%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP132^2 : 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 : n002.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 1.19s 0.54s
% Output : Refutation 1.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP132^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n002.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 20:00:53 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.22/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.50/0.42 % (1773792)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.50/0.42 % (1773797)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2393615440:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.50/0.42 % (1773803)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.50/0.42 % (1773803)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
% 0.50/0.42 % (1773799)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3906086718:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.50/0.42 % (1773801)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4206956122:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.50/0.42 % (1773800)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=3858409474: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)
% 0.50/0.42 % (1773802)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1893705458:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.50/0.42 % (1773803)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=1988332629:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.50/0.42 % (1773798)lrs+10_16_si=on:nwc=1.5:random_seed=190941784:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.50/0.42 % (1773799)Instruction limit reached!
% 0.50/0.42 % (1773799)------------------------------
% 0.50/0.42 % (1773799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.42 % (1773799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.42 % (1773799)CaDiCaL version: 2.1.3
% 0.50/0.42 % (1773799)Termination reason: Instruction limit
% 0.50/0.42 % (1773799)Termination phase: shuffling
% 0.50/0.42 % (1773799)Time elapsed: 0.003 s
% 0.50/0.42 % (1773799)Peak memory usage: 10 MB
% 0.50/0.42 % (1773799)Instructions burned: 4 (million)
% 0.50/0.42 % (1773798)Instruction limit reached!
% 0.50/0.42 % (1773798)------------------------------
% 0.50/0.42 % (1773798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.42 % (1773798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.42 % (1773798)CaDiCaL version: 2.1.3
% 0.50/0.42 % (1773798)Termination reason: Instruction limit
% 0.50/0.42 % (1773798)Termination phase: Property scanning
% 0.50/0.42 % (1773798)Time elapsed: 0.010 s
% 0.50/0.42 % (1773798)Peak memory usage: 10 MB
% 0.50/0.42 % (1773798)Instructions burned: 19 (million)
% 0.50/0.42 % (1773801)Instruction limit reached!
% 0.50/0.42 % (1773801)------------------------------
% 0.50/0.42 % (1773801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.42 % (1773801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.42 % (1773801)CaDiCaL version: 2.1.3
% 0.50/0.42 % (1773801)Termination reason: Instruction limit
% 0.50/0.42 % (1773801)Termination phase: Property scanning
% 0.50/0.42 % (1773801)Time elapsed: 0.012 s
% 0.50/0.42 % (1773801)Peak memory usage: 10 MB
% 0.50/0.42 % (1773801)Instructions burned: 24 (million)
% 0.50/0.42 % (1773797)Instruction limit reached!
% 0.50/0.42 % (1773797)------------------------------
% 0.50/0.42 % (1773797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.42 % (1773797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.42 % (1773797)CaDiCaL version: 2.1.3
% 0.50/0.42 % (1773797)Termination reason: Instruction limit
% 0.50/0.42 % (1773797)Termination phase: Property scanning
% 0.50/0.42 % (1773797)Time elapsed: 0.022 s
% 0.50/0.42 % (1773797)Peak memory usage: 12 MB
% 0.50/0.42 % (1773797)Instructions burned: 87 (million)
% 0.50/0.42 % (1773811)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3555281471:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.50/0.42 % (1773814)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1200639026:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.50/0.45 % (1773811)Instruction limit reached!
% 0.50/0.45 % (1773811)------------------------------
% 0.50/0.45 % (1773811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (1773811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (1773811)CaDiCaL version: 2.1.3
% 0.50/0.45 % (1773811)Termination reason: Instruction limit
% 0.50/0.45 % (1773811)Termination phase: shuffling
% 0.50/0.45 % (1773811)Time elapsed: 0.002 s
% 0.50/0.45 % (1773811)Peak memory usage: 10 MB
% 0.50/0.45 % (1773811)Instructions burned: 2 (million)
% 0.50/0.45 % (1773813)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.50/0.45 % (1773814)Instruction limit reached!
% 0.50/0.45 % (1773814)------------------------------
% 0.50/0.45 % (1773814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (1773814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (1773814)CaDiCaL version: 2.1.3
% 0.50/0.45 % (1773814)Termination reason: Instruction limit
% 0.50/0.45 % (1773814)Termination phase: shuffling
% 0.50/0.45 % (1773814)Time elapsed: 0.004 s
% 0.50/0.45 % (1773814)Peak memory usage: 10 MB
% 0.50/0.45 % (1773814)Instructions burned: 14 (million)
% 0.50/0.45 % (1773812)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1053684792:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.50/0.45 % (1773813)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2500577547:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.50/0.45 % (1773812)Instruction limit reached!
