%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT317^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 07:48:46 AM UTC 2026
% Result : Theorem 0.91s 0.45s
% Output : Refutation 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT317^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n026.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % 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 18:29:27 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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
% 0.91/0.40 % (983532)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.91/0.40 % (983547)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3562287630:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.91/0.40 % (983544)lrs+10_16_si=on:nwc=1.5:random_seed=459315697:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.91/0.40 % (983545)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2462187916:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.91/0.40 % (983543)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2201239946:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.91/0.40 % (983549)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.91/0.40 % (983549)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
% 0.91/0.40 % (983547)Instruction limit reached!
% 0.91/0.40 % (983547)------------------------------
% 0.91/0.40 % (983547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.40 % (983547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.40 % (983547)CaDiCaL version: 2.1.3
% 0.91/0.40 % (983547)Termination reason: Instruction limit
% 0.91/0.40 % (983547)Termination phase: Saturation
% 0.91/0.40 % (983547)Time elapsed: 0.007 s
% 0.91/0.40 % (983547)Peak memory usage: 12 MB
% 0.91/0.40 % (983547)Instructions burned: 24 (million)
% 0.91/0.40 % (983548)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2431292131:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.91/0.40 % (983546)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=3986304500: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)
% 0.91/0.40 % (983545)Instruction limit reached!
% 0.91/0.40 % (983545)------------------------------
% 0.91/0.40 % (983545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.40 % (983545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.40 % (983545)CaDiCaL version: 2.1.3
% 0.91/0.40 % (983545)Termination reason: Instruction limit
% 0.91/0.40 % (983545)Termination phase: Saturation
% 0.91/0.40 % (983545)Time elapsed: 0.004 s
% 0.91/0.40 % (983545)Peak memory usage: 12 MB
% 0.91/0.40 % (983545)Instructions burned: 4 (million)
% 0.91/0.40 % (983549)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=2187399450:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.91/0.40 % (983557)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4235786540:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.91/0.40 % (983544)Instruction limit reached!
% 0.91/0.40 % (983544)------------------------------
% 0.91/0.40 % (983544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.40 % (983544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.40 % (983544)CaDiCaL version: 2.1.3
% 0.91/0.40 % (983544)Termination reason: Instruction limit
% 0.91/0.40 % (983544)Termination phase: Saturation
% 0.91/0.40 % (983544)Time elapsed: 0.012 s
% 0.91/0.40 % (983544)Peak memory usage: 12 MB
% 0.91/0.40 % (983544)Instructions burned: 19 (million)
% 0.91/0.40 % (983557)Instruction limit reached!
% 0.91/0.40 % (983557)------------------------------
% 0.91/0.40 % (983557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.40 % (983557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.40 % (983557)CaDiCaL version: 2.1.3
% 0.91/0.40 % (983557)Termination reason: Instruction limit
% 0.91/0.40 % (983557)Termination phase: Saturation
% 0.91/0.40 % (983557)Time elapsed: 0.001 s
% 0.91/0.40 % (983557)Peak memory usage: 12 MB
% 0.91/0.40 % (983557)Instructions burned: 3 (million)
% 0.91/0.40 % (983567)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.91/0.40 % (983562)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2486043316:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.91/0.44 % (983567)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2135635100:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.91/0.44 % (983567)Instruction limit reached!
% 0.91/0.44 % (983567)------------------------------
% 0.91/0.44 % (983567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.44 % (983567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.44 % (983567)CaDiCaL version: 2.1.3
% 0.91/0.44 % (983567)Termination reason: Instruction limit
% 0.91/0.44 % (983567)Termination phase: Saturation
% 0.91/0.44 % (983567)Time elapsed: 0.003 s
% 0.91/0.44 % (983567)Peak memory usage: 12 MB
% 0.91/0.44 % (983567)Instructions burned: 8 (million)
% 0.91/0.44 % (983562)Instruction limit reached!
% 0.91/0.44 % (983562)------------------------------
% 0.91/0.44 % (983562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.44 % (983562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.44 % (983562)CaDiCaL version: 2.1.3
% 0.91/0.44 % (983562)Termination reason: Instruction limit
% 0.91/0.44 % (983562)Termination phase: Saturation
% 0.91/0.44 % (983562)Time elapsed: 0.004 s
% 0.91/0.44 % (983562)Peak memory usage: 12 MB
% 0.91/0.44 % (983562)Instructions burned: 5 (million)
% 0.91/0.44 % (983568)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=421413716:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.91/0.44 % (983568)Instruction limit reached!
% 0.91/0.44 % (983568)------------------------------
% 0.91/0.44 % (983568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.44 % (983568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.44 % (983568)CaDiCaL version: 2.1.3
% 0.91/0.44 % (983568)Termination reason: Instruction limit
% 0.91/0.44 % (983568)Termination phase: Saturation
% 0.91/0.44 % (983568)Time elapsed: 0.009 s
% 0.91/0.44 % (983568)Peak memory usage: 12 MB
% 0.91/0.44 % (983568)Instructions burned: 13 (million)
% 0.91/0.44 % (983576)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=432775814:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.91/0.44 % (983548)Instruction limit reached!
