%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP043^2 : 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 : n013.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 08:08:05 AM UTC 2026
% Result : Theorem 1.65s 0.50s
% Output : Refutation 1.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP043^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.14 % Computer : n013.cluster.edu
% 0.11/0.14 % Model : x86_64 x86_64
% 0.11/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.14 % Memory : 8046.5625MB
% 0.11/0.14 % OS : Linux 6.8.0-71-generic
% 0.11/0.14 % CPULimit : 300
% 0.11/0.14 % WCLimit : 300
% 0.11/0.14 % DateTime : Tue Sep 29 19:40:06 UTC 2026
% 0.11/0.15 % CPUTime :
% 0.11/0.15 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 Running higher-order theorem proving
% 0.11/0.23 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
% 0.86/0.36 % (2560985)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.86/0.36 % (2560994)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3388083406:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.86/0.36 % (2560994)Instruction limit reached!
% 0.86/0.36 % (2560994)------------------------------
% 0.86/0.36 % (2560994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.36 % (2560994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.36 % (2560994)CaDiCaL version: 2.1.3
% 0.86/0.36 % (2560994)Termination reason: Instruction limit
% 0.86/0.36 % (2560994)Termination phase: Property scanning
% 0.86/0.36 % (2560994)Time elapsed: 0.006 s
% 0.86/0.36 % (2560994)Peak memory usage: 10 MB
% 0.86/0.36 % (2560994)Instructions burned: 25 (million)
% 0.86/0.36 % (2560990)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=857871172:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.86/0.36 % (2560991)lrs+10_16_si=on:nwc=1.5:random_seed=1913314835:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.86/0.36 % (2560993)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=4101059689: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)
% 0.86/0.36 % (2560995)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2002664374:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.86/0.36 % (2560996)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.86/0.36 % (2560996)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
% 0.86/0.36 % (2560998)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3480085225:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.86/0.36 % (2560991)Instruction limit reached!
% 0.86/0.36 % (2560991)------------------------------
% 0.86/0.36 % (2560991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.36 % (2560991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.36 % (2560991)CaDiCaL version: 2.1.3
% 0.86/0.36 % (2560991)Termination reason: Instruction limit
% 0.86/0.36 % (2560991)Termination phase: Property scanning
% 0.86/0.36 % (2560991)Time elapsed: 0.010 s
% 0.86/0.36 % (2560991)Peak memory usage: 10 MB
% 0.86/0.36 % (2560991)Instructions burned: 19 (million)
% 0.86/0.36 % (2560998)Instruction limit reached!
% 0.86/0.36 % (2560998)------------------------------
% 0.86/0.36 % (2560998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.36 % (2560998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.36 % (2560998)CaDiCaL version: 2.1.3
% 0.86/0.36 % (2560998)Termination reason: Instruction limit
% 0.86/0.36 % (2560998)Termination phase: shuffling
% 0.86/0.36 % (2560998)Time elapsed: 0.001 s
% 0.86/0.36 % (2560998)Peak memory usage: 10 MB
% 0.86/0.36 % (2560998)Instructions burned: 3 (million)
% 0.86/0.36 % (2560992)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1572265602:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.86/0.36 % (2560996)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=2964838835:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.86/0.36 % (2560992)Instruction limit reached!
% 0.86/0.36 % (2560992)------------------------------
% 0.86/0.36 % (2560992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.36 % (2560992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.36 % (2560992)CaDiCaL version: 2.1.3
% 0.86/0.36 % (2560992)Termination reason: Instruction limit
% 0.86/0.36 % (2560992)Termination phase: shuffling
% 0.86/0.36 % (2560992)Time elapsed: 0.004 s
% 0.86/0.36 % (2560992)Peak memory usage: 10 MB
% 0.86/0.36 % (2560992)Instructions burned: 4 (million)
% 0.86/0.36 % (2561005)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.86/0.40 % (2561005)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=960891650:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.86/0.40 % (2561005)Instruction limit reached!
% 0.86/0.40 % (2561005)------------------------------
% 0.86/0.40 % (2561005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.40 % (2561005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.40 % (2561005)CaDiCaL version: 2.1.3
% 0.86/0.40 % (2561005)Termination reason: Instruction limit
% 0.86/0.40 % (2561005)Termination phase: shuffling
% 0.86/0.40 % (2561005)Time elapsed: 0.002 s
% 0.86/0.40 % (2561005)Peak memory usage: 10 MB
% 0.86/0.40 % (2561005)Instructions burned: 8 (million)
% 0.86/0.40 % (2561004)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3067940256:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.86/0.40 % (2561010)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
% 0.86/0.40 % (2561010)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.86/0.40 % (2561004)Instruction limit reached!
% 0.86/0.40 % (2561004)------------------------------
% 0.86/0.40 % (2561004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.40 % (2561004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.40 % (2561004)CaDiCaL version: 2.1.3
% 0.86/0.40 % (2561004)Termination reason: Instruction limit
% 0.86/0.40 % (2561004)Termination phase: shuffling
% 0.86/0.40 % (2561004)Time elapsed: 0.003 s
% 0.86/0.40 % (2561004)Peak memory usage: 10 MB
% 0.86/0.40 % (2561004)Instructions burned: 5 (million)
% 0.86/0.40 % (2561010)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3095881941:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.86/0.40 % (2561008)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=303835152:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.86/0.40 % (2560990)Instruction limit reached!
% 0.86/0.40 % (2560990)------------------------------
% 0.86/0.40 % (2560990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.40 % (2560990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.40 % (2560990)CaDiCaL version: 2.1.3
% 0.86/0.40 % (2560990)Termination reason: Instruction limit
% 0.86/0.40 % (2560990)Termination phase: Property scanning
% 0.86/0.40 % (2560990)Time elapsed: 0.041 s
% 0.86/0.40 % (2560990)Peak memory usage: 12 MB
% 0.86/0.40 % (2560990)Instructions burned: 87 (million)
% 0.86/0.40 % (2561010)Instruction limit reached!
% 0.86/0.40 % (2561010)------------------------------
% 0.86/0.40 % (2561010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.40 % (2561010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.40 % (2561010)CaDiCaL version: 2.1.3
% 0.86/0.40 % (2561010)Termination reason: Instruction limit
% 0.86/0.40 % (2561010)Termination phase: shuffling
% 0.86/0.40 % (2561010)Time elapsed: 0.007 s
% 0.86/0.40 % (2561010)Peak memory usage: 10 MB
% 0.86/0.40 % (2561010)Instructions burned: 31 (million)
% 0.86/0.40 % (2561008)Instruction limit reached!
