%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP101^2 : 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 : n008.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 0.61s 0.40s
% Output : Refutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP101^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.17 % Computer : n008.cluster.edu
% 0.05/0.17 % Model : x86_64 x86_64
% 0.05/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.17 % Memory : 8046.5625MB
% 0.05/0.17 % OS : Linux 6.8.0-71-generic
% 0.05/0.17 % CPULimit : 300
% 0.05/0.17 % WCLimit : 300
% 0.05/0.17 % DateTime : Tue Sep 29 19:54:24 UTC 2026
% 0.05/0.17 % CPUTime :
% 0.05/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.21 Running higher-order theorem proving
% 0.22/0.26 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
% 0.61/0.39 % (3649676)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.61/0.39 % (3649686)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3101659969:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.61/0.39 % (3649687)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.61/0.39 % (3649687)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
% 0.61/0.39 % (3649681)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=416104870:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.61/0.39 % (3649682)lrs+10_16_si=on:nwc=1.5:random_seed=595262490:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.61/0.39 % (3649683)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3463138732:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.61/0.39 % (3649684)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=2065363722: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)
% 0.61/0.39 % (3649685)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4833846:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.61/0.39 % (3649687)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=4237623550:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.61/0.39 % (3649683)Instruction limit reached!
% 0.61/0.39 % (3649683)------------------------------
% 0.61/0.39 % (3649683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3649683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3649683)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3649683)Termination reason: Instruction limit
% 0.61/0.39 % (3649683)Termination phase: shuffling
% 0.61/0.39 % (3649683)Time elapsed: 0.002 s
% 0.61/0.39 % (3649683)Peak memory usage: 10 MB
% 0.61/0.39 % (3649683)Instructions burned: 3 (million)
% 0.61/0.39 % (3649682)Instruction limit reached!
% 0.61/0.39 % (3649682)------------------------------
% 0.61/0.39 % (3649682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3649682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3649682)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3649682)Termination reason: Instruction limit
% 0.61/0.39 % (3649682)Termination phase: Property scanning
% 0.61/0.39 % (3649682)Time elapsed: 0.010 s
% 0.61/0.39 % (3649682)Peak memory usage: 10 MB
% 0.61/0.39 % (3649682)Instructions burned: 20 (million)
% 0.61/0.39 % (3649685)Instruction limit reached!
% 0.61/0.39 % (3649685)------------------------------
% 0.61/0.39 % (3649685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3649685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3649685)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3649685)Termination reason: Instruction limit
% 0.61/0.39 % (3649685)Termination phase: Property scanning
% 0.61/0.39 % (3649685)Time elapsed: 0.011 s
% 0.61/0.39 % (3649685)Peak memory usage: 10 MB
% 0.61/0.39 % (3649685)Instructions burned: 24 (million)
% 0.61/0.39 % (3649686)Instruction limit reached!
% 0.61/0.39 % (3649686)------------------------------
% 0.61/0.39 % (3649686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.39 % (3649686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.39 % (3649686)CaDiCaL version: 2.1.3
% 0.61/0.39 % (3649686)Termination reason: Instruction limit
% 0.61/0.39 % (3649686)Termination phase: Function definition elimination
% 0.61/0.39 % (3649686)Time elapsed: 0.020 s
% 0.61/0.39 % (3649686)Peak memory usage: 12 MB
% 0.61/0.39 % (3649686)Instructions burned: 78 (million)
% 0.61/0.39 % (3649695)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1547406947:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.39 % (3649698)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=743744240:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.61/0.40 % (3649695)Instruction limit reached!
% 0.61/0.40 % (3649695)------------------------------
% 0.61/0.40 % (3649695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (3649695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (3649695)CaDiCaL version: 2.1.3
% 0.61/0.40 % (3649695)Termination reason: Instruction limit
% 0.61/0.40 % (3649695)Termination phase: shuffling
% 0.61/0.40 % (3649695)Time elapsed: 0.003 s
% 0.61/0.40 % (3649695)Peak memory usage: 10 MB
% 0.61/0.40 % (3649695)Instructions burned: 4 (million)
% 0.61/0.40 % (3649698)Instruction limit reached!