% 0.91/0.44 % (983548)------------------------------
% 0.91/0.44 % (983548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.44 % (983548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.44 % (983548)CaDiCaL version: 2.1.3
% 0.91/0.44 % (983548)Termination reason: Instruction limit
% 0.91/0.44 % (983548)Termination phase: Saturation
% 0.91/0.44 % (983548)Time elapsed: 0.044 s
% 0.91/0.44 % (983548)Peak memory usage: 13 MB
% 0.91/0.44 % (983548)Instructions burned: 75 (million)
% 0.91/0.44 % (983575)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
% 0.91/0.44 % (983575)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.91/0.44 % (983543)Instruction limit reached!
% 0.91/0.44 % (983543)------------------------------
% 0.91/0.44 % (983543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.44 % (983543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.44 % (983543)CaDiCaL version: 2.1.3
% 0.91/0.44 % (983543)Termination reason: Instruction limit
% 0.91/0.44 % (983543)Termination phase: Saturation
% 0.91/0.44 % (983543)Time elapsed: 0.049 s
% 0.91/0.44 % (983543)Peak memory usage: 12 MB
% 0.91/0.44 % (983543)Instructions burned: 88 (million)
% 0.91/0.44 % (983575)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3429138154:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.91/0.44 % (983579)lrs+10_1_si=on:cs=on:random_seed=1705826680:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.91/0.44 % (983581)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.91/0.45 % (983581)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=1156764997:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.91/0.45 % (983579)Instruction limit reached!
% 0.91/0.45 % (983579)------------------------------
% 0.91/0.45 % (983579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.45 % (983579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.45 % (983579)CaDiCaL version: 2.1.3
% 0.91/0.45 % (983579)Termination reason: Instruction limit
% 0.91/0.45 % (983579)Termination phase: Saturation
% 0.91/0.45 % (983579)Time elapsed: 0.008 s
% 0.91/0.45 % (983579)Peak memory usage: 12 MB
% 0.91/0.45 % (983579)Instructions burned: 16 (million)
% 0.91/0.45 % (983581)Instruction limit reached!
% 0.91/0.45 % (983581)------------------------------
% 0.91/0.45 % (983581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.45 % (983581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.45 % (983581)CaDiCaL version: 2.1.3
% 0.91/0.45 % (983581)Termination reason: Instruction limit
% 0.91/0.45 % (983581)Termination phase: Saturation
% 0.91/0.45 % (983581)Time elapsed: 0.003 s
% 0.91/0.45 % (983581)Peak memory usage: 12 MB
% 0.91/0.45 % (983581)Instructions burned: 4 (million)
% 0.91/0.45 % (983582)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=188813912:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.91/0.45 % (983575)Instruction limit reached!
% 0.91/0.45 % (983575)------------------------------
% 0.91/0.45 % (983575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.45 % (983575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.45 % (983575)CaDiCaL version: 2.1.3
% 0.91/0.45 % (983575)Termination reason: Instruction limit
% 0.91/0.45 % (983575)Termination phase: Saturation
% 0.91/0.45 % (983575)Time elapsed: 0.018 s
% 0.91/0.45 % (983575)Peak memory usage: 12 MB
% 0.91/0.45 % (983575)Instructions burned: 28 (million)
% 0.91/0.45 % (983549)Instruction limit reached!
% 0.91/0.45 % (983549)------------------------------
% 0.91/0.45 % (983549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.45 % (983549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.45 % (983549)CaDiCaL version: 2.1.3
% 0.91/0.45 % (983549)Termination reason: Instruction limit
% 0.91/0.45 % (983549)Termination phase: Saturation
% 0.91/0.45 % (983549)Time elapsed: 0.081 s
% 0.91/0.45 % (983549)Peak memory usage: 12 MB
% 0.91/0.45 % (983549)Instructions burned: 157 (million)
% 0.91/0.45 % (983594)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2349894767:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.91/0.45 % (983608)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2641057570:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.91/0.45 % (983576)Instruction limit reached!
% 0.91/0.45 % (983576)------------------------------
% 0.91/0.45 % (983576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.45 % (983576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.45 % (983576)CaDiCaL version: 2.1.3
% 0.91/0.45 % (983576)Termination reason: Instruction limit
% 0.91/0.45 % (983576)Termination phase: Saturation
% 0.91/0.45 % (983576)Time elapsed: 0.054 s
% 0.91/0.45 % (983576)Peak memory usage: 13 MB
% 0.91/0.45 % (983576)Instructions burned: 86 (million)
% 0.91/0.45 % (983595)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1349206932:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.91/0.45 % (983595)Instruction limit reached!
% 0.91/0.45 % (983595)------------------------------
% 0.91/0.45 % (983595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.45 % (983595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.45 % (983595)CaDiCaL version: 2.1.3
% 0.91/0.45 % (983595)Termination reason: Instruction limit
% 0.91/0.45 % (983595)Termination phase: Saturation
% 0.91/0.45 % (983595)Time elapsed: 0.014 s
% 0.91/0.45 % (983595)Peak memory usage: 12 MB
% 0.91/0.45 % (983595)Instructions burned: 14 (million)
% 0.91/0.45 % (983594)Instruction limit reached!
