%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP133^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:08:29 AM UTC 2026
% Result : Theorem 1.81s 0.63s
% Output : Refutation 1.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP133^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 % Computer : n004.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 19:58:22 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.28 Running higher-order theorem proving
% 0.25/0.32 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
% 1.18/0.50 % (1767547)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.18/0.50 % (1767556)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=186232486:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.18/0.50 % (1767558)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.18/0.50 % (1767558)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.18/0.50 % (1767556)Instruction limit reached!
% 1.18/0.50 % (1767556)------------------------------
% 1.18/0.50 % (1767556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.50 % (1767556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.50 % (1767556)CaDiCaL version: 2.1.3
% 1.18/0.50 % (1767556)Termination reason: Instruction limit
% 1.18/0.50 % (1767556)Termination phase: Property scanning
% 1.18/0.50 % (1767556)Time elapsed: 0.010 s
% 1.18/0.50 % (1767556)Peak memory usage: 10 MB
% 1.18/0.50 % (1767556)Instructions burned: 24 (million)
% 1.18/0.50 % (1767552)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1293014624:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.18/0.50 % (1767554)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3482460892:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.18/0.50 % (1767553)lrs+10_16_si=on:nwc=1.5:random_seed=2755841906:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.18/0.50 % (1767555)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=832590485:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 1.18/0.50 % (1767557)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3428244659:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.18/0.50 % (1767558)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=666432113:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.18/0.50 % (1767554)Instruction limit reached!
% 1.18/0.50 % (1767554)------------------------------
% 1.18/0.50 % (1767554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.50 % (1767554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.50 % (1767554)CaDiCaL version: 2.1.3
% 1.18/0.50 % (1767554)Termination reason: Instruction limit
% 1.18/0.50 % (1767554)Termination phase: shuffling
% 1.18/0.50 % (1767554)Time elapsed: 0.003 s
% 1.18/0.50 % (1767554)Peak memory usage: 10 MB
% 1.18/0.50 % (1767554)Instructions burned: 3 (million)
% 1.18/0.50 % (1767560)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3040670003:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.18/0.50 % (1767553)Instruction limit reached!
% 1.18/0.50 % (1767553)------------------------------
% 1.18/0.50 % (1767553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.50 % (1767553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.50 % (1767553)CaDiCaL version: 2.1.3
% 1.18/0.50 % (1767553)Termination reason: Instruction limit
% 1.18/0.50 % (1767553)Termination phase: Property scanning
% 1.18/0.50 % (1767553)Time elapsed: 0.016 s
% 1.18/0.50 % (1767553)Peak memory usage: 10 MB
% 1.18/0.50 % (1767553)Instructions burned: 19 (million)
% 1.18/0.50 % (1767560)Instruction limit reached!
% 1.18/0.50 % (1767560)------------------------------
% 1.18/0.50 % (1767560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.50 % (1767560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.50 % (1767560)CaDiCaL version: 2.1.3
% 1.18/0.50 % (1767560)Termination reason: Instruction limit
% 1.18/0.50 % (1767560)Termination phase: shuffling
% 1.18/0.50 % (1767560)Time elapsed: 0.002 s
% 1.18/0.50 % (1767560)Peak memory usage: 10 MB
% 1.18/0.50 % (1767560)Instructions burned: 4 (million)
% 1.18/0.50 % (1767567)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2546478487:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.18/0.56 % (1767567)Instruction limit reached!
% 1.18/0.56 % (1767567)------------------------------
% 1.18/0.56 % (1767567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.56 % (1767567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.56 % (1767567)CaDiCaL version: 2.1.3
% 1.18/0.56 % (1767567)Termination reason: Instruction limit
% 1.18/0.56 % (1767567)Termination phase: shuffling
% 1.18/0.56 % (1767567)Time elapsed: 0.003 s
% 1.18/0.56 % (1767567)Peak memory usage: 10 MB
% 1.18/0.56 % (1767567)Instructions burned: 6 (million)
% 1.18/0.56 % (1767570)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2881794517:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.18/0.56 % (1767570)Instruction limit reached!
% 1.18/0.56 % (1767570)------------------------------
% 1.18/0.56 % (1767570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.56 % (1767570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.56 % (1767570)CaDiCaL version: 2.1.3
% 1.18/0.56 % (1767570)Termination reason: Instruction limit
% 1.18/0.56 % (1767570)Termination phase: shuffling
% 1.18/0.56 % (1767570)Time elapsed: 0.006 s
% 1.18/0.56 % (1767570)Peak memory usage: 10 MB
% 1.18/0.56 % (1767570)Instructions burned: 14 (million)
% 1.18/0.56 % (1767569)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.18/0.56 % (1767572)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.18/0.56 % (1767572)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.18/0.56 % (1767569)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=681217093:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.18/0.56 % (1767572)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1416835584:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.18/0.56 % (1767569)Instruction limit reached!
% 1.18/0.56 % (1767569)------------------------------
% 1.18/0.56 % (1767569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.56 % (1767569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.56 % (1767569)CaDiCaL version: 2.1.3
% 1.18/0.56 % (1767569)Termination reason: Instruction limit
% 1.18/0.56 % (1767569)Termination phase: shuffling
% 1.18/0.56 % (1767569)Time elapsed: 0.007 s
% 1.18/0.56 % (1767569)Peak memory usage: 10 MB
% 1.18/0.56 % (1767569)Instructions burned: 7 (million)
% 1.18/0.56 % (1767574)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=3308209293:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.18/0.56 % (1767557)Instruction limit reached!
% 1.18/0.56 % (1767557)------------------------------
% 1.18/0.56 % (1767557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.56 % (1767557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.56 % (1767557)CaDiCaL version: 2.1.3
% 1.18/0.56 % (1767557)Termination reason: Instruction limit
% 1.18/0.56 % (1767557)Termination phase: Property scanning
% 1.18/0.56 % (1767557)Time elapsed: 0.061 s
% 1.18/0.56 % (1767557)Peak memory usage: 12 MB
% 1.18/0.56 % (1767557)Instructions burned: 76 (million)
% 1.18/0.56 % (1767572)Instruction limit reached!
% 1.18/0.56 % (1767572)------------------------------
% 1.18/0.56 % (1767572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.56 % (1767572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.56 % (1767572)CaDiCaL version: 2.1.3
% 1.18/0.56 % (1767572)Termination reason: Instruction limit
% 1.18/0.56 % (1767572)Termination phase: Property scanning
% 1.18/0.56 % (1767572)Time elapsed: 0.014 s
% 1.18/0.56 % (1767572)Peak memory usage: 10 MB
% 1.18/0.56 % (1767572)Instructions burned: 29 (million)
% 1.18/0.56 % (1767552)Instruction limit reached!
% 1.18/0.56 % (1767552)------------------------------
% 1.18/0.56 % (1767552)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (1767552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (1767552)CaDiCaL version: 2.1.3
% 1.81/0.61 % (1767552)Termination reason: Instruction limit
% 1.81/0.61 % (1767552)Termination phase: Property scanning
% 1.81/0.61 % (1767552)Time elapsed: 0.070 s
% 1.81/0.61 % (1767552)Peak memory usage: 12 MB
% 1.81/0.61 % (1767552)Instructions burned: 88 (million)
% 1.81/0.61 % (1767577)lrs+10_1_si=on:cs=on:random_seed=4264815552:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.81/0.61 % (1767579)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.81/0.61 % (1767574)Instruction limit reached!
% 1.81/0.61 % (1767574)------------------------------
% 1.81/0.61 % (1767574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (1767574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (1767574)CaDiCaL version: 2.1.3
% 1.81/0.61 % (1767574)Termination reason: Instruction limit
% 1.81/0.61 % (1767574)Termination phase: Property scanning
% 1.81/0.61 % (1767574)Time elapsed: 0.036 s
% 1.81/0.61 % (1767574)Peak memory usage: 11 MB
% 1.81/0.61 % (1767574)Instructions burned: 88 (million)
% 1.81/0.61 % (1767577)Instruction limit reached!
% 1.81/0.61 % (1767577)------------------------------
% 1.81/0.61 % (1767577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (1767577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (1767577)CaDiCaL version: 2.1.3
% 1.81/0.61 % (1767577)Termination reason: Instruction limit
% 1.81/0.61 % (1767577)Termination phase: shuffling
% 1.81/0.61 % (1767577)Time elapsed: 0.007 s
% 1.81/0.61 % (1767577)Peak memory usage: 10 MB
% 1.81/0.61 % (1767577)Instructions burned: 8 (million)
% 1.81/0.61 % (1767580)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4158315128:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.81/0.61 % (1767579)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=597893366:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.81/0.61 % (1767579)Instruction limit reached!
