%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL044-8 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 : Tue Sep 29 09:37:44 AM UTC 2026
% Result : Unsatisfiable 26.60s 4.85s
% Output : Refutation 26.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 28 unt; 2 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 42 ( 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(n,X0),X1),X2) = apply(apply(apply(X0,X2),X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_definition) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n)),b)),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f5,definition,
sF0 = apply(strong_fixed_point,fixed_pt),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
apply(strong_fixed_point,fixed_pt) = sF0,
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
sF1 = apply(fixed_pt,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
apply(fixed_pt,sF0) = sF1,
inference(reorient_equations,[],[f7]) ).
fof(f9,plain,
sF0 != sF1,
inference(definition_folding,[],[f4,f8,f6,f6]) ).
fof(f11,plain,
! [X2,X3,X0,X1] : apply(apply(apply(n,apply(apply(b,X0),X1)),X3),X2) = apply(apply(apply(X0,apply(X1,X2)),X3),X2),
inference(superposition,[],[f2,f1]) ).
fof(f16,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(b,X0)),X2),X1) = apply(apply(X0,apply(X1,X2)),X1),
inference(superposition,[],[f2,f1]) ).
fof(f18,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(X0,X2)),X2),X1) = apply(apply(apply(apply(n,X0),X1),X2),X1),
inference(superposition,[],[f2,f2]) ).
fof(f22,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(X0,X2)),X2),X1) = apply(apply(apply(n,apply(n,X0)),X2),X1),
inference(forward_demodulation,[],[f18,f2]) ).
fof(f26,plain,
! [X0] : apply(apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n)),b),apply(b,X0)) = apply(strong_fixed_point,X0),
inference(superposition,[],[f1,f3]) ).
fof(f30,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n),apply(b,apply(b,X0))),
inference(forward_demodulation,[],[f26,f1]) ).
fof(f54,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(b,apply(b,X0))),X1),X2) = apply(X0,apply(apply(X2,X1),X2)),
inference(superposition,[],[f1,f16]) ).
fof(f137,plain,
! [X2,X3,X0,X1] : apply(apply(apply(n,apply(apply(b,apply(b,X0)),X1)),X3),X2) = apply(apply(X0,apply(apply(X1,X2),X3)),X2),
inference(superposition,[],[f11,f1]) ).
fof(f160,plain,
! [X2,X0,X1] : apply(apply(apply(n,apply(apply(b,b),X0)),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(superposition,[],[f1,f11]) ).
fof(f296,plain,
! [X0,X1] : apply(apply(apply(n,apply(n,apply(b,b))),X0),X1) = apply(apply(X0,X1),apply(X0,X1)),
inference(superposition,[],[f22,f160]) ).
fof(f614,plain,
! [X2,X3,X0,X1] : apply(apply(apply(n,apply(n,apply(apply(b,apply(b,X0)),X1))),X2),X3) = apply(apply(apply(X0,apply(apply(X1,X2),X3)),X2),X3),
inference(superposition,[],[f2,f137]) ).
fof(f785,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(b,apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,X0)))),n),apply(b,apply(b,X0))),
inference(superposition,[],[f30,f614]) ).
fof(f849,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))),
inference(forward_demodulation,[],[f785,f1]) ).
fof(f879,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))),
inference(forward_demodulation,[],[f849,f22]) ).
fof(f1088,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(n,apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))),apply(n,apply(b,apply(b,X0)))),
inference(superposition,[],[f879,f296]) ).
fof(f1197,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(superposition,[],[f54,f1088]) ).
fof(f1240,plain,
sF0 = apply(fixed_pt,sF0),
inference(superposition,[],[f1197,f6]) ).
fof(f1330,plain,
sF0 = sF1,
inference(superposition,[],[f8,f1240]) ).
fof(f1335,plain,
$false,
inference(forward_subsumption_resolution,[],[f1330,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL044-8 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.29 % Computer : n005.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8046.5625MB
% 0.12/0.29 % OS : Linux 6.8.0-71-generic
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Mon Sep 28 21:30:46 UTC 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.31/0.35 Running first-order theorem proving
% 0.31/0.35 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.60/4.85 % (1208141)Detected a unit-equality problem, will run specialized UEQ schedule.
% 26.60/4.85 % (1208150)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2135747506:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 26.60/4.85 % (1208146)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=387850114:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 26.60/4.85 % (1208147)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1948402093:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 26.60/4.85 % (1208149)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1846698411:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 26.60/4.85 % (1208148)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2239356919:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 26.60/4.85 % (1208151)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=128802085:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 26.60/4.85 % (1208152)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2178952760:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 26.60/4.85 % (1208150)Instruction limit reached!
% 26.60/4.85 % (1208150)------------------------------
% 26.60/4.85 % (1208150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.60/4.85 % (1208150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.60/4.85 % (1208150)CaDiCaL version: 2.1.3
% 26.60/4.85 % (1208150)Termination reason: Instruction limit
% 26.60/4.85 % (1208150)Termination phase: Saturation
% 26.60/4.85 % (1208150)Time elapsed: 0.088 s
% 26.60/4.85 % (1208150)Peak memory usage: 90 MB
% 26.60/4.85 % (1208150)Instructions burned: 182 (million)
% 26.60/4.85 % (1208149)Instruction limit reached!
