%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP103^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:21 AM UTC 2026
% Result : Theorem 0.54s 0.44s
% Output : Refutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP103^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 19:54:03 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.23/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.54/0.41 % (1269395)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.54/0.41 % (1269404)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=693075380:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.54/0.41 % (1269406)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.54/0.41 % (1269406)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
% 0.54/0.41 % (1269404)Instruction limit reached!
% 0.54/0.41 % (1269404)------------------------------
% 0.54/0.41 % (1269404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1269404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1269404)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1269404)Termination reason: Instruction limit
% 0.54/0.41 % (1269404)Termination phase: Property scanning
% 0.54/0.41 % (1269404)Time elapsed: 0.006 s
% 0.54/0.41 % (1269404)Peak memory usage: 10 MB
% 0.54/0.41 % (1269404)Instructions burned: 26 (million)
% 0.54/0.41 % (1269400)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2026166507:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.54/0.41 % (1269401)lrs+10_16_si=on:nwc=1.5:random_seed=1580421232:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.54/0.41 % (1269402)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3915626287:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.54/0.41 % (1269403)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=1895358502: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)
% 0.54/0.41 % (1269405)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2851074217:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.54/0.41 % (1269406)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=3813243623:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.54/0.41 % (1269402)Instruction limit reached!
% 0.54/0.41 % (1269402)------------------------------
% 0.54/0.41 % (1269402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1269402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1269402)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1269402)Termination reason: Instruction limit
% 0.54/0.41 % (1269402)Termination phase: shuffling
% 0.54/0.41 % (1269402)Time elapsed: 0.005 s
% 0.54/0.41 % (1269402)Peak memory usage: 10 MB
% 0.54/0.41 % (1269402)Instructions burned: 10 (million)
% 0.54/0.41 % (1269408)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1252053108:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.41 % (1269401)Instruction limit reached!
% 0.54/0.41 % (1269401)------------------------------
% 0.54/0.41 % (1269401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1269401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1269401)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1269401)Termination reason: Instruction limit
% 0.54/0.41 % (1269401)Termination phase: Property scanning
% 0.54/0.41 % (1269401)Time elapsed: 0.011 s
% 0.54/0.41 % (1269401)Peak memory usage: 10 MB
% 0.54/0.41 % (1269401)Instructions burned: 19 (million)
% 0.54/0.41 % (1269408)Instruction limit reached!
% 0.54/0.41 % (1269408)------------------------------
% 0.54/0.41 % (1269408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1269408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1269408)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1269408)Termination reason: Instruction limit
% 0.54/0.41 % (1269408)Termination phase: shuffling
% 0.54/0.41 % (1269408)Time elapsed: 0.001 s
% 0.54/0.41 % (1269408)Peak memory usage: 10 MB
% 0.54/0.41 % (1269408)Instructions burned: 5 (million)
% 0.54/0.41 % (1269418)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2121327301:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.54/0.44 % (1269415)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2782066845:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.54/0.44 % (1269417)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.44 % (1269418)Instruction limit reached!
% 0.54/0.44 % (1269418)------------------------------
% 0.54/0.44 % (1269418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269418)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269418)Termination reason: Instruction limit
% 0.54/0.44 % (1269418)Termination phase: shuffling
% 0.54/0.44 % (1269418)Time elapsed: 0.004 s
% 0.54/0.44 % (1269418)Peak memory usage: 10 MB
% 0.54/0.44 % (1269418)Instructions burned: 15 (million)
% 0.54/0.44 % (1269415)Instruction limit reached!
% 0.54/0.44 % (1269415)------------------------------
% 0.54/0.44 % (1269415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269415)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269415)Termination reason: Instruction limit
% 0.54/0.44 % (1269415)Termination phase: shuffling
% 0.54/0.44 % (1269415)Time elapsed: 0.003 s
% 0.54/0.44 % (1269415)Peak memory usage: 10 MB
% 0.54/0.44 % (1269415)Instructions burned: 5 (million)
% 0.54/0.44 % (1269417)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=897719959:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.54/0.44 % (1269417)Instruction limit reached!
% 0.54/0.44 % (1269417)------------------------------
% 0.54/0.44 % (1269417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269417)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269417)Termination reason: Instruction limit
% 0.54/0.44 % (1269417)Termination phase: shuffling
% 0.54/0.44 % (1269417)Time elapsed: 0.004 s
% 0.54/0.44 % (1269417)Peak memory usage: 10 MB
% 0.54/0.44 % (1269417)Instructions burned: 7 (million)
% 0.54/0.44 % (1269405)Instruction limit reached!