% 1.81/0.61 % (1767579)------------------------------
% 1.81/0.61 % (1767579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (1767579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (1767579)CaDiCaL version: 2.1.3
% 1.81/0.61 % (1767579)Termination reason: Instruction limit
% 1.81/0.61 % (1767579)Termination phase: shuffling
% 1.81/0.61 % (1767579)Time elapsed: 0.003 s
% 1.81/0.61 % (1767579)Peak memory usage: 10 MB
% 1.81/0.61 % (1767579)Instructions burned: 3 (million)
% 1.81/0.61 % (1767581)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=286230922:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.81/0.61 % (1767585)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=718747147:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.81/0.61 % (1767585)Instruction limit reached!
% 1.81/0.61 % (1767585)------------------------------
% 1.81/0.61 % (1767585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (1767585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (1767585)CaDiCaL version: 2.1.3
% 1.81/0.61 % (1767585)Termination reason: Instruction limit
% 1.81/0.61 % (1767585)Termination phase: Property scanning
% 1.81/0.61 % (1767585)Time elapsed: 0.007 s
% 1.81/0.61 % (1767585)Peak memory usage: 10 MB
% 1.81/0.61 % (1767585)Instructions burned: 16 (million)
% 1.81/0.61 % (1767583)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=95049770:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.81/0.61 % (1767580)Instruction limit reached!
% 1.81/0.61 % (1767580)------------------------------
% 1.81/0.61 % (1767580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.61 % (1767580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.61 % (1767580)CaDiCaL version: 2.1.3
% 1.81/0.61 % (1767580)Termination reason: Instruction limit
% 1.81/0.61 % (1767580)Termination phase: Preprocessing 3
% 1.81/0.63 % (1767580)Time elapsed: 0.033 s
% 1.81/0.63 % (1767580)Peak memory usage: 11 MB
% 1.81/0.63 % (1767580)Instructions burned: 39 (million)
% 1.81/0.63 % (1767588)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3724709876:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.81/0.63 % (1767558)Instruction limit reached!
% 1.81/0.63 % (1767558)------------------------------
% 1.81/0.63 % (1767558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.63 % (1767558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.63 % (1767558)CaDiCaL version: 2.1.3
% 1.81/0.63 % (1767558)Termination reason: Instruction limit
% 1.81/0.63 % (1767558)Termination phase: Saturation
% 1.81/0.63 % (1767558)Time elapsed: 0.132 s
% 1.81/0.63 % (1767558)Peak memory usage: 13 MB
% 1.81/0.63 % (1767558)Instructions burned: 157 (million)
% 1.81/0.63 % (1767590)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=751636386:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.81/0.63 % (1767583)Instruction limit reached!
% 1.81/0.63 % (1767583)------------------------------
% 1.81/0.63 % (1767583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.63 % (1767583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.63 % (1767583)CaDiCaL version: 2.1.3
% 1.81/0.63 % (1767583)Termination reason: Instruction limit
% 1.81/0.63 % (1767583)Termination phase: SInE selection
% 1.81/0.63 % (1767583)Time elapsed: 0.021 s
% 1.81/0.63 % (1767583)Peak memory usage: 10 MB
% 1.81/0.63 % (1767583)Instructions burned: 25 (million)
% 1.81/0.63 % (1767590)Instruction limit reached!
% 1.81/0.63 % (1767590)------------------------------
% 1.81/0.63 % (1767590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.63 % (1767590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.63 % (1767590)CaDiCaL version: 2.1.3
% 1.81/0.63 % (1767590)Termination reason: Instruction limit
% 1.81/0.63 % (1767590)Termination phase: shuffling
% 1.81/0.63 % (1767590)Time elapsed: 0.007 s
% 1.81/0.63 % (1767590)Peak memory usage: 10 MB
% 1.81/0.63 % (1767590)Instructions burned: 14 (million)
% 1.81/0.63 % (1767592)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1138363802: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)
% 1.81/0.63 % (1767592)Instruction limit reached!
% 1.81/0.63 % (1767592)------------------------------
% 1.81/0.63 % (1767592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.63 % (1767592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.63 % (1767592)CaDiCaL version: 2.1.3
% 1.81/0.63 % (1767592)Termination reason: Instruction limit
% 1.81/0.63 % (1767592)Termination phase: shuffling
% 1.81/0.63 % (1767592)Time elapsed: 0.003 s
% 1.81/0.63 % (1767592)Peak memory usage: 9 MB
% 1.81/0.63 % (1767592)Instructions burned: 2 (million)
% 1.81/0.63 % (1767596)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=994966805:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.81/0.63 % (1767594)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=472745678:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.81/0.63 % (1767597)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1137009702:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.81/0.63 % (1767596)Instruction limit reached!
% 1.81/0.63 % (1767596)------------------------------
% 1.81/0.63 % (1767596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.63 % (1767596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.63 % (1767596)CaDiCaL version: 2.1.3
% 1.81/0.63 % (1767596)Termination reason: Instruction limit
% 1.81/0.63 % (1767596)Termination phase: Property scanning
% 1.81/0.63 % (1767596)Time elapsed: 0.011 s
% 1.81/0.63 % (1767596)Peak memory usage: 10 MB
% 1.81/0.63 % (1767596)Instructions burned: 25 (million)
% 1.81/0.63 % (1767599)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
% 1.81/0.63 % (1767599)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.81/0.63 % (1767599)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=3721809543:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.81/0.63 % (1767594)Instruction limit reached!
% 1.81/0.63 % (1767594)------------------------------
% 1.81/0.63 % (1767594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.63 % (1767594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.63 % (1767594)CaDiCaL version: 2.1.3
% 1.81/0.63 % (1767594)Termination reason: Instruction limit
% 1.81/0.63 % (1767594)Termination phase: Property scanning
% 1.81/0.63 % (1767594)Time elapsed: 0.022 s
% 1.81/0.63 % (1767594)Peak memory usage: 10 MB
% 1.81/0.63 % (1767594)Instructions burned: 26 (million)
% 1.81/0.63 % (1767603)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.81/0.63 % (1767603)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=1727963072:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 1.81/0.63 % (1767599)Instruction limit reached!
% 1.81/0.63 % (1767599)------------------------------
% 1.81/0.63 % (1767599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.63 % (1767599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.63 % (1767599)CaDiCaL version: 2.1.3
% 1.81/0.63 % (1767599)Termination reason: Instruction limit
% 1.81/0.63 % (1767599)Termination phase: shuffling
% 1.81/0.63 % (1767599)Time elapsed: 0.013 s
% 1.81/0.63 % (1767599)Peak memory usage: 10 MB
% 1.81/0.63 % (1767599)Instructions burned: 14 (million)
% 1.81/0.63 % (1767603)Instruction limit reached!
% 1.81/0.63 % (1767603)------------------------------
% 1.81/0.63 % (1767603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.63 % (1767603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.63 % (1767603)CaDiCaL version: 2.1.3
% 1.81/0.63 % (1767603)Termination reason: Instruction limit
% 1.81/0.63 % (1767603)Termination phase: shuffling
% 1.81/0.63 % (1767603)Time elapsed: 0.004 s
% 1.81/0.63 % (1767603)Peak memory usage: 10 MB
% 1.81/0.63 % (1767603)Instructions burned: 9 (million)
% 1.81/0.63 % (1767605)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=2271330131:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 1.81/0.63 % (1767608)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1481469674:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.81/0.63 % (1767597)Instruction limit reached!
% 1.81/0.63 % (1767597)------------------------------
% 1.81/0.63 % (1767597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.63 % (1767597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.63 % (1767597)CaDiCaL version: 2.1.3
% 1.81/0.63 % (1767597)Termination reason: Instruction limit
% 1.81/0.63 % (1767597)Termination phase: Property scanning
% 1.81/0.63 % (1767597)Time elapsed: 0.051 s
% 1.81/0.63 % (1767597)Peak memory usage: 11 MB
% 1.81/0.63 % (1767597)Instructions burned: 60 (million)
% 1.81/0.63 % (1767607)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3904367321:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 1.81/0.63 % (1767608)Instruction limit reached!
% 1.81/0.63 % (1767608)------------------------------
% 1.81/0.63 % (1767608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.63 % (1767608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.63 % (1767608)CaDiCaL version: 2.1.3
% 1.81/0.63 % (1767608)Termination reason: Instruction limit
% 1.81/0.63 % (1767608)Termination phase: shuffling
% 1.81/0.63 % (1767608)Time elapsed: 0.012 s
% 1.81/0.63 % (1767608)Peak memory usage: 10 MB
% 1.81/0.63 % (1767608)Instructions burned: 24 (million)
% 1.81/0.63 % (1767607)Instruction limit reached!