% 26.60/4.85 % (1208149)------------------------------
% 26.60/4.85 % (1208149)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.60/4.85 % (1208149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.60/4.85 % (1208149)CaDiCaL version: 2.1.3
% 26.60/4.85 % (1208149)Termination reason: Instruction limit
% 26.60/4.85 % (1208149)Termination phase: Saturation
% 26.60/4.85 % (1208149)Time elapsed: 0.136 s
% 26.60/4.85 % (1208149)Peak memory usage: 89 MB
% 26.60/4.85 % (1208149)Instructions burned: 136 (million)
% 26.60/4.85 % (1208160)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2932072508:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 26.60/4.85 % (1208151)Instruction limit reached!
% 26.60/4.85 % (1208151)------------------------------
% 26.60/4.85 % (1208151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.60/4.85 % (1208151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.60/4.85 % (1208151)CaDiCaL version: 2.1.3
% 26.60/4.85 % (1208151)Termination reason: Instruction limit
% 26.60/4.85 % (1208151)Termination phase: Saturation
% 26.60/4.85 % (1208151)Time elapsed: 0.281 s
% 26.60/4.85 % (1208151)Peak memory usage: 91 MB
% 26.60/4.85 % (1208151)Instructions burned: 257 (million)
% 26.60/4.85 % (1208161)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3092907488:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 26.60/4.85 % (1208163)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2088611773:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 26.60/4.85 % (1208163)Refutation not found, incomplete strategy
% 26.60/4.85 % (1208163)------------------------------
% 26.60/4.85 % (1208163)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.60/4.85 % (1208163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.60/4.85 % (1208163)CaDiCaL version: 2.1.3
% 26.60/4.85 % (1208163)Termination reason: Refutation not found, incomplete strategy
% 26.60/4.85 % (1208163)Time elapsed: 0.003 s
% 26.60/4.85 % (1208163)Peak memory usage: 88 MB
% 26.60/4.85 % (1208163)Instructions burned: 1 (million)
% 26.60/4.85 % (1208163)------------------------------
% 26.60/4.85 % (1208163)------------------------------
% 26.60/4.85 % (1208152)Instruction limit reached!
% 26.60/4.85 % (1208152)------------------------------
% 26.60/4.85 % (1208152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.60/4.85 % (1208152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.60/4.85 % (1208152)CaDiCaL version: 2.1.3
% 26.60/4.85 % (1208152)Termination reason: Instruction limit
% 26.60/4.85 % (1208152)Termination phase: Saturation
% 26.60/4.85 % (1208152)Time elapsed: 1.074 s
% 26.60/4.85 % (1208152)Peak memory usage: 99 MB
% 26.60/4.85 % (1208152)Instructions burned: 1188 (million)
% 26.60/4.85 % (1208166)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=3515261745:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2987 on theBenchmark for (2987ds/317Mi)
% 26.60/4.85 % (1208167)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=3895288863:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/12125Mi)
% 26.60/4.85 % (1208160)Instruction limit reached!
% 26.60/4.85 % (1208160)------------------------------
% 26.60/4.85 % (1208160)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.60/4.85 % (1208160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.60/4.85 % (1208160)CaDiCaL version: 2.1.3
% 26.60/4.85 % (1208160)Termination reason: Instruction limit
% 26.60/4.85 % (1208160)Termination phase: Saturation
% 26.60/4.85 % (1208160)Time elapsed: 1.237 s
% 26.60/4.85 % (1208160)Peak memory usage: 138 MB
% 26.60/4.85 % (1208160)Instructions burned: 2051 (million)
% 26.60/4.85 % (1208166)Instruction limit reached!
% 26.60/4.85 % (1208166)------------------------------
% 26.60/4.85 % (1208166)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.60/4.85 % (1208166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.60/4.85 % (1208166)CaDiCaL version: 2.1.3
% 26.60/4.85 % (1208166)Termination reason: Instruction limit
% 26.60/4.85 % (1208166)Termination phase: Saturation
% 26.60/4.85 % (1208166)Time elapsed: 0.286 s
% 26.60/4.85 % (1208166)Peak memory usage: 90 MB
% 26.60/4.85 % (1208166)Instructions burned: 317 (million)
% 26.60/4.85 % (1208170)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=3867344726:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2981 on theBenchmark for (2981ds/2836Mi)
% 26.60/4.85 % (1208171)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=3668661502:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2981 on theBenchmark for (2981ds/14534Mi)
% 26.60/4.85 % (1208167)First to succeed.
% 26.60/4.85 % (1208167)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1208141"
% 26.60/4.85 % (1208167)Refutation found. Thanks to Tanya!
% 26.60/4.85 % SZS status Unsatisfiable for theBenchmark
% 26.60/4.85 % SZS output start Proof for theBenchmark
% See solution above
% 26.60/4.85 % (1208167)------------------------------
% 26.60/4.85 % (1208167)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.60/4.85 % (1208167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.60/4.85 % (1208167)CaDiCaL version: 2.1.3
% 26.60/4.85 % (1208167)Termination reason: Refutation
% 26.60/4.85 % (1208167)Time elapsed: 1.547 s
% 26.60/4.85 % (1208167)Peak memory usage: 135 MB
% 26.60/4.85 % (1208167)Instructions burned: 1508 (million)
% 26.60/4.85 % (1208167)------------------------------
% 26.60/4.85 % (1208167)------------------------------
% 26.60/4.85 % (1208141)Success in time 3.625 s
% 26.60/4.85 % Vampire exiting
%------------------------------------------------------------------------------