% 0.61/0.40 % (3649698)------------------------------
% 0.61/0.40 % (3649698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (3649698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (3649698)CaDiCaL version: 2.1.3
% 0.61/0.40 % (3649698)Termination reason: Instruction limit
% 0.61/0.40 % (3649698)Termination phase: shuffling
% 0.61/0.40 % (3649698)Time elapsed: 0.003 s
% 0.61/0.40 % (3649698)Peak memory usage: 10 MB
% 0.61/0.40 % (3649698)Instructions burned: 12 (million)
% 0.61/0.40 % (3649697)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.40 % (3649696)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=320603882:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.61/0.40 % (3649697)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1403878764:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.61/0.40 % (3649696)Instruction limit reached!
% 0.61/0.40 % (3649696)------------------------------
% 0.61/0.40 % (3649696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (3649696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (3649696)CaDiCaL version: 2.1.3
% 0.61/0.40 % (3649696)Termination reason: Instruction limit
% 0.61/0.40 % (3649696)Termination phase: shuffling
% 0.61/0.40 % (3649696)Time elapsed: 0.003 s
% 0.61/0.40 % (3649696)Peak memory usage: 10 MB
% 0.61/0.40 % (3649696)Instructions burned: 5 (million)
% 0.61/0.40 % (3649697)Instruction limit reached!
% 0.61/0.40 % (3649697)------------------------------
% 0.61/0.40 % (3649697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (3649697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (3649697)CaDiCaL version: 2.1.3
% 0.61/0.40 % (3649697)Termination reason: Instruction limit
% 0.61/0.40 % (3649697)Termination phase: shuffling
% 0.61/0.40 % (3649697)Time elapsed: 0.004 s
% 0.61/0.40 % (3649697)Peak memory usage: 10 MB
% 0.61/0.40 % (3649697)Instructions burned: 8 (million)
% 0.61/0.40 % (3649702)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=4137265880:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.61/0.40 % (3649681)Instruction limit reached!
% 0.61/0.40 % (3649681)------------------------------
% 0.61/0.40 % (3649681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (3649681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (3649681)CaDiCaL version: 2.1.3
% 0.61/0.40 % (3649681)Termination reason: Instruction limit
% 0.61/0.40 % (3649681)Termination phase: Property scanning
% 0.61/0.40 % (3649681)Time elapsed: 0.041 s
% 0.61/0.40 % (3649681)Peak memory usage: 12 MB
% 0.61/0.40 % (3649681)Instructions burned: 88 (million)
% 0.61/0.40 % (3649701)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
% 0.61/0.40 % (3649701)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.40 % (3649701)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=95933568:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.61/0.40 % (3649705)lrs+10_1_si=on:cs=on:random_seed=714501779:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.61/0.40 % (3649706)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.61/0.40 % (3649706)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=3848647957:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.40 % (3649705)Instruction limit reached!
% 0.61/0.40 % (3649705)------------------------------
% 0.61/0.40 % (3649705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (3649705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (3649705)CaDiCaL version: 2.1.3
% 0.61/0.40 % (3649705)Termination reason: Instruction limit
% 0.61/0.40 % (3649705)Termination phase: shuffling
% 0.61/0.40 % (3649705)Time elapsed: 0.005 s
% 0.61/0.40 % (3649705)Peak memory usage: 10 MB
% 0.61/0.40 % (3649705)Instructions burned: 10 (million)
% 0.61/0.40 % (3649706)Instruction limit reached!
% 0.61/0.40 % (3649706)------------------------------
% 0.61/0.40 % (3649706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (3649706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (3649706)CaDiCaL version: 2.1.3
% 0.61/0.40 % (3649706)Termination reason: Instruction limit
% 0.61/0.40 % (3649706)Termination phase: shuffling
% 0.61/0.40 % (3649706)Time elapsed: 0.002 s
% 0.61/0.40 % (3649706)Peak memory usage: 10 MB
% 0.61/0.40 % (3649706)Instructions burned: 3 (million)
% 0.61/0.40 % (3649702)Instruction limit reached!
% 0.61/0.40 % (3649702)------------------------------
% 0.61/0.40 % (3649702)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (3649702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (3649702)CaDiCaL version: 2.1.3
% 0.61/0.40 % (3649702)Termination reason: Instruction limit
% 0.61/0.40 % (3649702)Termination phase: Property scanning
% 0.61/0.40 % (3649702)Time elapsed: 0.020 s
% 0.61/0.40 % (3649702)Peak memory usage: 11 MB
% 0.61/0.40 % (3649702)Instructions burned: 89 (million)
% 0.61/0.40 % (3649701)Instruction limit reached!