% 1.81/0.63 % (1767607)------------------------------
% 1.81/0.63 % (1767607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.63 % (1767607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.63 % (1767607)CaDiCaL version: 2.1.3
% 1.81/0.63 % (1767607)Termination reason: Instruction limit
% 1.81/0.63 % (1767607)Termination phase: shuffling
% 1.81/0.63 % (1767607)Time elapsed: 0.007 s
% 1.81/0.63 % (1767607)Peak memory usage: 10 MB
% 1.81/0.63 % (1767607)Instructions burned: 8 (million)
% 1.81/0.63 % (1767581) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1767547-1767581"...
% 1.81/0.63 % (1767611)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2702053988:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.81/0.63 % (1767605)Instruction limit reached!
% 1.81/0.63 % (1767605)------------------------------
% 1.81/0.63 % (1767605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.63 % (1767605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.63 % (1767605)CaDiCaL version: 2.1.3
% 1.81/0.63 % (1767605)Termination reason: Instruction limit
% 1.81/0.63 % (1767605)Termination phase: Property scanning
% 1.81/0.63 % (1767605)Time elapsed: 0.026 s
% 1.81/0.63 % (1767605)Peak memory usage: 10 MB
% 1.81/0.63 % (1767605)Instructions burned: 32 (million)
% 1.81/0.63 % (1767581)...printing done.
% 1.81/0.63 % (1767611)Instruction limit reached!
% 1.81/0.63 % (1767611)------------------------------
% 1.81/0.63 % (1767611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.63 % (1767611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.63 % (1767611)CaDiCaL version: 2.1.3
% 1.81/0.63 % (1767611)Termination reason: Instruction limit
% 1.81/0.63 % (1767611)Termination phase: Property scanning
% 1.81/0.63 % (1767611)Time elapsed: 0.009 s
% 1.81/0.63 % (1767611)Peak memory usage: 10 MB
% 1.81/0.63 % (1767611)Instructions burned: 20 (million)
% 1.81/0.63 % (1767581)Refutation found. Thanks to Tanya!
% 1.81/0.63 % SZS status Theorem for theBenchmark
% 1.81/0.63 % SZS output start Proof for theBenchmark
% 1.81/0.63 thf(type_def_5, type, set_set_nat: $tType).
% 1.81/0.63 thf(type_def_6, type, set_nat: $tType).
% 1.81/0.63 thf(type_def_7, type, nat: $tType).
% 1.81/0.63 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 1.81/0.63 thf(func_def_0, type, one_one_nat: nat).
% 1.81/0.63 thf(func_def_1, type, times_times_nat: (nat > nat > nat)).
% 1.81/0.63 thf(func_def_2, type, zero_zero_nat: nat).
% 1.81/0.64 thf(func_def_3, type, groups1842438620at_nat: ((nat > nat) > set_nat > nat)).
% 1.81/0.64 thf(func_def_4, type, number1551313001itions: ((nat > nat) > nat > $o)).
% 1.81/0.64 thf(func_def_5, type, ord_less_nat: (nat > nat > $o)).
% 1.81/0.64 thf(func_def_6, type, ord_less_set_nat: (set_nat > set_nat > $o)).
% 1.81/0.64 thf(func_def_7, type, ord_less_eq_nat_o: ((nat > $o) > (nat > $o) > $o)).
% 1.81/0.64 thf(func_def_8, type, ord_less_eq_nat: (nat > nat > $o)).
% 1.81/0.64 thf(func_def_9, type, ord_less_eq_set_nat: (set_nat > set_nat > $o)).
% 1.81/0.64 thf(func_def_10, type, ord_le1613022364et_nat: (set_set_nat > set_set_nat > $o)).
% 1.81/0.64 thf(func_def_11, type, collect_nat: ((nat > $o) > set_nat)).
% 1.81/0.64 thf(func_def_12, type, collect_set_nat: ((set_nat > $o) > set_set_nat)).
% 1.81/0.64 thf(func_def_13, type, set_ord_atMost_nat: (nat > set_nat)).
% 1.81/0.64 thf(func_def_14, type, set_or1086813439et_nat: (set_nat > set_set_nat)).
% 1.81/0.64 thf(func_def_15, type, member_nat: (nat > set_nat > $o)).
% 1.81/0.64 thf(func_def_16, type, member_set_nat: (set_nat > set_set_nat > $o)).
% 1.81/0.64 thf(func_def_17, type, p: (nat > nat)).
% 1.81/0.64 thf(func_def_19, type, vAND: ($o > $o > $o)).
% 1.81/0.64 thf(func_def_20, type, db0: !>[X0: $tType]:(X0)).
% 1.81/0.64 thf(func_def_21, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.81/0.64 thf(func_def_24, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.81/0.64 thf(func_def_25, type, vNOT: ($o > $o)).
% 1.81/0.64 thf(func_def_26, type, db1: !>[X0: $tType]:(X0)).
% 1.81/0.64 thf(func_def_27, type, vOR: ($o > $o > $o)).
% 1.81/0.64 thf(func_def_28, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.81/0.64 thf(func_def_29, type, vIMP: ($o > $o > $o)).
% 1.81/0.64 thf(func_def_30, type, db2: !>[X0: $tType]:(X0)).
% 1.81/0.64 thf(func_def_31, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.81/0.64 thf(func_def_32, type, sP0: (set_nat > (nat > nat) > (nat > nat) > $o)).
% 1.81/0.64 thf(func_def_33, type, sP1: ((nat > nat) > (nat > nat) > set_nat > $o)).
% 1.81/0.64 thf(func_def_34, type, sP2: (nat > nat > nat > $o)).
% 1.81/0.64 thf(func_def_35, type, sP3: (nat > nat > nat > $o)).
% 1.81/0.64 thf(func_def_36, type, sP4: (nat > nat > nat > $o)).
% 1.81/0.64 thf(func_def_37, type, sK5: (set_nat > (nat > nat) > nat)).
% 1.81/0.64 thf(func_def_38, type, sK6: ((nat > nat) > nat)).
% 1.81/0.64 thf(func_def_39, type, sK7: ((nat > nat) > nat)).
% 1.81/0.64 thf(func_def_40, type, sK8: ((nat > nat) > nat)).
% 1.81/0.64 thf(func_def_41, type, sK9: ((nat > nat) > nat)).
% 1.81/0.64 thf(func_def_42, type, sK10: ((nat > nat) > set_nat > (nat > nat) > (nat > nat) > set_nat > (nat > nat) > nat)).
% 1.81/0.64 thf(func_def_43, type, sK11: (set_nat > (nat > nat) > set_nat > (nat > nat) > nat)).
% 1.81/0.64 thf(func_def_44, type, sK12: (set_nat > (nat > nat) > nat)).
% 1.81/0.64 thf(func_def_45, type, sK13: ((nat > nat) > (nat > nat) > set_nat > nat)).
% 1.81/0.64 thf(func_def_46, type, sK14: (set_nat > (nat > nat) > (nat > nat) > nat)).
% 1.81/0.64 thf(func_def_47, type, sK15: (set_nat > (nat > nat) > set_nat > nat)).
% 1.81/0.64 thf(func_def_48, type, sK16: ((nat > nat) > set_nat > set_nat > nat)).
% 1.81/0.64 thf(func_def_49, type, sK17: ((nat > nat) > (nat > nat) > set_nat > (nat > nat) > nat)).
% 1.81/0.64 thf(func_def_50, type, sK18: ((nat > $o) > nat)).
% 1.81/0.64 thf(func_def_51, type, sK19: ((nat > $o) > nat > nat)).
% 1.81/0.64 thf(func_def_52, type, sK20: ((set_nat > nat) > set_nat)).
% 1.81/0.64 thf(func_def_53, type, sK21: ((set_nat > nat) > set_nat)).
% 1.81/0.64 thf(func_def_54, type, sK22: ((set_nat > set_nat) > set_nat)).
% 1.81/0.64 thf(func_def_55, type, sK23: ((set_nat > set_nat) > set_nat)).
% 1.81/0.64 thf(func_def_56, type, sK24: ((nat > nat) > nat)).
% 1.81/0.64 thf(func_def_57, type, sK25: ((nat > nat) > nat)).
% 1.81/0.64 thf(func_def_58, type, sK26: ((nat > nat) > set_nat > (nat > nat) > nat)).
% 1.81/0.64 thf(func_def_59, type, sK27: ((set_nat > nat) > set_nat)).
% 1.81/0.64 thf(func_def_60, type, sK28: ((set_nat > nat) > set_nat)).
