%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO068-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 09:36:00 AM UTC 2026
% Result : Unsatisfiable 8.51s 2.25s
% Output : Refutation 8.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 126 ( 126 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6))),multiply(X3,multiply(X6,X5,X4),X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(b,a,a) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_tba_axioms_2) ).
fof(f3,plain,
a != multiply(b,a,a),
inference(reorient_equations,[],[f2]) ).
fof(f4,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : multiply(X1,multiply(X2,inverse(multiply(X0,X1,X3)),X3),X0) = multiply(multiply(X0,X1,X2),inverse(multiply(multiply(X4,X5,X6),X7,multiply(X4,X5,X8))),multiply(X5,multiply(X8,X7,X6),X4)),
inference(superposition,[],[f1,f1]) ).
fof(f7,plain,
! [X2,X3,X10,X0,X1,X8,X6,X9,X7,X4,X5] : multiply(multiply(X1,inverse(X1),X2),inverse(multiply(multiply(X3,X4,multiply(X5,multiply(X6,X7,X8),X9)),inverse(multiply(multiply(X9,X5,X8),X7,multiply(X9,X5,X6))),multiply(X3,X4,multiply(X10,inverse(X10),X0)))),multiply(X4,X0,X3)) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f27,plain,
! [X2,X0,X1] : multiply(inverse(X1),multiply(X0,inverse(multiply(X1,inverse(X1),X2)),X2),X1) = X0,
inference(superposition,[],[f4,f1]) ).
fof(f44,plain,
! [X2,X3,X0,X1,X4] : multiply(multiply(X1,inverse(X1),X2),inverse(multiply(multiply(X3,inverse(X3),X4),inverse(multiply(X3,inverse(X3),X4)),multiply(X3,inverse(X3),X0))),X0) = X2,
inference(superposition,[],[f1,f27]) ).
fof(f274,plain,
! [X2,X3,X10,X0,X1,X8,X6,X9,X7,X4,X5] : multiply(multiply(X9,inverse(X9),X10),inverse(multiply(X0,multiply(multiply(X1,inverse(X1),inverse(X0)),inverse(multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6))),multiply(X3,multiply(X6,X5,X4),X2)),multiply(X7,inverse(X7),X8))),multiply(inverse(X0),X8,X0)) = X10,
inference(superposition,[],[f7,f7]) ).
fof(f301,plain,
! [X10,X0,X8,X9,X7] : multiply(multiply(X9,inverse(X9),X10),inverse(multiply(X0,inverse(X0),multiply(X7,inverse(X7),X8))),multiply(inverse(X0),X8,X0)) = X10,
inference(forward_demodulation,[],[f274,f1]) ).
fof(f326,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X3,X4,multiply(X5,multiply(X6,X7,X8),X9)),inverse(multiply(multiply(X9,X5,X8),X7,multiply(X9,X5,X6))),multiply(X3,X4,multiply(X10,inverse(X10),X11)))),multiply(X4,X11,X3)) = multiply(inverse(X2),X1,X2),
inference(superposition,[],[f7,f301]) ).
fof(f357,plain,
! [X2,X1] : multiply(inverse(X2),X1,X2) = X1,
inference(forward_demodulation,[],[f326,f7]) ).
fof(f384,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(X0),inverse(multiply(X0,inverse(X0),X1)),X0),
inference(superposition,[],[f27,f357]) ).
fof(f418,plain,
! [X0,X1] : inverse(X1) = inverse(multiply(X0,inverse(X0),X1)),
inference(forward_demodulation,[],[f384,f357]) ).
fof(f595,plain,
! [X2,X0,X1] : multiply(inverse(X1),multiply(X2,inverse(X0),X0),X1) = X2,
inference(superposition,[],[f27,f418]) ).
fof(f629,plain,
! [X2,X0] : multiply(X2,inverse(X0),X0) = X2,
inference(forward_demodulation,[],[f595,f357]) ).