% 0.54/0.44 % (1269405)------------------------------
% 0.54/0.44 % (1269405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269405)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269405)Termination reason: Instruction limit
% 0.54/0.44 % (1269405)Termination phase: Property scanning
% 0.54/0.44 % (1269405)Time elapsed: 0.035 s
% 0.54/0.44 % (1269405)Peak memory usage: 12 MB
% 0.54/0.44 % (1269405)Instructions burned: 77 (million)
% 0.54/0.44 % (1269421)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
% 0.54/0.44 % (1269421)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.44 % (1269421)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3912633589:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.54/0.44 % (1269400)Instruction limit reached!
% 0.54/0.44 % (1269400)------------------------------
% 0.54/0.44 % (1269400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269400)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269400)Termination reason: Instruction limit
% 0.54/0.44 % (1269400)Termination phase: Saturation
% 0.54/0.44 % (1269400)Time elapsed: 0.040 s
% 0.54/0.44 % (1269400)Peak memory usage: 13 MB
% 0.54/0.44 % (1269400)Instructions burned: 88 (million)
% 0.54/0.44 % (1269421)Instruction limit reached!
% 0.54/0.44 % (1269421)------------------------------
% 0.54/0.44 % (1269421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269421)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269421)Termination reason: Instruction limit
% 0.54/0.44 % (1269421)Termination phase: Property scanning
% 0.54/0.44 % (1269421)Time elapsed: 0.007 s
% 0.54/0.44 % (1269421)Peak memory usage: 11 MB
% 0.54/0.44 % (1269421)Instructions burned: 31 (million)
% 0.54/0.44 % (1269422)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=424615628:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.54/0.44 % (1269425)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.54/0.44 % (1269424)lrs+10_1_si=on:cs=on:random_seed=3184073125:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.54/0.44 % (1269425)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=2905701029:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.44 % (1269428)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3349836482:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.54/0.44 % (1269425)Instruction limit reached!
% 0.54/0.44 % (1269425)------------------------------
% 0.54/0.44 % (1269425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269425)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269425)Termination reason: Instruction limit
% 0.54/0.44 % (1269425)Termination phase: shuffling
% 0.54/0.44 % (1269425)Time elapsed: 0.002 s
% 0.54/0.44 % (1269425)Peak memory usage: 10 MB
% 0.54/0.44 % (1269425)Instructions burned: 3 (million)
% 0.54/0.44 % (1269424)Instruction limit reached!
% 0.54/0.44 % (1269424)------------------------------
% 0.54/0.44 % (1269424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269424)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269424)Termination reason: Instruction limit
% 0.54/0.44 % (1269424)Termination phase: shuffling
% 0.54/0.44 % (1269424)Time elapsed: 0.004 s
% 0.54/0.44 % (1269424)Peak memory usage: 10 MB
% 0.54/0.44 % (1269424)Instructions burned: 8 (million)
% 0.54/0.44 % (1269427)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=855113067:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.54/0.44 % (1269433)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2318876574:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.54/0.44 % (1269435)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1834391130:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.54/0.44 % (1269427)Instruction limit reached!
% 0.54/0.44 % (1269427)------------------------------
% 0.54/0.44 % (1269427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269427)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269427)Termination reason: Instruction limit
% 0.54/0.44 % (1269427)Termination phase: Property scanning
% 0.54/0.44 % (1269427)Time elapsed: 0.018 s
% 0.54/0.44 % (1269427)Peak memory usage: 11 MB
% 0.54/0.44 % (1269427)Instructions burned: 40 (million)
% 0.54/0.44 % (1269406)Instruction limit reached!
% 0.54/0.44 % (1269406)------------------------------
% 0.54/0.44 % (1269406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269406)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269406)Termination reason: Instruction limit
% 0.54/0.44 % (1269406)Termination phase: Saturation
% 0.54/0.44 % (1269406)Time elapsed: 0.078 s
% 0.54/0.44 % (1269406)Peak memory usage: 13 MB
% 0.54/0.44 % (1269406)Instructions burned: 157 (million)
% 0.54/0.44 % (1269435)Instruction limit reached!
% 0.54/0.44 % (1269435)------------------------------
% 0.54/0.44 % (1269435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269435)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269435)Termination reason: Instruction limit
% 0.54/0.44 % (1269435)Termination phase: shuffling
% 0.54/0.44 % (1269435)Time elapsed: 0.007 s
% 0.54/0.44 % (1269435)Peak memory usage: 10 MB
% 0.54/0.44 % (1269435)Instructions burned: 16 (million)
% 0.54/0.44 % (1269422)Instruction limit reached!
% 0.54/0.44 % (1269422)------------------------------
% 0.54/0.44 % (1269422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269422)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269422)Termination reason: Instruction limit
% 0.54/0.44 % (1269422)Termination phase: Property scanning
% 0.54/0.44 % (1269422)Time elapsed: 0.037 s
% 0.54/0.44 % (1269422)Peak memory usage: 11 MB
% 0.54/0.44 % (1269422)Instructions burned: 88 (million)
% 0.54/0.44 % (1269433)Instruction limit reached!