% 1.81/0.64 thf(func_def_61, type, sK29: ((set_nat > nat) > set_nat)).
% 1.81/0.64 thf(func_def_62, type, sK30: ((set_nat > nat) > set_nat)).
% 1.81/0.64 thf(func_def_63, type, sK31: ((nat > nat) > set_nat > nat)).
% 1.81/0.64 thf(func_def_64, type, sK32: (set_nat > set_nat > (nat > nat) > nat)).
% 1.81/0.64 thf(func_def_65, type, sK33: (nat > set_nat > set_nat > (nat > nat) > nat)).
% 1.81/0.64 thf(func_def_66, type, sK34: (set_nat > (nat > nat) > (nat > nat) > set_nat > (nat > nat) > nat)).
% 1.81/0.64 thf(func_def_67, type, sK35: ((nat > set_nat) > nat)).
% 1.81/0.64 thf(func_def_68, type, sK36: ((nat > set_nat) > nat)).
% 1.81/0.64 thf(func_def_69, type, sK37: ((nat > set_nat) > nat)).
% 1.81/0.64 thf(func_def_70, type, sK38: ((nat > set_nat) > nat)).
% 1.81/0.64 thf(func_def_71, type, sK39: ((nat > nat > $o) > nat)).
% 1.81/0.64 thf(func_def_72, type, sK40: ((nat > nat > $o) > nat)).
% 1.81/0.64 thf(func_def_73, type, sK41: ((nat > nat > $o) > nat)).
% 1.81/0.64 thf(func_def_74, type, sK42: ((nat > nat > $o) > nat)).
% 1.81/0.64 thf(func_def_75, type, sK43: ((nat > nat) > set_nat > (nat > nat) > nat)).
% 1.81/0.64 thf(func_def_76, type, sK44: ((set_nat > set_nat) > set_nat)).
% 1.81/0.64 thf(func_def_77, type, sK45: ((set_nat > set_nat) > set_nat)).
% 1.81/0.64 thf(func_def_78, type, sK46: ((set_nat > nat) > set_nat)).
% 1.81/0.64 thf(func_def_79, type, sK47: ((set_nat > nat) > set_nat)).
% 1.81/0.64 thf(func_def_80, type, sK48: ((set_nat > set_nat) > set_nat)).
% 1.81/0.64 thf(func_def_81, type, sK49: ((set_nat > set_nat) > set_nat)).
% 1.81/0.64 thf(func_def_82, type, sK50: ((nat > $o) > nat)).
% 1.81/0.64 thf(func_def_83, type, sK51: ((nat > nat) > nat)).
% 1.81/0.64 thf(func_def_84, type, sK52: ((nat > nat) > nat)).
% 1.81/0.64 thf(func_def_85, type, sK53: ((nat > set_nat) > nat)).
% 1.81/0.64 thf(func_def_86, type, sK54: ((nat > set_nat) > nat)).
% 1.81/0.64 thf(func_def_87, type, sK55: ((nat > nat) > nat)).
% 1.81/0.64 thf(func_def_88, type, sK56: ((nat > nat) > nat)).
% 1.81/0.64 thf(func_def_89, type, sK57: ((set_nat > set_nat) > set_nat)).
% 1.81/0.64 thf(func_def_90, type, sK58: ((set_nat > set_nat) > set_nat)).
% 1.81/0.64 thf(func_def_91, type, sK59: ((nat > set_nat) > nat)).
% 1.81/0.64 thf(func_def_92, type, sK60: ((nat > set_nat) > nat)).
% 1.81/0.64 thf(func_def_93, type, sK61: (nat > (nat > $o) > nat)).
% 1.81/0.64 thf(func_def_94, type, sK62: ((nat > $o) > nat)).
% 1.81/0.64 thf(func_def_95, type, sK63: (set_nat > (nat > nat) > nat)).
% 1.81/0.64 thf(func_def_96, type, db3: !>[X0: $tType]:(X0)).
% 1.81/0.64 thf(func_def_97, type, sK64: nat).
% 1.81/0.64 thf(func_def_99, type, sK66: nat).
% 1.81/0.64 thf(f1,axiom,(
% 1.81/0.64 ! [X0 : set_nat] : (((groups1842438620at_nat @ (^[X1 : nat] : (zero_zero_nat)) @ X0)) = zero_zero_nat)),
% 1.81/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_sum_Oneutral__const)).
% 1.81/0.64 thf(f33,axiom,(
% 1.81/0.64 ! [X1 : set_nat,X3 : (nat > nat),X0 : set_nat,X2 : (nat > nat)] : ((X0 = X1) => (! [X4 : nat] : ((member_nat @ X4 @ X1) => (((X2 @ X4)) = ((X3 @ X4)))) => (((groups1842438620at_nat @ X2 @ X0)) = ((groups1842438620at_nat @ X3 @ X1)))))),
% 1.81/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_sum_Ocong)).
% 1.81/0.64 thf(f39,axiom,(
% 1.81/0.64 ! [X0 : nat,X1 : nat] : ((((times_times_nat @ X0 @ X1)) != zero_zero_nat) => ((X1 != zero_zero_nat) & (X0 != zero_zero_nat)))),
% 1.81/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_mult__not__zero)).
% 1.81/0.64 thf(f50,axiom,(
% 1.81/0.64 ! [X0 : nat] : (((times_times_nat @ zero_zero_nat @ X0)) = zero_zero_nat)),
% 1.81/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_mult__0)).
% 1.81/0.64 thf(f58,axiom,(
% 1.81/0.64 (((times_times_nat @ zero_zero_nat)) = (^[X0 : nat] : (zero_zero_nat)))),
% 1.81/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_lambda__zero)).
% 1.81/0.64 thf(f65,axiom,(
% 1.81/0.64 ((^[X0 : nat] : ((collect_nat @ (^[X1 : nat] : ((ord_less_eq_nat @ X1 @ X0)))))) = set_ord_atMost_nat)),
% 1.81/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_atMost__def)).
% 1.81/0.64 thf(f76,axiom,(
% 1.81/0.64 ~(ord_less_eq_nat @ one_one_nat @ zero_zero_nat)),
% 1.81/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_not__one__le__zero)).
% 1.81/0.64 thf(f227,axiom,(
% 1.81/0.64 ! [X0 : nat] : ~(ord_less_nat @ X0 @ zero_zero_nat)),
% 1.81/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_less__zeroE)).
% 1.81/0.64 thf(f255,axiom,(
% 1.81/0.64 (ord_less_nat = (^[X0 : nat, X1 : nat] : ((X0 != X1) & (ord_less_eq_nat @ X0 @ X1))))),
% 1.81/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_order_Ostrict__iff__order)).
% 1.81/0.64 thf(f262,conjecture,(
% 1.81/0.64 (((^[X0 : nat] : (zero_zero_nat)) = p) = ! [X0 : nat] : ((((p @ X0)) != zero_zero_nat) => ((ord_less_eq_nat @ one_one_nat @ X0) & (ord_less_eq_nat @ X0 @ zero_zero_nat))) & (zero_zero_nat = ((groups1842438620at_nat @ (^[X0 : nat] : ((times_times_nat @ (p @ X0) @ X0))) @ (set_ord_atMost_nat @ zero_zero_nat)))))),
% 1.81/0.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 1.81/0.64 thf(f263,negated_conjecture,(
% 1.81/0.64 ~ (((^[X0 : nat] : (zero_zero_nat)) = p) = ! [X0 : nat] : ((((p @ X0)) != zero_zero_nat) => ((ord_less_eq_nat @ one_one_nat @ X0) & (ord_less_eq_nat @ X0 @ zero_zero_nat))) & (zero_zero_nat = ((groups1842438620at_nat @ (^[X0 : nat] : ((times_times_nat @ (p @ X0) @ X0))) @ (set_ord_atMost_nat @ zero_zero_nat)))))),
% 1.81/0.64 inference(negated_conjecture,[status(cth)],[f262])).
% 1.81/0.64 thf(f308,plain,(
% 1.81/0.64 ((^[X0 : nat] : ((collect_nat @ (^[X1 : nat] : ((ord_less_eq_nat @ X1 @ X0)))))) = set_ord_atMost_nat)),
% 1.81/0.64 inference(rectify,[],[f65])).
% 1.81/0.64 thf(f309,plain,(
% 1.81/0.64 (set_ord_atMost_nat = (^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))))),
% 1.81/0.64 inference(fool_elimination,[],[f308])).