% 0.86/0.40 % (2561008)------------------------------
% 0.86/0.40 % (2561008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.40 % (2561008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.40 % (2561008)CaDiCaL version: 2.1.3
% 0.86/0.40 % (2561008)Termination reason: Instruction limit
% 0.86/0.40 % (2561008)Termination phase: shuffling
% 0.86/0.40 % (2561008)Time elapsed: 0.006 s
% 0.86/0.40 % (2561008)Peak memory usage: 10 MB
% 0.86/0.40 % (2561008)Instructions burned: 12 (million)
% 0.86/0.40 % (2560995)Instruction limit reached!
% 0.86/0.40 % (2560995)------------------------------
% 0.86/0.40 % (2560995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.40 % (2560995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.40 % (2560995)CaDiCaL version: 2.1.3
% 0.86/0.40 % (2560995)Termination reason: Instruction limit
% 0.86/0.43 % (2560995)Termination phase: Property scanning
% 0.86/0.43 % (2560995)Time elapsed: 0.047 s
% 0.86/0.43 % (2560995)Peak memory usage: 12 MB
% 0.86/0.43 % (2560995)Instructions burned: 76 (million)
% 0.86/0.43 % (2561015)lrs+10_1_si=on:cs=on:random_seed=2692330766:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.86/0.43 % (2561012)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=4278022928:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.86/0.43 % (2561015)Instruction limit reached!
% 0.86/0.43 % (2561015)------------------------------
% 0.86/0.43 % (2561015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.43 % (2561015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.43 % (2561015)CaDiCaL version: 2.1.3
% 0.86/0.43 % (2561015)Termination reason: Instruction limit
% 0.86/0.43 % (2561015)Termination phase: shuffling
% 0.86/0.43 % (2561015)Time elapsed: 0.003 s
% 0.86/0.43 % (2561015)Peak memory usage: 10 MB
% 0.86/0.43 % (2561015)Instructions burned: 10 (million)
% 0.86/0.43 % (2561016)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.86/0.43 % (2561016)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=428812488:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.86/0.43 % (2561017)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4109958156:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.86/0.43 % (2561016)Instruction limit reached!
% 0.86/0.43 % (2561016)------------------------------
% 0.86/0.43 % (2561016)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.43 % (2561016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.43 % (2561016)CaDiCaL version: 2.1.3
% 0.86/0.43 % (2561016)Termination reason: Instruction limit
% 0.86/0.43 % (2561016)Termination phase: shuffling
% 0.86/0.43 % (2561016)Time elapsed: 0.004 s
% 0.86/0.43 % (2561016)Peak memory usage: 10 MB
% 0.86/0.43 % (2561016)Instructions burned: 7 (million)
% 0.86/0.43 % (2561021)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=414907063:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.86/0.43 % (2561018)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=320949336:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.86/0.43 % (2561021)Instruction limit reached!
% 0.86/0.43 % (2561021)------------------------------
% 0.86/0.43 % (2561021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.43 % (2561021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.43 % (2561021)CaDiCaL version: 2.1.3
% 0.86/0.43 % (2561021)Termination reason: Instruction limit
% 0.86/0.43 % (2561021)Termination phase: Property scanning
% 0.86/0.43 % (2561021)Time elapsed: 0.006 s
% 0.86/0.43 % (2561021)Peak memory usage: 10 MB
% 0.86/0.43 % (2561021)Instructions burned: 25 (million)
% 0.86/0.43 % (2561017)Instruction limit reached!
% 0.86/0.43 % (2561017)------------------------------
% 0.86/0.43 % (2561017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.43 % (2561017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.43 % (2561017)CaDiCaL version: 2.1.3
% 0.86/0.43 % (2561017)Termination reason: Instruction limit
% 0.86/0.43 % (2561017)Termination phase: Preprocessing 3
% 0.86/0.43 % (2561017)Time elapsed: 0.019 s
% 0.86/0.43 % (2561017)Peak memory usage: 11 MB
% 0.86/0.43 % (2561017)Instructions burned: 39 (million)
% 0.86/0.43 % (2561027)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2388240943:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.86/0.43 % (2561025)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3822988721:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.86/0.43 % (2561025)Instruction limit reached!
% 0.86/0.43 % (2561025)------------------------------
% 0.86/0.43 % (2561025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.43 % (2561025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.48 % (2561025)CaDiCaL version: 2.1.3
% 0.86/0.48 % (2561025)Termination reason: Instruction limit
% 0.86/0.48 % (2561025)Termination phase: shuffling
% 0.86/0.48 % (2561025)Time elapsed: 0.008 s
% 0.86/0.48 % (2561025)Peak memory usage: 10 MB
% 0.86/0.48 % (2561025)Instructions burned: 15 (million)
% 0.86/0.48 % (2561028)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2234765089:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.86/0.48 % (2560996)Instruction limit reached!
% 0.86/0.48 % (2560996)------------------------------
% 0.86/0.48 % (2560996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.48 % (2560996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.48 % (2560996)CaDiCaL version: 2.1.3
% 0.86/0.48 % (2560996)Termination reason: Instruction limit
% 0.86/0.48 % (2560996)Termination phase: Saturation
% 0.86/0.48 % (2560996)Time elapsed: 0.090 s
% 0.86/0.48 % (2560996)Peak memory usage: 14 MB
% 0.86/0.48 % (2560996)Instructions burned: 157 (million)
% 0.86/0.48 % (2561028)Instruction limit reached!
% 0.86/0.48 % (2561028)------------------------------
% 0.86/0.48 % (2561028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.48 % (2561028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.48 % (2561028)CaDiCaL version: 2.1.3
% 0.86/0.48 % (2561028)Termination reason: Instruction limit
% 0.86/0.48 % (2561028)Termination phase: shuffling
% 0.86/0.48 % (2561028)Time elapsed: 0.008 s
% 0.86/0.48 % (2561028)Peak memory usage: 10 MB
% 0.86/0.48 % (2561028)Instructions burned: 16 (million)
% 0.86/0.48 % (2561012)Instruction limit reached!