% 0.54/0.44 % (1269433)------------------------------
% 0.54/0.44 % (1269433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269433)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269433)Termination reason: Instruction limit
% 0.54/0.44 % (1269433)Termination phase: Property scanning
% 0.54/0.44 % (1269433)Time elapsed: 0.012 s
% 0.54/0.44 % (1269433)Peak memory usage: 10 MB
% 0.54/0.44 % (1269433)Instructions burned: 27 (million)
% 0.54/0.44 % (1269438)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1750652902:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.54/0.44 % (1269439)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=937341320:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.54/0.44 % (1269440)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1901989830:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.54/0.44 % (1269439)Instruction limit reached!
% 0.54/0.44 % (1269439)------------------------------
% 0.54/0.44 % (1269439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269439)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269439)Termination reason: Instruction limit
% 0.54/0.44 % (1269439)Termination phase: shuffling
% 0.54/0.44 % (1269439)Time elapsed: 0.007 s
% 0.54/0.44 % (1269439)Peak memory usage: 10 MB
% 0.54/0.44 % (1269439)Instructions burned: 16 (million)
% 0.54/0.44 % (1269441)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2803351837:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.54/0.44 % (1269440)Instruction limit reached!
% 0.54/0.44 % (1269440)------------------------------
% 0.54/0.44 % (1269440)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269440)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269440)Termination reason: Instruction limit
% 0.54/0.44 % (1269440)Termination phase: shuffling
% 0.54/0.44 % (1269440)Time elapsed: 0.002 s
% 0.54/0.44 % (1269440)Peak memory usage: 10 MB
% 0.54/0.44 % (1269440)Instructions burned: 3 (million)
% 0.54/0.44 % (1269442)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1888346259:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.54/0.44 % (1269428) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1269395-1269428"...
% 0.54/0.44 % (1269428)...printing done.
% 0.54/0.44 % (1269428)Refutation found. Thanks to Tanya!
% 0.54/0.44 % SZS status Theorem for theBenchmark
% 0.54/0.44 % SZS output start Proof for theBenchmark
% 0.54/0.44 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.54/0.44 thf(type_def_6, type, list: $tType > $tType).
% 0.54/0.44 thf(type_def_7, type, nat: $tType).
% 0.54/0.44 thf(type_def_8, type, a: $tType).
% 0.54/0.44 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.54/0.44 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_1, type, size: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_2, type, zero: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_3, type, field: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_5, type, mult_zero: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_6, type, linorder: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_7, type, ordered_ring: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_8, type, wellorder: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_9, type, division_ring: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_10, type, semiring_bits: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_11, type, semidom_divide: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_12, type, semigroup_mult: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_13, type, linordered_idom: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_14, type, linordered_ring: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_15, type, ordered_semiring: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_16, type, linordered_field: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_17, type, ab_semigroup_mult: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_18, type, ordered_semiring_0: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_19, type, ordere1490568538miring: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_20, type, linord581940658strict: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_21, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_22, type, linord20386208strict: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_23, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_24, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_25, type, linord893533164strict: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_26, type, semiri1923998003cancel: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_27, type, euclid191655569cancel: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_28, type, times_times: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.54/0.44 thf(func_def_29, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.54/0.44 thf(func_def_30, type, product: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > list @ product_prod @ X0 @ X1))).
% 0.54/0.44 thf(func_def_31, type, suc: (nat > nat)).
% 0.54/0.44 thf(func_def_32, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 0.54/0.44 thf(func_def_33, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.54/0.44 thf(func_def_34, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.54/0.44 thf(func_def_35, type, divide_divide: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.54/0.44 thf(func_def_36, type, k: nat).
% 0.54/0.44 thf(func_def_37, type, n: nat).
% 0.54/0.44 thf(func_def_38, type, xs: list @ a).
% 0.54/0.44 thf(func_def_42, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.54/0.44 thf(func_def_43, type, vNOT: ($o > $o)).
% 0.54/0.44 thf(func_def_44, type, vAND: ($o > $o > $o)).
% 0.54/0.44 thf(func_def_45, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.54/0.44 thf(func_def_46, type, vIMP: ($o > $o > $o)).
% 0.54/0.44 thf(func_def_47, type, db0: !>[X0: $tType]:(X0)).
% 0.54/0.44 thf(func_def_48, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.54/0.44 thf(func_def_49, type, vOR: ($o > $o > $o)).
% 0.54/0.44 thf(func_def_50, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.54/0.44 thf(func_def_51, type, db1: !>[X0: $tType]:(X0)).
% 0.54/0.44 thf(func_def_52, type, db2: !>[X0: $tType]:(X0)).
% 0.54/0.44 thf(func_def_53, type, sK0: ((nat > $o) > nat > nat)).