% 0.50/0.45 % (1773812)------------------------------
% 0.50/0.45 % (1773812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (1773812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (1773812)CaDiCaL version: 2.1.3
% 0.50/0.45 % (1773812)Termination reason: Instruction limit
% 0.50/0.45 % (1773812)Termination phase: shuffling
% 0.50/0.45 % (1773812)Time elapsed: 0.003 s
% 0.50/0.45 % (1773812)Peak memory usage: 10 MB
% 0.50/0.45 % (1773812)Instructions burned: 5 (million)
% 0.50/0.45 % (1773813)Instruction limit reached!
% 0.50/0.45 % (1773813)------------------------------
% 0.50/0.45 % (1773813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (1773813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (1773813)CaDiCaL version: 2.1.3
% 0.50/0.45 % (1773813)Termination reason: Instruction limit
% 0.50/0.45 % (1773813)Termination phase: shuffling
% 0.50/0.45 % (1773813)Time elapsed: 0.004 s
% 0.50/0.45 % (1773813)Peak memory usage: 10 MB
% 0.50/0.45 % (1773813)Instructions burned: 8 (million)
% 0.50/0.45 % (1773802)Instruction limit reached!
% 0.50/0.45 % (1773802)------------------------------
% 0.50/0.45 % (1773802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.45 % (1773802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.45 % (1773802)CaDiCaL version: 2.1.3
% 0.50/0.45 % (1773802)Termination reason: Instruction limit
% 0.50/0.45 % (1773802)Termination phase: Property scanning
% 0.50/0.45 % (1773802)Time elapsed: 0.038 s
% 0.50/0.45 % (1773802)Peak memory usage: 12 MB
% 0.50/0.45 % (1773802)Instructions burned: 81 (million)
% 0.50/0.45 % (1773817)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
% 0.50/0.45 % (1773817)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.50/0.45 % (1773819)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=3676634371:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.50/0.45 % (1773817)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=364543319:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.50/0.45 % (1773822)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.19/0.49 % (1773821)lrs+10_1_si=on:cs=on:random_seed=3411396208:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.19/0.49 % (1773822)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=3500255556:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.19/0.49 % (1773822)Instruction limit reached!
% 1.19/0.49 % (1773822)------------------------------
% 1.19/0.49 % (1773822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.49 % (1773822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.49 % (1773822)CaDiCaL version: 2.1.3
% 1.19/0.49 % (1773822)Termination reason: Instruction limit
% 1.19/0.49 % (1773822)Termination phase: shuffling
% 1.19/0.49 % (1773822)Time elapsed: 0.002 s
% 1.19/0.49 % (1773822)Peak memory usage: 10 MB
% 1.19/0.49 % (1773822)Instructions burned: 3 (million)
% 1.19/0.49 % (1773823)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=612541906:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.19/0.49 % (1773821)Instruction limit reached!
% 1.19/0.49 % (1773821)------------------------------
% 1.19/0.49 % (1773821)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.49 % (1773821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.49 % (1773821)CaDiCaL version: 2.1.3
% 1.19/0.49 % (1773821)Termination reason: Instruction limit
% 1.19/0.49 % (1773821)Termination phase: shuffling
% 1.19/0.49 % (1773821)Time elapsed: 0.005 s
% 1.19/0.49 % (1773817)Instruction limit reached!
% 1.19/0.49 % (1773817)------------------------------
% 1.19/0.49 % (1773817)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.49 % (1773821)Peak memory usage: 10 MB
% 1.19/0.49 % (1773821)Instructions burned: 10 (million)
% 1.19/0.49 % (1773817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.49 % (1773817)CaDiCaL version: 2.1.3
% 1.19/0.49 % (1773817)Termination reason: Instruction limit
% 1.19/0.49 % (1773817)Termination phase: shuffling
% 1.19/0.49 % (1773817)Time elapsed: 0.014 s
% 1.19/0.49 % (1773817)Peak memory usage: 10 MB
% 1.19/0.49 % (1773817)Instructions burned: 30 (million)
% 1.19/0.49 % (1773819)Instruction limit reached!
