%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP002-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 10:16:19 AM UTC 2026
% Result : Unsatisfiable 0.92s 0.63s
% Output : Refutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 63 ( 63 unt; 0 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 16 ( 16 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 85 ( 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0,X1] : commutator(X0,X1) = multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
fof(f6,axiom,
! [X0] : multiply(X0,multiply(X0,X0)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity) ).
fof(f7,plain,
! [X0] : identity = multiply(X0,multiply(X0,X0)),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
commutator(commutator(a,b),b) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutator) ).
fof(f9,plain,
identity != commutator(commutator(a,b),b),
inference(reorient_equations,[],[f8]) ).
fof(f10,plain,
identity != multiply(multiply(a,multiply(b,multiply(inverse(a),inverse(b)))),multiply(b,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b)))),
inference(definition_unfolding,[],[f9,f5,f5]) ).
fof(f11,plain,
identity != multiply(a,multiply(multiply(b,multiply(inverse(a),inverse(b))),multiply(b,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b))))),
inference(backward_demodulation,[],[f10,f4]) ).
fof(f12,plain,
identity != multiply(a,multiply(b,multiply(multiply(inverse(a),inverse(b)),multiply(b,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b)))))),
inference(forward_demodulation,[],[f11,f4]) ).
fof(f13,plain,
identity != multiply(a,multiply(b,multiply(inverse(a),multiply(inverse(b),multiply(b,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b))))))),
inference(forward_demodulation,[],[f12,f4]) ).
fof(f18,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f19,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(multiply(X0,X0),X1)),
inference(superposition,[],[f4,f7]) ).
fof(f28,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(X0,multiply(X0,X1))),
inference(forward_demodulation,[],[f19,f4]) ).
fof(f29,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f18,f1]) ).
fof(f31,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(X0,X1))) = X1,
inference(forward_demodulation,[],[f28,f1]) ).
fof(f32,plain,
identity != multiply(a,multiply(b,multiply(inverse(a),multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b))))),
inference(backward_demodulation,[],[f13,f29]) ).
fof(f34,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f29,f3]) ).
fof(f35,plain,
! [X0] : multiply(X0,X0) = multiply(inverse(X0),identity),
inference(superposition,[],[f29,f7]) ).
fof(f36,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f29,f29]) ).
fof(f37,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[],[f29,f4]) ).
fof(f40,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f34,f36]) ).
fof(f41,plain,
! [X0] : inverse(X0) = multiply(X0,X0),
inference(backward_demodulation,[],[f35,f40]) ).
fof(f42,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(backward_demodulation,[],[f7,f41]) ).
fof(f46,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[],[f4,f42]) ).
fof(f48,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(superposition,[],[f4,f42]) ).
fof(f50,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f46,f1]) ).
fof(f58,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[],[f50,f42]) ).
fof(f67,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f58,f40]) ).
fof(f84,plain,
! [X0,X1] : multiply(inverse(X1),X0) = multiply(X1,multiply(X1,X0)),
inference(superposition,[],[f29,f31]) ).
fof(f133,plain,
! [X0,X1] : multiply(inverse(X0),identity) = multiply(X1,inverse(multiply(X0,X1))),
inference(superposition,[],[f29,f48]) ).
fof(f144,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f133,f40]) ).
fof(f172,plain,
! [X0,X1] : multiply(X0,multiply(X1,multiply(X0,X1))) = inverse(multiply(X0,X1)),
inference(superposition,[],[f4,f41]) ).
fof(f189,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(superposition,[],[f29,f144]) ).
fof(f193,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(superposition,[],[f50,f144]) ).
fof(f196,plain,
identity != multiply(a,multiply(b,multiply(inverse(a),inverse(multiply(b,multiply(a,multiply(b,multiply(inverse(a),inverse(b))))))))),
inference(backward_demodulation,[],[f32,f189]) ).
fof(f205,plain,
identity != multiply(a,multiply(b,inverse(multiply(multiply(b,multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),a)))),
inference(forward_demodulation,[],[f196,f189]) ).
fof(f209,plain,
identity != multiply(a,multiply(b,inverse(multiply(b,multiply(multiply(a,multiply(b,multiply(inverse(a),inverse(b)))),a))))),
inference(forward_demodulation,[],[f205,f4]) ).
fof(f211,plain,
identity != multiply(a,multiply(b,inverse(multiply(b,multiply(a,multiply(multiply(b,multiply(inverse(a),inverse(b))),a)))))),
inference(forward_demodulation,[],[f209,f4]) ).
fof(f212,plain,
identity != multiply(a,multiply(b,inverse(multiply(b,multiply(a,multiply(b,multiply(multiply(inverse(a),inverse(b)),a))))))),
inference(forward_demodulation,[],[f211,f4]) ).
