%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP002-4 : 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 : n009.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 10:16:20 AM UTC 2026
% Result : Unsatisfiable 0.83s 0.61s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 59 unt; 0 def)
% Number of atoms : 59 ( 58 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 ( 3 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 : 77 ( 77 !; 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] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f6,axiom,
! [X0] : multiply(X0,inverse(X0)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f7,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0,X1] : commutator(X0,X1) = multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
fof(f9,axiom,
! [X0] : multiply(X0,multiply(X0,X0)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity) ).
fof(f10,plain,
! [X0] : identity = multiply(X0,multiply(X0,X0)),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
commutator(commutator(a,b),b) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutator) ).
fof(f12,plain,
identity != commutator(commutator(a,b),b),
inference(reorient_equations,[],[f11]) ).
fof(f13,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,[],[f12,f8,f8]) ).
fof(f14,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,[],[f13,f4]) ).
fof(f15,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,[],[f14,f4]) ).
fof(f16,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,[],[f15,f4]) ).
fof(f28,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[],[f4,f7]) ).
fof(f32,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f39,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(superposition,[],[f7,f4]) ).
fof(f43,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f32,f1]) ).
fof(f46,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f28,f1]) ).
fof(f47,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,[],[f16,f43]) ).
fof(f53,plain,
! [X0] : multiply(X0,X0) = multiply(inverse(X0),identity),
inference(superposition,[],[f43,f10]) ).
fof(f55,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[],[f43,f4]) ).
fof(f56,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f43,f3]) ).
fof(f60,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f56,f5]) ).
fof(f62,plain,
! [X0] : inverse(X0) = multiply(X0,X0),
inference(forward_demodulation,[],[f53,f5]) ).
fof(f89,plain,
! [X0,X1] : multiply(inverse(X0),X1) = multiply(X0,multiply(X0,X1)),
inference(superposition,[],[f4,f62]) ).
fof(f92,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(X0,multiply(X1,multiply(X0,X1))),
inference(superposition,[],[f4,f62]) ).
fof(f114,plain,
! [X0,X1] : multiply(X1,inverse(multiply(X0,X1))) = multiply(inverse(X0),identity),
inference(superposition,[],[f43,f39]) ).
fof(f125,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f114,f5]) ).
fof(f158,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(superposition,[],[f43,f125]) ).
fof(f162,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(superposition,[],[f46,f125]) ).
fof(f165,plain,
identity != multiply(a,multiply(b,multiply(inverse(a),inverse(multiply(b,multiply(a,multiply(b,multiply(inverse(a),inverse(b))))))))),
inference(backward_demodulation,[],[f47,f158]) ).
fof(f174,plain,
identity != multiply(a,multiply(b,inverse(multiply(multiply(b,multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),a)))),
inference(forward_demodulation,[],[f165,f158]) ).
fof(f178,plain,
identity != multiply(a,multiply(b,inverse(multiply(b,multiply(multiply(a,multiply(b,multiply(inverse(a),inverse(b)))),a))))),
inference(forward_demodulation,[],[f174,f4]) ).
fof(f180,plain,
identity != multiply(a,multiply(b,inverse(multiply(b,multiply(a,multiply(multiply(b,multiply(inverse(a),inverse(b))),a)))))),
inference(forward_demodulation,[],[f178,f4]) ).
fof(f181,plain,
identity != multiply(a,multiply(b,inverse(multiply(b,multiply(a,multiply(b,multiply(multiply(inverse(a),inverse(b)),a))))))),
inference(forward_demodulation,[],[f180,f4]) ).
fof(f182,plain,
identity != multiply(a,multiply(b,inverse(multiply(b,multiply(a,multiply(b,multiply(inverse(a),multiply(inverse(b),a)))))))),
inference(forward_demodulation,[],[f181,f4]) ).
fof(f238,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),multiply(X0,identity)),
inference(superposition,[],[f55,f7]) ).
fof(f273,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
inference(forward_demodulation,[],[f238,f5]) ).