% 1.19/0.49 % (1773819)------------------------------
% 1.19/0.49 % (1773819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.49 % (1773819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.49 % (1773819)CaDiCaL version: 2.1.3
% 1.19/0.49 % (1773819)Termination reason: Instruction limit
% 1.19/0.49 % (1773819)Termination phase: Property scanning
% 1.19/0.49 % (1773819)Time elapsed: 0.020 s
% 1.19/0.49 % (1773819)Peak memory usage: 11 MB
% 1.19/0.49 % (1773819)Instructions burned: 87 (million)
% 1.19/0.49 % (1773832)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3272513479:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.19/0.49 % (1773829)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2982873437:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.19/0.49 % (1773831)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1471064680:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.19/0.49 % (1773830)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3741017968:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.19/0.49 % (1773823)Instruction limit reached!
% 1.19/0.49 % (1773823)------------------------------
% 1.19/0.49 % (1773823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.49 % (1773823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.49 % (1773823)CaDiCaL version: 2.1.3
% 1.19/0.49 % (1773823)Termination reason: Instruction limit
% 1.19/0.49 % (1773823)Termination phase: Property scanning
% 1.19/0.49 % (1773823)Time elapsed: 0.019 s
% 1.19/0.49 % (1773823)Peak memory usage: 11 MB
% 1.19/0.49 % (1773823)Instructions burned: 38 (million)
% 1.19/0.49 % (1773803)Instruction limit reached!
% 1.19/0.49 % (1773803)------------------------------
% 1.19/0.49 % (1773803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.49 % (1773803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1773803)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1773803)Termination reason: Instruction limit
% 1.19/0.53 % (1773803)Termination phase: Saturation
% 1.19/0.53 % (1773803)Time elapsed: 0.083 s
% 1.19/0.53 % (1773803)Peak memory usage: 14 MB
% 1.19/0.53 % (1773803)Instructions burned: 158 (million)
% 1.19/0.53 % (1773831)Instruction limit reached!
% 1.19/0.53 % (1773831)------------------------------
% 1.19/0.53 % (1773831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1773831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1773831)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1773831)Termination reason: Instruction limit
% 1.19/0.53 % (1773831)Termination phase: shuffling
% 1.19/0.53 % (1773831)Time elapsed: 0.007 s
% 1.19/0.53 % (1773831)Peak memory usage: 10 MB
% 1.19/0.53 % (1773831)Instructions burned: 15 (million)
% 1.19/0.53 % (1773830)Instruction limit reached!
% 1.19/0.53 % (1773830)------------------------------
% 1.19/0.53 % (1773830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1773830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1773830)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1773830)Termination reason: Instruction limit
% 1.19/0.53 % (1773830)Termination phase: Property scanning
% 1.19/0.53 % (1773830)Time elapsed: 0.012 s
% 1.19/0.53 % (1773830)Peak memory usage: 10 MB
% 1.19/0.53 % (1773830)Instructions burned: 25 (million)
% 1.19/0.53 % (1773837)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=59384141:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.19/0.53 % (1773838)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3514097126: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)
% 1.19/0.53 % (1773839)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1114648244:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.19/0.53 % (1773837)Instruction limit reached!
% 1.19/0.53 % (1773837)------------------------------
% 1.19/0.53 % (1773837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1773837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1773837)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1773837)Termination reason: Instruction limit
% 1.19/0.53 % (1773837)Termination phase: shuffling
% 1.19/0.53 % (1773837)Time elapsed: 0.007 s
% 1.19/0.53 % (1773837)Peak memory usage: 10 MB
% 1.19/0.53 % (1773837)Instructions burned: 14 (million)
% 1.19/0.53 % (1773838)Instruction limit reached!
% 1.19/0.53 % (1773838)------------------------------
% 1.19/0.53 % (1773838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1773838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1773838)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1773838)Termination reason: Instruction limit
% 1.19/0.53 % (1773838)Termination phase: shuffling
% 1.19/0.53 % (1773838)Time elapsed: 0.003 s
% 1.19/0.53 % (1773838)Peak memory usage: 10 MB
% 1.19/0.53 % (1773838)Instructions burned: 6 (million)
% 1.19/0.53 % (1773840)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2030214764:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.19/0.53 % (1773839)Instruction limit reached!
% 1.19/0.53 % (1773839)------------------------------
% 1.19/0.53 % (1773839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1773839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1773839)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1773839)Termination reason: Instruction limit
% 1.19/0.53 % (1773839)Termination phase: shuffling
% 1.19/0.53 % (1773839)Time elapsed: 0.013 s
% 1.19/0.53 % (1773839)Peak memory usage: 10 MB
% 1.19/0.53 % (1773839)Instructions burned: 27 (million)
% 1.19/0.53 % (1773840)Instruction limit reached!