fof(f213,plain,
identity != multiply(a,multiply(b,inverse(multiply(b,multiply(a,multiply(b,multiply(inverse(a),multiply(inverse(b),a)))))))),
inference(forward_demodulation,[],[f212,f4]) ).
fof(f272,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),X2) = multiply(inverse(X1),multiply(inverse(X0),X2)),
inference(superposition,[],[f4,f189]) ).
fof(f273,plain,
identity != multiply(a,multiply(b,inverse(multiply(b,multiply(a,multiply(b,multiply(inverse(multiply(b,a)),a))))))),
inference(backward_demodulation,[],[f213,f272]) ).
fof(f308,plain,
! [X2,X0,X1] : inverse(multiply(multiply(X1,inverse(X0)),X2)) = multiply(inverse(X2),multiply(X0,inverse(X1))),
inference(superposition,[],[f189,f193]) ).
fof(f311,plain,
! [X2,X0,X1] : multiply(inverse(X2),multiply(X0,inverse(X1))) = inverse(multiply(X1,multiply(inverse(X0),X2))),
inference(forward_demodulation,[],[f308,f4]) ).
fof(f357,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),multiply(X0,identity)),
inference(superposition,[],[f37,f42]) ).
fof(f387,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
inference(forward_demodulation,[],[f357,f40]) ).
fof(f473,plain,
! [X0,X1] : multiply(inverse(inverse(multiply(X1,X0))),X1) = multiply(inverse(multiply(X1,X0)),inverse(X0)),
inference(superposition,[],[f84,f387]) ).
fof(f482,plain,
! [X0,X1] : multiply(inverse(inverse(multiply(X1,X0))),X1) = inverse(multiply(X0,multiply(X1,X0))),
inference(forward_demodulation,[],[f473,f189]) ).
fof(f496,plain,
! [X0,X1] : inverse(multiply(X0,multiply(X1,X0))) = multiply(multiply(X1,X0),X1),
inference(forward_demodulation,[],[f482,f67]) ).
fof(f504,plain,
! [X0,X1] : multiply(X1,multiply(X0,X1)) = inverse(multiply(X0,multiply(X1,X0))),
inference(forward_demodulation,[],[f496,f4]) ).
fof(f537,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,multiply(X0,X1))) = multiply(X0,inverse(multiply(X0,X1))),
inference(superposition,[],[f84,f172]) ).
fof(f3270,plain,
! [X0,X1] : multiply(X1,inverse(inverse(multiply(X0,multiply(X1,X0))))) = multiply(inverse(X1),multiply(multiply(X0,X1),inverse(multiply(X0,multiply(X1,X0))))),
inference(superposition,[],[f537,f504]) ).
fof(f3396,plain,
! [X0,X1] : multiply(X1,inverse(inverse(multiply(X0,multiply(X1,X0))))) = inverse(multiply(multiply(X0,multiply(X1,X0)),multiply(inverse(multiply(X0,X1)),X1))),
inference(forward_demodulation,[],[f3270,f311]) ).
fof(f3466,plain,
! [X0,X1] : multiply(X1,inverse(inverse(multiply(X0,multiply(X1,X0))))) = inverse(multiply(X0,multiply(multiply(X1,X0),multiply(inverse(multiply(X0,X1)),X1)))),
inference(forward_demodulation,[],[f3396,f4]) ).
fof(f3529,plain,
! [X0,X1] : multiply(X1,inverse(inverse(multiply(X0,multiply(X1,X0))))) = inverse(multiply(X0,multiply(X1,multiply(X0,multiply(inverse(multiply(X0,X1)),X1))))),
inference(forward_demodulation,[],[f3466,f4]) ).
fof(f3585,plain,
! [X0,X1] : multiply(X1,multiply(X0,multiply(X1,X0))) = inverse(multiply(X0,multiply(X1,multiply(X0,multiply(inverse(multiply(X0,X1)),X1))))),
inference(forward_demodulation,[],[f3529,f67]) ).
fof(f3627,plain,
! [X0,X1] : inverse(multiply(X1,X0)) = inverse(multiply(X0,multiply(X1,multiply(X0,multiply(inverse(multiply(X0,X1)),X1))))),
inference(forward_demodulation,[],[f3585,f172]) ).
fof(f3662,plain,
identity != multiply(a,multiply(b,inverse(multiply(a,b)))),
inference(backward_demodulation,[],[f273,f3627]) ).
fof(f3691,plain,
identity != multiply(a,inverse(a)),
inference(forward_demodulation,[],[f3662,f144]) ).
fof(f3707,plain,
$false,
inference(forward_subsumption_resolution,[],[f3691,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n014.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:12:47 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.92/0.63 % (535410)Will run a generic schedule for satisfiability detection.