% 0.86/0.48 % (2561012)------------------------------
% 0.86/0.48 % (2561012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.48 % (2561012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.48 % (2561012)CaDiCaL version: 2.1.3
% 0.86/0.48 % (2561012)Termination reason: Instruction limit
% 0.86/0.48 % (2561012)Termination phase: Preprocessing 3
% 0.86/0.48 % (2561012)Time elapsed: 0.057 s
% 0.86/0.48 % (2561012)Peak memory usage: 11 MB
% 0.86/0.48 % (2561012)Instructions burned: 86 (million)
% 0.86/0.48 % (2561031)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1653671182:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.86/0.48 % (2561018)Refutation not found, incomplete strategy
% 0.86/0.48 % (2561018)------------------------------
% 0.86/0.48 % (2561018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.48 % (2561018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.48 % (2561018)CaDiCaL version: 2.1.3
% 0.86/0.48 % (2561018)Termination reason: Refutation not found, incomplete strategy
% 0.86/0.48 % (2561018)Time elapsed: 0.044 s
% 0.86/0.48 % (2561018)Peak memory usage: 13 MB
% 0.86/0.48 % (2561018)Instructions burned: 64 (million)
% 0.86/0.48 % (2561031)Instruction limit reached!
% 0.86/0.48 % (2561031)------------------------------
% 0.86/0.48 % (2561031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.48 % (2561031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.48 % (2561031)CaDiCaL version: 2.1.3
% 0.86/0.48 % (2561031)Termination reason: Instruction limit
% 0.86/0.48 % (2561031)Termination phase: shuffling
% 0.86/0.48 % (2561031)Time elapsed: 0.003 s
% 0.86/0.48 % (2561031)Peak memory usage: 10 MB
% 0.86/0.48 % (2561031)Instructions burned: 5 (million)
% 0.86/0.48 % (2561018)------------------------------
% 0.86/0.48 % (2561018)------------------------------
% 0.86/0.48 % (2561035)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2121747333:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.86/0.48 % (2561034)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=597742580:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.86/0.48 % (2561037)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.86/0.48 % (2561037)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.86/0.48 % (2561037)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=83907397:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.65/0.50 % (2561038)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.65/0.50 % (2561033)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1281636459:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.65/0.50 % (2561038)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=876047471:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.65/0.50 % (2561034)Instruction limit reached!
% 1.65/0.50 % (2561034)------------------------------
% 1.65/0.50 % (2561034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.50 % (2561034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.50 % (2561034)CaDiCaL version: 2.1.3
% 1.65/0.50 % (2561034)Termination reason: Instruction limit
% 1.65/0.50 % (2561034)Termination phase: Property scanning
% 1.65/0.50 % (2561034)Time elapsed: 0.011 s
% 1.65/0.50 % (2561034)Peak memory usage: 10 MB
% 1.65/0.50 % (2561034)Instructions burned: 23 (million)
% 1.65/0.50 % (2561037)Instruction limit reached!
% 1.65/0.50 % (2561037)------------------------------
% 1.65/0.50 % (2561037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.50 % (2561037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.50 % (2561037)CaDiCaL version: 2.1.3
% 1.65/0.50 % (2561037)Termination reason: Instruction limit
% 1.65/0.50 % (2561037)Termination phase: shuffling
% 1.65/0.50 % (2561037)Time elapsed: 0.007 s
% 1.65/0.50 % (2561037)Peak memory usage: 10 MB
% 1.65/0.50 % (2561037)Instructions burned: 15 (million)
% 1.65/0.50 % (2561038)Instruction limit reached!
% 1.65/0.50 % (2561038)------------------------------
% 1.65/0.50 % (2561038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.50 % (2561038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.50 % (2561038)CaDiCaL version: 2.1.3
% 1.65/0.50 % (2561038)Termination reason: Instruction limit
% 1.65/0.50 % (2561038)Termination phase: shuffling
% 1.65/0.50 % (2561038)Time elapsed: 0.007 s
% 1.65/0.50 % (2561038)Peak memory usage: 10 MB
% 1.65/0.50 % (2561038)Instructions burned: 9 (million)
% 1.65/0.50 % (2561033)Instruction limit reached!
% 1.65/0.50 % (2561033)------------------------------
% 1.65/0.50 % (2561033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.50 % (2561033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.50 % (2561033)CaDiCaL version: 2.1.3
% 1.65/0.50 % (2561033)Termination reason: Instruction limit
% 1.65/0.50 % (2561033)Termination phase: shuffling
% 1.65/0.50 % (2561033)Time elapsed: 0.012 s
% 1.65/0.50 % (2561033)Peak memory usage: 10 MB
% 1.65/0.50 % (2561033)Instructions burned: 27 (million)
% 1.65/0.50 % (2561035)Instruction limit reached!
% 1.65/0.50 % (2561035)------------------------------
% 1.65/0.50 % (2561035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.50 % (2561035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.50 % (2561035)CaDiCaL version: 2.1.3
% 1.65/0.50 % (2561035)Termination reason: Instruction limit
% 1.65/0.50 % (2561035)Termination phase: Property scanning
% 1.65/0.50 % (2561035)Time elapsed: 0.028 s
% 1.65/0.50 % (2561035)Peak memory usage: 11 MB
% 1.65/0.50 % (2561035)Instructions burned: 60 (million)
% 1.65/0.50 % (2561045)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=4114554701:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.65/0.50 % (2561044)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=1657111220:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.65/0.50 % (2561046)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=830304186:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.65/0.50 % (2561045)Instruction limit reached!
% 1.65/0.50 % (2561045)------------------------------
% 1.65/0.50 % (2561045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.50 % (2561045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.50 % (2561045)CaDiCaL version: 2.1.3
% 1.65/0.50 % (2561045)Termination reason: Instruction limit
% 1.65/0.50 % (2561045)Termination phase: shuffling
% 1.65/0.50 % (2561045)Time elapsed: 0.005 s
% 1.65/0.50 % (2561045)Peak memory usage: 10 MB
% 1.65/0.50 % (2561045)Instructions burned: 9 (million)
% 1.65/0.50 % (2561047)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2148669499:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.65/0.50 % (2561044)Instruction limit reached!