% 0.54/0.44 thf(func_def_54, type, sK1: ((nat > $o) > nat > nat)).
% 0.54/0.44 thf(func_def_55, type, sK2: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.54/0.44 thf(func_def_56, type, sK3: ((nat > $o) > nat)).
% 0.54/0.44 thf(func_def_57, type, sK4: (nat > nat)).
% 0.54/0.44 thf(func_def_58, type, sK5: ((nat > $o) > nat)).
% 0.54/0.44 thf(func_def_59, type, sK6: (nat > nat > nat)).
% 0.54/0.44 thf(func_def_60, type, sK7: ((nat > nat > $o) > nat)).
% 0.54/0.44 thf(func_def_61, type, sK8: ((nat > nat > $o) > nat)).
% 0.54/0.44 thf(func_def_62, type, sK9: ((nat > nat > $o) > nat)).
% 0.54/0.44 thf(func_def_63, type, sK10: ((nat > nat > $o) > nat)).
% 0.54/0.44 thf(func_def_64, type, sK11: (nat > nat)).
% 0.54/0.44 thf(func_def_65, type, sK12: ((nat > $o) > nat)).
% 0.54/0.44 thf(func_def_66, type, sK13: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat > X0))).
% 0.54/0.44 thf(func_def_67, type, sK14: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > X0))).
% 0.54/0.44 thf(func_def_68, type, sK15: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat))).
% 0.54/0.44 thf(func_def_69, type, sK16: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.54/0.44 thf(func_def_70, type, sK17: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.54/0.44 thf(func_def_71, type, sK18: ((nat > $o) > nat)).
% 0.54/0.44 thf(func_def_72, type, sK19: ((nat > $o) > nat)).
% 0.54/0.44 thf(func_def_73, type, sK20: ((nat > $o) > nat)).
% 0.54/0.44 thf(func_def_74, type, sK21: ((nat > nat > $o) > nat)).
% 0.54/0.44 thf(func_def_75, type, sK22: ((nat > nat > $o) > nat)).
% 0.54/0.44 thf(func_def_76, type, sK23: ((nat > nat > $o) > nat)).
% 0.54/0.44 thf(func_def_77, type, sK24: ((nat > nat > $o) > nat)).
% 0.54/0.44 thf(func_def_78, type, sK25: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.54/0.44 thf(func_def_79, type, sK26: ((nat > $o) > nat)).
% 0.54/0.44 thf(func_def_80, type, sK27: (nat > nat > nat)).
% 0.54/0.44 thf(func_def_81, type, sK28: (nat > nat)).
% 0.54/0.44 thf(func_def_82, type, sK29: !>[X0: $tType]:((nat > list @ X0))).
% 0.54/0.44 thf(func_def_83, type, sK30: (nat > nat)).
% 0.54/0.44 thf(f1,axiom,(
% 0.54/0.44 ! [X3 : nat,X2 : nat] : ((ord_less @ nat @ zero_zero @ nat @ X2) => (((divide_divide @ nat @ (times_times @ nat @ X3 @ X2) @ X2)) = X3))),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_div__mult__self__is__m)).
% 0.54/0.44 thf(f30,axiom,(
% 0.54/0.44 ! [X0 : nat] : (X0 != ((suc @ X0)))),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_n__not__Suc__n)).
% 0.54/0.44 thf(f33,axiom,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(ord_less @ nat @ X0 @ X1) => (ord_less @ nat @ X1 @ X0)))),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_linorder__neqE__nat)).
% 0.54/0.44 thf(f37,axiom,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ X0 @ X1) => (X0 != X1))),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_less__not__refl3)).
% 0.54/0.44 thf(f58,axiom,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ X0 @ X1) => (X1 != zero_zero @ nat))),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_gr__implies__not0)).
% 0.54/0.44 thf(f78,axiom,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ (suc @ X0) @ X1) => (ord_less @ nat @ X0 @ X1))),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Suc__lessD)).
% 0.54/0.44 thf(f97,axiom,(
% 0.54/0.44 ! [X1 : nat,X2 : nat,X0 : nat] : ((ord_less @ nat @ X0 @ (times_times @ nat @ X1 @ X2)) => (ord_less @ nat @ (divide_divide @ nat @ X0 @ X2) @ X1))),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Euclidean__Division_Oless__mult__imp__div__less)).
% 0.54/0.44 thf(f279,axiom,(
% 0.54/0.44 (((divide_divide @ nat @ (size_size @ list @ a @ xs) @ k)) = ((suc @ n)))),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.54/0.44 thf(f280,axiom,(
% 0.54/0.44 (k != zero_zero @ nat)),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.54/0.44 thf(f281,conjecture,(
% 0.54/0.44 (ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)).