fof(f718,plain,
! [X2,X3,X0,X1] : multiply(multiply(X2,inverse(X2),X3),inverse(multiply(X0,inverse(X0),X1)),X1) = X3,
inference(superposition,[],[f44,f629]) ).
fof(f723,plain,
! [X2,X3,X1] : multiply(multiply(X2,inverse(X2),X3),inverse(X1),X1) = X3,
inference(forward_demodulation,[],[f718,f418]) ).
fof(f742,plain,
! [X2,X3] : multiply(X2,inverse(X2),X3) = X3,
inference(forward_demodulation,[],[f723,f629]) ).
fof(f795,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(multiply(X1,inverse(X1),X2),inverse(multiply(multiply(X3,inverse(X3),X4),X5,X0)),multiply(inverse(X3),multiply(X0,X5,X4),X3)) = X2,
inference(superposition,[],[f1,f742]) ).
fof(f863,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(multiply(X1,inverse(X1),X2),inverse(multiply(multiply(X3,inverse(X3),X4),X5,X0)),multiply(X0,X5,X4)) = X2,
inference(forward_demodulation,[],[f795,f357]) ).
fof(f911,plain,
! [X2,X0,X1,X4,X5] : multiply(multiply(X1,inverse(X1),X2),inverse(multiply(X4,X5,X0)),multiply(X0,X5,X4)) = X2,
inference(forward_demodulation,[],[f863,f742]) ).
fof(f935,plain,
! [X2,X0,X4,X5] : multiply(X2,inverse(multiply(X4,X5,X0)),multiply(X0,X5,X4)) = X2,
inference(forward_demodulation,[],[f911,f742]) ).
fof(f3351,plain,
! [X2,X0,X1] : multiply(X0,X1,X2) = multiply(X2,X1,X0),
inference(superposition,[],[f935,f742]) ).
fof(f3597,plain,
! [X2,X3,X0,X1] : multiply(multiply(X3,X2,X1),inverse(multiply(X1,X2,X3)),X0) = X0,
inference(superposition,[],[f3351,f935]) ).
fof(f5349,plain,
! [X2,X3,X0,X1] : multiply(X0,X1,multiply(X2,inverse(X2),X3)) = multiply(multiply(X2,inverse(X2),X3),X0,multiply(inverse(X2),multiply(X1,X0,X3),X2)),
inference(superposition,[],[f7,f3597]) ).
fof(f5519,plain,
! [X2,X3,X0,X1] : multiply(X0,X1,multiply(X2,inverse(X2),X3)) = multiply(multiply(X2,inverse(X2),X3),X0,multiply(X1,X0,X3)),
inference(forward_demodulation,[],[f5349,f357]) ).
fof(f5613,plain,
! [X3,X0,X1] : multiply(X0,X1,X3) = multiply(X3,X0,multiply(X1,X0,X3)),
inference(forward_demodulation,[],[f5519,f742]) ).
fof(f5722,plain,
! [X0,X1] : multiply(X0,inverse(X1),X1) = multiply(X1,X0,X0),
inference(superposition,[],[f5613,f357]) ).
fof(f5924,plain,
! [X0,X1] : multiply(X1,X0,X0) = X0,
inference(forward_demodulation,[],[f5722,f629]) ).
fof(f6464,plain,
a != a,
inference(superposition,[],[f3,f5924]) ).
fof(f6465,plain,
$false,
inference(trivial_inequality_removal,[],[f6464]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO068-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 % Computer : n001.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Mon Sep 28 21:13:52 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.31 Running first-order theorem proving
% 0.26/0.31 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
% 8.51/2.25 % (754850)Detected a unit-equality problem, will run specialized UEQ schedule.