% 1.65/0.50 % (2561044)------------------------------
% 1.65/0.50 % (2561044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.50 % (2561044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.50 % (2561044)CaDiCaL version: 2.1.3
% 1.65/0.50 % (2561044)Termination reason: Instruction limit
% 1.65/0.50 % (2561044)Termination phase: shuffling
% 1.65/0.50 % (2561044)Time elapsed: 0.015 s
% 1.65/0.50 % (2561044)Peak memory usage: 10 MB
% 1.65/0.50 % (2561044)Instructions burned: 32 (million)
% 1.65/0.50 % (2561048)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=819165938:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.65/0.50 % (2561046)Instruction limit reached!
% 1.65/0.50 % (2561046)------------------------------
% 1.65/0.50 % (2561046)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.50 % (2561046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.50 % (2561046)CaDiCaL version: 2.1.3
% 1.65/0.50 % (2561046)Termination reason: Instruction limit
% 1.65/0.50 % (2561046)Termination phase: shuffling
% 1.65/0.50 % (2561046)Time elapsed: 0.013 s
% 1.65/0.50 % (2561046)Peak memory usage: 10 MB
% 1.65/0.50 % (2561046)Instructions burned: 23 (million)
% 1.65/0.50 % (2561027)Instruction limit reached!
% 1.65/0.50 % (2561027)------------------------------
% 1.65/0.50 % (2561027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.50 % (2561027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.50 % (2561027)CaDiCaL version: 2.1.3
% 1.65/0.50 % (2561027)Termination reason: Instruction limit
% 1.65/0.50 % (2561027)Termination phase: Saturation
% 1.65/0.50 % (2561027)Time elapsed: 0.095 s
% 1.65/0.50 % (2561027)Peak memory usage: 15 MB
% 1.65/0.50 % (2561027)Instructions burned: 330 (million)
% 1.65/0.50 % (2561052)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=896576954:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.65/0.50 % (2561047)Instruction limit reached!
% 1.65/0.50 % (2561047)------------------------------
% 1.65/0.50 % (2561047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.50 % (2561047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.50 % (2561047)CaDiCaL version: 2.1.3
% 1.65/0.50 % (2561047)Termination reason: Instruction limit
% 1.65/0.50 % (2561047)Termination phase: Property scanning
% 1.65/0.50 % (2561047)Time elapsed: 0.018 s
% 1.65/0.50 % (2561047)Peak memory usage: 10 MB
% 1.65/0.50 % (2561047)Instructions burned: 21 (million)
% 1.65/0.50 % (2561055)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1713400395:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.65/0.50 % (2561057)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.65/0.50 % (2561056)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3252167100:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.65/0.50 % (2561057)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2854954512:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.65/0.50 % (2561057)Instruction limit reached!
% 1.65/0.50 % (2561057)------------------------------
% 1.65/0.50 % (2561057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.50 % (2561057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.50 % (2561057)CaDiCaL version: 2.1.3
% 1.65/0.50 % (2561057)Termination reason: Instruction limit
% 1.65/0.50 % (2561057)Termination phase: shuffling
% 1.65/0.50 % (2561057)Time elapsed: 0.007 s
% 1.65/0.50 % (2561057)Peak memory usage: 10 MB
% 1.65/0.50 % (2561057)Instructions burned: 8 (million)
% 1.65/0.50 % (2561056)Instruction limit reached!
% 1.65/0.50 % (2561056)------------------------------
% 1.65/0.50 % (2561056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.50 % (2561056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.50 % (2561056)CaDiCaL version: 2.1.3
% 1.65/0.50 % (2561056)Termination reason: Instruction limit
% 1.65/0.50 % (2561056)Termination phase: Preprocessing 3
% 1.65/0.50 % (2561056)Time elapsed: 0.020 s
% 1.65/0.50 % (2561056)Peak memory usage: 11 MB
% 1.65/0.50 % (2561056)Instructions burned: 43 (million)
% 1.65/0.50 % (2561059)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=461457255:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.65/0.50 % (2561063)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=597237361:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 1.65/0.50 % (2561055) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2560985-2561055"...
% 1.65/0.50 % (2561055)...printing done.
% 1.65/0.50 % (2561055)Refutation found. Thanks to Tanya!
% 1.65/0.50 % SZS status Theorem for theBenchmark
% 1.65/0.50 % SZS output start Proof for theBenchmark
% 1.65/0.50 thf(type_def_5, type, list: $tType > $tType).
% 1.65/0.50 thf(type_def_6, type, nat: $tType).
% 1.65/0.50 thf(type_def_7, type, int: $tType).
% 1.65/0.50 thf(type_def_8, type, a: $tType).
% 1.65/0.50 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 1.65/0.50 thf(func_def_0, type, linordered_idom: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_2, type, size: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_3, type, plus: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_4, type, zero: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_5, type, ord: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_6, type, order: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_7, type, group_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_8, type, monoid_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_9, type, linorder: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_10, type, preorder: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_11, type, semigroup_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_12, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_13, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_14, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_15, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_16, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_17, type, ordere216010020id_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_18, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_19, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_20, type, ordere1818651114id_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_21, type, strict797366125id_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_22, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_23, type, ordere223160158up_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_24, type, strict2144017051up_add: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_25, type, ordere516151231imp_le: !>[X0: $tType]:($o)).
% 1.65/0.50 thf(func_def_26, type, descar1668888542_psums: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.65/0.50 thf(func_def_27, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 1.65/0.50 thf(func_def_28, type, zero_zero: !>[X0: $tType]:(X0)).
% 1.65/0.50 thf(func_def_29, type, append: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 1.65/0.50 thf(func_def_30, type, last: !>[X0: $tType]:((list @ X0 > X0))).
% 1.65/0.50 thf(func_def_31, type, cons: !>[X0: $tType]:((X0 > list @ X0 > list @ X0))).
% 1.65/0.50 thf(func_def_32, type, nil: !>[X0: $tType]:(list @ X0)).
% 1.65/0.50 thf(func_def_33, type, nth: !>[X0: $tType]:((list @ X0 > nat > X0))).
% 1.65/0.50 thf(func_def_34, type, replicate: !>[X0: $tType]:((nat > X0 > list @ X0))).
% 1.65/0.50 thf(func_def_35, type, take: !>[X0: $tType]:((nat > list @ X0 > list @ X0))).
% 1.65/0.50 thf(func_def_36, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 1.65/0.50 thf(func_def_37, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.65/0.50 thf(func_def_38, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.65/0.50 thf(func_def_39, type, p: nat).
