%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP002-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 07:26:08 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.74s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 7
% Syntax : Number of formulae : 86 ( 86 unt; 0 def)
% Number of atoms : 86 ( 85 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 39 ( 39 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 17 ( 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 : 105 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(right_identity,axiom,
! [VAR_0] : multiply(VAR_0,identity) = VAR_0,
file('theBenchmark.p',right_identity) ).
cnf(c_4,plain,
multiply(A,identity) = A,
inference(clausify,[status(thm)],[right_identity]) ).
fof(commutator,axiom,
! [VAR_0,VAR_1] : commutator(VAR_0,VAR_1) = multiply(VAR_0,multiply(VAR_1,multiply(inverse(VAR_0),inverse(VAR_1)))),
file('theBenchmark.p',commutator) ).
cnf(c_6,plain,
commutator(A,B) = multiply(A,multiply(B,multiply(inverse(A),inverse(B)))),
inference(clausify,[status(thm)],[commutator]) ).
fof(x_cubed_is_identity,axiom,
! [VAR_0] : multiply(VAR_0,multiply(VAR_0,VAR_0)) = identity,
file('theBenchmark.p',x_cubed_is_identity) ).
cnf(c_7,plain,
multiply(A,multiply(A,A)) = identity,
inference(clausify,[status(thm)],[x_cubed_is_identity]) ).
fof(prove_commutator,axiom,
commutator(commutator(a,b),b) != identity,
file('theBenchmark.p',prove_commutator) ).
cnf(c_8,plain,
commutator(commutator(a,b),b) != identity,
inference(clausify,[status(thm)],[prove_commutator]) ).
cnf(c_62,plain,
commutator(multiply(a,multiply(b,multiply(inverse(a),inverse(b)))),b) != identity,
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_63,plain,
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)))) != identity,
inference(paramod,[status(thm)],[c_6,c_62]) ).
cnf(c_64,plain,
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))))) != identity,
inference(paramod,[status(thm)],[c_3,c_63]) ).
cnf(c_65,plain,
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)))))) != identity,
inference(paramod,[status(thm)],[c_3,c_64]) ).
cnf(c_9,plain,
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))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_65]) ).
cnf(c_66,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_67,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_66]) ).
cnf(c_10,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_67]) ).
cnf(c_11,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_10,c_9]) ).
cnf(c_68,plain,
multiply(identity,A) = multiply(B,multiply(multiply(B,B),A)),
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_69,plain,
A = multiply(B,multiply(multiply(B,B),A)),
inference(paramod,[status(thm)],[c_1,c_68]) ).
cnf(c_70,plain,
A = multiply(B,multiply(B,multiply(B,A))),
inference(paramod,[status(thm)],[c_3,c_69]) ).
cnf(c_15,plain,
multiply(A,multiply(A,multiply(A,B))) = B,
inference(copy,[status(thm)],[c_70]) ).
cnf(c_71,plain,
identity = multiply(A,multiply(B,multiply(multiply(A,B),multiply(A,B)))),
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_72,plain,
identity = multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,B))))),
inference(paramod,[status(thm)],[c_3,c_71]) ).
cnf(c_16,plain,
multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,B))))) = identity,
inference(copy,[status(thm)],[c_72]) ).
cnf(c_73,plain,
multiply(inverse(A),identity) = multiply(A,A),
inference(paramod,[status(thm)],[c_7,c_10]) ).
cnf(c_19,plain,
inverse(A) = multiply(A,A),
inference(paramod,[status(thm)],[c_4,c_73]) ).
cnf(c_74,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_19,c_11]) ).
cnf(c_75,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(inverse(multiply(a,multiply(b,multiply(multiply(a,a),inverse(b))))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_19,c_74]) ).
cnf(c_76,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(inverse(multiply(a,multiply(b,multiply(multiply(a,a),multiply(b,b))))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_19,c_75]) ).
cnf(c_77,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(inverse(multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b)))))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_3,c_76]) ).
cnf(c_78,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(multiply(multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b))))),multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b)))))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_19,c_77]) ).
cnf(c_79,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(multiply(a,multiply(multiply(b,multiply(a,multiply(a,multiply(b,b)))),multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b))))))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_3,c_78]) ).
cnf(c_80,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(multiply(a,multiply(b,multiply(multiply(a,multiply(a,multiply(b,b))),multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b)))))))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_3,c_79]) ).
cnf(c_81,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(multiply(a,multiply(b,multiply(a,multiply(multiply(a,multiply(b,b)),multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b))))))))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_3,c_80]) ).
cnf(c_82,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(multiply(a,multiply(b,multiply(a,multiply(a,multiply(multiply(b,b),multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b)))))))))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_3,c_81]) ).