% 0.91/0.45 % (983594)------------------------------
% 0.91/0.45 % (983594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.45 % (983594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.45 % (983594)CaDiCaL version: 2.1.3
% 0.91/0.45 % (983594)Termination reason: Instruction limit
% 0.91/0.45 % (983594)Termination phase: Saturation
% 0.91/0.45 % (983594)Time elapsed: 0.023 s
% 0.91/0.45 % (983594)Peak memory usage: 12 MB
% 0.91/0.45 % (983594)Instructions burned: 26 (million)
% 0.91/0.45 % (983611)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=4231716491:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.91/0.45 % (983582)Instruction limit reached!
% 0.91/0.45 % (983582)------------------------------
% 0.91/0.45 % (983582)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.45 % (983582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.45 % (983582)CaDiCaL version: 2.1.3
% 0.91/0.45 % (983582)Termination reason: Instruction limit
% 0.91/0.45 % (983582)Termination phase: Saturation
% 0.91/0.45 % (983582)Time elapsed: 0.053 s
% 0.91/0.45 % (983582)Peak memory usage: 12 MB
% 0.91/0.45 % (983582)Instructions burned: 38 (million)
% 0.91/0.45 % (983611)Instruction limit reached!
% 0.91/0.45 % (983611)------------------------------
% 0.91/0.45 % (983611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.45 % (983611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.45 % (983611)CaDiCaL version: 2.1.3
% 0.91/0.45 % (983611)Termination reason: Instruction limit
% 0.91/0.45 % (983611)Termination phase: Saturation
% 0.91/0.45 % (983611)Time elapsed: 0.007 s
% 0.91/0.45 % (983611)Peak memory usage: 12 MB
% 0.91/0.45 % (983611)Instructions burned: 15 (million)
% 0.91/0.45 % (983593)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3474962542:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.91/0.45 % (983593)Refutation not found, incomplete strategy
% 0.91/0.45 % (983593)------------------------------
% 0.91/0.45 % (983593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.45 % (983593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.45 % (983593)CaDiCaL version: 2.1.3
% 0.91/0.45 % (983593)Termination reason: Refutation not found, incomplete strategy
% 0.91/0.45 % (983593)Time elapsed: 0.002 s
% 0.91/0.45 % (983593)Peak memory usage: 12 MB
% 0.91/0.45 % (983593)------------------------------
% 0.91/0.45 % (983593)------------------------------
% 0.91/0.45 % (983624)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2767792201:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.91/0.45 % (983620)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2889444767:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.91/0.45 % (983621)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=250852701:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.91/0.45 % (983619)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2896185711: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)
% 0.91/0.45 % (983619)Instruction limit reached!
% 0.91/0.45 % (983619)------------------------------
% 0.91/0.45 % (983619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.45 % (983619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.45 % (983619)CaDiCaL version: 2.1.3
% 0.91/0.45 % (983619)Termination reason: Instruction limit
% 0.91/0.45 % (983619)Termination phase: Saturation
% 0.91/0.45 % (983619)Time elapsed: 0.003 s
% 0.91/0.45 % (983619)Peak memory usage: 12 MB
% 0.91/0.45 % (983619)Instructions burned: 2 (million)
% 0.91/0.45 % (983627)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 0.91/0.45 % (983627)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.91/0.45 % (983627)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=205963283:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.91/0.45 % (983624) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-983532-983624"...
% 0.91/0.45 % (983621)Instruction limit reached!
% 0.91/0.45 % (983621)------------------------------
% 0.91/0.45 % (983621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.45 % (983621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.45 % (983621)CaDiCaL version: 2.1.3
% 0.91/0.45 % (983621)Termination reason: Instruction limit
% 0.91/0.45 % (983621)Termination phase: Saturation
% 0.91/0.45 % (983621)Time elapsed: 0.018 s
% 0.91/0.45 % (983621)Peak memory usage: 11 MB
% 0.91/0.45 % (983621)Instructions burned: 24 (million)
% 0.91/0.45 % (983620)Instruction limit reached!
% 0.91/0.45 % (983620)------------------------------
% 0.91/0.45 % (983620)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.45 % (983620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.45 % (983620)CaDiCaL version: 2.1.3
% 0.91/0.45 % (983620)Termination reason: Instruction limit
% 0.91/0.45 % (983620)Termination phase: Saturation
% 0.91/0.45 % (983620)Time elapsed: 0.025 s
% 0.91/0.45 % (983620)Peak memory usage: 12 MB
% 0.91/0.45 % (983620)Instructions burned: 26 (million)
% 0.91/0.45 % (983624)...printing done.
% 0.91/0.45 % (983627)Instruction limit reached!