% 1.65/0.50 thf(func_def_40, type, v: (list @ a > int)).
% 1.65/0.50 thf(func_def_41, type, xa: a).
% 1.65/0.50 thf(func_def_42, type, xs: list @ a).
% 1.65/0.50 thf(func_def_43, type, xs1: list @ a).
% 1.65/0.50 thf(func_def_44, type, xs2: list @ a).
% 1.65/0.50 thf(func_def_45, type, xsa: list @ a).
% 1.65/0.50 thf(func_def_49, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.65/0.50 thf(func_def_50, type, vAND: ($o > $o > $o)).
% 1.65/0.50 thf(func_def_51, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.65/0.50 thf(func_def_52, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.65/0.50 thf(func_def_53, type, db2: !>[X0: $tType]:(X0)).
% 1.65/0.50 thf(func_def_54, type, db0: !>[X0: $tType]:(X0)).
% 1.65/0.50 thf(func_def_55, type, db1: !>[X0: $tType]:(X0)).
% 1.65/0.50 thf(func_def_56, type, vNOT: ($o > $o)).
% 1.65/0.50 thf(func_def_57, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.65/0.50 thf(func_def_58, type, vIMP: ($o > $o > $o)).
% 1.65/0.50 thf(func_def_59, type, vOR: ($o > $o > $o)).
% 1.65/0.50 thf(func_def_60, type, sK0: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X0 > list @ X3 > list @ X2 > $o) > list @ X0))).
% 1.65/0.50 thf(func_def_61, type, sK1: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X0 > list @ X3 > list @ X2 > $o) > X0))).
% 1.65/0.50 thf(func_def_62, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X0 > list @ X3 > list @ X2 > $o) > X3))).
% 1.65/0.50 thf(func_def_63, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X0 > list @ X3 > list @ X2 > $o) > list @ X3))).
% 1.65/0.50 thf(func_def_64, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X0 > list @ X3 > list @ X2 > $o) > X1))).
% 1.65/0.50 thf(func_def_65, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X0 > list @ X3 > list @ X2 > $o) > list @ X2))).
% 1.65/0.50 thf(func_def_66, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X0 > list @ X3 > list @ X2 > $o) > list @ X1))).
% 1.65/0.50 thf(func_def_67, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X0 > list @ X3 > list @ X2 > $o) > X2))).
% 1.65/0.50 thf(func_def_68, type, sK8: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.65/0.50 thf(func_def_69, type, sK9: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.65/0.50 thf(func_def_70, type, sK10: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.65/0.50 thf(func_def_71, type, sK11: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 1.65/0.50 thf(func_def_72, type, sK12: !>[X0: $tType]:((list @ X0 > list @ X0 > X0))).
% 1.65/0.50 thf(func_def_73, type, sK13: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 1.65/0.50 thf(func_def_74, type, sK14: !>[X0: $tType]:((list @ X0 > list @ X0 > X0))).
% 1.65/0.50 thf(func_def_75, type, sK15: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 1.65/0.50 thf(func_def_76, type, sK16: ((nat > nat) > nat)).
% 1.65/0.50 thf(func_def_77, type, sK17: ((nat > nat) > nat)).
% 1.65/0.50 thf(func_def_78, type, sK18: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > X1 > X0))).
% 1.65/0.50 thf(func_def_79, type, sK19: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > list @ X0))).
% 1.65/0.50 thf(func_def_80, type, sK20: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > list @ X0))).
% 1.65/0.50 thf(func_def_81, type, sK21: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > X1))).
% 1.65/0.51 thf(func_def_82, type, sK22: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > list @ X1))).
% 1.65/0.51 thf(func_def_83, type, sK23: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > X1 > X0))).
% 1.65/0.51 thf(func_def_84, type, sK24: !>[X0: $tType]:((nat > list @ X0))).
% 1.65/0.51 thf(func_def_85, type, sK25: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 1.65/0.51 thf(func_def_86, type, sK26: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 1.65/0.51 thf(func_def_87, type, sK27: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 1.65/0.51 thf(func_def_88, type, sK28: !>[X0: $tType]:((list @ X0 > X0))).
% 1.65/0.51 thf(func_def_89, type, sK29: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.65/0.51 thf(func_def_90, type, sK30: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.65/0.51 thf(func_def_91, type, sK31: !>[X0: $tType]:((list @ X0 > X0))).
% 1.65/0.51 thf(func_def_92, type, sK32: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_93, type, sK33: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_94, type, sK34: (nat > (nat > $o) > nat)).
% 1.65/0.51 thf(func_def_95, type, sK35: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 1.65/0.51 thf(func_def_96, type, sK36: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_97, type, sK37: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 1.65/0.51 thf(func_def_98, type, sK38: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_99, type, sK39: !>[X0: $tType]:((list @ X0 > X0))).
% 1.65/0.51 thf(func_def_100, type, sK40: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.65/0.51 thf(func_def_101, type, sK41: !>[X0: $tType]:((list @ X0 > X0))).
% 1.65/0.51 thf(func_def_102, type, sK42: !>[X0: $tType]:((list @ X0 > X0))).
% 1.65/0.51 thf(func_def_103, type, sK43: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_104, type, sK44: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_105, type, sK45: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_106, type, sK46: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_107, type, sK47: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_108, type, sK48: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_109, type, sK49: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_110, type, sK50: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_111, type, sK51: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_112, type, sK52: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1 > X0))).
% 1.65/0.51 thf(func_def_113, type, sK53: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > list @ X1))).
% 1.65/0.51 thf(func_def_114, type, sK54: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1 > X0))).
% 1.65/0.51 thf(func_def_115, type, sK55: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1))).
% 1.65/0.51 thf(func_def_116, type, sK56: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1))).
% 1.65/0.51 thf(func_def_117, type, sK57: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1))).
% 1.65/0.51 thf(func_def_118, type, sK58: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1 > X0))).
% 1.65/0.51 thf(func_def_119, type, sK59: !>[X0: $tType]:((list @ X0 > nat > list @ X0 > nat))).
% 1.65/0.51 thf(func_def_120, type, sK60: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 1.65/0.51 thf(func_def_121, type, sK61: !>[X0: $tType]:((list @ list @ X0 > list @ X0))).