% 0.54/0.44 thf(f282,negated_conjecture,(
% 0.54/0.44 ~(ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))),
% 0.54/0.44 inference(negated_conjecture,[status(cth)],[f281])).
% 0.54/0.44 thf(f348,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ zero_zero @ nat @ X1) => (((divide_divide @ nat @ (times_times @ nat @ X0 @ X1) @ X1)) = X0))),
% 0.54/0.44 inference(rectify,[],[f1])).
% 0.54/0.44 thf(f349,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ zero_zero @ nat @ X1)) = $true) => (((divide_divide @ nat @ (times_times @ nat @ X0 @ X1) @ X1)) = X0))),
% 0.54/0.44 inference(fool_elimination,[],[f348])).
% 0.54/0.44 thf(f370,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ (suc @ X0) @ X1) => (ord_less @ nat @ X0 @ X1))),
% 0.54/0.44 inference(rectify,[],[f78])).
% 0.54/0.44 thf(f371,plain,(
% 0.54/0.44 ! [X1 : nat,X0 : nat] : ((((ord_less @ nat @ (suc @ X0) @ X1)) = $true) => (((ord_less @ nat @ X0 @ X1)) = $true))),
% 0.54/0.44 inference(fool_elimination,[],[f370])).
% 0.54/0.44 thf(f409,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less @ nat @ X2 @ (times_times @ nat @ X0 @ X1)) => (ord_less @ nat @ (divide_divide @ nat @ X2 @ X1) @ X0))),
% 0.54/0.44 inference(rectify,[],[f97])).
% 0.54/0.44 thf(f410,plain,(
% 0.54/0.44 ! [X2 : nat,X0 : nat,X1 : nat] : (($true = ((ord_less @ nat @ X2 @ (times_times @ nat @ X0 @ X1)))) => ($true = ((ord_less @ nat @ (divide_divide @ nat @ X2 @ X1) @ X0))))),
% 0.54/0.44 inference(fool_elimination,[],[f409])).
% 0.54/0.44 thf(f437,plain,(
% 0.54/0.44 ~(ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))),
% 0.54/0.44 inference(rectify,[],[f282])).
% 0.54/0.44 thf(f438,plain,(
% 0.54/0.44 ~ (((ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))) = $true)),
% 0.54/0.44 inference(fool_elimination,[],[f437])).
% 0.54/0.44 thf(f564,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(ord_less @ nat @ X0 @ X1) => (ord_less @ nat @ X1 @ X0)))),
% 0.54/0.44 inference(rectify,[],[f33])).
% 0.54/0.44 thf(f565,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~ (((ord_less @ nat @ X0 @ X1)) = $true) => (((ord_less @ nat @ X1 @ X0)) = $true)))),
% 0.54/0.44 inference(fool_elimination,[],[f564])).
% 0.54/0.44 thf(f578,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ X0 @ X1) => (X1 != zero_zero @ nat))),
% 0.54/0.44 inference(rectify,[],[f58])).
% 0.54/0.44 thf(f579,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X0 @ X1)) = $true) => (zero_zero @ nat != X1))),
% 0.54/0.44 inference(fool_elimination,[],[f578])).
% 0.54/0.44 thf(f699,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ X0 @ X1) => (X0 != X1))),
% 0.54/0.44 inference(rectify,[],[f37])).
% 0.54/0.44 thf(f700,plain,(
% 0.54/0.44 ! [X1 : nat,X0 : nat] : ((((ord_less @ nat @ X0 @ X1)) = $true) => (X0 != X1))),
% 0.54/0.44 inference(fool_elimination,[],[f699])).
% 0.54/0.44 thf(f783,plain,(
% 0.54/0.44 (((ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))) != $true)),
% 0.54/0.44 inference(flattening,[],[f438])).
% 0.54/0.44 thf(f788,plain,(
% 0.54/0.44 ! [X1 : nat,X0 : nat] : ((X0 != X1) => ((((ord_less @ nat @ X0 @ X1)) != $true) => (((ord_less @ nat @ X1 @ X0)) = $true)))),
% 0.54/0.44 inference(flattening,[],[f565])).
% 0.54/0.44 thf(f821,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((X0 != X1) | (((ord_less @ nat @ X0 @ X1)) != $true))),
% 0.54/0.44 inference(ennf_transformation,[],[f700])).
% 0.54/0.44 thf(f841,plain,(
% 0.54/0.44 ! [X1 : nat,X0 : nat] : ((((ord_less @ nat @ X0 @ X1)) != $true) | (zero_zero @ nat != X1))),
% 0.54/0.44 inference(ennf_transformation,[],[f579])).
% 0.54/0.44 thf(f854,plain,(
% 0.54/0.44 ! [X2 : nat,X0 : nat,X1 : nat] : (($true != ((ord_less @ nat @ X2 @ (times_times @ nat @ X0 @ X1)))) | ($true = ((ord_less @ nat @ (divide_divide @ nat @ X2 @ X1) @ X0))))),
% 0.54/0.44 inference(ennf_transformation,[],[f410])).