% 0.61/0.40 % (3649701)------------------------------
% 0.61/0.40 % (3649701)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (3649701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (3649701)CaDiCaL version: 2.1.3
% 0.61/0.40 % (3649701)Termination reason: Instruction limit
% 0.61/0.40 % (3649701)Termination phase: shuffling
% 0.61/0.40 % (3649701)Time elapsed: 0.014 s
% 0.61/0.40 % (3649701)Peak memory usage: 10 MB
% 0.61/0.40 % (3649701)Instructions burned: 30 (million)
% 0.61/0.40 % (3649708)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2689242478:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.61/0.40 % (3649713)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2969845869:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.61/0.40 % (3649713)Instruction limit reached!
% 0.61/0.40 % (3649713)------------------------------
% 0.61/0.40 % (3649713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (3649713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (3649713)CaDiCaL version: 2.1.3
% 0.61/0.40 % (3649713)Termination reason: Instruction limit
% 0.61/0.40 % (3649713)Termination phase: Property scanning
% 0.61/0.40 % (3649713)Time elapsed: 0.006 s
% 0.61/0.40 % (3649713)Peak memory usage: 10 MB
% 0.61/0.40 % (3649713)Instructions burned: 26 (million)
% 0.61/0.40 % (3649712)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3588115559:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.61/0.40 % (3649714)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3867785546:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.61/0.40 % (3649684) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3649676-3649684"...
% 0.61/0.40 % (3649687)Instruction limit reached!
% 0.61/0.40 % (3649687)------------------------------
% 0.61/0.40 % (3649687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (3649687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (3649687)CaDiCaL version: 2.1.3
% 0.61/0.40 % (3649687)Termination reason: Instruction limit
% 0.61/0.40 % (3649687)Termination phase: Saturation
% 0.61/0.40 % (3649687)Time elapsed: 0.079 s
% 0.61/0.40 % (3649687)Peak memory usage: 14 MB
% 0.61/0.40 % (3649687)Instructions burned: 157 (million)
% 0.61/0.40 % (3649708)Instruction limit reached!
% 0.61/0.40 % (3649708)------------------------------
% 0.61/0.40 % (3649708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (3649715)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2876258468:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.61/0.40 % (3649708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (3649708)CaDiCaL version: 2.1.3
% 0.61/0.40 % (3649708)Termination reason: Instruction limit
% 0.61/0.40 % (3649708)Termination phase: Property scanning
% 0.61/0.40 % (3649708)Time elapsed: 0.018 s
% 0.61/0.40 % (3649708)Peak memory usage: 11 MB
% 0.61/0.40 % (3649708)Instructions burned: 38 (million)
% 0.61/0.40 % (3649684)...printing done.
% 0.61/0.40 % (3649684)Refutation found. Thanks to Tanya!
% 0.61/0.40 % SZS status Theorem for theBenchmark
% 0.61/0.40 % SZS output start Proof for theBenchmark
% 0.61/0.40 thf(type_def_5, type, list: $tType > $tType).
% 0.61/0.40 thf(type_def_6, type, set: $tType > $tType).
% 0.61/0.40 thf(type_def_7, type, nat: $tType).
% 0.61/0.40 thf(type_def_8, type, a: $tType).
% 0.61/0.40 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.61/0.40 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_1, type, size: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_2, type, one: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_3, type, minus: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_4, type, ord: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_5, type, order: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_6, type, group_add: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_7, type, no_bot: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_8, type, no_top: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_9, type, linorder: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_10, type, preorder: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_11, type, wellorder: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_12, type, dense_order: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_13, type, dense_linorder: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_14, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_15, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_16, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 0.61/0.40 thf(func_def_17, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.61/0.40 thf(func_def_18, type, one_one: !>[X0: $tType]:(X0)).
% 0.61/0.40 thf(func_def_19, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.61/0.40 thf(func_def_20, type, list_asc: !>[X0: $tType]:((list @ X0 > $o))).