% 1.65/0.51 thf(func_def_122, type, sK62: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 1.65/0.51 thf(func_def_123, type, sK63: !>[X0: $tType]:((list @ list @ X0 > X0))).
% 1.65/0.51 thf(func_def_124, type, sK64: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 1.65/0.51 thf(func_def_125, type, sK65: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_126, type, sK66: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 1.65/0.51 thf(func_def_127, type, sK67: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_128, type, sK68: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 1.65/0.51 thf(func_def_129, type, sK69: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_130, type, sK70: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_131, type, sK71: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 1.65/0.51 thf(func_def_132, type, sK72: !>[X0: $tType]:((list @ X0 > list @ X0 > nat))).
% 1.65/0.51 thf(func_def_133, type, sK73: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X1))).
% 1.65/0.51 thf(func_def_134, type, sK74: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X1))).
% 1.65/0.51 thf(func_def_135, type, sK75: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_136, type, sK76: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_137, type, sK77: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X1))).
% 1.65/0.51 thf(func_def_138, type, sK78: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X1))).
% 1.65/0.51 thf(func_def_139, type, sK79: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_140, type, sK80: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_141, type, sK81: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_142, type, sK82: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_143, type, sK83: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_144, type, sK84: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_145, type, sK85: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_146, type, sK86: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_147, type, sK87: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_148, type, sK88: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X1))).
% 1.65/0.51 thf(func_def_149, type, sK89: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_150, type, sK90: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X1))).
% 1.65/0.51 thf(func_def_151, type, sK91: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_152, type, sK92: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_153, type, sK93: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_154, type, sK94: !>[X0: $tType]:((list @ X0 > X0))).
% 1.65/0.51 thf(func_def_155, type, sK95: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.65/0.51 thf(func_def_156, type, sK96: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_157, type, sK97: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_158, type, sK98: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_159, type, sK99: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_160, type, sK100: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_161, type, sK101: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_162, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X1 > list @ X0 > list @ X2 > $o) > X2))).
% 1.65/0.51 thf(func_def_163, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X1 > list @ X0 > list @ X2 > $o) > X1))).
% 1.65/0.51 thf(func_def_164, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X1))).
% 1.65/0.51 thf(func_def_165, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_166, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X1 > list @ X0 > list @ X2 > $o) > X0))).
% 1.65/0.51 thf(func_def_167, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X2))).
% 1.65/0.51 thf(func_def_168, type, sK108: !>[X0: $tType]:((list @ X0 > X0))).
% 1.65/0.51 thf(func_def_169, type, sK109: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.65/0.51 thf(func_def_170, type, sK110: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_171, type, sK111: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 1.65/0.51 thf(func_def_172, type, sK112: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_173, type, sK113: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 1.65/0.51 thf(func_def_174, type, sK114: !>[X0: $tType]:(((nat > X0 > $o) > nat > nat))).
% 1.65/0.51 thf(func_def_175, type, sK115: !>[X0: $tType]:(((nat > X0 > $o) > nat > list @ X0))).
% 1.65/0.51 thf(func_def_176, type, sK116: !>[X0: $tType]:(((nat > X0 > $o) > nat > X0))).
% 1.65/0.51 thf(func_def_177, type, sK117: !>[X0: $tType]:((list @ X0 > (nat > X0 > $o) > nat > nat))).
% 1.65/0.51 thf(f5,axiom,(
% 1.65/0.51 (xs1 = ((replicate @ a @ p @ zero_zero @ a)))),
% 1.65/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_xs1__def)).
% 1.65/0.51 thf(f6,axiom,(
% 1.65/0.51 (xsa = ((append @ a @ xs1 @ (cons @ a @ (nth @ a @ xsa @ p) @ xs2))))),
% 1.65/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_xs__decompose)).
% 1.65/0.51 thf(f7,axiom,(
% 1.65/0.51 ! [X0 : $tType] : (monoid_add @ X0 => ! [X1 : nat,X2 : list @ X0] : (((descar1668888542_psums @ X0 @ (append @ X0 @ (replicate @ X0 @ X1 @ zero_zero @ X0) @ X2))) = ((append @ X0 @ (replicate @ X0 @ X1 @ zero_zero @ X0) @ (descar1668888542_psums @ X0 @ X2)))))),
% 1.65/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_psums__replicate__0__append)).
% 1.65/0.51 thf(f260,axiom,(
% 1.65/0.51 ! [X0 : $tType] : (linordered_idom @ X0 => monoid_add @ X0)),
% 1.65/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Omonoid__add)).
% 1.65/0.51 thf(f329,axiom,(
% 1.65/0.51 linordered_idom @ a),
% 1.65/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0)).
% 1.65/0.51 thf(f330,conjecture,(
% 1.65/0.51 (((descar1668888542_psums @ a @ xsa)) = ((append @ a @ (replicate @ a @ p @ zero_zero @ a) @ (descar1668888542_psums @ a @ (cons @ a @ (nth @ a @ xsa @ p) @ xs2)))))),
% 1.65/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 1.65/0.51 thf(f331,negated_conjecture,(
% 1.65/0.51 ~ (((descar1668888542_psums @ a @ xsa)) = ((append @ a @ (replicate @ a @ p @ zero_zero @ a) @ (descar1668888542_psums @ a @ (cons @ a @ (nth @ a @ xsa @ p) @ xs2)))))),
% 1.65/0.51 inference(negated_conjecture,[status(cth)],[f330])).
% 1.65/0.51 thf(f372,plain,(
% 1.65/0.51 ! [X0 : $tType] : (linordered_idom @ X0 => monoid_add @ X0)),
% 1.65/0.51 inference(rectify,[],[f260])).
% 1.65/0.51 thf(f373,plain,(
% 1.65/0.51 ! [X0 : $tType] : ((linordered_idom @ X0 = $true) => (monoid_add @ X0 = $true))),
% 1.65/0.51 inference(fool_elimination,[],[f372])).
% 1.65/0.51 thf(f511,plain,(
% 1.65/0.51 ! [X0 : $tType] : (monoid_add @ X0 => ! [X1 : nat,X2 : list @ X0] : (((descar1668888542_psums @ X0 @ (append @ X0 @ (replicate @ X0 @ X1 @ zero_zero @ X0) @ X2))) = ((append @ X0 @ (replicate @ X0 @ X1 @ zero_zero @ X0) @ (descar1668888542_psums @ X0 @ X2)))))),
% 1.65/0.51 inference(rectify,[],[f7])).