% 0.54/0.44 thf(f858,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ (suc @ X0) @ X1)) != $true) | (((ord_less @ nat @ X0 @ X1)) = $true))),
% 0.54/0.44 inference(ennf_transformation,[],[f371])).
% 0.54/0.44 thf(f864,plain,(
% 0.54/0.44 ! [X1 : nat,X0 : nat] : (((((ord_less @ nat @ X1 @ X0)) = $true) | (((ord_less @ nat @ X0 @ X1)) = $true)) | (X0 = X1))),
% 0.54/0.44 inference(ennf_transformation,[],[f788])).
% 0.54/0.44 thf(f865,plain,(
% 0.54/0.44 ! [X1 : nat,X0 : nat] : ((((ord_less @ nat @ X1 @ X0)) = $true) | (X0 = X1) | (((ord_less @ nat @ X0 @ X1)) = $true))),
% 0.54/0.44 inference(flattening,[],[f864])).
% 0.54/0.44 thf(f868,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ zero_zero @ nat @ X1)) != $true) | (((divide_divide @ nat @ (times_times @ nat @ X0 @ X1) @ X1)) = X0))),
% 0.54/0.44 inference(ennf_transformation,[],[f349])).
% 0.54/0.44 thf(f891,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat,X2 : nat] : ((((ord_less @ nat @ X0 @ (times_times @ nat @ X1 @ X2))) != $true) | (((ord_less @ nat @ (divide_divide @ nat @ X0 @ X2) @ X1)) = $true))),
% 0.54/0.44 inference(rectify,[],[f854])).
% 0.54/0.44 thf(f892,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X0 @ X1)) = $true) | (X0 = X1) | (((ord_less @ nat @ X1 @ X0)) = $true))),
% 0.54/0.44 inference(rectify,[],[f865])).
% 0.54/0.44 thf(f897,plain,(
% 0.54/0.44 ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X1 @ X0)) != $true) | (zero_zero @ nat != X0))),
% 0.54/0.44 inference(rectify,[],[f841])).
% 0.54/0.44 thf(f938,plain,(
% 0.54/0.44 ( ! [X0 : nat] : ((((suc @ X0)) != X0)) )),
% 0.54/0.44 inference(cnf_transformation,[],[f30])).
% 0.54/0.44 thf(f948,plain,(
% 0.54/0.44 ( ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ (suc @ X0) @ X1)) != $true) | (((ord_less @ nat @ X0 @ X1)) = $true)) )),
% 0.54/0.44 inference(cnf_transformation,[],[f858])).
% 0.54/0.44 thf(f957,plain,(
% 0.54/0.44 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((ord_less @ nat @ (divide_divide @ nat @ X0 @ X2) @ X1)) = $true) | (((ord_less @ nat @ X0 @ (times_times @ nat @ X1 @ X2))) != $true)) )),
% 0.54/0.44 inference(cnf_transformation,[],[f891])).
% 0.54/0.44 thf(f958,plain,(
% 0.54/0.44 ( ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X1 @ X0)) = $true) | (((ord_less @ nat @ X0 @ X1)) = $true) | (X0 = X1)) )),
% 0.54/0.44 inference(cnf_transformation,[],[f892])).
% 0.54/0.44 thf(f965,plain,(
% 0.54/0.44 ( ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X1 @ X0)) != $true) | (zero_zero @ nat != X0)) )),
% 0.54/0.44 inference(cnf_transformation,[],[f897])).
% 0.54/0.44 thf(f996,plain,(
% 0.54/0.44 ( ! [X0 : nat,X1 : nat] : ((X0 != X1) | (((ord_less @ nat @ X0 @ X1)) != $true)) )),
% 0.54/0.44 inference(cnf_transformation,[],[f821])).
% 0.54/0.44 thf(f1005,plain,(
% 0.54/0.44 (((divide_divide @ nat @ (size_size @ list @ a @ xs) @ k)) = ((suc @ n)))),
% 0.54/0.44 inference(cnf_transformation,[],[f279])).
% 0.54/0.44 thf(f1007,plain,(
% 0.54/0.44 (zero_zero @ nat != k)),
% 0.54/0.44 inference(cnf_transformation,[],[f280])).
% 0.54/0.44 thf(f1033,plain,(
% 0.54/0.44 ( ! [X0 : nat,X1 : nat] : ((((divide_divide @ nat @ (times_times @ nat @ X0 @ X1) @ X1)) = X0) | (((ord_less @ nat @ zero_zero @ nat @ X1)) != $true)) )),
% 0.54/0.44 inference(cnf_transformation,[],[f868])).