% 0.91/0.45 % (983627)------------------------------
% 0.91/0.45 % (983627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.45 % (983627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.45 % (983627)CaDiCaL version: 2.1.3
% 0.91/0.45 % (983627)Termination reason: Instruction limit
% 0.91/0.45 % (983627)Termination phase: Saturation
% 0.91/0.45 % (983627)Time elapsed: 0.011 s
% 0.91/0.45 % (983627)Peak memory usage: 12 MB
% 0.91/0.45 % (983627)Instructions burned: 14 (million)
% 0.91/0.45 % (983624)Refutation found. Thanks to Tanya!
% 0.91/0.45 % SZS status Theorem for theBenchmark
% 0.91/0.45 % SZS output start Proof for theBenchmark
% 0.91/0.45 thf(type_def_5, type, 'type/ind_types/list': $tType > $tType).
% 0.91/0.45 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.91/0.45 thf(type_def_7, type, sK2: $tType).
% 0.91/0.45 thf(func_def_0, type, 'const/lists/TL': !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.91/0.46 thf(func_def_1, type, 'const/lists/HD': !>[X0: $tType]:(('type/ind_types/list' @ X0 > X0))).
% 0.91/0.46 thf(func_def_2, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 0.91/0.46 thf(func_def_3, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.91/0.46 thf(func_def_7, type, sK0: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0))).
% 0.91/0.46 thf(func_def_8, type, sK1: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > X0))).
% 0.91/0.46 thf(func_def_9, type, sK3: 'type/ind_types/list' @ sK2).
% 0.91/0.46 thf(func_def_10, type, sF4: 'type/ind_types/list' @ sK2).
% 0.91/0.46 thf(func_def_11, type, sF5: sK2).
% 0.91/0.46 thf(func_def_12, type, sF6: 'type/ind_types/list' @ sK2).
% 0.91/0.46 thf(func_def_13, type, sF7: 'type/ind_types/list' @ sK2).
% 0.91/0.46 thf(func_def_14, type, vNOT: ($o > $o)).
% 0.91/0.46 thf(func_def_15, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.91/0.46 thf(func_def_16, type, db0: !>[X0: $tType]:(X0)).
% 0.91/0.46 thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.91/0.46 thf(f1,axiom,(
% 0.91/0.46 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((! [X3 : 'type/ind_types/list' @ X0,X2 : X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) & (X1 @ 'const/ind_types/NIL' @ X0)) => ! [X2 : 'type/ind_types/list' @ X0] : (X1 @ X2))),
% 0.91/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/ind_types/list_INDUCT_')).
% 0.91/0.46 thf(f2,axiom,(
% 0.91/0.46 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = X2)),
% 0.91/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/TL_')).
% 0.91/0.46 thf(f3,axiom,(
% 0.91/0.46 ! [X0 : $tType,X2 : X0,X1 : 'type/ind_types/list' @ X0] : ((('const/lists/HD' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1))) = X2)),
% 0.91/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/HD_')).
% 0.91/0.46 thf(f5,conjecture,(
% 0.91/0.46 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((X1 != 'const/ind_types/NIL' @ X0) => (X1 = (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ ('const/lists/TL' @ X0 @ X1)))))),
% 0.91/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/CONS_HD_TL_')).
% 0.91/0.46 thf(f6,negated_conjecture,(
% 0.91/0.46 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((X1 != 'const/ind_types/NIL' @ X0) => (X1 = (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ ('const/lists/TL' @ X0 @ X1)))))),
% 0.91/0.46 inference(negated_conjecture,[status(cth)],[f5])).
% 0.91/0.46 thf(f7,plain,(
% 0.91/0.46 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((! [X2 : 'type/ind_types/list' @ X0,X3 : X0] : ((X1 @ X2) => (X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2))) & (X1 @ 'const/ind_types/NIL' @ X0)) => ! [X4 : 'type/ind_types/list' @ X0] : (X1 @ X4))),
% 0.91/0.46 inference(rectify,[],[f1])).
% 0.91/0.46 thf(f8,plain,(
% 0.91/0.46 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((! [X3 : X0,X2 : 'type/ind_types/list' @ X0] : ((((X1 @ X2)) = $true) => ($true = ((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2))))) & (((X1 @ 'const/ind_types/NIL' @ X0)) = $true)) => ! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true))),
% 0.91/0.46 inference(fool_elimination,[],[f7])).
% 0.91/0.46 thf(f10,plain,(
% 0.91/0.46 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true) | (? [X2 : 'type/ind_types/list' @ X0,X3 : X0] : (($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2)))) & (((X1 @ X2)) = $true)) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true)))),
% 0.91/0.46 inference(ennf_transformation,[],[f8])).
% 0.91/0.46 thf(f11,plain,(
% 0.91/0.46 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | ? [X2 : 'type/ind_types/list' @ X0,X3 : X0] : (($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2)))) & (((X1 @ X2)) = $true)) | ! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true))),
% 0.91/0.46 inference(flattening,[],[f10])).
% 0.91/0.46 thf(f12,plain,(
% 0.91/0.46 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((X1 != 'const/ind_types/NIL' @ X0) & ((('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ ('const/lists/TL' @ X0 @ X1))) != X1))),
% 0.91/0.46 inference(ennf_transformation,[],[f6])).