% 0.61/0.40 thf(func_def_21, type, list_desc: !>[X0: $tType]:((list @ X0 > $o))).
% 0.61/0.40 thf(func_def_22, type, list_strict_asc: !>[X0: $tType]:((list @ X0 > $o))).
% 0.61/0.40 thf(func_def_23, type, list_strict_desc: !>[X0: $tType]:((list @ X0 > $o))).
% 0.61/0.40 thf(func_def_24, type, listIn521021761append: !>[X0: $tType]:((list @ X0 > (nat > X0) > nat > X0))).
% 0.61/0.40 thf(func_def_25, type, append: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.40 thf(func_def_26, type, butlast: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.61/0.40 thf(func_def_27, type, set2: !>[X0: $tType]:((list @ X0 > set @ X0))).
% 0.61/0.40 thf(func_def_28, type, list_ex: !>[X0: $tType]:(((X0 > $o) > list @ X0 > $o))).
% 0.61/0.40 thf(func_def_29, type, list_update: !>[X0: $tType]:((list @ X0 > nat > X0 > list @ X0))).
% 0.61/0.40 thf(func_def_30, type, nth: !>[X0: $tType]:((list @ X0 > nat > X0))).
% 0.61/0.40 thf(func_def_31, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 0.61/0.40 thf(func_def_32, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.40 thf(func_def_33, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.40 thf(func_def_34, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.61/0.40 thf(func_def_35, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.61/0.40 thf(func_def_36, type, f: (nat > a)).
% 0.61/0.40 thf(func_def_37, type, g: (nat > a)).
% 0.61/0.40 thf(func_def_38, type, x: nat).
% 0.61/0.40 thf(func_def_39, type, xs: list @ a).
% 0.61/0.40 thf(func_def_40, type, ys: list @ a).
% 0.61/0.40 thf(func_def_44, type, vAND: ($o > $o > $o)).
% 0.61/0.40 thf(func_def_45, type, db1: !>[X0: $tType]:(X0)).
% 0.61/0.40 thf(func_def_46, type, db0: !>[X0: $tType]:(X0)).
% 0.61/0.40 thf(func_def_47, type, vNOT: ($o > $o)).
% 0.61/0.40 thf(func_def_48, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.61/0.40 thf(func_def_49, type, db2: !>[X0: $tType]:(X0)).
% 0.61/0.40 thf(func_def_50, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.40 thf(func_def_51, type, vIMP: ($o > $o > $o)).
% 0.61/0.40 thf(func_def_52, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.40 thf(func_def_53, type, vOR: ($o > $o > $o)).
% 0.61/0.40 thf(func_def_54, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.40 thf(func_def_55, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.61/0.40 thf(func_def_56, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.61/0.40 thf(func_def_57, type, sK2: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_58, type, sK3: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_59, type, sK4: !>[X0: $tType]:((set @ X0 > list @ X0 > X0))).
% 0.61/0.40 thf(func_def_60, type, sK5: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_61, type, sK6: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_62, type, sK7: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_63, type, sK8: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.61/0.40 thf(func_def_64, type, sK9: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.61/0.40 thf(func_def_65, type, sK10: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_66, type, sK11: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_67, type, sK12: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.61/0.40 thf(func_def_68, type, sK13: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_69, type, sK14: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_70, type, sK15: !>[X0: $tType]:((nat > list @ X0))).
% 0.61/0.40 thf(func_def_71, type, sK16: !>[X0: $tType]:((list @ X0 > X0 > nat))).
% 0.61/0.40 thf(func_def_72, type, sK17: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_73, type, sK18: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_74, type, sK19: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_75, type, sK20: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_76, type, sK21: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_77, type, sK22: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_78, type, sK23: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.40 thf(func_def_79, type, sK24: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.40 thf(func_def_80, type, sK25: ((nat > $o) > nat > nat)).
% 0.61/0.40 thf(func_def_81, type, sK26: ((nat > $o) > nat > nat)).
% 0.61/0.40 thf(func_def_82, type, sK27: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_83, type, sK28: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_84, type, sK29: ((nat > $o) > nat)).
% 0.61/0.40 thf(func_def_85, type, sK30: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.40 thf(func_def_86, type, sK31: !>[X0: $tType]:((list @ X0 > (X0 > $o) > nat))).