% 1.19/0.53 % (1773840)------------------------------
% 1.19/0.53 % (1773840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1773840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1773840)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1773840)Termination reason: Instruction limit
% 1.19/0.53 % (1773840)Termination phase: Property scanning
% 1.19/0.53 % (1773840)Time elapsed: 0.011 s
% 1.19/0.53 % (1773840)Peak memory usage: 10 MB
% 1.19/0.53 % (1773840)Instructions burned: 23 (million)
% 1.19/0.53 % (1773845)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
% 1.19/0.53 % (1773845)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.19/0.53 % (1773844)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=210582582:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.19/0.53 % (1773845)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=3069247956:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.19/0.53 % (1773847)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.19/0.53 % (1773845)Instruction limit reached!
% 1.19/0.53 % (1773845)------------------------------
% 1.19/0.53 % (1773845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1773845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1773845)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1773845)Termination reason: Instruction limit
% 1.19/0.53 % (1773845)Termination phase: shuffling
% 1.19/0.53 % (1773845)Time elapsed: 0.007 s
% 1.19/0.53 % (1773845)Peak memory usage: 10 MB
% 1.19/0.53 % (1773845)Instructions burned: 15 (million)
% 1.19/0.53 % (1773847)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=3591432966:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.19/0.53 % (1773848)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=2639945016:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.19/0.53 % (1773847)Instruction limit reached!
% 1.19/0.53 % (1773847)------------------------------
% 1.19/0.53 % (1773847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1773847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1773847)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1773847)Termination reason: Instruction limit
% 1.19/0.53 % (1773847)Termination phase: shuffling
% 1.19/0.53 % (1773847)Time elapsed: 0.004 s
% 1.19/0.53 % (1773847)Peak memory usage: 10 MB
% 1.19/0.53 % (1773847)Instructions burned: 8 (million)
% 1.19/0.53 % (1773851)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=375005281:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.19/0.53 % (1773844)Instruction limit reached!
% 1.19/0.53 % (1773844)------------------------------
% 1.19/0.53 % (1773844)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1773844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1773844)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1773844)Termination reason: Instruction limit
% 1.19/0.53 % (1773844)Termination phase: Property scanning
% 1.19/0.53 % (1773844)Time elapsed: 0.030 s
% 1.19/0.53 % (1773844)Peak memory usage: 11 MB
% 1.19/0.53 % (1773844)Instructions burned: 61 (million)
% 1.19/0.53 % (1773848)Instruction limit reached!
% 1.19/0.53 % (1773848)------------------------------
% 1.19/0.53 % (1773848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1773848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1773848)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1773848)Termination reason: Instruction limit
% 1.19/0.53 % (1773848)Termination phase: Property scanning
% 1.19/0.53 % (1773848)Time elapsed: 0.015 s
% 1.19/0.53 % (1773848)Peak memory usage: 11 MB
% 1.19/0.53 % (1773848)Instructions burned: 33 (million)
% 1.19/0.53 % (1773851)Instruction limit reached!
% 1.19/0.53 % (1773851)------------------------------
% 1.19/0.53 % (1773851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1773851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1773851)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1773851)Termination reason: Instruction limit
% 1.19/0.53 % (1773851)Termination phase: shuffling
% 1.19/0.53 % (1773851)Time elapsed: 0.004 s
% 1.19/0.53 % (1773851)Peak memory usage: 10 MB
% 1.19/0.53 % (1773851)Instructions burned: 8 (million)
% 1.19/0.53 % (1773854)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3155086923:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.19/0.53 % (1773832)Instruction limit reached!
% 1.19/0.53 % (1773832)------------------------------
% 1.19/0.53 % (1773832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1773832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1773832)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1773832)Termination reason: Instruction limit
% 1.19/0.53 % (1773832)Termination phase: Saturation
% 1.19/0.53 % (1773832)Time elapsed: 0.092 s
% 1.19/0.53 % (1773832)Peak memory usage: 14 MB
% 1.19/0.53 % (1773832)Instructions burned: 329 (million)
% 1.19/0.53 % (1773854)Instruction limit reached!
% 1.19/0.53 % (1773854)------------------------------
% 1.19/0.53 % (1773854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1773854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1773854)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1773854)Termination reason: Instruction limit
% 1.19/0.53 % (1773854)Termination phase: shuffling
% 1.19/0.53 % (1773854)Time elapsed: 0.011 s
% 1.19/0.53 % (1773854)Peak memory usage: 10 MB
% 1.19/0.53 % (1773854)Instructions burned: 25 (million)
% 1.19/0.53 % (1773856)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3942423217:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.19/0.53 % (1773857)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=4095179683:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.19/0.53 % (1773858)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=4038698009:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.19/0.53 % (1773860)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3929257294:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.19/0.53 % (1773856)Instruction limit reached!
