) & (((ord_less_nat @ sK13 @ (size_size_list_a @ xs))) = $true)),
% 1.07/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f764])).
% 1.07/0.55 thf(f912,plain,(
% 1.07/0.55 ! [X0 : nat,X1 : nat,X2 : nat] : ((((ord_less_nat @ X2 @ X0)) = $true) | (((ord_less_nat @ X1 @ X0)) != $true) | (((ord_less_eq_nat @ X2 @ X1)) != $true))),
% 1.07/0.55 inference(rectify,[],[f757])).
% 1.07/0.55 thf(f1000,plain,(
% 1.07/0.55 ( ! [X0 : nat,X1 : nat] : ((((ord_less_nat @ X1 @ X0)) != $true) | (((ord_less_nat @ X0 @ X1)) != $true)) )),
% 1.07/0.55 inference(cnf_transformation,[],[f892])).
% 1.07/0.55 thf(f1001,plain,(
% 1.07/0.55 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X1 @ X0)) != $true) | (((ord_less_nat @ X0 @ X1)) != $true)) )),
% 1.07/0.55 inference(cnf_transformation,[],[f893])).
% 1.07/0.55 thf(f1013,plain,(
% 1.07/0.55 ( ! [X2 : (nat > a),X0 : list_a,X1 : nat] : ((((listIn1312259492pend_a @ X0 @ X2 @ X1)) = ((nth_a @ X0 @ X1))) | (((ord_less_nat @ X1 @ (size_size_list_a @ X0))) != $true)) )),
% 1.07/0.55 inference(cnf_transformation,[],[f905])).
% 1.07/0.55 thf(f1018,plain,(
% 1.07/0.55 (((ord_less_nat @ sK13 @ (size_size_list_a @ xs))) = $true)),
% 1.07/0.55 inference(cnf_transformation,[],[f909])).
% 1.07/0.55 thf(f1019,plain,(
% 1.07/0.55 (((nth_a @ xs @ sK13)) != ((nth_a @ ys @ sK13)))),
% 1.07/0.55 inference(cnf_transformation,[],[f909])).
% 1.07/0.55 thf(f1024,plain,(
% 1.07/0.55 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((ord_less_nat @ X2 @ X0)) = $true) | (((ord_less_eq_nat @ X2 @ X1)) != $true) | (((ord_less_nat @ X1 @ X0)) != $true)) )),
% 1.07/0.55 inference(cnf_transformation,[],[f912])).
% 1.07/0.55 thf(f1064,plain,(
% 1.07/0.55 (((ord_less_eq_nat @ (size_size_list_a @ xs) @ (size_size_list_a @ ys))) = $true)),
% 1.07/0.55 inference(cnf_transformation,[],[f704])).
% 1.07/0.55 thf(f1078,plain,(
% 1.07/0.55 ( ! [X0 : nat,X1 : nat] : ((((ord_less_nat @ X1 @ X0)) = $true) | (((ord_less_nat @ X0 @ X1)) = $true) | (X0 = X1)) )),
% 1.07/0.55 inference(cnf_transformation,[],[f822])).
% 1.07/0.55 thf(f1082,plain,(
% 1.07/0.55 ( ! [X0 : nat] : ((((listIn1312259492pend_a @ xs @ f @ X0)) = ((listIn1312259492pend_a @ ys @ g @ X0)))) )),
% 1.07/0.55 inference(cnf_transformation,[],[f253])).
% 1.07/0.55 thf(f1167,definition,(
% 1.07/0.55 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.07/0.55 introduced(theory,[fool_exhaustiveness_axiom])).
% 1.07/0.55 thf(f1200,plain,(
% 1.07/0.55 ($true != $true) | (((ord_less_nat @ (size_size_list_a @ xs) @ sK13)) != $true)),
% 1.07/0.55 inference(superposition,[],[f1000,f1018])).
% 1.07/0.55 thf(f1207,plain,(
% 1.07/0.55 (((ord_less_nat @ (size_size_list_a @ xs) @ sK13)) != $true)),
% 1.07/0.55 inference(trivial_inequality_removal,[],[f1200])).
% 1.07/0.55 thf(f1218,plain,(
% 1.07/0.55 ( ! [X0 : nat] : ((((ord_less_nat @ X0 @ sK13)) != $true) | (((ord_less_eq_nat @ (size_size_list_a @ xs) @ X0)) != $true) | ($true != $true)) )),
% 1.07/0.55 inference(superposition,[],[f1207,f1024])).