cnf(c_83,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b))))))))))),inverse(b))))) != identity,
inference(paramod,[status(thm)],[c_3,c_82]) ).
cnf(c_84,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b))))))))))),multiply(b,b))))) != identity,
inference(paramod,[status(thm)],[c_19,c_83]) ).
cnf(c_85,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(a,multiply(multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b)))))))))),multiply(b,b)))))) != identity,
inference(paramod,[status(thm)],[c_3,c_84]) ).
cnf(c_86,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(a,multiply(b,multiply(multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b))))))))),multiply(b,b))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_85]) ).
cnf(c_87,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(a,multiply(b,multiply(a,multiply(multiply(a,multiply(b,multiply(b,multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b)))))))),multiply(b,b)))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_86]) ).
cnf(c_88,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(a,multiply(b,multiply(a,multiply(a,multiply(multiply(b,multiply(b,multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b))))))),multiply(b,b))))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_87]) ).
cnf(c_89,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(multiply(b,multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b)))))),multiply(b,b)))))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_88]) ).
cnf(c_90,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,b))))),multiply(b,b))))))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_89]) ).
cnf(c_91,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,multiply(multiply(b,multiply(a,multiply(a,multiply(b,b)))),multiply(b,b)))))))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_90]) ).
cnf(c_92,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,multiply(b,multiply(multiply(a,multiply(a,multiply(b,b))),multiply(b,b))))))))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_91]) ).
cnf(c_93,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,multiply(b,multiply(a,multiply(multiply(a,multiply(b,b)),multiply(b,b)))))))))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_92]) ).
cnf(c_94,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,multiply(b,multiply(a,multiply(a,multiply(multiply(b,b),multiply(b,b))))))))))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_93]) ).
cnf(c_95,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b)))))))))))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_94]) ).
cnf(c_96,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,identity)))))))))))))) != identity,
inference(paramod,[status(thm)],[c_7,c_95]) ).
cnf(c_97,plain,
multiply(a,multiply(b,multiply(multiply(a,a),multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,multiply(b,multiply(a,multiply(a,b))))))))))))) != identity,
inference(paramod,[status(thm)],[c_4,c_96]) ).
cnf(c_98,plain,
multiply(a,multiply(b,multiply(a,multiply(a,multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,multiply(b,multiply(a,multiply(a,b)))))))))))))) != identity,
inference(paramod,[status(thm)],[c_3,c_97]) ).
cnf(c_21,plain,
multiply(a,multiply(b,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,multiply(b,multiply(a,multiply(a,b))))))))))) != identity,
inference(paramod,[status(thm)],[c_15,c_98]) ).
cnf(c_99,plain,
multiply(A,multiply(A,identity)) = multiply(B,multiply(A,multiply(B,multiply(A,B)))),
inference(paramod,[status(thm)],[c_16,c_15]) ).
cnf(c_100,plain,
multiply(A,A) = multiply(B,multiply(A,multiply(B,multiply(A,B)))),
inference(paramod,[status(thm)],[c_4,c_99]) ).
cnf(c_24,plain,
multiply(A,multiply(B,multiply(A,multiply(B,A)))) = multiply(B,B),
inference(copy,[status(thm)],[c_100]) ).
cnf(c_101,plain,
multiply(multiply(A,A),B) = multiply(C,multiply(multiply(A,multiply(C,multiply(A,C))),B)),
inference(paramod,[status(thm)],[c_24,c_3]) ).
cnf(c_102,plain,
multiply(A,multiply(A,B)) = multiply(C,multiply(multiply(A,multiply(C,multiply(A,C))),B)),
inference(paramod,[status(thm)],[c_3,c_101]) ).
cnf(c_103,plain,
multiply(A,multiply(A,B)) = multiply(C,multiply(A,multiply(multiply(C,multiply(A,C)),B))),
inference(paramod,[status(thm)],[c_3,c_102]) ).
cnf(c_104,plain,
multiply(A,multiply(A,B)) = multiply(C,multiply(A,multiply(C,multiply(multiply(A,C),B)))),
inference(paramod,[status(thm)],[c_3,c_103]) ).
cnf(c_105,plain,
multiply(A,multiply(A,B)) = multiply(C,multiply(A,multiply(C,multiply(A,multiply(C,B))))),
inference(paramod,[status(thm)],[c_3,c_104]) ).
cnf(c_25,plain,
multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,C))))) = multiply(B,multiply(B,C)),
inference(copy,[status(thm)],[c_105]) ).
cnf(c_106,plain,
multiply(A,multiply(A,multiply(B,B))) = multiply(B,multiply(A,multiply(B,A))),
inference(paramod,[status(thm)],[c_24,c_15]) ).
