%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL038-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 09:37:41 AM UTC 2026
% Result : Unsatisfiable 0.19s 1.70s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 11 unt; 0 def)
% Number of atoms : 11 ( 10 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0] : apply(m,X0) = apply(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_definition) ).
fof(f3,axiom,
! [X2,X0,X1] : apply(apply(apply(v,X0),X1),X2) = apply(apply(X2,X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_definition) ).
fof(f4,negated_conjecture,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
fof(f6,plain,
! [X0,X1] : apply(m,apply(apply(b,X0),X1)) = apply(X0,apply(X1,apply(apply(b,X0),X1))),
inference(superposition,[],[f1,f2]) ).
fof(f7,plain,
! [X0,X1] : apply(X0,apply(X1,f(apply(apply(b,X0),X1)))) != apply(f(apply(apply(b,X0),X1)),apply(X0,apply(X1,f(apply(apply(b,X0),X1))))),
inference(superposition,[],[f4,f1]) ).
fof(f32,plain,
! [X2,X0,X1] : apply(X0,apply(X1,apply(X2,f(apply(apply(b,X0),apply(apply(b,X1),X2)))))) != apply(f(apply(apply(b,X0),apply(apply(b,X1),X2))),apply(X0,apply(X1,apply(X2,f(apply(apply(b,X0),apply(apply(b,X1),X2))))))),
inference(superposition,[],[f7,f1]) ).
fof(f60,plain,
! [X2,X3,X0,X1] : apply(X1,apply(apply(apply(X0,f(apply(apply(b,X1),apply(apply(b,apply(apply(v,X2),X3)),X0)))),X2),X3)) != apply(f(apply(apply(b,X1),apply(apply(b,apply(apply(v,X2),X3)),X0))),apply(X1,apply(apply(apply(X0,f(apply(apply(b,X1),apply(apply(b,apply(apply(v,X2),X3)),X0)))),X2),X3))),
inference(superposition,[],[f32,f3]) ).
fof(f150,plain,
! [X2,X0,X1] : apply(X1,apply(apply(X0,f(apply(apply(b,X1),apply(apply(b,apply(apply(v,X2),X0)),v)))),X2)) != apply(f(apply(apply(b,X1),apply(apply(b,apply(apply(v,X2),X0)),v))),apply(X1,apply(apply(X0,f(apply(apply(b,X1),apply(apply(b,apply(apply(v,X2),X0)),v)))),X2))),
inference(superposition,[],[f60,f3]) ).
fof(f188,plain,
! [X0] : apply(m,apply(apply(b,f(apply(apply(b,X0),apply(apply(b,apply(apply(v,X0),b)),v)))),X0)) != apply(X0,apply(apply(b,f(apply(apply(b,X0),apply(apply(b,apply(apply(v,X0),b)),v)))),X0)),
inference(superposition,[],[f150,f6]) ).
fof(f202,plain,
$false,
inference(equality_resolution,[],[f188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL038-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n010.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 21:30:32 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running first-order theorem proving
% 0.06/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/1.70 % (2372001)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.19/1.70 % (2372010)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=493545674:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.19/1.70 % (2372006)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=2736044825:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.19/1.70 % (2372009)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4082205391:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.19/1.70 % (2372008)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=558049519:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.19/1.70 % (2372007)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=2043224961:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.19/1.70 % (2372012)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3424957326:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.19/1.70 % (2372011)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3472800111:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.19/1.70 % (2372010)Instruction limit reached!
% 0.19/1.70 % (2372010)------------------------------
% 0.19/1.70 % (2372010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.70 % (2372010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.70 % (2372010)CaDiCaL version: 2.1.3
% 0.19/1.70 % (2372010)Termination reason: Instruction limit
% 0.19/1.70 % (2372010)Termination phase: Saturation
% 0.19/1.70 % (2372010)Time elapsed: 0.054 s
% 0.19/1.70 % (2372010)Peak memory usage: 89 MB
% 0.19/1.70 % (2372010)Instructions burned: 184 (million)
% 0.19/1.70 % (2372009)Instruction limit reached!