% 1.07/0.55 thf(f1238,plain,(
% 1.07/0.55 ( ! [X0 : nat] : ((((ord_less_eq_nat @ (size_size_list_a @ xs) @ X0)) != $true) | (((ord_less_nat @ X0 @ sK13)) != $true)) )),
% 1.07/0.55 inference(trivial_inequality_removal,[],[f1218])).
% 1.07/0.55 thf(f1262,plain,(
% 1.07/0.55 (((ord_less_nat @ (size_size_list_a @ ys) @ (size_size_list_a @ xs))) != $true) | ($true != $true)),
% 1.07/0.55 inference(superposition,[],[f1001,f1064])).
% 1.07/0.55 thf(f1271,plain,(
% 1.07/0.55 (((ord_less_nat @ (size_size_list_a @ ys) @ (size_size_list_a @ xs))) != $true)),
% 1.07/0.55 inference(trivial_inequality_removal,[],[f1262])).
% 1.07/0.55 thf(f1366,plain,(
% 1.07/0.55 ( ! [X0 : nat] : ((((listIn1312259492pend_a @ xs @ f @ X0)) = ((nth_a @ ys @ X0))) | ($true != ((ord_less_nat @ X0 @ (size_size_list_a @ ys))))) )),
% 1.07/0.55 inference(superposition,[],[f1082,f1013])).
% 1.07/0.55 thf(f1702,plain,(
% 1.07/0.55 (((ord_less_nat @ sK13 @ (size_size_list_a @ ys))) != $true) | (((nth_a @ xs @ sK13)) != ((listIn1312259492pend_a @ xs @ f @ sK13)))),
% 1.07/0.55 inference(superposition,[],[f1019,f1366])).
% 1.07/0.55 thf(f1706,definition,(
% 1.07/0.55 spl64_10 <=> (((nth_a @ xs @ sK13)) = ((listIn1312259492pend_a @ xs @ f @ sK13)))),
% 1.07/0.55 introduced(definition,[new_symbols(definition,[spl64_10])],[avatar_definition])).
% 1.07/0.55 thf(f1708,plain,(
% 1.07/0.55 (((nth_a @ xs @ sK13)) != ((listIn1312259492pend_a @ xs @ f @ sK13))) | spl64_10),
% 1.07/0.55 inference(avatar_component_clause,[],[f1706])).
% 1.07/0.55 thf(f1710,definition,(
% 1.07/0.55 spl64_11 <=> (((ord_less_nat @ sK13 @ (size_size_list_a @ ys))) = $true)),
% 1.07/0.55 introduced(definition,[new_symbols(definition,[spl64_11])],[avatar_definition])).
% 1.07/0.55 thf(f1713,plain,(
% 1.07/0.55 ~spl64_10 | ~spl64_11),
% 1.07/0.55 inference(avatar_split_clause,[],[f1702,f1710,f1706])).
% 1.07/0.55 thf(f1938,plain,(
% 1.07/0.55 (((ord_less_nat @ (size_size_list_a @ ys) @ sK13)) != $true) | ($true != $true)),
% 1.07/0.55 inference(superposition,[],[f1238,f1064])).
% 1.07/0.55 thf(f1983,plain,(
% 1.07/0.55 (((ord_less_nat @ (size_size_list_a @ ys) @ sK13)) != $true)),
% 1.07/0.55 inference(trivial_inequality_removal,[],[f1938])).
% 1.07/0.55 thf(f2027,plain,(
% 1.07/0.55 (((ord_less_nat @ (size_size_list_a @ ys) @ sK13)) = $false) | ($true != $true)),
% 1.07/0.55 inference(superposition,[],[f1983,f1167])).
% 1.07/0.55 thf(f2040,plain,(
% 1.07/0.55 (((ord_less_nat @ (size_size_list_a @ ys) @ sK13)) = $false)),
% 1.07/0.55 inference(trivial_inequality_removal,[],[f2027])).
% 1.07/0.55 thf(f2047,definition,(
% 1.07/0.55 spl64_17 <=> (((size_size_list_a @ ys)) = sK13)),
% 1.07/0.55 introduced(definition,[new_symbols(definition,[spl64_17])],[avatar_definition])).