cnf(c_28,plain,
multiply(A,multiply(B,multiply(A,B))) = multiply(B,multiply(B,multiply(A,A))),
inference(copy,[status(thm)],[c_106]) ).
cnf(c_107,plain,
multiply(multiply(A,multiply(A,multiply(B,B))),C) = multiply(B,multiply(multiply(A,multiply(B,A)),C)),
inference(paramod,[status(thm)],[c_28,c_3]) ).
cnf(c_108,plain,
multiply(A,multiply(multiply(A,multiply(B,B)),C)) = multiply(B,multiply(multiply(A,multiply(B,A)),C)),
inference(paramod,[status(thm)],[c_3,c_107]) ).
cnf(c_109,plain,
multiply(A,multiply(A,multiply(multiply(B,B),C))) = multiply(B,multiply(multiply(A,multiply(B,A)),C)),
inference(paramod,[status(thm)],[c_3,c_108]) ).
cnf(c_110,plain,
multiply(A,multiply(A,multiply(B,multiply(B,C)))) = multiply(B,multiply(multiply(A,multiply(B,A)),C)),
inference(paramod,[status(thm)],[c_3,c_109]) ).
cnf(c_111,plain,
multiply(A,multiply(A,multiply(B,multiply(B,C)))) = multiply(B,multiply(A,multiply(multiply(B,A),C))),
inference(paramod,[status(thm)],[c_3,c_110]) ).
cnf(c_112,plain,
multiply(A,multiply(A,multiply(B,multiply(B,C)))) = multiply(B,multiply(A,multiply(B,multiply(A,C)))),
inference(paramod,[status(thm)],[c_3,c_111]) ).
cnf(c_29,plain,
multiply(A,multiply(B,multiply(A,multiply(B,C)))) = multiply(B,multiply(B,multiply(A,multiply(A,C)))),
inference(copy,[status(thm)],[c_112]) ).
cnf(c_113,plain,
multiply(A,multiply(multiply(B,C),multiply(A,multiply(B,multiply(C,multiply(A,D)))))) = multiply(multiply(B,C),multiply(multiply(B,C),D)),
inference(paramod,[status(thm)],[c_3,c_25]) ).
cnf(c_114,plain,
multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,multiply(C,multiply(A,D))))))) = multiply(multiply(B,C),multiply(multiply(B,C),D)),
inference(paramod,[status(thm)],[c_3,c_113]) ).
cnf(c_115,plain,
multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,multiply(C,multiply(A,D))))))) = multiply(multiply(B,C),multiply(B,multiply(C,D))),
inference(paramod,[status(thm)],[c_3,c_114]) ).
cnf(c_38,plain,
multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,multiply(C,multiply(A,D))))))) = multiply(B,multiply(C,multiply(B,multiply(C,D)))),
inference(paramod,[status(thm)],[c_3,c_115]) ).
cnf(c_116,plain,
multiply(a,multiply(b,multiply(b,multiply(a,multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(b,multiply(a,b))))))))))) != identity,
inference(paramod,[status(thm)],[c_29,c_21]) ).
cnf(c_117,plain,
multiply(a,multiply(b,multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(a,b)))))))) != identity,
inference(paramod,[status(thm)],[c_38,c_116]) ).
cnf(c_118,plain,
multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))) != identity,
inference(paramod,[status(thm)],[c_15,c_117]) ).
cnf(c_119,plain,
multiply(a,multiply(a,a)) != identity,
inference(paramod,[status(thm)],[c_24,c_118]) ).
cnf(c_120,plain,
identity != identity,
inference(paramod,[status(thm)],[c_7,c_119]) ).
cnf(c_61,plain,
$false,
inference(copy,[status(thm)],[c_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP002-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.71 % Computer : n014.cluster.edu
% 0.07/0.71 % Model : x86_64 x86_64
% 0.07/0.71 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.71 % Memory : 8046.5625MB
% 0.07/0.71 % OS : Linux 6.8.0-71-generic
% 0.07/0.71 % CPULimit : 300
% 0.07/0.71 % WCLimit : 300
% 0.07/0.71 % DateTime : Fri Sep 25 14:15:49 UTC 2026
% 0.07/0.71 % CPUTime :
% 0.07/0.71 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.71 % Process 402152 was started by sandbox2 on n014,
% 0.07/0.71 % Fri Sep 25 14:15:49 2026
% 0.07/0.71 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.71
% 0.07/0.71 % From the command line: assign(max_seconds, 300).
% 0.07/0.74
% 0.07/0.74 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.74
% 0.07/0.74 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.07/0.74 % Length of proof is 20.
% 0.07/0.74 % Level of proof is 5.
% 0.07/0.74 % Maximum clause weight is 27.000.
% 0.07/0.74 % Given clauses 18.
% 0.07/0.74
% 0.07/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
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