% 0.61/0.40 thf(func_def_87, type, sK32: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_88, type, sK33: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_89, type, sK34: !>[X0: $tType]:((nat > (nat > X0 > $o) > list @ X0))).
% 0.61/0.40 thf(func_def_90, type, sK35: !>[X0: $tType]:((nat > (nat > X0 > $o) > nat))).
% 0.61/0.40 thf(func_def_91, type, sK36: !>[X0: $tType]:((nat > (nat > X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_92, type, sK37: !>[X0: $tType]:((list @ X0 > nat > (nat > X0 > $o) > nat))).
% 0.61/0.40 thf(func_def_93, type, sK38: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.40 thf(func_def_94, type, sK39: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_95, type, sK40: ((nat > $o) > nat)).
% 0.61/0.40 thf(func_def_96, type, sK41: !>[X0: $tType]:(((X0 > $o) > list @ X0 > X0))).
% 0.61/0.40 thf(func_def_97, type, sK42: !>[X0: $tType]:(((X0 > $o) > list @ X0 > nat))).
% 0.61/0.40 thf(func_def_98, type, sK43: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > $o) > X1))).
% 0.61/0.40 thf(func_def_99, type, sK44: ((nat > nat) > nat)).
% 0.61/0.40 thf(func_def_100, type, sK45: ((nat > nat) > nat)).
% 0.61/0.40 thf(func_def_101, type, sK46: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.61/0.40 thf(func_def_102, type, sK47: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.40 thf(func_def_103, type, sK48: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_104, type, sK49: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_105, type, sK50: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_106, type, sK51: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.40 thf(func_def_107, type, sK52: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.40 thf(func_def_108, type, sK53: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.40 thf(func_def_109, type, sK54: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.40 thf(func_def_110, type, sK55: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.40 thf(func_def_111, type, sK56: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.40 thf(func_def_112, type, sK57: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > list @ X0 > X0))).
% 0.61/0.40 thf(func_def_113, type, sK58: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.40 thf(func_def_114, type, sK59: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.61/0.40 thf(func_def_115, type, sK60: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_116, type, sK61: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_117, type, sK62: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.40 thf(func_def_118, type, sK63: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.40 thf(func_def_119, type, sK64: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.61/0.40 thf(func_def_120, type, sK65: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_121, type, sK66: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_122, type, sK67: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_123, type, sK68: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_124, type, sK69: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_125, type, sK70: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_126, type, sK71: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.40 thf(func_def_127, type, sK72: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.40 thf(func_def_128, type, sK73: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.61/0.40 thf(func_def_129, type, sK74: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_130, type, sK75: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_131, type, sK76: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_132, type, sK77: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.61/0.40 thf(func_def_133, type, sK78: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_134, type, sK79: !>[X0: $tType]:((nat > (X0 > nat) > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_135, type, sK80: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.40 thf(func_def_136, type, sK81: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.61/0.40 thf(func_def_137, type, sK82: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.40 thf(func_def_138, type, sK83: !>[X0: $tType]:((list @ X0 > list @ X0 > nat))).
% 0.61/0.40 thf(func_def_139, type, sK84: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_140, type, sK85: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_141, type, sK86: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.61/0.40 thf(func_def_142, type, sK87: (nat > (nat > $o) > nat)).
% 0.61/0.40 thf(func_def_143, type, sK88: ((nat > $o) > nat)).
% 0.61/0.40 thf(func_def_144, type, sK89: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.40 thf(func_def_145, type, sK90: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_146, type, sK91: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_147, type, sK92: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_148, type, sK93: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_149, type, sK94: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.61/0.40 thf(func_def_150, type, sK95: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 0.61/0.40 thf(func_def_151, type, sK96: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_152, type, sK97: !>[X0: $tType]:((list @ X0 > (X0 > $o) > X0))).
% 0.61/0.40 thf(func_def_153, type, sK98: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.40 thf(func_def_154, type, sK99: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.40 thf(func_def_155, type, sK100: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.61/0.40 thf(func_def_156, type, sK101: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.61/0.40 thf(func_def_157, type, sK102: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.40 thf(f285,axiom,(
% 0.61/0.40 ! [X0 : nat] : (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((nth @ a @ xs @ X0)) = ((nth @ a @ ys @ X0)))) & (~(ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))) = ((nth @ a @ ys @ X0)))))) & (~(ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((nth @ a @ xs @ X0)) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))) & (~(ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))))))),
% 0.61/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.61/0.40 thf(f286,axiom,(
% 0.61/0.40 (ord_less @ nat @ x @ (size_size @ list @ a @ ys))),
% 0.61/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)).