% 0.54/0.44 thf(f1053,plain,(
% 0.54/0.44 (((ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))) != $true)),
% 0.54/0.44 inference(cnf_transformation,[],[f783])).
% 0.54/0.44 thf(f1058,plain,(
% 0.54/0.44 ( ! [X1 : nat] : (($true != ((ord_less @ nat @ X1 @ zero_zero @ nat)))) )),
% 0.54/0.44 inference(equality_resolution,[],[f965])).
% 0.54/0.44 thf(f1061,plain,(
% 0.54/0.44 ( ! [X1 : nat] : (($true != ((ord_less @ nat @ X1 @ X1)))) )),
% 0.54/0.44 inference(equality_resolution,[],[f996])).
% 0.54/0.44 thf(f1065,plain,(
% 0.54/0.44 ($true = ((ord_less @ nat @ (size_size @ list @ a @ xs) @ (times_times @ nat @ n @ k)))) | (((size_size @ list @ a @ xs)) = ((times_times @ nat @ n @ k))) | ($true != $true)),
% 0.54/0.44 inference(superposition,[],[f1053,f958])).
% 0.54/0.44 thf(f1068,plain,(
% 0.54/0.44 (((size_size @ list @ a @ xs)) = ((times_times @ nat @ n @ k))) | ($true = ((ord_less @ nat @ (size_size @ list @ a @ xs) @ (times_times @ nat @ n @ k))))),
% 0.54/0.44 inference(trivial_inequality_removal,[],[f1065])).
% 0.54/0.44 thf(f1072,definition,(
% 0.54/0.44 spl31_1 <=> (((size_size @ list @ a @ xs)) = ((times_times @ nat @ n @ k)))),
% 0.54/0.44 introduced(definition,[new_symbols(definition,[spl31_1])],[avatar_definition])).
% 0.54/0.44 thf(f1074,plain,(
% 0.54/0.44 (((size_size @ list @ a @ xs)) = ((times_times @ nat @ n @ k))) | ~spl31_1),
% 0.54/0.44 inference(avatar_component_clause,[],[f1072])).
% 0.54/0.44 thf(f1076,definition,(
% 0.54/0.44 spl31_2 <=> ($true = ((ord_less @ nat @ (size_size @ list @ a @ xs) @ (times_times @ nat @ n @ k))))),
% 0.54/0.44 introduced(definition,[new_symbols(definition,[spl31_2])],[avatar_definition])).
% 0.54/0.44 thf(f1078,plain,(
% 0.54/0.44 ($true = ((ord_less @ nat @ (size_size @ list @ a @ xs) @ (times_times @ nat @ n @ k)))) | ~spl31_2),
% 0.54/0.44 inference(avatar_component_clause,[],[f1076])).
% 0.54/0.44 thf(f1079,plain,(
% 0.54/0.44 spl31_1 | spl31_2),
% 0.54/0.44 inference(avatar_split_clause,[],[f1068,f1076,f1072])).
% 0.54/0.44 thf(f1104,plain,(
% 0.54/0.44 ( ! [X0 : nat] : (($true != ((ord_less @ nat @ (size_size @ list @ a @ xs) @ (times_times @ nat @ X0 @ k)))) | ($true = ((ord_less @ nat @ (suc @ n) @ X0)))) )),
% 0.54/0.44 inference(superposition,[],[f957,f1005])).
% 0.54/0.44 thf(f1127,definition,(
% 0.54/0.44 spl31_5 <=> ($true = ((ord_less @ nat @ zero_zero @ nat @ k)))),
% 0.54/0.44 introduced(definition,[new_symbols(definition,[spl31_5])],[avatar_definition])).
% 0.54/0.44 thf(f1128,plain,(
% 0.54/0.44 ($true = ((ord_less @ nat @ zero_zero @ nat @ k))) | ~spl31_5),
% 0.54/0.44 inference(avatar_component_clause,[],[f1127])).
% 0.54/0.44 thf(f1129,plain,(
% 0.54/0.44 ($true != ((ord_less @ nat @ zero_zero @ nat @ k))) | spl31_5),
% 0.54/0.44 inference(avatar_component_clause,[],[f1127])).
% 0.54/0.44 thf(f1157,plain,(
% 0.54/0.44 ($true = ((ord_less @ nat @ k @ zero_zero @ nat))) | ($true != $true) | (zero_zero @ nat = k) | spl31_5),
% 0.54/0.44 inference(superposition,[],[f1129,f958])).
% 0.54/0.44 thf(f1160,plain,(
% 0.54/0.44 (zero_zero @ nat = k) | ($true = ((ord_less @ nat @ k @ zero_zero @ nat))) | spl31_5),
% 0.54/0.44 inference(trivial_inequality_removal,[],[f1157])).