% 1.19/0.53 % (1773856)------------------------------
% 1.19/0.54 % (1773856)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.54 % (1773856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.54 % (1773856)CaDiCaL version: 2.1.3
% 1.19/0.54 % (1773856)Termination reason: Instruction limit
% 1.19/0.54 % (1773856)Termination phase: Property scanning
% 1.19/0.54 % (1773856)Time elapsed: 0.009 s
% 1.19/0.54 % (1773856)Peak memory usage: 10 MB
% 1.19/0.54 % (1773856)Instructions burned: 20 (million)
% 1.19/0.54 % (1773861)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1837831113:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.19/0.54 % (1773866)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.19/0.54 % (1773860) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1773792-1773860"...
% 1.19/0.54 % (1773860)...printing done.
% 1.19/0.54 % (1773866)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3434244450:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.19/0.54 % (1773860)Refutation found. Thanks to Tanya!
% 1.19/0.54 % SZS status Theorem for theBenchmark
% 1.19/0.54 % SZS output start Proof for theBenchmark
% 1.19/0.54 thf(type_def_5, type, set: $tType > $tType).
% 1.19/0.54 thf(type_def_6, type, nat: $tType).
% 1.19/0.54 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 1.19/0.54 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_1, type, dvd: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_2, type, one: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_3, type, ring: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_4, type, zero: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_5, type, minus: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_6, type, ord: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_7, type, neg_numeral: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_8, type, order: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_9, type, comm_ring: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_10, type, mult_zero: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_11, type, group_add: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_12, type, no_bot: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_13, type, no_top: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_14, type, semiring_0: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_15, type, monoid_mult: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_16, type, linorder: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_17, type, preorder: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_18, type, ordered_ring: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_19, type, zero_neq_one: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_20, type, ab_group_add: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_21, type, wellorder: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_22, type, semigroup_mult: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_23, type, dense_order: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_24, type, linordered_idom: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_25, type, linordered_ring: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_26, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_27, type, ordered_semiring: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_28, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_29, type, comm_monoid_mult: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_30, type, ab_semigroup_mult: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_31, type, ordered_semiring_0: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_32, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_33, type, ordere1490568538miring: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_34, type, comm_s1003936772cancel: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_35, type, linord581940658strict: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_36, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_37, type, ring_11004092258visors: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_38, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_39, type, ordere216010020id_add: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_40, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_41, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_42, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_43, type, semiri1923998003cancel: !>[X0: $tType]:($o)).
% 1.19/0.54 thf(func_def_44, type, fun_upd: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0 > X1 > X0 > X1))).
% 1.19/0.54 thf(func_def_45, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 1.19/0.54 thf(func_def_46, type, one_one: !>[X0: $tType]:(X0)).
% 1.19/0.54 thf(func_def_47, type, times_times: !>[X0: $tType]:((X0 > X0 > X0))).
% 1.19/0.54 thf(func_def_48, type, zero_zero: !>[X0: $tType]:(X0)).
% 1.19/0.54 thf(func_def_49, type, groups1340683514dd_sum: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > X1))).
% 1.19/0.54 thf(func_def_50, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 1.19/0.54 thf(func_def_51, type, number2016821345itions: ((nat > nat) > nat > $o)).
% 1.19/0.54 thf(func_def_52, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.19/0.54 thf(func_def_53, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.19/0.54 thf(func_def_54, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 1.19/0.54 thf(func_def_55, type, set_ord_atMost: !>[X0: $tType]:((X0 > set @ X0))).
% 1.19/0.54 thf(func_def_56, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 1.19/0.54 thf(func_def_57, type, k: nat).
% 1.19/0.54 thf(func_def_58, type, n: nat).
% 1.19/0.54 thf(func_def_59, type, p: (nat > nat)).
% 1.19/0.54 thf(func_def_61, type, db2: !>[X0: $tType]:(X0)).
% 1.19/0.54 thf(func_def_62, type, db0: !>[X0: $tType]:(X0)).
% 1.19/0.54 thf(func_def_63, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.19/0.54 thf(func_def_64, type, db1: !>[X0: $tType]:(X0)).
% 1.19/0.54 thf(func_def_65, type, db3: !>[X0: $tType]:(X0)).
% 1.19/0.54 thf(func_def_66, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.19/0.54 thf(func_def_69, type, vAND: ($o > $o > $o)).