% 0.19/1.70 % (2372009)------------------------------
% 0.19/1.70 % (2372009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.70 % (2372009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.70 % (2372009)CaDiCaL version: 2.1.3
% 0.19/1.70 % (2372009)Termination reason: Instruction limit
% 0.19/1.70 % (2372009)Termination phase: Saturation
% 0.19/1.70 % (2372009)Time elapsed: 0.083 s
% 0.19/1.70 % (2372009)Peak memory usage: 89 MB
% 0.19/1.70 % (2372009)Instructions burned: 137 (million)
% 0.19/1.70 % (2372020)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2110189011:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 0.19/1.70 % (2372011)Instruction limit reached!
% 0.19/1.70 % (2372011)------------------------------
% 0.19/1.70 % (2372011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.70 % (2372011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.70 % (2372011)CaDiCaL version: 2.1.3
% 0.19/1.70 % (2372011)Termination reason: Instruction limit
% 0.19/1.70 % (2372011)Termination phase: Saturation
% 0.19/1.70 % (2372011)Time elapsed: 0.167 s
% 0.19/1.70 % (2372011)Peak memory usage: 90 MB
% 0.19/1.70 % (2372011)Instructions burned: 257 (million)
% 0.19/1.70 % (2372021)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=469749178:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 0.19/1.70 % (2372023)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2831815600:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 0.19/1.70 % (2372023)Instruction limit reached!
% 0.19/1.70 % (2372023)------------------------------
% 0.19/1.70 % (2372023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.70 % (2372023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.70 % (2372023)CaDiCaL version: 2.1.3
% 0.19/1.70 % (2372023)Termination reason: Instruction limit
% 0.19/1.70 % (2372023)Termination phase: Saturation
% 0.19/1.70 % (2372023)Time elapsed: 0.128 s
% 0.19/1.70 % (2372023)Peak memory usage: 89 MB
% 0.19/1.70 % (2372023)Instructions burned: 215 (million)
% 0.19/1.70 % (2372020)First to succeed.
% 0.19/1.70 % (2372020)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2372001"
% 0.19/1.70 % (2372026)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=476323964:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 0.19/1.70 % (2372006)Also succeeded, but the first one will report.
% 0.19/1.70 % (2372012)Instruction limit reached!
% 0.19/1.70 % (2372012)------------------------------
% 0.19/1.70 % (2372012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.70 % (2372012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.70 % (2372012)CaDiCaL version: 2.1.3
% 0.19/1.70 % (2372012)Termination reason: Instruction limit
% 0.19/1.70 % (2372012)Termination phase: Saturation
% 0.19/1.70 % (2372012)Time elapsed: 0.646 s
% 0.19/1.70 % (2372012)Peak memory usage: 100 MB
% 0.19/1.70 % (2372012)Instructions burned: 1188 (million)
% 0.19/1.70 % (2372007)Also succeeded, but the first one will report.
% 0.19/1.70 % (2372008)Also succeeded, but the first one will report.
% 0.19/1.70 % (2372020)Refutation found. Thanks to Tanya!
% 0.19/1.70 % SZS status Unsatisfiable for theBenchmark
% 0.19/1.70 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.70 % (2372020)------------------------------
% 0.19/1.70 % (2372020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.70 % (2372020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.70 % (2372020)CaDiCaL version: 2.1.3
% 0.19/1.70 % (2372020)Termination reason: Refutation
% 0.19/1.70 % (2372020)Time elapsed: 0.422 s
% 0.19/1.70 % (2372020)Peak memory usage: 129 MB
% 0.19/1.70 % (2372020)Instructions burned: 1039 (million)
% 0.19/1.70 % (2372020)------------------------------
% 0.19/1.70 % (2372020)------------------------------
% 0.19/1.70 % (2372001)Success in time 0.858 s
% 0.19/1.70 % Vampire exiting
%------------------------------------------------------------------------------