% 0.54/0.44 thf(f1165,plain,(
% 0.54/0.44 ($true = ((ord_less @ nat @ k @ zero_zero @ nat))) | spl31_5),
% 0.54/0.44 inference(forward_subsumption_resolution,[],[f1160,f1007])).
% 0.54/0.44 thf(f1168,plain,(
% 0.54/0.44 $false | spl31_5),
% 0.54/0.44 inference(forward_subsumption_resolution,[],[f1165,f1058])).
% 0.54/0.44 thf(f1169,plain,(
% 0.54/0.44 spl31_5),
% 0.54/0.44 inference(avatar_contradiction_clause,[],[f1168])).
% 0.54/0.44 thf(f1561,plain,(
% 0.54/0.44 ($true != $true) | ($true = ((ord_less @ nat @ (suc @ n) @ n))) | ~spl31_2),
% 0.54/0.44 inference(superposition,[],[f1104,f1078])).
% 0.54/0.44 thf(f1572,plain,(
% 0.54/0.44 ($true = ((ord_less @ nat @ (suc @ n) @ n))) | ~spl31_2),
% 0.54/0.44 inference(trivial_inequality_removal,[],[f1561])).
% 0.54/0.44 thf(f1695,plain,(
% 0.54/0.44 ($true != $true) | ($true = ((ord_less @ nat @ n @ n))) | ~spl31_2),
% 0.54/0.44 inference(superposition,[],[f948,f1572])).
% 0.54/0.44 thf(f1699,plain,(
% 0.54/0.44 ($true = ((ord_less @ nat @ n @ n))) | ~spl31_2),
% 0.54/0.44 inference(trivial_inequality_removal,[],[f1695])).
% 0.54/0.44 thf(f1710,plain,(
% 0.54/0.44 $false | ~spl31_2),
% 0.54/0.44 inference(forward_subsumption_resolution,[],[f1699,f1061])).
% 0.54/0.44 thf(f1711,plain,(
% 0.54/0.44 ~spl31_2),
% 0.54/0.44 inference(avatar_contradiction_clause,[],[f1710])).
% 0.54/0.44 thf(f1718,plain,(
% 0.54/0.44 (((suc @ n)) = ((divide_divide @ nat @ (times_times @ nat @ n @ k) @ k))) | ~spl31_1),
% 0.54/0.44 inference(superposition,[],[f1005,f1074])).
% 0.54/0.44 thf(f2447,plain,(
% 0.54/0.44 ($true != ((ord_less @ nat @ zero_zero @ nat @ k))) | (n = ((suc @ n))) | ~spl31_1),
% 0.54/0.44 inference(superposition,[],[f1033,f1718])).
% 0.54/0.44 thf(f2462,plain,(
% 0.54/0.44 (n = ((suc @ n))) | (~spl31_1 | ~spl31_5)),
% 0.54/0.44 inference(forward_subsumption_resolution,[],[f2447,f1128])).
% 0.54/0.44 thf(f2465,plain,(
% 0.54/0.44 $false | (~spl31_1 | ~spl31_5)),
% 0.54/0.44 inference(forward_subsumption_resolution,[],[f2462,f938])).
% 0.54/0.44 thf(f2466,plain,(
% 0.54/0.44 ~spl31_1 | ~spl31_5),
% 0.54/0.44 inference(avatar_contradiction_clause,[],[f2465])).
% 0.54/0.44 cnf(s1, plain, spl31_1 | spl31_2, inference(sat_conversion,[],[f1079])).
% 0.54/0.44 cnf(s9, plain, spl31_5, inference(sat_conversion,[],[f1169])).
% 0.54/0.44 cnf(s22, plain, ~spl31_2, inference(sat_conversion,[],[f1711])).
% 0.54/0.44 cnf(s41, plain, ~spl31_1 | ~spl31_5, inference(sat_conversion,[],[f2466])).
% 0.54/0.44 cnf(s42, plain, ~spl31_1, inference(rat,[],[s41,s9])).
% 0.54/0.44 cnf(s47, plain, $false, inference(rat,[],[s1,s22,s42])).
% 0.54/0.44 thf(f2467,plain,(
% 0.54/0.44 $false),
% 0.54/0.44 inference(avatar_sat_refutation,[],[s47])).
% 0.54/0.44 % SZS output end Proof for theBenchmark
% 0.54/0.44 % (1269428)------------------------------
% 0.54/0.44 % (1269428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (1269428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (1269428)CaDiCaL version: 2.1.3
% 0.54/0.44 % (1269428)Termination reason: Refutation
% 0.54/0.44 % (1269428)Time elapsed: 0.055 s
% 0.54/0.44 % (1269428)Peak memory usage: 15 MB
% 0.54/0.44 % (1269428)Instructions burned: 196 (million)
% 0.54/0.44 % (1269395)Success in time 0.159 s
% 0.54/0.44 % Vampire exiting
%------------------------------------------------------------------------------