% 1.81/0.64 thf(f335,plain,(
% 1.81/0.64 ! [X0 : set_nat,X1 : (nat > nat),X2 : set_nat,X3 : (nat > nat)] : ((X0 = X2) => (! [X4 : nat] : ((member_nat @ X4 @ X0) => (((X3 @ X4)) = ((X1 @ X4)))) => (((groups1842438620at_nat @ X1 @ X0)) = ((groups1842438620at_nat @ X3 @ X2)))))),
% 1.81/0.64 inference(rectify,[],[f33])).
% 1.81/0.64 thf(f336,plain,(
% 1.81/0.64 ! [X3 : (nat > nat),X1 : (nat > nat),X0 : set_nat,X2 : set_nat] : ((X0 = X2) => (! [X4 : nat] : ((((member_nat @ X4 @ X0)) = $true) => (((X3 @ X4)) = ((X1 @ X4)))) => (((groups1842438620at_nat @ X1 @ X0)) = ((groups1842438620at_nat @ X3 @ X2)))))),
% 1.81/0.64 inference(fool_elimination,[],[f335])).
% 1.81/0.64 thf(f339,plain,(
% 1.81/0.64 ! [X0 : set_nat] : (((groups1842438620at_nat @ (^[X1 : nat] : (zero_zero_nat)) @ X0)) = zero_zero_nat)),
% 1.81/0.64 inference(rectify,[],[f1])).
% 1.81/0.64 thf(f340,plain,(
% 1.81/0.64 ! [X0 : set_nat] : (zero_zero_nat = ((groups1842438620at_nat @ (^[Y0 : nat]: (zero_zero_nat)) @ X0)))),
% 1.81/0.64 inference(fool_elimination,[],[f339])).
% 1.81/0.64 thf(f418,plain,(
% 1.81/0.64 (ord_less_nat = (^[X0 : nat, X1 : nat] : ((X0 != X1) & (ord_less_eq_nat @ X0 @ X1))))),
% 1.81/0.64 inference(rectify,[],[f255])).
% 1.81/0.64 thf(f419,plain,(
% 1.81/0.64 (ord_less_nat = (^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_eq_nat @ Y0 @ Y1) & (~ (Y0 = Y1)))))))),
% 1.81/0.64 inference(fool_elimination,[],[f418])).
% 1.81/0.64 thf(f442,plain,(
% 1.81/0.64 ~(ord_less_eq_nat @ one_one_nat @ zero_zero_nat)),
% 1.81/0.64 inference(rectify,[],[f76])).
% 1.81/0.64 thf(f443,plain,(
% 1.81/0.64 ~ (((ord_less_eq_nat @ one_one_nat @ zero_zero_nat)) = $true)),
% 1.81/0.64 inference(fool_elimination,[],[f442])).
% 1.81/0.64 thf(f462,plain,(
% 1.81/0.64 (((times_times_nat @ zero_zero_nat)) = (^[Y0 : nat]: (zero_zero_nat)))),
% 1.81/0.64 inference(fool_elimination,[],[f58])).
% 1.81/0.64 thf(f493,plain,(
% 1.81/0.64 ~ (((^[X0 : nat] : (zero_zero_nat)) = p) = ! [X1 : nat] : ((zero_zero_nat != ((p @ X1))) => ((ord_less_eq_nat @ one_one_nat @ X1) & (ord_less_eq_nat @ X1 @ zero_zero_nat))) & (zero_zero_nat = ((groups1842438620at_nat @ (^[X2 : nat] : ((times_times_nat @ (p @ X2) @ X2))) @ (set_ord_atMost_nat @ zero_zero_nat)))))),
% 1.81/0.64 inference(rectify,[],[f263])).
% 1.81/0.64 thf(f494,plain,(
% 1.81/0.64 ~ ((((^[Y0 : nat]: (zero_zero_nat)) = p)) = (((zero_zero_nat = (groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost_nat @ zero_zero_nat))) & (!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ Y0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ Y0))))))))),
% 1.81/0.64 inference(fool_elimination,[],[f493])).
% 1.81/0.64 thf(f503,plain,(
% 1.81/0.64 ! [X0 : nat] : ~(ord_less_nat @ X0 @ zero_zero_nat)),
% 1.81/0.64 inference(rectify,[],[f227])).
% 1.81/0.64 thf(f504,plain,(
% 1.81/0.64 ! [X0 : nat] : ~ (((ord_less_nat @ X0 @ zero_zero_nat)) = $true)),
% 1.81/0.64 inference(fool_elimination,[],[f503])).
% 1.81/0.64 thf(f724,plain,(
% 1.81/0.64 ((((^[Y0 : nat]: (zero_zero_nat)) = p)) != (((zero_zero_nat = (groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost_nat @ zero_zero_nat))) & (!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ Y0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ Y0))))))))),
% 1.81/0.64 inference(flattening,[],[f494])).
% 1.81/0.64 thf(f726,plain,(
% 1.81/0.64 (((ord_less_eq_nat @ one_one_nat @ zero_zero_nat)) != $true)),
% 1.81/0.64 inference(flattening,[],[f443])).
% 1.81/0.64 thf(f737,plain,(
% 1.81/0.64 ! [X0 : nat] : (((ord_less_nat @ X0 @ zero_zero_nat)) != $true)),
% 1.81/0.64 inference(flattening,[],[f504])).
% 1.81/0.64 thf(f755,plain,(
% 1.81/0.64 ! [X0 : nat,X1 : nat] : (((X1 != zero_zero_nat) & (X0 != zero_zero_nat)) | (zero_zero_nat = ((times_times_nat @ X0 @ X1))))),
% 1.81/0.64 inference(ennf_transformation,[],[f39])).
% 1.81/0.64 thf(f821,plain,(
% 1.81/0.64 ! [X3 : (nat > nat),X1 : (nat > nat),X0 : set_nat,X2 : set_nat] : (((((groups1842438620at_nat @ X1 @ X0)) = ((groups1842438620at_nat @ X3 @ X2))) | ? [X4 : nat] : ((((X3 @ X4)) != ((X1 @ X4))) & (((member_nat @ X4 @ X0)) = $true))) | (X0 != X2))),
% 1.81/0.64 inference(ennf_transformation,[],[f336])).
% 1.81/0.64 thf(f822,plain,(
% 1.81/0.64 ! [X2 : set_nat,X3 : (nat > nat),X0 : set_nat,X1 : (nat > nat)] : (? [X4 : nat] : ((((X3 @ X4)) != ((X1 @ X4))) & (((member_nat @ X4 @ X0)) = $true)) | (X0 != X2) | (((groups1842438620at_nat @ X1 @ X0)) = ((groups1842438620at_nat @ X3 @ X2))))),
% 1.81/0.64 inference(flattening,[],[f821])).
% 1.81/0.64 thf(f964,plain,(
% 1.81/0.64 ! [X0 : set_nat,X1 : (nat > nat),X2 : set_nat,X3 : (nat > nat)] : (? [X4 : nat] : ((((X3 @ X4)) != ((X1 @ X4))) & (((member_nat @ X4 @ X2)) = $true)) | (X0 != X2) | (((groups1842438620at_nat @ X1 @ X0)) = ((groups1842438620at_nat @ X3 @ X2))))),
% 1.81/0.64 inference(rectify,[],[f822])).
% 1.81/0.64 thf(f965,plain,(
% 1.81/0.64 ! [X0 : set_nat,X1 : (nat > nat),X2 : set_nat,X3 : (nat > nat)] : (((((X3 @ (sK26 @ X3 @ X2 @ X1))) != ((X1 @ (sK26 @ X3 @ X2 @ X1)))) & ($true = ((member_nat @ (sK26 @ X3 @ X2 @ X1) @ X2)))) | (X0 != X2) | (((groups1842438620at_nat @ X1 @ X0)) = ((groups1842438620at_nat @ X3 @ X2))))),
% 1.81/0.64 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK5 @ X1 @ X0)],[f964])).
% 1.81/0.64 thf(f1074,plain,(
% 1.81/0.64 (((ord_less_eq_nat @ one_one_nat @ zero_zero_nat)) != $true)),
% 1.81/0.64 inference(cnf_transformation,[],[f726])).
% 1.81/0.64 thf(f1075,plain,(
% 1.81/0.64 ( ! [X0 : nat] : ((zero_zero_nat = ((times_times_nat @ zero_zero_nat @ X0)))) )),
% 1.81/0.64 inference(cnf_transformation,[],[f50])).
% 1.81/0.64 thf(f1121,plain,(
% 1.81/0.64 ( ! [X0 : nat,X1 : nat] : ((zero_zero_nat != X0) | (zero_zero_nat = ((times_times_nat @ X0 @ X1)))) )),
% 1.81/0.64 inference(cnf_transformation,[],[f755])).