% 0.92/0.63 % (535417)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2773910736:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.92/0.63 % (535416)% WARNING: option uhcvi not known.
% 0.92/0.63 % (535415)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1260469415_2999 on theBenchmark for (2999ds/0Mi)
% 0.92/0.63 % (535416)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3036274141:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.92/0.63 % (535418)dis+10_1_sil=32000:sp=arity:random_seed=3055811403:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.92/0.63 % (535419)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1352887353:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.92/0.63 % (535420)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1972612241:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.92/0.63 % (535421)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=567821412:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.92/0.63 % TRYING [1]
% 0.92/0.63 % TRYING [2]
% 0.92/0.63 % TRYING [3]
% 0.92/0.63 % TRYING [4]
% 0.92/0.63 % TRYING [5]
% 0.92/0.63 % TRYING [6]
% 0.92/0.63 % TRYING [7]
% 0.92/0.63 % (535418)Instruction limit reached!
% 0.92/0.63 % (535418)------------------------------
% 0.92/0.63 % (535418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.63 % (535418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.63 % (535418)CaDiCaL version: 2.1.3
% 0.92/0.63 % (535418)Termination reason: Instruction limit
% 0.92/0.63 % (535418)Termination phase: Saturation
% 0.92/0.63 % (535418)Time elapsed: 0.055 s
% 0.92/0.63 % (535418)Peak memory usage: 12 MB
% 0.92/0.63 % (535418)Instructions burned: 104 (million)
% 0.92/0.63 % (535419)Instruction limit reached!
% 0.92/0.63 % (535419)------------------------------
% 0.92/0.63 % (535419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.63 % (535419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.63 % (535419)CaDiCaL version: 2.1.3
% 0.92/0.63 % (535419)Termination reason: Instruction limit
% 0.92/0.63 % (535419)Termination phase: Saturation
% 0.92/0.63 % (535419)Time elapsed: 0.065 s
% 0.92/0.63 % (535419)Peak memory usage: 12 MB
% 0.92/0.63 % (535419)Instructions burned: 117 (million)
% 0.92/0.63 % (535420)Instruction limit reached!
% 0.92/0.63 % (535420)------------------------------
% 0.92/0.63 % (535420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.63 % (535420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.63 % (535420)CaDiCaL version: 2.1.3
% 0.92/0.63 % (535420)Termination reason: Instruction limit
% 0.92/0.63 % (535420)Termination phase: Saturation
% 0.92/0.63 % (535420)Time elapsed: 0.069 s
% 0.92/0.63 % (535420)Peak memory usage: 12 MB
% 0.92/0.63 % (535420)Instructions burned: 135 (million)
% 0.92/0.63 % (535429)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4200146681:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.92/0.63 % TRYING [1]
% 0.92/0.63 % TRYING [2]
% 0.92/0.63 % TRYING [3]
% 0.92/0.63 % TRYING [4]
% 0.92/0.63 % (535430)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3825679481:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.92/0.63 % TRYING [5]
% 0.92/0.63 % (535431)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3625500557:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.92/0.63 % (535421)Instruction limit reached!
% 0.92/0.63 % (535421)------------------------------
% 0.92/0.63 % (535421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.63 % (535421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.63 % (535421)CaDiCaL version: 2.1.3
% 0.92/0.63 % (535421)Termination reason: Instruction limit
% 0.92/0.63 % (535421)Termination phase: Saturation
% 0.92/0.63 % (535421)Time elapsed: 0.094 s
% 0.92/0.63 % (535421)Peak memory usage: 13 MB
% 0.92/0.63 % (535421)Instructions burned: 160 (million)
% 0.92/0.63 % TRYING [6]
% 0.92/0.63 % (535435)ott-21_1_sil=16000:fs=off:random_seed=3616337553:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.92/0.63 % TRYING [8]
% 0.92/0.63 % (535430) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-535410-535430"...
% 0.92/0.63 % (535430)...printing done.
% 0.92/0.63 % (535430)Refutation found. Thanks to Tanya!
% 0.92/0.63 % SZS status Unsatisfiable for theBenchmark
% 0.92/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 0.92/0.63 % (535430)------------------------------
% 0.92/0.63 % (535430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.92/0.63 % (535430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.92/0.63 % (535430)CaDiCaL version: 2.1.3
% 0.92/0.63 % (535430)Termination reason: Refutation
% 0.92/0.63 % (535430)Time elapsed: 0.068 s
% 0.92/0.63 % (535430)Peak memory usage: 12 MB
% 0.92/0.63 % (535430)Instructions burned: 113 (million)
% 0.92/0.63 % (535410)Success in time 0.199 s
% 0.92/0.63 % Vampire exiting
%------------------------------------------------------------------------------