% 8.51/2.25 % (754857)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=685446863:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 8.51/2.25 % (754862)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1595157578:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 8.51/2.25 % (754860)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3805318488:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 8.51/2.25 % (754863)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2979609013:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 8.51/2.25 % (754861)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3920727516:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 8.51/2.25 % (754859)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1089967766:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 8.51/2.25 % (754858)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=1072937972:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 8.51/2.25 % (754860)Instruction limit reached!
% 8.51/2.25 % (754860)------------------------------
% 8.51/2.25 % (754860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/2.25 % (754860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/2.25 % (754860)CaDiCaL version: 2.1.3
% 8.51/2.25 % (754860)Termination reason: Instruction limit
% 8.51/2.25 % (754860)Termination phase: Saturation
% 8.51/2.25 % (754860)Time elapsed: 0.137 s
% 8.51/2.25 % (754860)Peak memory usage: 89 MB
% 8.51/2.25 % (754860)Instructions burned: 137 (million)
% 8.51/2.25 % (754861)Instruction limit reached!
% 8.51/2.25 % (754861)------------------------------
% 8.51/2.25 % (754861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/2.25 % (754861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/2.25 % (754861)CaDiCaL version: 2.1.3
% 8.51/2.25 % (754861)Termination reason: Instruction limit
% 8.51/2.25 % (754861)Termination phase: Saturation
% 8.51/2.25 % (754861)Time elapsed: 0.170 s
% 8.51/2.25 % (754861)Peak memory usage: 89 MB
% 8.51/2.25 % (754861)Instructions burned: 181 (million)
% 8.51/2.25 % (754862)Instruction limit reached!
% 8.51/2.25 % (754862)------------------------------
% 8.51/2.25 % (754862)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/2.25 % (754862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/2.25 % (754862)CaDiCaL version: 2.1.3
% 8.51/2.25 % (754862)Termination reason: Instruction limit
% 8.51/2.25 % (754862)Termination phase: Saturation
% 8.51/2.25 % (754862)Time elapsed: 0.246 s
% 8.51/2.25 % (754862)Peak memory usage: 89 MB
% 8.51/2.25 % (754862)Instructions burned: 257 (million)
% 8.51/2.25 % (754863)First to succeed.
% 8.51/2.25 % (754863)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-754850"
% 8.51/2.25 % (754871)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=4175786662:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 8.51/2.25 % (754872)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3889038851:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 8.51/2.25 % (754873)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=102343657:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 8.51/2.25 % (754857)Also succeeded, but the first one will report.
% 8.51/2.25 % (754873)Instruction limit reached!
% 8.51/2.25 % (754873)------------------------------
% 8.51/2.25 % (754873)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/2.25 % (754873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/2.25 % (754873)CaDiCaL version: 2.1.3
% 8.51/2.25 % (754873)Termination reason: Instruction limit
% 8.51/2.25 % (754873)Termination phase: Saturation
% 8.51/2.25 % (754873)Time elapsed: 0.189 s
% 8.51/2.25 % (754873)Peak memory usage: 89 MB
% 8.51/2.25 % (754873)Instructions burned: 215 (million)
% 8.51/2.25 % (754863)Refutation found. Thanks to Tanya!
% 8.51/2.25 % SZS status Unsatisfiable for theBenchmark
% 8.51/2.25 % SZS output start Proof for theBenchmark
% See solution above
% 8.51/2.25 % (754863)------------------------------
% 8.51/2.25 % (754863)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/2.25 % (754863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/2.25 % (754863)CaDiCaL version: 2.1.3
% 8.51/2.25 % (754863)Termination reason: Refutation
% 8.51/2.25 % (754863)Time elapsed: 0.370 s
% 8.51/2.25 % (754863)Peak memory usage: 92 MB
% 8.51/2.25 % (754863)Instructions burned: 405 (million)
% 8.51/2.25 % (754863)------------------------------
% 8.51/2.25 % (754863)------------------------------
% 8.51/2.25 % (754850)Success in time 1.066 s
% 8.51/2.25 % Vampire exiting
%------------------------------------------------------------------------------