% 0.91/0.46 thf(f13,plain,(
% 0.91/0.46 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/HD' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = X1)),
% 0.91/0.46 inference(rectify,[],[f3])).
% 0.91/0.46 thf(f14,plain,(
% 0.91/0.46 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | (($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ X1) @ (sK0 @ X0 @ X1))))) & ($true = ((X1 @ (sK0 @ X0 @ X1))))) | ! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true))),
% 0.91/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X3,sK1 @ X0 @ X1),skolemize(X3,sK1 @ X0 @ X1)],[f11])).
% 0.91/0.46 thf(f16,plain,(
% 0.91/0.46 ('const/ind_types/NIL' @ sK2 != sK3) & ((('const/ind_types/CONS' @ sK2 @ ('const/lists/HD' @ sK2 @ sK3) @ ('const/lists/TL' @ sK2 @ sK3))) != sK3)),
% 0.91/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f12])).
% 0.91/0.46 thf(f17,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/HD' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = X1)) )),
% 0.91/0.46 inference(cnf_transformation,[],[f13])).
% 0.91/0.46 thf(f19,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o),X4 : 'type/ind_types/list' @ X0] : (($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ X1) @ (sK0 @ X0 @ X1))))) | (((X1 @ X4)) = $true) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true)) )),
% 0.91/0.46 inference(cnf_transformation,[],[f14])).
% 0.91/0.46 thf(f20,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = X2)) )),
% 0.91/0.46 inference(cnf_transformation,[],[f2])).
% 0.91/0.46 thf(f22,plain,(
% 0.91/0.46 ((('const/ind_types/CONS' @ sK2 @ ('const/lists/HD' @ sK2 @ sK3) @ ('const/lists/TL' @ sK2 @ sK3))) != sK3)),
% 0.91/0.46 inference(cnf_transformation,[],[f16])).
% 0.91/0.46 thf(f23,plain,(
% 0.91/0.46 ('const/ind_types/NIL' @ sK2 != sK3)),
% 0.91/0.46 inference(cnf_transformation,[],[f16])).
% 0.91/0.46 thf(f26,definition,(
% 0.91/0.46 (sF4 = 'const/ind_types/NIL' @ sK2)),
% 0.91/0.46 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 0.91/0.46 thf(f27,plain,(
% 0.91/0.46 ('const/ind_types/NIL' @ sK2 = sF4)),
% 0.91/0.46 inference(reorient_equations,[],[f26])).
% 0.91/0.46 thf(f28,plain,(
% 0.91/0.46 (sF4 != sK3)),
% 0.91/0.46 inference(definition_folding,[],[f23,f27])).
% 0.91/0.46 thf(f29,definition,(
% 0.91/0.46 (sF5 = (('const/lists/HD' @ sK2 @ sK3)))),
% 0.91/0.46 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 0.91/0.46 thf(f30,plain,(
% 0.91/0.46 ((('const/lists/HD' @ sK2 @ sK3)) = sF5)),
% 0.91/0.46 inference(reorient_equations,[],[f29])).
% 0.91/0.46 thf(f31,definition,(
% 0.91/0.46 (sF6 = (('const/lists/TL' @ sK2 @ sK3)))),
% 0.91/0.46 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
% 0.91/0.46 thf(f32,plain,(
% 0.91/0.46 ((('const/lists/TL' @ sK2 @ sK3)) = sF6)),
% 0.91/0.46 inference(reorient_equations,[],[f31])).
% 0.91/0.46 thf(f33,definition,(
% 0.91/0.46 (sF7 = (('const/ind_types/CONS' @ sK2 @ sF5 @ sF6)))),
% 0.91/0.46 introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
% 0.91/0.46 thf(f34,plain,(
% 0.91/0.46 (sF7 != sK3)),
% 0.91/0.46 inference(definition_folding,[],[f22,f33,f32,f30])).
% 0.91/0.46 thf(f104,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ($true != (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ 'const/ind_types/NIL' @ X0)))) )),
% 0.91/0.46 inference(leibniz_equality_elimination,[],[f19])).
% 0.91/0.46 thf(f107,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X4 : 'type/ind_types/list' @ X0,X5 : ('type/ind_types/list' @ X0 > $o)] : (((((^[Y0 : 'type/ind_types/list' @ X0]: (~ (X5 @ Y0))) @ X4)) = $true) | ($true != (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (X5 @ Y0))) @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X5 @ Y0)))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X5 @ Y0)))))))) | ($true != (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (X5 @ Y0))) @ 'const/ind_types/NIL' @ X0)))) )),
% 0.91/0.46 inference(primitive_instantiation,[],[f19])).
% 0.91/0.46 thf(f116,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ($true != ((~ ('const/ind_types/NIL' @ X0 = X1))))) )),
% 0.91/0.46 inference(beta-eta_normalization,[],[f104])).