% 0.61/0.40 thf(f287,conjecture,(
% 0.61/0.40 (((nth @ a @ xs @ x)) = ((nth @ a @ ys @ x)))),
% 0.61/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3)).
% 0.61/0.40 thf(f288,negated_conjecture,(
% 0.61/0.40 ~ (((nth @ a @ xs @ x)) = ((nth @ a @ ys @ x)))),
% 0.61/0.40 inference(negated_conjecture,[status(cth)],[f287])).
% 0.61/0.40 thf(f494,plain,(
% 0.61/0.40 (ord_less @ nat @ x @ (size_size @ list @ a @ ys))),
% 0.61/0.40 inference(rectify,[],[f286])).
% 0.61/0.40 thf(f495,plain,(
% 0.61/0.40 (((ord_less @ nat @ x @ (size_size @ list @ a @ ys))) = $true)),
% 0.61/0.40 inference(fool_elimination,[],[f494])).
% 0.61/0.40 thf(f628,plain,(
% 0.61/0.40 ! [X0 : nat] : (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((nth @ a @ xs @ X0)) = ((nth @ a @ ys @ X0)))) & (~(ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))) = ((nth @ a @ ys @ X0)))))) & (~(ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((nth @ a @ xs @ X0)) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))) & (~(ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))))))),
% 0.61/0.40 inference(rectify,[],[f285])).
% 0.61/0.40 thf(f629,plain,(
% 0.61/0.40 ! [X0 : nat] : (((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((nth @ a @ xs @ X0)) = ((nth @ a @ ys @ X0)))) & (~ (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((nth @ a @ ys @ X0)) = ((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))))))) & (~ (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((nth @ a @ xs @ X0)) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))) & (~ (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))))))),
% 0.61/0.40 inference(fool_elimination,[],[f628])).
% 0.61/0.40 thf(f831,plain,(
% 0.61/0.40 (((nth @ a @ xs @ x)) != ((nth @ a @ ys @ x)))),
% 0.61/0.40 inference(flattening,[],[f288])).
% 0.61/0.40 thf(f848,plain,(
% 0.61/0.40 ! [X0 : nat] : (((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true) => (((nth @ a @ ys @ X0)) = ((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))))) & ((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((nth @ a @ xs @ X0)) = ((nth @ a @ ys @ X0)))))) & ((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true) => (((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((nth @ a @ xs @ X0)) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))) & ((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true) => (((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))))))),
% 0.61/0.40 inference(flattening,[],[f629])).
% 0.61/0.40 thf(f1121,plain,(
% 0.61/0.40 ! [X0 : nat] : (((((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true) | (((nth @ a @ xs @ X0)) = ((nth @ a @ ys @ X0)))) & ((((nth @ a @ ys @ X0)) = ((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs))))) | (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true))) | (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true)) & ((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) | (((((nth @ a @ xs @ X0)) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys))))) | (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true)) & ((((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys))))) | (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true)))))),
% 0.61/0.40 inference(ennf_transformation,[],[f848])).
% 0.61/0.40 thf(f1488,plain,(
% 0.61/0.40 ( ! [X0 : nat] : ((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true) | (((nth @ a @ xs @ X0)) = ((nth @ a @ ys @ X0))) | (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true)) )),
% 0.61/0.40 inference(cnf_transformation,[],[f1121])).
% 0.61/0.40 thf(f1641,plain,(
% 0.61/0.40 (((nth @ a @ xs @ x)) != ((nth @ a @ ys @ x)))),
% 0.61/0.40 inference(cnf_transformation,[],[f831])).
% 0.61/0.40 thf(f1795,plain,(
% 0.61/0.40 (((ord_less @ nat @ x @ (size_size @ list @ a @ ys))) = $true)),
% 0.61/0.40 inference(cnf_transformation,[],[f495])).