% 1.19/0.54 thf(func_def_70, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.19/0.54 thf(func_def_71, type, vIMP: ($o > $o > $o)).
% 1.19/0.54 thf(func_def_72, type, vNOT: ($o > $o)).
% 1.19/0.54 thf(func_def_73, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.19/0.54 thf(func_def_74, type, vOR: ($o > $o > $o)).
% 1.19/0.54 thf(func_def_75, type, sP0: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > (X1 > X0) > $o))).
% 1.19/0.54 thf(func_def_76, type, sP1: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > set @ X0 > $o))).
% 1.19/0.54 thf(func_def_77, type, sK2: !>[X0: $tType]:(((X0 > nat) > set @ X0 > (X0 > nat) > X0))).
% 1.19/0.54 thf(func_def_78, type, sK3: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 1.19/0.54 thf(func_def_79, type, sK4: ((nat > nat) > nat > nat)).
% 1.19/0.54 thf(func_def_80, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X1 > (X1 > X2) > (X1 > X0) > (X0 > X2) > set @ X0 > X1))).
% 1.19/0.54 thf(func_def_81, type, sK6: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > X0))).
% 1.19/0.54 thf(func_def_82, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > set @ X1 > (X1 > X0) > set @ X0 > X1))).
% 1.19/0.54 thf(func_def_83, type, sK8: (nat > (nat > $o) > nat)).
% 1.19/0.54 thf(func_def_84, type, sK9: ((nat > $o) > nat)).
% 1.19/0.54 thf(func_def_85, type, sK10: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 1.19/0.54 thf(func_def_86, type, sK11: ((nat > $o) > nat)).
% 1.19/0.54 thf(func_def_87, type, sK12: ((nat > $o) > nat > nat)).
% 1.19/0.54 thf(func_def_88, type, sK13: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > (X1 > X0) > X1))).
% 1.19/0.54 thf(func_def_89, type, sK14: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 1.19/0.54 thf(func_def_90, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > set @ X0 > X0))).
% 1.19/0.54 thf(func_def_91, type, sK16: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > (X1 > X0) > X1))).
% 1.19/0.54 thf(func_def_92, type, sK17: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0 > X0))).
% 1.19/0.54 thf(func_def_93, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X0) > set @ X2 > (X2 > X1) > (X0 > X1) > X2))).
% 1.19/0.54 thf(func_def_94, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > X1))).
% 1.19/0.54 thf(func_def_95, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > set @ X0 > set @ X1 > X1))).
% 1.19/0.54 thf(func_def_96, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X2) > (X1 > X0) > (X0 > X1) > set @ X0 > set @ X1 > (X0 > X2) > X0))).
% 1.19/0.54 thf(func_def_97, type, sK22: ((nat > $o) > nat)).
% 1.19/0.54 thf(func_def_98, type, sK23: ((nat > $o) > nat)).
% 1.19/0.54 thf(func_def_99, type, sK24: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X0))).
% 1.19/0.54 thf(func_def_100, type, sK25: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 1.19/0.54 thf(func_def_101, type, sK26: (nat > (nat > nat) > nat)).
% 1.19/0.54 thf(func_def_102, type, sK27: ((nat > nat) > nat > nat)).
% 1.19/0.54 thf(func_def_103, type, sK28: (nat > (nat > nat) > nat)).
% 1.19/0.54 thf(func_def_104, type, sK29: (nat > (nat > nat) > nat)).
% 1.19/0.54 thf(func_def_105, type, sK30: ((nat > nat) > nat)).
% 1.19/0.54 thf(f1,axiom,(
% 1.19/0.54 (number2016821345itions @ p @ n)),
% 1.19/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_partitions)).
% 1.19/0.54 thf(f64,axiom,(
% 1.19/0.54 (number2016821345itions = (^[X0 : (nat > nat), X1 : nat] : (! [X2 : nat] : ((((X0 @ X2)) != zero_zero @ nat) => ((ord_less_eq @ nat @ X2 @ X1) & (ord_less_eq @ nat @ one_one @ nat @ X2))) & (X1 = ((groups1340683514dd_sum @ nat @ nat @ (^[X2 : nat] : ((times_times @ nat @ (X0 @ X2) @ X2))) @ (set_ord_atMost @ nat @ X1)))))))),
% 1.19/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_partitions__def)).