% 0.91/0.46 thf(f117,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (($true = (('const/ind_types/NIL' @ X0 = X1))) | ((('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1)) )),
% 0.91/0.46 inference(not_proxy_clausification,[],[f116])).
% 0.91/0.46 thf(f118,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 0.91/0.46 inference(equality_proxy_clausification,[],[f117])).
% 0.91/0.46 thf(f132,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X4 : 'type/ind_types/list' @ X0,X5 : ('type/ind_types/list' @ X0 > $o)] : (($true != ((~ (X5 @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X5 @ Y0)))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X5 @ Y0))))))))) | ($true = ((~ (X5 @ X4)))) | (((~ (X5 @ 'const/ind_types/NIL' @ X0))) != $true)) )),
% 0.91/0.46 inference(beta-eta_normalization,[],[f107])).
% 0.91/0.46 thf(f133,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X4 : 'type/ind_types/list' @ X0,X5 : ('type/ind_types/list' @ X0 > $o)] : ((((X5 @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X5 @ Y0)))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X5 @ Y0))))))) = $true) | (((~ (X5 @ 'const/ind_types/NIL' @ X0))) != $true) | ($true = ((~ (X5 @ X4))))) )),
% 0.91/0.46 inference(not_proxy_clausification,[],[f132])).
% 0.91/0.46 thf(f134,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X4 : 'type/ind_types/list' @ X0,X5 : ('type/ind_types/list' @ X0 > $o)] : (($true = ((X5 @ 'const/ind_types/NIL' @ X0))) | ($true = ((~ (X5 @ X4)))) | (((X5 @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X5 @ Y0)))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X5 @ Y0))))))) = $true)) )),
% 0.91/0.46 inference(not_proxy_clausification,[],[f133])).
% 0.91/0.46 thf(f135,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X4 : 'type/ind_types/list' @ X0,X5 : ('type/ind_types/list' @ X0 > $o)] : ((((X5 @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X5 @ Y0)))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X5 @ Y0))))))) = $true) | ($true = ((X5 @ 'const/ind_types/NIL' @ X0))) | (((X5 @ X4)) = $false)) )),
% 0.91/0.46 inference(not_proxy_clausification,[],[f134])).
% 0.91/0.46 thf(f187,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X6 : ('type/ind_types/list' @ X0 > $o),X4 : 'type/ind_types/list' @ X0] : (($true = (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (X6 @ Y0))) @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ ((^[Y1 : 'type/ind_types/list' @ X0]: (~ (X6 @ Y1))) @ Y0)))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ ((^[Y1 : 'type/ind_types/list' @ X0]: (~ (X6 @ Y1))) @ Y0)))))))) | ($false = (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (X6 @ Y0))) @ X4))) | ($true = (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (X6 @ Y0))) @ 'const/ind_types/NIL' @ X0)))) )),
% 0.91/0.46 inference(primitive_instantiation,[],[f135])).
% 0.91/0.46 thf(f199,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X6 : ('type/ind_types/list' @ X0 > $o),X4 : 'type/ind_types/list' @ X0] : ((((~ (X6 @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (~ (X6 @ Y0))))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (~ (X6 @ Y0))))))))) = $true) | ($false = ((~ (X6 @ X4)))) | (((~ (X6 @ 'const/ind_types/NIL' @ X0))) = $true)) )),
% 0.91/0.46 inference(beta-eta_normalization,[],[f187])).
% 0.91/0.46 thf(f200,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X6 : ('type/ind_types/list' @ X0 > $o),X4 : 'type/ind_types/list' @ X0] : (($false = ((~ (X6 @ X4)))) | ($false = ((X6 @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (~ (X6 @ Y0))))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (~ (X6 @ Y0))))))))) | (((~ (X6 @ 'const/ind_types/NIL' @ X0))) = $true)) )),
% 0.91/0.46 inference(not_proxy_clausification,[],[f199])).
% 0.91/0.46 thf(f201,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X6 : ('type/ind_types/list' @ X0 > $o),X4 : 'type/ind_types/list' @ X0] : (($false = ((X6 @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (~ (X6 @ Y0))))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (~ (X6 @ Y0))))))))) | (((X6 @ X4)) = $true) | (((~ (X6 @ 'const/ind_types/NIL' @ X0))) = $true)) )),
% 0.91/0.46 inference(not_proxy_clausification,[],[f200])).
% 0.91/0.46 thf(f202,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X6 : ('type/ind_types/list' @ X0 > $o),X4 : 'type/ind_types/list' @ X0] : (($false = ((X6 @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (~ (X6 @ Y0))))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (~ (X6 @ Y0))))))))) | (((X6 @ 'const/ind_types/NIL' @ X0)) = $false) | (((X6 @ X4)) = $true)) )),
% 0.91/0.46 inference(not_proxy_clausification,[],[f201])).
% 0.91/0.46 thf(f203,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X6 : ('type/ind_types/list' @ X0 > $o),X4 : 'type/ind_types/list' @ X0] : ((((X6 @ X4)) = $true) | ($false = ((X6 @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (X6 @ Y0))) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (X6 @ Y0))))))) | (((X6 @ 'const/ind_types/NIL' @ X0)) = $false)) )),
% 0.91/0.46 inference(boolean_simplification,[],[f202])).