% 1.65/0.51 thf(f512,plain,(
% 1.65/0.51 ! [X0 : $tType] : ((monoid_add @ X0 = $true) => ! [X1 : nat,X2 : list @ X0] : (((descar1668888542_psums @ X0 @ (append @ X0 @ (replicate @ X0 @ X1 @ zero_zero @ X0) @ X2))) = ((append @ X0 @ (replicate @ X0 @ X1 @ zero_zero @ X0) @ (descar1668888542_psums @ X0 @ X2)))))),
% 1.65/0.51 inference(fool_elimination,[],[f511])).
% 1.65/0.51 thf(f830,plain,(
% 1.65/0.51 linordered_idom @ a),
% 1.65/0.51 inference(rectify,[],[f329])).
% 1.65/0.51 thf(f831,plain,(
% 1.65/0.51 (linordered_idom @ a = $true)),
% 1.65/0.51 inference(fool_elimination,[],[f830])).
% 1.65/0.51 thf(f878,plain,(
% 1.65/0.51 (((descar1668888542_psums @ a @ xsa)) != ((append @ a @ (replicate @ a @ p @ zero_zero @ a) @ (descar1668888542_psums @ a @ (cons @ a @ (nth @ a @ xsa @ p) @ xs2)))))),
% 1.65/0.51 inference(flattening,[],[f331])).
% 1.65/0.51 thf(f953,plain,(
% 1.65/0.51 ! [X0 : $tType] : (! [X1 : nat,X2 : list @ X0] : (((descar1668888542_psums @ X0 @ (append @ X0 @ (replicate @ X0 @ X1 @ zero_zero @ X0) @ X2))) = ((append @ X0 @ (replicate @ X0 @ X1 @ zero_zero @ X0) @ (descar1668888542_psums @ X0 @ X2)))) | (monoid_add @ X0 != $true))),
% 1.65/0.51 inference(ennf_transformation,[],[f512])).
% 1.65/0.51 thf(f993,plain,(
% 1.65/0.51 ! [X0 : $tType] : ((linordered_idom @ X0 != $true) | (monoid_add @ X0 = $true))),
% 1.65/0.51 inference(ennf_transformation,[],[f373])).
% 1.65/0.51 thf(f1148,plain,(
% 1.65/0.51 (xs1 = ((replicate @ a @ p @ zero_zero @ a)))),
% 1.65/0.51 inference(cnf_transformation,[],[f5])).
% 1.65/0.51 thf(f1224,plain,(
% 1.65/0.51 (xsa = ((append @ a @ xs1 @ (cons @ a @ (nth @ a @ xsa @ p) @ xs2))))),
% 1.65/0.51 inference(cnf_transformation,[],[f6])).
% 1.65/0.51 thf(f1288,plain,(
% 1.65/0.51 ( ! [X0 : $tType] : ((monoid_add @ X0 = $true) | (linordered_idom @ X0 != $true)) )),
% 1.65/0.51 inference(cnf_transformation,[],[f993])).
% 1.65/0.51 thf(f1305,plain,(
% 1.65/0.51 (((descar1668888542_psums @ a @ xsa)) != ((append @ a @ (replicate @ a @ p @ zero_zero @ a) @ (descar1668888542_psums @ a @ (cons @ a @ (nth @ a @ xsa @ p) @ xs2)))))),
% 1.65/0.51 inference(cnf_transformation,[],[f878])).
% 1.65/0.51 thf(f1307,plain,(
% 1.65/0.51 (linordered_idom @ a = $true)),
% 1.65/0.51 inference(cnf_transformation,[],[f831])).
% 1.65/0.51 thf(f1308,plain,(
% 1.65/0.51 ( ! [X0 : $tType,X2 : list @ X0,X1 : nat] : ((((descar1668888542_psums @ X0 @ (append @ X0 @ (replicate @ X0 @ X1 @ zero_zero @ X0) @ X2))) = ((append @ X0 @ (replicate @ X0 @ X1 @ zero_zero @ X0) @ (descar1668888542_psums @ X0 @ X2)))) | (monoid_add @ X0 != $true)) )),
% 1.65/0.51 inference(cnf_transformation,[],[f953])).
% 1.65/0.51 thf(f1545,definition,(
% 1.65/0.51 spl118_1 <=> (xsa = ((append @ a @ xs1 @ (cons @ a @ (nth @ a @ xsa @ p) @ xs2))))),
% 1.65/0.51 introduced(definition,[new_symbols(definition,[spl118_1])],[avatar_definition])).
% 1.65/0.51 thf(f1547,plain,(
% 1.65/0.51 (xsa = ((append @ a @ xs1 @ (cons @ a @ (nth @ a @ xsa @ p) @ xs2)))) | ~spl118_1),
% 1.65/0.51 inference(avatar_component_clause,[],[f1545])).
% 1.65/0.51 thf(f1548,plain,(
% 1.65/0.51 spl118_1),
% 1.65/0.51 inference(avatar_split_clause,[],[f1224,f1545])).
% 1.65/0.51 thf(f1550,definition,(
% 1.65/0.51 spl118_2 <=> (((descar1668888542_psums @ a @ xsa)) = ((append @ a @ (replicate @ a @ p @ zero_zero @ a) @ (descar1668888542_psums @ a @ (cons @ a @ (nth @ a @ xsa @ p) @ xs2)))))),
% 1.65/0.51 introduced(definition,[new_symbols(definition,[spl118_2])],[avatar_definition])).
% 1.65/0.51 thf(f1552,plain,(
% 1.65/0.51 (((descar1668888542_psums @ a @ xsa)) != ((append @ a @ (replicate @ a @ p @ zero_zero @ a) @ (descar1668888542_psums @ a @ (cons @ a @ (nth @ a @ xsa @ p) @ xs2))))) | spl118_2),
% 1.65/0.51 inference(avatar_component_clause,[],[f1550])).
% 1.65/0.51 thf(f1553,plain,(
% 1.65/0.51 ~spl118_2),
% 1.65/0.51 inference(avatar_split_clause,[],[f1305,f1550])).
% 1.65/0.51 thf(f1560,definition,(
% 1.65/0.51 spl118_4 <=> (linordered_idom @ a = $true)),
% 1.65/0.51 introduced(definition,[new_symbols(definition,[spl118_4])],[avatar_definition])).