% 1.19/0.54 thf(f300,conjecture,(
% 1.19/0.54 (((minus_minus @ nat @ n @ k)) = ((minus_minus @ nat @ (groups1340683514dd_sum @ nat @ nat @ (^[X0 : nat] : ((times_times @ nat @ (p @ X0) @ X0))) @ (set_ord_atMost @ nat @ n)) @ k)))),
% 1.19/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 1.19/0.54 thf(f301,negated_conjecture,(
% 1.19/0.54 ~ (((minus_minus @ nat @ n @ k)) = ((minus_minus @ nat @ (groups1340683514dd_sum @ nat @ nat @ (^[X0 : nat] : ((times_times @ nat @ (p @ X0) @ X0))) @ (set_ord_atMost @ nat @ n)) @ k)))),
% 1.19/0.54 inference(negated_conjecture,[status(cth)],[f300])).
% 1.19/0.54 thf(f316,plain,(
% 1.19/0.54 (number2016821345itions = (^[X0 : (nat > nat), X1 : nat] : (! [X2 : nat] : ((((X0 @ X2)) != zero_zero @ nat) => ((ord_less_eq @ nat @ X2 @ X1) & (ord_less_eq @ nat @ one_one @ nat @ X2))) & (X1 = ((groups1340683514dd_sum @ nat @ nat @ (^[X3 : nat] : ((times_times @ nat @ (X0 @ X3) @ X3))) @ (set_ord_atMost @ nat @ X1)))))))),
% 1.19/0.54 inference(rectify,[],[f64])).
% 1.19/0.54 thf(f317,plain,(
% 1.19/0.54 (number2016821345itions = (^[Y0 : nat > nat]: ((^[Y1 : nat]: ((Y1 = (groups1340683514dd_sum @ nat @ nat @ (^[Y2 : nat]: (times_times @ nat @ (Y0 @ Y2) @ Y2)) @ (set_ord_atMost @ nat @ Y1))) & (!! @ nat @ (^[Y2 : nat]: ((~ ((Y0 @ Y2) = zero_zero @ nat)) => ((ord_less_eq @ nat @ one_one @ nat @ Y2) & (ord_less_eq @ nat @ Y2 @ Y1))))))))))),
% 1.19/0.54 inference(fool_elimination,[],[f316])).
% 1.19/0.54 thf(f644,plain,(
% 1.19/0.54 ~ (((minus_minus @ nat @ n @ k)) = ((minus_minus @ nat @ (groups1340683514dd_sum @ nat @ nat @ (^[X0 : nat] : ((times_times @ nat @ (p @ X0) @ X0))) @ (set_ord_atMost @ nat @ n)) @ k)))),
% 1.19/0.54 inference(rectify,[],[f301])).
% 1.19/0.54 thf(f645,plain,(
% 1.19/0.54 ~ (((minus_minus @ nat @ n @ k)) = ((minus_minus @ nat @ (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ n)) @ k)))),
% 1.19/0.54 inference(fool_elimination,[],[f644])).
% 1.19/0.54 thf(f737,plain,(
% 1.19/0.54 (number2016821345itions @ p @ n)),
% 1.19/0.54 inference(rectify,[],[f1])).
% 1.19/0.54 thf(f738,plain,(
% 1.19/0.54 (((number2016821345itions @ p @ n)) = $true)),
% 1.19/0.54 inference(fool_elimination,[],[f737])).
% 1.19/0.54 thf(f847,plain,(
% 1.19/0.54 (((minus_minus @ nat @ n @ k)) != ((minus_minus @ nat @ (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ n)) @ k)))),
% 1.19/0.54 inference(flattening,[],[f645])).
% 1.19/0.54 thf(f978,plain,(
% 1.19/0.54 (number2016821345itions = (^[Y0 : nat > nat]: ((^[Y1 : nat]: ((Y1 = (groups1340683514dd_sum @ nat @ nat @ (^[Y2 : nat]: (times_times @ nat @ (Y0 @ Y2) @ Y2)) @ (set_ord_atMost @ nat @ Y1))) & (!! @ nat @ (^[Y2 : nat]: ((~ ((Y0 @ Y2) = zero_zero @ nat)) => ((ord_less_eq @ nat @ one_one @ nat @ Y2) & (ord_less_eq @ nat @ Y2 @ Y1))))))))))),
% 1.19/0.54 inference(cnf_transformation,[],[f317])).
% 1.19/0.54 thf(f1045,plain,(
% 1.19/0.54 (((number2016821345itions @ p @ n)) = $true)),
% 1.19/0.54 inference(cnf_transformation,[],[f738])).
% 1.19/0.54 thf(f1090,plain,(
% 1.19/0.54 (((minus_minus @ nat @ n @ k)) != ((minus_minus @ nat @ (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ n)) @ k)))),
% 1.19/0.54 inference(cnf_transformation,[],[f847])).