fof(f336,plain,
! [X0,X1] : multiply(inverse(inverse(multiply(X1,X0))),X1) = multiply(inverse(multiply(X1,X0)),inverse(X0)),
inference(superposition,[],[f89,f273]) ).
fof(f343,plain,
! [X0,X1] : multiply(inverse(inverse(multiply(X1,X0))),X1) = inverse(multiply(X0,multiply(X1,X0))),
inference(forward_demodulation,[],[f336,f158]) ).
fof(f354,plain,
! [X0,X1] : inverse(multiply(X0,multiply(X1,X0))) = multiply(multiply(X1,X0),X1),
inference(forward_demodulation,[],[f343,f60]) ).
fof(f360,plain,
! [X0,X1] : multiply(X1,multiply(X0,X1)) = inverse(multiply(X0,multiply(X1,X0))),
inference(forward_demodulation,[],[f354,f4]) ).
fof(f382,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),X2) = multiply(inverse(X1),multiply(inverse(X0),X2)),
inference(superposition,[],[f4,f158]) ).
fof(f383,plain,
identity != multiply(a,multiply(b,inverse(multiply(b,multiply(a,multiply(b,multiply(inverse(multiply(b,a)),a))))))),
inference(backward_demodulation,[],[f182,f382]) ).
fof(f425,plain,
! [X2,X0,X1] : inverse(multiply(multiply(X1,inverse(X0)),X2)) = multiply(inverse(X2),multiply(X0,inverse(X1))),
inference(superposition,[],[f158,f162]) ).
fof(f428,plain,
! [X2,X0,X1] : multiply(inverse(X2),multiply(X0,inverse(X1))) = inverse(multiply(X1,multiply(inverse(X0),X2))),
inference(forward_demodulation,[],[f425,f4]) ).
fof(f549,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,multiply(X0,X1))) = multiply(X0,inverse(multiply(X0,X1))),
inference(superposition,[],[f89,f92]) ).
fof(f2246,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,[],[f549,f360]) ).
fof(f2366,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,[],[f2246,f428]) ).
fof(f2428,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,[],[f2366,f4]) ).
fof(f2485,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,[],[f2428,f4]) ).
fof(f2534,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,[],[f2485,f60]) ).
fof(f2570,plain,
! [X0,X1] : inverse(multiply(X1,X0)) = inverse(multiply(X0,multiply(X1,multiply(X0,multiply(inverse(multiply(X0,X1)),X1))))),
inference(forward_demodulation,[],[f2534,f92]) ).
fof(f2600,plain,
identity != multiply(a,multiply(b,inverse(multiply(a,b)))),
inference(backward_demodulation,[],[f383,f2570]) ).
fof(f2625,plain,
identity != multiply(a,inverse(a)),
inference(forward_demodulation,[],[f2600,f125]) ).
fof(f2639,plain,
$false,
inference(forward_subsumption_resolution,[],[f2625,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP002-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40 % Computer : n009.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 09:13:15 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.43 Running first-order model finding
% 0.14/0.43 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
% 0.83/0.60 % (1751824)Will run a generic schedule for satisfiability detection.
% 0.83/0.60 % (1751838)% WARNING: option uhcvi not known.
% 0.83/0.60 % (1751838)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2002972169:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.83/0.60 % (1751837)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=75411109_2999 on theBenchmark for (2999ds/0Mi)
% 0.83/0.60 % (1751840)dis+10_1_sil=32000:sp=arity:random_seed=999413946:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.83/0.60 % (1751839)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4054379253:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.83/0.60 % (1751841)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3410295909:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.83/0.60 % (1751842)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=256241050:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.83/0.60 % (1751843)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2953503305:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.83/0.60 % TRYING [1]
% 0.83/0.60 % TRYING [2]
% 0.83/0.60 % TRYING [3]
% 0.83/0.60 % TRYING [4]
% 0.83/0.60 % TRYING [5]
% 0.83/0.60 % TRYING [6]
% 0.83/0.60 % TRYING [7]
% 0.83/0.60 % (1751840)Instruction limit reached!