% 1.07/0.55 thf(f2049,plain,(
% 1.07/0.55 (((size_size_list_a @ ys)) = sK13) | ~spl64_17),
% 1.07/0.55 inference(avatar_component_clause,[],[f2047])).
% 1.07/0.55 thf(f2082,plain,(
% 1.07/0.55 (((ord_less_nat @ sK13 @ (size_size_list_a @ ys))) = $true) | ($true = $false) | (((size_size_list_a @ ys)) = sK13)),
% 1.07/0.55 inference(superposition,[],[f2040,f1078])).
% 1.07/0.55 thf(f2141,plain,(
% 1.07/0.55 (((size_size_list_a @ ys)) = sK13) | (((ord_less_nat @ sK13 @ (size_size_list_a @ ys))) = $true)),
% 1.07/0.55 inference(trivial_inequality_removal,[],[f2082])).
% 1.07/0.55 thf(f2154,plain,(
% 1.07/0.55 (((nth_a @ xs @ sK13)) != ((nth_a @ xs @ sK13))) | (((ord_less_nat @ sK13 @ (size_size_list_a @ xs))) != $true) | spl64_10),
% 1.07/0.55 inference(superposition,[],[f1708,f1013])).
% 1.07/0.55 thf(f2155,plain,(
% 1.07/0.55 (((ord_less_nat @ sK13 @ (size_size_list_a @ xs))) != $true) | spl64_10),
% 1.07/0.55 inference(trivial_inequality_removal,[],[f2154])).
% 1.07/0.55 thf(f2156,plain,(
% 1.07/0.55 $false | spl64_10),
% 1.07/0.55 inference(forward_subsumption_resolution,[],[f2155,f1018])).
% 1.07/0.55 thf(f2157,plain,(
% 1.07/0.55 spl64_10),
% 1.07/0.55 inference(avatar_contradiction_clause,[],[f2156])).
% 1.07/0.55 thf(f2158,plain,(
% 1.07/0.55 spl64_17 | spl64_11),
% 1.07/0.55 inference(avatar_split_clause,[],[f2141,f1710,f2047])).
% 1.07/0.55 thf(f2161,plain,(
% 1.07/0.55 (((ord_less_nat @ (size_size_list_a @ ys) @ (size_size_list_a @ xs))) = $true) | ~spl64_17),
% 1.07/0.55 inference(superposition,[],[f1018,f2049])).
% 1.07/0.55 thf(f2176,plain,(
% 1.07/0.55 $false | ~spl64_17),
% 1.07/0.55 inference(forward_subsumption_resolution,[],[f2161,f1271])).
% 1.07/0.55 thf(f2177,plain,(
% 1.07/0.55 ~spl64_17),
% 1.07/0.55 inference(avatar_contradiction_clause,[],[f2176])).
% 1.07/0.55 cnf(s25, plain, ~spl64_10 | ~spl64_11, inference(sat_conversion,[],[f1713])).
% 1.07/0.55 cnf(s38, plain, spl64_10, inference(sat_conversion,[],[f2157])).
% 1.07/0.55 cnf(s39, plain, spl64_11 | spl64_17, inference(sat_conversion,[],[f2158])).
% 1.07/0.55 cnf(s41, plain, ~spl64_17, inference(sat_conversion,[],[f2177])).
% 1.07/0.55 cnf(s44, plain, spl64_11, inference(rat,[],[s39,s41])).
% 1.07/0.55 cnf(s46, plain, $false, inference(rat,[],[s25,s44,s38])).
% 1.07/0.55 thf(f2183,plain,(
% 1.07/0.55 $false),
% 1.07/0.55 inference(avatar_sat_refutation,[],[s46])).
% 1.07/0.55 % SZS output end Proof for theBenchmark
% 1.07/0.55 % (4031722)------------------------------
% 1.07/0.55 % (4031722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (4031722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (4031722)CaDiCaL version: 2.1.3
% 1.07/0.55 % (4031722)Termination reason: Refutation
% 1.07/0.55 % (4031722)Time elapsed: 0.051 s
% 1.07/0.55 % (4031722)Peak memory usage: 14 MB
% 1.07/0.55 % (4031722)Instructions burned: 114 (million)
% 1.07/0.55 % (4031688)Success in time 0.207 s
% 1.07/0.55 % Vampire exiting
%------------------------------------------------------------------------------