% 1.19/0.54 thf(f1105,plain,(
% 1.19/0.54 ((((^[Y0 : nat > nat]: ((^[Y1 : nat]: ((Y1 = (groups1340683514dd_sum @ nat @ nat @ (^[Y2 : nat]: (times_times @ nat @ (Y0 @ Y2) @ Y2)) @ (set_ord_atMost @ nat @ Y1))) & (!! @ nat @ (^[Y2 : nat]: ((~ ((Y0 @ Y2) = zero_zero @ nat)) => ((ord_less_eq @ nat @ one_one @ nat @ Y2) & (ord_less_eq @ nat @ Y2 @ Y1))))))))) @ p @ n)) = $true)),
% 1.19/0.54 inference(definition_unfolding,[],[f1045,f978])).
% 1.19/0.54 thf(f1126,plain,(
% 1.19/0.54 ((((n = (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ n))) & (!! @ nat @ (^[Y0 : nat]: ((~ ((p @ Y0) = zero_zero @ nat)) => ((ord_less_eq @ nat @ one_one @ nat @ Y0) & (ord_less_eq @ nat @ Y0 @ n))))))) = $true)),
% 1.19/0.54 inference(beta-eta_normalization,[],[f1105])).
% 1.19/0.54 thf(f1128,plain,(
% 1.19/0.54 (((n = (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ n)))) = $true)),
% 1.19/0.54 inference(and_proxy_clausification,[],[f1126])).
% 1.19/0.54 thf(f1129,plain,(
% 1.19/0.54 (n = ((groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ n))))),
% 1.19/0.54 inference(equality_proxy_clausification,[],[f1128])).
% 1.19/0.54 thf(f1255,definition,(
% 1.19/0.54 spl31_2 <=> (n = ((groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ n))))),
% 1.19/0.54 introduced(definition,[new_symbols(definition,[spl31_2])],[avatar_definition])).
% 1.19/0.54 thf(f1258,plain,(
% 1.19/0.54 spl31_2),
% 1.19/0.54 inference(avatar_split_clause,[],[f1129,f1255])).
% 1.19/0.54 thf(f1275,definition,(
% 1.19/0.54 spl31_6 <=> (((minus_minus @ nat @ n @ k)) = ((minus_minus @ nat @ (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ n)) @ k)))),
% 1.19/0.54 introduced(definition,[new_symbols(definition,[spl31_6])],[avatar_definition])).
% 1.19/0.54 thf(f1278,plain,(
% 1.19/0.54 ~spl31_6),
% 1.19/0.54 inference(avatar_split_clause,[],[f1090,f1275])).
% 1.19/0.54 thf(f1289,definition,(
% 1.19/0.54 (n != ((groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ n)))) | (((minus_minus @ nat @ n @ k)) = ((minus_minus @ nat @ (groups1340683514dd_sum @ nat @ nat @ (^[Y0 : nat]: (times_times @ nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost @ nat @ n)) @ k)))),
% 1.19/0.54 introduced(theory,[theory_tautology_sat_conflict])).
% 1.19/0.54 cnf(s2, plain, spl31_2, inference(sat_conversion,[],[f1258])).
% 1.19/0.54 cnf(s6, plain, ~spl31_6, inference(sat_conversion,[],[f1278])).
% 1.19/0.54 cnf(s9, plain, ~spl31_2 | spl31_6, inference(sat_conversion,[],[f1289])).
% 1.19/0.54 cnf(s10, plain, ~spl31_2, inference(rat,[],[s9,s6])).
% 1.19/0.54 cnf(s11, plain, $false, inference(rat,[],[s2,s10])).
% 1.19/0.54 thf(f1290,plain,(
% 1.19/0.54 $false),
% 1.19/0.54 inference(avatar_sat_refutation,[],[s11])).
% 1.19/0.54 % SZS output end Proof for theBenchmark
% 1.19/0.54 % (1773860)------------------------------
% 1.19/0.54 % (1773860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.54 % (1773860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.54 % (1773860)CaDiCaL version: 2.1.3
% 1.19/0.54 % (1773860)Termination reason: Refutation
% 1.19/0.54 % (1773860)Time elapsed: 0.023 s
% 1.19/0.54 % (1773860)Peak memory usage: 14 MB
% 1.19/0.54 % (1773860)Instructions burned: 87 (million)
% 1.19/0.54 % (1773792)Success in time 0.252 s
% 1.19/0.54 % Vampire exiting
%------------------------------------------------------------------------------