% 1.81/0.64 thf(f1142,plain,(
% 1.81/0.64 ( ! [X2 : set_nat,X3 : (nat > nat),X0 : set_nat,X1 : (nat > nat)] : ((((X3 @ (sK26 @ X3 @ X2 @ X1))) != ((X1 @ (sK26 @ X3 @ X2 @ X1)))) | (X0 != X2) | (((groups1842438620at_nat @ X1 @ X0)) = ((groups1842438620at_nat @ X3 @ X2)))) )),
% 1.81/0.64 inference(cnf_transformation,[],[f965])).
% 1.81/0.64 thf(f1143,plain,(
% 1.81/0.64 (set_ord_atMost_nat = (^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))))),
% 1.81/0.64 inference(cnf_transformation,[],[f309])).
% 1.81/0.64 thf(f1152,plain,(
% 1.81/0.64 ((((^[Y0 : nat]: (zero_zero_nat)) = p)) != (((zero_zero_nat = (groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost_nat @ zero_zero_nat))) & (!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ Y0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ Y0))))))))),
% 1.81/0.64 inference(cnf_transformation,[],[f724])).
% 1.81/0.64 thf(f1199,plain,(
% 1.81/0.64 (((times_times_nat @ zero_zero_nat)) = (^[Y0 : nat]: (zero_zero_nat)))),
% 1.81/0.64 inference(cnf_transformation,[],[f462])).
% 1.81/0.64 thf(f1203,plain,(
% 1.81/0.64 (ord_less_nat = (^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_eq_nat @ Y0 @ Y1) & (~ (Y0 = Y1)))))))),
% 1.81/0.64 inference(cnf_transformation,[],[f419])).
% 1.81/0.64 thf(f1214,plain,(
% 1.81/0.64 ( ! [X0 : set_nat] : ((zero_zero_nat = ((groups1842438620at_nat @ (^[Y0 : nat]: (zero_zero_nat)) @ X0)))) )),
% 1.81/0.64 inference(cnf_transformation,[],[f340])).
% 1.81/0.64 thf(f1232,plain,(
% 1.81/0.64 ( ! [X0 : nat] : ((((ord_less_nat @ X0 @ zero_zero_nat)) != $true)) )),
% 1.81/0.64 inference(cnf_transformation,[],[f737])).
% 1.81/0.64 thf(f1330,plain,(
% 1.81/0.64 ((((^[Y0 : nat]: (zero_zero_nat)) = p)) != (((zero_zero_nat = (groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))) @ zero_zero_nat))) & (!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ Y0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ Y0))))))))),
% 1.81/0.64 inference(definition_unfolding,[],[f1152,f1143])).
% 1.81/0.64 thf(f1368,plain,(
% 1.81/0.64 ( ! [X0 : nat] : (($true != (((^[Y0 : nat]: ((^[Y1 : nat]: ((ord_less_eq_nat @ Y0 @ Y1) & (~ (Y0 = Y1)))))) @ X0 @ zero_zero_nat)))) )),
% 1.81/0.64 inference(definition_unfolding,[],[f1232,f1203])).
% 1.81/0.64 thf(f1411,plain,(
% 1.81/0.64 ( ! [X1 : nat] : ((zero_zero_nat = ((times_times_nat @ zero_zero_nat @ X1)))) )),
% 1.81/0.64 inference(equality_resolution,[],[f1121])).
% 1.81/0.64 thf(f1415,plain,(
% 1.81/0.64 ( ! [X2 : set_nat,X3 : (nat > nat),X1 : (nat > nat)] : ((((groups1842438620at_nat @ X1 @ X2)) = ((groups1842438620at_nat @ X3 @ X2))) | (((X3 @ (sK26 @ X3 @ X2 @ X1))) != ((X1 @ (sK26 @ X3 @ X2 @ X1))))) )),
% 1.81/0.64 inference(equality_resolution,[],[f1142])).
% 1.81/0.64 thf(f1448,plain,(
% 1.81/0.64 ( ! [X0 : nat] : (((((ord_less_eq_nat @ X0 @ zero_zero_nat) & (~ (X0 = zero_zero_nat)))) != $true)) )),
% 1.81/0.64 inference(beta-eta_normalization,[],[f1368])).
% 1.81/0.64 thf(f1544,plain,(
% 1.81/0.64 ((((zero_zero_nat = (groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))) @ zero_zero_nat))) & (!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ Y0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ Y0))))))) = $true) | ((((^[Y0 : nat]: (zero_zero_nat)) = p)) = $true)),
% 1.81/0.64 inference(xor_proxy_clausification,[],[f1330])).
% 1.81/0.64 thf(f1545,plain,(
% 1.81/0.64 ((((zero_zero_nat = (groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))) @ zero_zero_nat))) & (!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ Y0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ Y0))))))) = $false) | ((((^[Y0 : nat]: (zero_zero_nat)) = p)) = $false)),
% 1.81/0.64 inference(xor_proxy_clausification,[],[f1330])).
% 1.81/0.64 thf(f1546,plain,(
% 1.81/0.64 ((((^[Y0 : nat]: (zero_zero_nat)) = p)) = $false) | (((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ Y0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ Y0)))))) = $false) | ($false = ((zero_zero_nat = (groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))) @ zero_zero_nat)))))),
% 1.81/0.64 inference(and_proxy_clausification,[],[f1545])).
% 1.81/0.64 thf(f1547,plain,(
% 1.81/0.64 (((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ Y0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ Y0)))))) = $false) | (p != (^[Y0 : nat]: (zero_zero_nat))) | ($false = ((zero_zero_nat = (groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))) @ zero_zero_nat)))))),
% 1.81/0.64 inference(equality_proxy_clausification,[],[f1546])).
% 1.81/0.64 thf(f1548,plain,(
% 1.81/0.64 ($false = ((zero_zero_nat = (groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))) @ zero_zero_nat))))) | ($false = (((^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ Y0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ Y0)))) @ sK64))) | (p != (^[Y0 : nat]: (zero_zero_nat)))),
% 1.81/0.64 inference(sigma_proxy_clausification,[],[f1547])).
% 1.81/0.64 thf(f1549,plain,(
% 1.81/0.64 (p != (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))) @ zero_zero_nat)))) | ($false = (((^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ Y0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ Y0)))) @ sK64)))),
% 1.81/0.64 inference(equality_proxy_clausification,[],[f1548])).
% 1.81/0.64 thf(f1550,plain,(
% 1.81/0.64 (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat)))))) | ($false = (((~ (zero_zero_nat = (p @ sK64))) => ((ord_less_eq_nat @ sK64 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ sK64))))) | (p != (^[Y0 : nat]: (zero_zero_nat)))),
% 1.81/0.64 inference(beta-eta_normalization,[],[f1549])).
% 1.81/0.64 thf(f1552,plain,(
% 1.81/0.64 (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat)))))) | (p != (^[Y0 : nat]: (zero_zero_nat))) | ($true = ((~ (zero_zero_nat = (p @ sK64)))))),
% 1.81/0.64 inference(imp_proxy_clausification,[],[f1550])).
% 1.81/0.64 thf(f1553,plain,(
% 1.81/0.64 (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat)))))) | ($false = ((zero_zero_nat = (p @ sK64)))) | (p != (^[Y0 : nat]: (zero_zero_nat)))),
% 1.81/0.64 inference(not_proxy_clausification,[],[f1552])).
% 1.81/0.64 thf(f1554,plain,(
% 1.81/0.64 (zero_zero_nat != ((p @ sK64))) | (p != (^[Y0 : nat]: (zero_zero_nat))) | (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat))))))),
% 1.81/0.64 inference(equality_proxy_clausification,[],[f1553])).
% 1.81/0.64 thf(f1556,plain,(
% 1.81/0.64 ((((^[Y0 : nat]: (zero_zero_nat)) = p)) = $true) | (((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ Y0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ Y0)))))) = $true)),
% 1.81/0.64 inference(and_proxy_clausification,[],[f1544])).
% 1.81/0.64 thf(f1561,plain,(
% 1.81/0.64 (p = (^[Y0 : nat]: (zero_zero_nat))) | (((!! @ nat @ (^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ Y0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ Y0)))))) = $true)),
% 1.81/0.64 inference(equality_proxy_clausification,[],[f1556])).
% 1.81/0.64 thf(f1562,plain,(
% 1.81/0.64 ( ! [X1 : nat] : (((((^[Y0 : nat]: ((~ (zero_zero_nat = (p @ Y0))) => ((ord_less_eq_nat @ Y0 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ Y0)))) @ X1)) = $true) | (p = (^[Y0 : nat]: (zero_zero_nat)))) )),
% 1.81/0.64 inference(pi_proxy_clausification,[],[f1561])).
