%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO070-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 3.02s 0.94s
% Output : Refutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of formulae : 32 ( 32 unt; 0 def)
% Number of atoms : 32 ( 31 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 : 128 ( 128 !; 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/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(a,a,b) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_tba_axioms_4) ).
fof(f3,plain,
a != multiply(a,a,b),
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(f5347,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(f5517,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,[],[f5347,f357]) ).
fof(f5611,plain,
! [X3,X0,X1] : multiply(X0,X1,X3) = multiply(X3,X0,multiply(X1,X0,X3)),
inference(forward_demodulation,[],[f5517,f742]) ).
fof(f5720,plain,
! [X0,X1] : multiply(X0,inverse(X1),X1) = multiply(X1,X0,X0),
inference(superposition,[],[f5611,f357]) ).
fof(f5922,plain,
! [X0,X1] : multiply(X1,X0,X0) = X0,
inference(forward_demodulation,[],[f5720,f629]) ).
fof(f6350,plain,
! [X0,X1] : multiply(X0,X0,X1) = X0,
inference(superposition,[],[f5922,f3351]) ).
fof(f6712,plain,
a != a,
inference(superposition,[],[f3,f6350]) ).
fof(f6713,plain,
$false,
inference(trivial_inequality_removal,[],[f6712]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO070-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 % Computer : n026.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Mon Sep 28 21:10:57 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 Running first-order theorem proving
% 0.11/0.25 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
% 3.02/0.94 % (80782)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.02/0.94 % (80794)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=798126894:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.02/0.94 % (80788)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=407566512:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.02/0.94 % (80789)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=2403273930:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.02/0.94 % (80791)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4186146036:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.02/0.94 % (80790)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=598013524:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.02/0.94 % (80793)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1118490435:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.02/0.94 % (80792)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1129734024:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.02/0.94 % (80791)Instruction limit reached!
% 3.02/0.94 % (80791)------------------------------
% 3.02/0.94 % (80791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/0.94 % (80791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/0.94 % (80791)CaDiCaL version: 2.1.3
% 3.02/0.94 % (80791)Termination reason: Instruction limit
% 3.02/0.94 % (80791)Termination phase: Saturation
% 3.02/0.94 % (80791)Time elapsed: 0.082 s
% 3.02/0.94 % (80791)Peak memory usage: 89 MB
% 3.02/0.94 % (80791)Instructions burned: 138 (million)
% 3.02/0.94 % (80794)First to succeed.
% 3.02/0.94 % (80794)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-80782"
% 3.02/0.94 % (80792)Instruction limit reached!
% 3.02/0.94 % (80792)------------------------------
% 3.02/0.94 % (80792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/0.94 % (80792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/0.94 % (80792)CaDiCaL version: 2.1.3
% 3.02/0.94 % (80792)Termination reason: Instruction limit
% 3.02/0.94 % (80792)Termination phase: Saturation
% 3.02/0.94 % (80792)Time elapsed: 0.103 s
% 3.02/0.94 % (80792)Peak memory usage: 89 MB
% 3.02/0.94 % (80792)Instructions burned: 181 (million)
% 3.02/0.94 % (80793)Instruction limit reached!
% 3.02/0.94 % (80793)------------------------------
% 3.02/0.94 % (80793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/0.94 % (80793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/0.94 % (80793)CaDiCaL version: 2.1.3
% 3.02/0.94 % (80793)Termination reason: Instruction limit
% 3.02/0.94 % (80793)Termination phase: Saturation
% 3.02/0.94 % (80793)Time elapsed: 0.156 s
% 3.02/0.94 % (80793)Peak memory usage: 89 MB
% 3.02/0.94 % (80793)Instructions burned: 257 (million)
% 3.02/0.94 % (80802)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=650281107:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.02/0.94 % (80794)Refutation found. Thanks to Tanya!
% 3.02/0.94 % SZS status Unsatisfiable for theBenchmark
% 3.02/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 3.02/0.94 % (80794)------------------------------
% 3.02/0.94 % (80794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/0.94 % (80794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/0.94 % (80794)CaDiCaL version: 2.1.3
% 3.02/0.94 % (80794)Termination reason: Refutation
% 3.02/0.94 % (80794)Time elapsed: 0.123 s
% 3.02/0.94 % (80794)Peak memory usage: 93 MB
% 3.02/0.94 % (80794)Instructions burned: 418 (million)
% 3.02/0.94 % (80794)------------------------------
% 3.02/0.94 % (80794)------------------------------
% 3.02/0.94 % (80782)Success in time 0.376 s
% 3.02/0.94 % Vampire exiting
%------------------------------------------------------------------------------