% 0.83/0.60 % (1751840)------------------------------
% 0.83/0.60 % (1751840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.60 % (1751840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.60 % (1751840)CaDiCaL version: 2.1.3
% 0.83/0.60 % (1751840)Termination reason: Instruction limit
% 0.83/0.60 % (1751840)Termination phase: Saturation
% 0.83/0.60 % (1751840)Time elapsed: 0.056 s
% 0.83/0.60 % (1751840)Peak memory usage: 12 MB
% 0.83/0.60 % (1751840)Instructions burned: 103 (million)
% 0.83/0.60 % (1751841)Instruction limit reached!
% 0.83/0.60 % (1751841)------------------------------
% 0.83/0.60 % (1751841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.60 % (1751841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.60 % (1751841)CaDiCaL version: 2.1.3
% 0.83/0.60 % (1751841)Termination reason: Instruction limit
% 0.83/0.60 % (1751841)Termination phase: Saturation
% 0.83/0.60 % (1751841)Time elapsed: 0.064 s
% 0.83/0.60 % (1751841)Peak memory usage: 12 MB
% 0.83/0.60 % (1751841)Instructions burned: 117 (million)
% 0.83/0.60 % (1751842)Instruction limit reached!
% 0.83/0.60 % (1751842)------------------------------
% 0.83/0.60 % (1751842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.60 % (1751842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.60 % (1751842)CaDiCaL version: 2.1.3
% 0.83/0.60 % (1751842)Termination reason: Instruction limit
% 0.83/0.60 % (1751842)Termination phase: Saturation
% 0.83/0.60 % (1751842)Time elapsed: 0.067 s
% 0.83/0.60 % (1751842)Peak memory usage: 12 MB
% 0.83/0.60 % (1751842)Instructions burned: 132 (million)
% 0.83/0.60 % (1751878)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2506765052:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.83/0.60 % TRYING [1]
% 0.83/0.60 % TRYING [2]
% 0.83/0.60 % TRYING [3]
% 0.83/0.60 % TRYING [4]
% 0.83/0.60 % (1751880)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1465180335:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.83/0.61 % (1751883)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=123234163:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.83/0.61 % TRYING [5]
% 0.83/0.61 % (1751843)Instruction limit reached!
% 0.83/0.61 % (1751843)------------------------------
% 0.83/0.61 % (1751843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.61 % (1751843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.61 % (1751843)CaDiCaL version: 2.1.3
% 0.83/0.61 % (1751843)Termination reason: Instruction limit
% 0.83/0.61 % (1751843)Termination phase: Saturation
% 0.83/0.61 % (1751843)Time elapsed: 0.096 s
% 0.83/0.61 % (1751843)Peak memory usage: 12 MB
% 0.83/0.61 % (1751843)Instructions burned: 160 (million)
% 0.83/0.61 % TRYING [8]
% 0.83/0.61 % TRYING [6]
% 0.83/0.61 % (1751899)ott-21_1_sil=16000:fs=off:random_seed=3393659888:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.83/0.61 % (1751880) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1751824-1751880"...
% 0.83/0.61 % (1751880)...printing done.
% 0.83/0.61 % (1751880)Refutation found. Thanks to Tanya!
% 0.83/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.83/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 0.83/0.61 % (1751880)------------------------------
% 0.83/0.61 % (1751880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.61 % (1751880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.61 % (1751880)CaDiCaL version: 2.1.3
% 0.83/0.61 % (1751880)Termination reason: Refutation
% 0.83/0.61 % (1751880)Time elapsed: 0.048 s
% 0.83/0.61 % (1751880)Peak memory usage: 13 MB
% 0.83/0.61 % (1751880)Instructions burned: 80 (million)
% 0.83/0.61 % (1751824)Success in time 0.17 s
% 0.83/0.61 % Vampire exiting
%------------------------------------------------------------------------------