% 0.61/0.40 thf(f2172,plain,(
% 0.61/0.40 ( ! [X0 : nat] : ((((nth @ a @ xs @ X0)) = ((nth @ a @ ys @ X0))) | (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true)) )),
% 0.61/0.40 inference(duplicate_literal_removal,[],[f1488])).
% 0.61/0.40 thf(f2227,definition,(
% 0.61/0.40 spl103_11 <=> (((ord_less @ nat @ x @ (size_size @ list @ a @ ys))) = $true)),
% 0.61/0.40 introduced(definition,[new_symbols(definition,[spl103_11])],[avatar_definition])).
% 0.61/0.40 thf(f2229,plain,(
% 0.61/0.40 (((ord_less @ nat @ x @ (size_size @ list @ a @ ys))) = $true) | ~spl103_11),
% 0.61/0.40 inference(avatar_component_clause,[],[f2227])).
% 0.61/0.40 thf(f2230,plain,(
% 0.61/0.40 spl103_11),
% 0.61/0.40 inference(avatar_split_clause,[],[f1795,f2227])).
% 0.61/0.40 thf(f2283,definition,(
% 0.61/0.40 spl103_22 <=> (((nth @ a @ xs @ x)) = ((nth @ a @ ys @ x)))),
% 0.61/0.40 introduced(definition,[new_symbols(definition,[spl103_22])],[avatar_definition])).
% 0.61/0.40 thf(f2285,plain,(
% 0.61/0.40 (((nth @ a @ xs @ x)) != ((nth @ a @ ys @ x))) | spl103_22),
% 0.61/0.40 inference(avatar_component_clause,[],[f2283])).
% 0.61/0.40 thf(f2286,plain,(
% 0.61/0.40 ~spl103_22),
% 0.61/0.40 inference(avatar_split_clause,[],[f1641,f2283])).
% 0.61/0.40 thf(f2343,plain,(
% 0.61/0.40 (((ord_less @ nat @ x @ (size_size @ list @ a @ ys))) != $true) | (((nth @ a @ ys @ x)) != ((nth @ a @ ys @ x))) | spl103_22),
% 0.61/0.40 inference(superposition,[],[f2285,f2172])).
% 0.61/0.40 thf(f2345,plain,(
% 0.61/0.40 (((ord_less @ nat @ x @ (size_size @ list @ a @ ys))) != $true) | spl103_22),
% 0.61/0.40 inference(trivial_inequality_removal,[],[f2343])).
% 0.61/0.40 thf(f2346,plain,(
% 0.61/0.40 $false | (~spl103_11 | spl103_22)),
% 0.61/0.40 inference(forward_subsumption_resolution,[],[f2345,f2229])).
% 0.61/0.40 thf(f2347,plain,(
% 0.61/0.40 ~spl103_11 | spl103_22),
% 0.61/0.40 inference(avatar_contradiction_clause,[],[f2346])).
% 0.61/0.40 cnf(s10, plain, spl103_11, inference(sat_conversion,[],[f2230])).
% 0.61/0.40 cnf(s23, plain, ~spl103_22, inference(sat_conversion,[],[f2286])).
% 0.61/0.40 cnf(s26, plain, ~spl103_11 | spl103_22, inference(sat_conversion,[],[f2347])).
% 0.61/0.40 cnf(s27, plain, ~spl103_11, inference(rat,[],[s26,s23])).
% 0.61/0.40 cnf(s28, plain, $false, inference(rat,[],[s10,s27])).
% 0.61/0.40 thf(f2348,plain,(
% 0.61/0.40 $false),
% 0.61/0.40 inference(avatar_sat_refutation,[],[s28])).
% 0.61/0.40 % SZS output end Proof for theBenchmark
% 0.61/0.40 % (3649684)------------------------------
% 0.61/0.40 % (3649684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (3649684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (3649684)CaDiCaL version: 2.1.3
% 0.61/0.40 % (3649684)Termination reason: Refutation
% 0.61/0.40 % (3649684)Time elapsed: 0.080 s
% 0.61/0.40 % (3649684)Peak memory usage: 14 MB
% 0.61/0.40 % (3649684)Instructions burned: 168 (million)
% 0.61/0.40 % (3649676)Success in time 0.129 s
% 0.61/0.40 % Vampire exiting
%------------------------------------------------------------------------------