% 1.81/0.64 thf(f1563,plain,(
% 1.81/0.64 ( ! [X1 : nat] : (((((~ (zero_zero_nat = (p @ X1))) => ((ord_less_eq_nat @ X1 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ X1)))) = $true) | (p = (^[Y0 : nat]: (zero_zero_nat)))) )),
% 1.81/0.64 inference(beta-eta_normalization,[],[f1562])).
% 1.81/0.64 thf(f1564,plain,(
% 1.81/0.64 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero_nat))) | (((~ (zero_zero_nat = (p @ X1)))) = $false) | ((((ord_less_eq_nat @ X1 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ X1))) = $true)) )),
% 1.81/0.64 inference(imp_proxy_clausification,[],[f1563])).
% 1.81/0.64 thf(f1565,plain,(
% 1.81/0.64 ( ! [X1 : nat] : (((((ord_less_eq_nat @ X1 @ zero_zero_nat) & (ord_less_eq_nat @ one_one_nat @ X1))) = $true) | (p = (^[Y0 : nat]: (zero_zero_nat))) | (((zero_zero_nat = (p @ X1))) = $true)) )),
% 1.81/0.64 inference(not_proxy_clausification,[],[f1564])).
% 1.81/0.64 thf(f1566,plain,(
% 1.81/0.64 ( ! [X1 : nat] : ((((zero_zero_nat = (p @ X1))) = $true) | ($true = ((ord_less_eq_nat @ one_one_nat @ X1))) | (p = (^[Y0 : nat]: (zero_zero_nat)))) )),
% 1.81/0.64 inference(and_proxy_clausification,[],[f1565])).
% 1.81/0.64 thf(f1567,plain,(
% 1.81/0.64 ( ! [X1 : nat] : ((((zero_zero_nat = (p @ X1))) = $true) | (((ord_less_eq_nat @ X1 @ zero_zero_nat)) = $true) | (p = (^[Y0 : nat]: (zero_zero_nat)))) )),
% 1.81/0.64 inference(and_proxy_clausification,[],[f1565])).
% 1.81/0.64 thf(f1568,plain,(
% 1.81/0.64 ( ! [X1 : nat] : ((zero_zero_nat = ((p @ X1))) | (p = (^[Y0 : nat]: (zero_zero_nat))) | (((ord_less_eq_nat @ X1 @ zero_zero_nat)) = $true)) )),
% 1.81/0.64 inference(equality_proxy_clausification,[],[f1567])).
% 1.81/0.64 thf(f1569,plain,(
% 1.81/0.64 ( ! [X1 : nat] : ((p = (^[Y0 : nat]: (zero_zero_nat))) | ($true = ((ord_less_eq_nat @ one_one_nat @ X1))) | (zero_zero_nat = ((p @ X1)))) )),
% 1.81/0.64 inference(equality_proxy_clausification,[],[f1566])).
% 1.81/0.64 thf(f1571,definition,(
% 1.81/0.64 spl65_1 <=> (zero_zero_nat = ((p @ sK64)))),
% 1.81/0.64 introduced(definition,[new_symbols(definition,[spl65_1])],[avatar_definition])).
% 1.81/0.64 thf(f1573,plain,(
% 1.81/0.64 (zero_zero_nat != ((p @ sK64))) | spl65_1),
% 1.81/0.64 inference(avatar_component_clause,[],[f1571])).
% 1.81/0.64 thf(f1575,definition,(
% 1.81/0.64 spl65_2 <=> (p = (^[Y0 : nat]: (zero_zero_nat)))),
% 1.81/0.64 introduced(definition,[new_symbols(definition,[spl65_2])],[avatar_definition])).
% 1.81/0.64 thf(f1576,plain,(
% 1.81/0.64 (p = (^[Y0 : nat]: (zero_zero_nat))) | ~spl65_2),
% 1.81/0.64 inference(avatar_component_clause,[],[f1575])).
% 1.81/0.64 thf(f1577,plain,(
% 1.81/0.64 (p != (^[Y0 : nat]: (zero_zero_nat))) | spl65_2),
% 1.81/0.64 inference(avatar_component_clause,[],[f1575])).
% 1.81/0.64 thf(f1579,definition,(
% 1.81/0.64 spl65_3 <=> (zero_zero_nat = ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat))))))),
% 1.81/0.64 introduced(definition,[new_symbols(definition,[spl65_3])],[avatar_definition])).
% 1.81/0.64 thf(f1581,plain,(
% 1.81/0.64 (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat)))))) | spl65_3),
% 1.81/0.64 inference(avatar_component_clause,[],[f1579])).
% 1.81/0.64 thf(f1582,plain,(
% 1.81/0.64 ~spl65_1 | ~spl65_2 | ~spl65_3),
% 1.81/0.64 inference(avatar_split_clause,[],[f1554,f1579,f1575,f1571])).
% 1.81/0.64 thf(f1587,definition,(
% 1.81/0.64 spl65_4 <=> ! [X1 : nat] : ((zero_zero_nat = ((p @ X1))) | (((ord_less_eq_nat @ X1 @ zero_zero_nat)) = $true))),
% 1.81/0.64 introduced(definition,[new_symbols(definition,[spl65_4])],[avatar_definition])).
% 1.81/0.64 thf(f1588,plain,(
% 1.81/0.64 ( ! [X1 : nat] : ((((ord_less_eq_nat @ X1 @ zero_zero_nat)) = $true) | (zero_zero_nat = ((p @ X1)))) ) | ~spl65_4),
% 1.81/0.64 inference(avatar_component_clause,[],[f1587])).
% 1.81/0.64 thf(f1589,plain,(
% 1.81/0.64 spl65_4 | spl65_2),
% 1.81/0.64 inference(avatar_split_clause,[],[f1568,f1575,f1587])).
% 1.81/0.64 thf(f1591,definition,(
% 1.81/0.64 spl65_5 <=> ! [X1 : nat] : (($true = ((ord_less_eq_nat @ one_one_nat @ X1))) | (zero_zero_nat = ((p @ X1))))),
% 1.81/0.64 introduced(definition,[new_symbols(definition,[spl65_5])],[avatar_definition])).
% 1.81/0.64 thf(f1592,plain,(
% 1.81/0.64 ( ! [X1 : nat] : (($true = ((ord_less_eq_nat @ one_one_nat @ X1))) | (zero_zero_nat = ((p @ X1)))) ) | ~spl65_5),
% 1.81/0.64 inference(avatar_component_clause,[],[f1591])).
% 1.81/0.64 thf(f1593,plain,(
% 1.81/0.64 spl65_2 | spl65_5),
% 1.81/0.64 inference(avatar_split_clause,[],[f1569,f1591,f1575])).
% 1.81/0.64 thf(f1603,plain,(
% 1.81/0.64 ( ! [X1 : nat] : ((((p @ X1)) = (((^[Y0 : nat]: (zero_zero_nat)) @ X1)))) ) | ~spl65_2),
% 1.81/0.64 inference(argument_congruence,[],[f1576])).
% 1.81/0.64 thf(f1604,plain,(
% 1.81/0.64 ( ! [X1 : nat] : ((zero_zero_nat = ((p @ X1)))) ) | ~spl65_2),
% 1.81/0.64 inference(beta-eta_normalization,[],[f1603])).
% 1.81/0.64 thf(f1606,plain,(
% 1.81/0.64 ( ! [X0 : (nat > nat)] : ((zero_zero_nat != ((groups1842438620at_nat @ X0 @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat)))))) | (((X0 @ (sK26 @ X0 @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat))) @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0))))) != (((^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (sK26 @ X0 @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat))) @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0))))))) ) | spl65_3),
% 1.81/0.64 inference(superposition,[],[f1581,f1415])).
% 1.81/0.64 thf(f1607,plain,(
% 1.81/0.64 ( ! [X0 : (nat > nat)] : ((((X0 @ (sK26 @ X0 @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat))) @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0))))) != ((times_times_nat @ (p @ (sK26 @ X0 @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat))) @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)))) @ (sK26 @ X0 @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat))) @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)))))) | (zero_zero_nat != ((groups1842438620at_nat @ X0 @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat))))))) ) | spl65_3),
% 1.81/0.64 inference(beta-eta_normalization,[],[f1606])).
% 1.81/0.64 thf(f1609,plain,(
% 1.81/0.64 ( ! [X0 : (nat > nat)] : ((((times_times_nat @ zero_zero_nat @ (sK26 @ X0 @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat))) @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0))))) != ((X0 @ (sK26 @ X0 @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat))) @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)))))) | (zero_zero_nat != ((groups1842438620at_nat @ X0 @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat))))))) ) | (~spl65_2 | spl65_3)),
% 1.81/0.64 inference(forward_demodulation,[],[f1607,f1604])).