% 0.91/0.46 thf(f204,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X6 : ('type/ind_types/list' @ X0 > $o),X4 : 'type/ind_types/list' @ X0] : ((((X6 @ ('const/ind_types/CONS' @ X0 @ (sK1 @ X0 @ X6) @ (sK0 @ X0 @ X6)))) = $false) | (((X6 @ 'const/ind_types/NIL' @ X0)) = $false) | (((X6 @ X4)) = $true)) )),
% 0.91/0.46 inference(beta-eta_normalization,[],[f203])).
% 0.91/0.46 thf(f395,plain,(
% 0.91/0.46 ( ! [X1 : $tType,X0 : 'type/ind_types/list' @ X1] : (((('const/lists/HD' @ X1 @ X0)) = ((sK1 @ X1 @ (^[Y0 : 'type/ind_types/list' @ X1]: (~ (Y0 = X0)))))) | ('const/ind_types/NIL' @ X1 = X0)) )),
% 0.91/0.46 inference(superposition,[],[f17,f118])).
% 0.91/0.46 thf(f416,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) | ($false = (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ 'const/ind_types/NIL' @ X0))) | ((((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ X2)) = $true) | ((((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ ('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))))))) = $false)) )),
% 0.91/0.46 inference(superposition,[],[f204,f395])).
% 0.91/0.46 thf(f418,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (($true = ((~ (X2 = X1)))) | (((~ (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))))) = X1))) = $false) | (((~ ('const/ind_types/NIL' @ X0 = X1))) = $false) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 0.91/0.46 inference(beta-eta_normalization,[],[f416])).
% 0.91/0.46 thf(f419,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (($false = ((X2 = X1))) | (((~ ('const/ind_types/NIL' @ X0 = X1))) = $false) | ('const/ind_types/NIL' @ X0 = X1) | (((~ (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))))) = X1))) = $false)) )),
% 0.91/0.46 inference(not_proxy_clausification,[],[f418])).
% 0.91/0.46 thf(f420,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : ((((~ ('const/ind_types/NIL' @ X0 = X1))) = $false) | ('const/ind_types/NIL' @ X0 = X1) | (X1 != X2) | (((~ (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))))) = X1))) = $false)) )),
% 0.91/0.46 inference(equality_proxy_clausification,[],[f419])).
% 0.91/0.46 thf(f421,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (($true = (('const/ind_types/NIL' @ X0 = X1))) | (((~ (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))))) = X1))) = $false) | (X1 != X2) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 0.91/0.46 inference(not_proxy_clausification,[],[f420])).
% 0.91/0.46 thf(f422,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : ((((~ (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))))) = X1))) = $false) | (X1 != X2) | ('const/ind_types/NIL' @ X0 = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 0.91/0.46 inference(equality_proxy_clausification,[],[f421])).
% 0.91/0.46 thf(f423,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) | ($true = ((('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))))) = X1))) | ('const/ind_types/NIL' @ X0 = X1) | (X1 != X2)) )),
% 0.91/0.46 inference(not_proxy_clausification,[],[f422])).
% 0.91/0.46 thf(f424,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : ((X1 != X2) | ((('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ('const/ind_types/NIL' @ X0 = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 0.91/0.46 inference(equality_proxy_clausification,[],[f423])).
% 0.91/0.46 thf(f425,plain,(
% 0.91/0.46 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ('const/ind_types/NIL' @ X0 = X1) | (X1 != X2)) )),
% 0.91/0.46 inference(duplicate_literal_removal,[],[f424])).
% 0.91/0.46 thf(f479,plain,(
% 0.91/0.46 ( ! [X0 : 'type/ind_types/list' @ sK2] : (('const/ind_types/NIL' @ sK2 = sK3) | (sK3 != X0) | ((('const/ind_types/CONS' @ sK2 @ sF5 @ (sK0 @ sK2 @ (^[Y0 : 'type/ind_types/list' @ sK2]: (~ (Y0 = sK3)))))) = sK3)) )),
% 0.91/0.46 inference(superposition,[],[f425,f30])).
% 0.91/0.46 thf(f494,plain,(
% 0.91/0.46 ( ! [X0 : 'type/ind_types/list' @ sK2] : ((sK3 != X0) | ((('const/ind_types/CONS' @ sK2 @ sF5 @ (sK0 @ sK2 @ (^[Y0 : 'type/ind_types/list' @ sK2]: (~ (Y0 = sK3)))))) = sK3) | (sF4 = sK3)) )),
% 0.91/0.46 inference(forward_demodulation,[],[f479,f27])).
% 0.91/0.46 thf(f523,plain,(
% 0.91/0.46 ( ! [X0 : 'type/ind_types/list' @ sK2] : ((sK3 != X0) | ((('const/ind_types/CONS' @ sK2 @ sF5 @ (sK0 @ sK2 @ (^[Y0 : 'type/ind_types/list' @ sK2]: (~ (Y0 = sK3)))))) = sK3)) )),
% 0.91/0.46 inference(forward_subsumption_resolution,[],[f494,f28])).