% 1.65/0.51 thf(f1562,plain,(
% 1.65/0.51 (linordered_idom @ a = $true) | ~spl118_4),
% 1.65/0.51 inference(avatar_component_clause,[],[f1560])).
% 1.65/0.51 thf(f1563,plain,(
% 1.65/0.51 spl118_4),
% 1.65/0.51 inference(avatar_split_clause,[],[f1307,f1560])).
% 1.65/0.51 thf(f1565,definition,(
% 1.65/0.51 spl118_5 <=> (xs1 = ((replicate @ a @ p @ zero_zero @ a)))),
% 1.65/0.51 introduced(definition,[new_symbols(definition,[spl118_5])],[avatar_definition])).
% 1.65/0.51 thf(f1567,plain,(
% 1.65/0.51 (xs1 = ((replicate @ a @ p @ zero_zero @ a))) | ~spl118_5),
% 1.65/0.51 inference(avatar_component_clause,[],[f1565])).
% 1.65/0.51 thf(f1568,plain,(
% 1.65/0.51 spl118_5),
% 1.65/0.51 inference(avatar_split_clause,[],[f1148,f1565])).
% 1.65/0.51 thf(f2023,plain,(
% 1.65/0.51 ($true != monoid_add @ a) | (((descar1668888542_psums @ a @ xsa)) != ((descar1668888542_psums @ a @ (append @ a @ (replicate @ a @ p @ zero_zero @ a) @ (cons @ a @ (nth @ a @ xsa @ p) @ xs2))))) | spl118_2),
% 1.65/0.51 inference(superposition,[],[f1552,f1308])).
% 1.65/0.51 thf(f2026,plain,(
% 1.65/0.51 ($true != monoid_add @ a) | (((descar1668888542_psums @ a @ xsa)) != ((descar1668888542_psums @ a @ (append @ a @ xs1 @ (cons @ a @ (nth @ a @ xsa @ p) @ xs2))))) | (spl118_2 | ~spl118_5)),
% 1.65/0.51 inference(forward_demodulation,[],[f2023,f1567])).
% 1.65/0.51 thf(f2029,plain,(
% 1.65/0.51 ($true != monoid_add @ a) | (((descar1668888542_psums @ a @ xsa)) != ((descar1668888542_psums @ a @ xsa))) | (~spl118_1 | spl118_2 | ~spl118_5)),
% 1.65/0.51 inference(forward_demodulation,[],[f2026,f1547])).
% 1.65/0.51 thf(f2030,plain,(
% 1.65/0.51 ($true != monoid_add @ a) | (~spl118_1 | spl118_2 | ~spl118_5)),
% 1.65/0.51 inference(trivial_inequality_removal,[],[f2029])).
% 1.65/0.51 thf(f2032,definition,(
% 1.65/0.51 spl118_35 <=> ($true = monoid_add @ a)),
% 1.65/0.51 introduced(definition,[new_symbols(definition,[spl118_35])],[avatar_definition])).
% 1.65/0.51 thf(f2034,plain,(
% 1.65/0.51 ($true != monoid_add @ a) | spl118_35),
% 1.65/0.51 inference(avatar_component_clause,[],[f2032])).
% 1.65/0.51 thf(f2035,plain,(
% 1.65/0.51 ~spl118_35 | ~spl118_1 | spl118_2 | ~spl118_5),
% 1.65/0.51 inference(avatar_split_clause,[],[f2030,f1565,f1550,f1545,f2032])).
% 1.65/0.51 thf(f2036,plain,(
% 1.65/0.51 ($true != $true) | (linordered_idom @ a != $true) | spl118_35),
% 1.65/0.51 inference(superposition,[],[f2034,f1288])).
% 1.65/0.51 thf(f2038,plain,(
% 1.65/0.51 (linordered_idom @ a != $true) | spl118_35),
% 1.65/0.51 inference(trivial_inequality_removal,[],[f2036])).
% 1.65/0.51 thf(f2040,plain,(
% 1.65/0.51 $false | (~spl118_4 | spl118_35)),
% 1.65/0.51 inference(forward_subsumption_resolution,[],[f2038,f1562])).
% 1.65/0.51 thf(f2041,plain,(
% 1.65/0.51 ~spl118_4 | spl118_35),
% 1.65/0.51 inference(avatar_contradiction_clause,[],[f2040])).
% 1.65/0.51 cnf(s1, plain, spl118_1, inference(sat_conversion,[],[f1548])).
% 1.65/0.51 cnf(s2, plain, ~spl118_2, inference(sat_conversion,[],[f1553])).
% 1.65/0.51 cnf(s4, plain, spl118_4, inference(sat_conversion,[],[f1563])).
% 1.65/0.51 cnf(s5, plain, spl118_5, inference(sat_conversion,[],[f1568])).
% 1.65/0.51 cnf(s25, plain, ~spl118_1 | spl118_2 | ~spl118_5 | ~spl118_35, inference(sat_conversion,[],[f2035])).
% 1.65/0.51 cnf(s26, plain, ~spl118_4 | spl118_35, inference(sat_conversion,[],[f2041])).
% 1.65/0.51 cnf(s28, plain, spl118_35, inference(rat,[],[s26,s4])).
% 1.65/0.51 cnf(s31, plain, ~spl118_1, inference(rat,[],[s25,s28,s5,s2])).
% 1.65/0.51 cnf(s32, plain, $false, inference(rat,[],[s1,s31])).
% 1.65/0.51 thf(f2047,plain,(
% 1.65/0.51 $false),
% 1.65/0.51 inference(avatar_sat_refutation,[],[s32])).
% 1.65/0.51 % SZS output end Proof for theBenchmark
% 1.65/0.51 % (2561055)------------------------------
% 1.65/0.51 % (2561055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.65/0.51 % (2561055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.65/0.51 % (2561055)CaDiCaL version: 2.1.3
% 1.65/0.51 % (2561055)Termination reason: Refutation
% 1.65/0.51 % (2561055)Time elapsed: 0.041 s
% 1.65/0.51 % (2561055)Peak memory usage: 15 MB
% 1.65/0.51 % (2561055)Instructions burned: 139 (million)
% 1.65/0.51 % (2560985)Success in time 0.27 s
% 1.65/0.51 % Vampire exiting
%------------------------------------------------------------------------------