% 1.81/0.64 thf(f1611,plain,(
% 1.81/0.64 ( ! [X0 : (nat > nat)] : ((zero_zero_nat != ((X0 @ (sK26 @ X0 @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat))) @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)))))) | (zero_zero_nat != ((groups1842438620at_nat @ X0 @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat))))))) ) | (~spl65_2 | spl65_3)),
% 1.81/0.64 inference(forward_demodulation,[],[f1609,f1075])).
% 1.81/0.64 thf(f1739,plain,(
% 1.81/0.64 (zero_zero_nat != ((groups1842438620at_nat @ (times_times_nat @ zero_zero_nat) @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat)))))) | (zero_zero_nat != zero_zero_nat) | (~spl65_2 | spl65_3)),
% 1.81/0.64 inference(superposition,[],[f1611,f1411])).
% 1.81/0.64 thf(f1751,plain,(
% 1.81/0.64 (zero_zero_nat != ((groups1842438620at_nat @ (times_times_nat @ zero_zero_nat) @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat)))))) | (~spl65_2 | spl65_3)),
% 1.81/0.64 inference(trivial_inequality_removal,[],[f1739])).
% 1.81/0.64 thf(f1759,plain,(
% 1.81/0.64 (zero_zero_nat != ((groups1842438620at_nat @ (^[Y0 : nat]: (zero_zero_nat)) @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ zero_zero_nat)))))) | (~spl65_2 | spl65_3)),
% 1.81/0.64 inference(forward_demodulation,[],[f1751,f1199])).
% 1.81/0.64 thf(f1771,plain,(
% 1.81/0.64 $false | (~spl65_2 | spl65_3)),
% 1.81/0.64 inference(forward_subsumption_resolution,[],[f1759,f1214])).
% 1.81/0.64 thf(f1772,plain,(
% 1.81/0.64 ~spl65_2 | spl65_3),
% 1.81/0.64 inference(avatar_contradiction_clause,[],[f1771])).
% 1.81/0.64 thf(f1785,plain,(
% 1.81/0.64 $false | (spl65_1 | ~spl65_2)),
% 1.81/0.64 inference(forward_subsumption_resolution,[],[f1573,f1604])).
% 1.81/0.64 thf(f1786,plain,(
% 1.81/0.64 spl65_1 | ~spl65_2),
% 1.81/0.64 inference(avatar_contradiction_clause,[],[f1785])).
% 1.81/0.64 thf(f1787,plain,(
% 1.81/0.64 (((p @ sK66)) != (((^[Y0 : nat]: (zero_zero_nat)) @ sK66))) | spl65_2),
% 1.81/0.64 inference(negative_extensionality,[],[f1577])).
% 1.81/0.64 thf(f1788,plain,(
% 1.81/0.64 (zero_zero_nat != ((p @ sK66))) | spl65_2),
% 1.81/0.64 inference(beta-eta_normalization,[],[f1787])).
% 1.81/0.64 thf(f1810,plain,(
% 1.81/0.64 ( ! [X0 : nat] : ((zero_zero_nat = ((p @ X0))) | ((($true & (~ (X0 = zero_zero_nat)))) != $true)) ) | ~spl65_4),
% 1.81/0.64 inference(superposition,[],[f1448,f1588])).
% 1.81/0.64 thf(f1878,plain,(
% 1.81/0.64 ( ! [X0 : nat] : (($true = $false) | ($false = ((~ (X0 = zero_zero_nat)))) | (zero_zero_nat = ((p @ X0)))) ) | ~spl65_4),
% 1.81/0.64 inference(and_proxy_clausification,[],[f1810])).
% 1.81/0.64 thf(f1879,plain,(
% 1.81/0.64 ( ! [X0 : nat] : (($true = ((X0 = zero_zero_nat))) | ($true = $false) | (zero_zero_nat = ((p @ X0)))) ) | ~spl65_4),
% 1.81/0.64 inference(not_proxy_clausification,[],[f1878])).
% 1.81/0.64 thf(f1880,plain,(
% 1.81/0.64 ( ! [X0 : nat] : (($true = $false) | (zero_zero_nat = X0) | (zero_zero_nat = ((p @ X0)))) ) | ~spl65_4),
% 1.81/0.64 inference(equality_proxy_clausification,[],[f1879])).
% 1.81/0.64 thf(f1881,plain,(
% 1.81/0.64 ( ! [X0 : nat] : ((zero_zero_nat = ((p @ X0))) | (zero_zero_nat = X0)) ) | ~spl65_4),
% 1.81/0.64 inference(trivial_inequality_removal,[],[f1880])).
% 1.81/0.64 thf(f2515,plain,(
% 1.81/0.64 (zero_zero_nat = ((p @ zero_zero_nat))) | ($true != $true) | ~spl65_5),
% 1.81/0.64 inference(superposition,[],[f1074,f1592])).
% 1.81/0.64 thf(f2638,plain,(
% 1.81/0.64 (zero_zero_nat = ((p @ zero_zero_nat))) | ~spl65_5),
% 1.81/0.64 inference(trivial_inequality_removal,[],[f2515])).
% 1.81/0.64 thf(f2945,plain,(
% 1.81/0.64 (zero_zero_nat != zero_zero_nat) | (zero_zero_nat = sK66) | (spl65_2 | ~spl65_4)),
% 1.81/0.64 inference(superposition,[],[f1788,f1881])).
% 1.81/0.64 thf(f2981,plain,(
% 1.81/0.64 (zero_zero_nat = sK66) | (spl65_2 | ~spl65_4)),
% 1.81/0.64 inference(trivial_inequality_removal,[],[f2945])).
% 1.81/0.64 thf(f3089,plain,(
% 1.81/0.64 (zero_zero_nat != ((p @ zero_zero_nat))) | (spl65_2 | ~spl65_4)),
% 1.81/0.64 inference(superposition,[],[f1788,f2981])).
% 1.81/0.64 thf(f3090,plain,(
% 1.81/0.64 $false | (spl65_2 | ~spl65_4 | ~spl65_5)),
% 1.81/0.64 inference(forward_subsumption_resolution,[],[f3089,f2638])).
% 1.81/0.64 thf(f3091,plain,(
% 1.81/0.64 spl65_2 | ~spl65_4 | ~spl65_5),
% 1.81/0.64 inference(avatar_contradiction_clause,[],[f3090])).
% 1.81/0.64 cnf(s1, plain, ~spl65_1 | ~spl65_2 | ~spl65_3, inference(sat_conversion,[],[f1582])).
% 1.81/0.64 cnf(s3, plain, spl65_2 | spl65_4, inference(sat_conversion,[],[f1589])).
% 1.81/0.64 cnf(s4, plain, spl65_2 | spl65_5, inference(sat_conversion,[],[f1593])).
% 1.81/0.64 cnf(s10, plain, ~spl65_2 | spl65_3, inference(sat_conversion,[],[f1772])).
% 1.81/0.64 cnf(s14, plain, spl65_1 | ~spl65_2, inference(sat_conversion,[],[f1786])).
% 1.81/0.64 cnf(s26, plain, spl65_2 | ~spl65_4 | ~spl65_5, inference(sat_conversion,[],[f3091])).
% 1.81/0.64 cnf(s27, plain, spl65_2, inference(rat,[],[s26,s3,s4])).
% 1.81/0.64 cnf(s28, plain, spl65_1, inference(rat,[],[s14,s27])).
% 1.81/0.64 cnf(s29, plain, spl65_3, inference(rat,[],[s10,s27])).
% 1.81/0.64 cnf(s30, plain, $false, inference(rat,[],[s1,s28,s29,s27])).
% 1.81/0.64 thf(f3092,plain,(
% 1.81/0.64 $false),
% 1.81/0.64 inference(avatar_sat_refutation,[],[s30])).
% 1.81/0.64 % SZS output end Proof for theBenchmark
% 1.81/0.64 % (1767581)------------------------------
% 1.81/0.64 % (1767581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.64 % (1767581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.64 % (1767581)CaDiCaL version: 2.1.3
% 1.81/0.64 % (1767581)Termination reason: Refutation
% 1.81/0.64 % (1767581)Time elapsed: 0.151 s
% 1.81/0.64 % (1767581)Peak memory usage: 15 MB
% 1.81/0.64 % (1767581)Instructions burned: 178 (million)
% 1.81/0.64 % (1767547)Success in time 0.306 s
% 1.81/0.64 % Vampire exiting
%------------------------------------------------------------------------------