% 0.91/0.46 thf(f528,definition,(
% 0.91/0.46 spl8_16 <=> ((('const/ind_types/CONS' @ sK2 @ sF5 @ (sK0 @ sK2 @ (^[Y0 : 'type/ind_types/list' @ sK2]: (~ (Y0 = sK3)))))) = sK3)),
% 0.91/0.46 introduced(definition,[new_symbols(definition,[spl8_16])],[avatar_definition])).
% 0.91/0.46 thf(f530,plain,(
% 0.91/0.46 ((('const/ind_types/CONS' @ sK2 @ sF5 @ (sK0 @ sK2 @ (^[Y0 : 'type/ind_types/list' @ sK2]: (~ (Y0 = sK3)))))) = sK3) | ~spl8_16),
% 0.91/0.46 inference(avatar_component_clause,[],[f528])).
% 0.91/0.46 thf(f532,definition,(
% 0.91/0.46 spl8_17 <=> ! [X0 : 'type/ind_types/list' @ sK2] : (sK3 != X0)),
% 0.91/0.46 introduced(definition,[new_symbols(definition,[spl8_17])],[avatar_definition])).
% 0.91/0.46 thf(f533,plain,(
% 0.91/0.46 ( ! [X0 : 'type/ind_types/list' @ sK2] : ((sK3 != X0)) ) | ~spl8_17),
% 0.91/0.46 inference(avatar_component_clause,[],[f532])).
% 0.91/0.46 thf(f534,plain,(
% 0.91/0.46 spl8_16 | spl8_17),
% 0.91/0.46 inference(avatar_split_clause,[],[f523,f532,f528])).
% 0.91/0.46 thf(f560,plain,(
% 0.91/0.46 ((('const/lists/TL' @ sK2 @ sK3)) = ((sK0 @ sK2 @ (^[Y0 : 'type/ind_types/list' @ sK2]: (~ (Y0 = sK3)))))) | ~spl8_16),
% 0.91/0.46 inference(superposition,[],[f20,f530])).
% 0.91/0.46 thf(f564,plain,(
% 0.91/0.46 (sF6 = ((sK0 @ sK2 @ (^[Y0 : 'type/ind_types/list' @ sK2]: (~ (Y0 = sK3)))))) | ~spl8_16),
% 0.91/0.46 inference(forward_demodulation,[],[f560,f32])).
% 0.91/0.46 thf(f566,plain,(
% 0.91/0.46 ((('const/ind_types/CONS' @ sK2 @ sF5 @ sF6)) = sK3) | ~spl8_16),
% 0.91/0.46 inference(superposition,[],[f530,f564])).
% 0.91/0.46 thf(f606,plain,(
% 0.91/0.46 $false | ~spl8_17),
% 0.91/0.46 inference(equality_resolution,[],[f533])).
% 0.91/0.46 thf(f609,plain,(
% 0.91/0.46 ~spl8_17),
% 0.91/0.46 inference(avatar_contradiction_clause,[],[f606])).
% 0.91/0.46 thf(f611,plain,(
% 0.91/0.46 (sF7 = sK3) | ~spl8_16),
% 0.91/0.46 inference(superposition,[],[f33,f566])).
% 0.91/0.46 thf(f619,plain,(
% 0.91/0.46 $false | ~spl8_16),
% 0.91/0.46 inference(forward_subsumption_resolution,[],[f611,f34])).
% 0.91/0.46 thf(f620,plain,(
% 0.91/0.46 ~spl8_16),
% 0.91/0.46 inference(avatar_contradiction_clause,[],[f619])).
% 0.91/0.46 cnf(s15, plain, spl8_16 | spl8_17, inference(sat_conversion,[],[f534])).
% 0.91/0.46 cnf(s23, plain, ~spl8_17, inference(sat_conversion,[],[f609])).
% 0.91/0.46 cnf(s25, plain, ~spl8_16, inference(sat_conversion,[],[f620])).
% 0.91/0.46 cnf(s26, plain, $false, inference(rat,[],[s15,s23,s25])).
% 0.91/0.46 thf(f621,plain,(
% 0.91/0.46 $false),
% 0.91/0.46 inference(avatar_sat_refutation,[],[s26])).
% 0.91/0.46 % SZS output end Proof for theBenchmark
% 0.91/0.46 % (983624)------------------------------
% 0.91/0.46 % (983624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.91/0.46 % (983624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.91/0.46 % (983624)CaDiCaL version: 2.1.3
% 0.91/0.46 % (983624)Termination reason: Refutation
% 0.91/0.46 % (983624)Time elapsed: 0.026 s
% 0.91/0.46 % (983624)Peak memory usage: 13 MB
% 0.91/0.46 % (983624)Instructions burned: 49 (million)
% 0.91/0.46 % (983532)Success in time 0.219 s
% 0.91/0.46 % Vampire exiting
%------------------------------------------------------------------------------