%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP510-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 07:30:15 AM UTC 2026
% Result : Unsatisfiable 0.14s 10.61s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 52 ( 52 unt; 0 def)
% Number of atoms : 52 ( 51 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 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; 0-2 aty)
% Number of variables : 154 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(multiply(VAR_0,VAR_1),VAR_2),inverse(multiply(VAR_0,VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_these_axioms_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_2,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_3,plain,
multiply(multiply(A,B),inverse(multiply(multiply(multiply(C,A),D),B))) = inverse(multiply(C,D)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_4,plain,
multiply(A,inverse(multiply(multiply(B,A),inverse(multiply(B,C))))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_11,plain,
multiply(multiply(A,inverse(multiply(B,C))),inverse(A)) = inverse(multiply(B,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_16,plain,
multiply(A,inverse(multiply(B,inverse(multiply(multiply(C,multiply(B,D)),inverse(multiply(C,A))))))) = D,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_186,plain,
multiply(multiply(inverse(multiply(multiply(A,B),inverse(multiply(A,C)))),D),inverse(multiply(multiply(C,E),D))) = inverse(multiply(B,E)),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_20,plain,
inverse(multiply(A,B)) = multiply(multiply(inverse(multiply(multiply(C,A),inverse(multiply(C,D)))),E),inverse(multiply(multiply(D,B),E))),
inference(copy,[status(thm)],[c_186]) ).
cnf(c_187,plain,
multiply(multiply(A,B),inverse(multiply(C,B))) = inverse(multiply(D,inverse(multiply(multiply(E,multiply(D,A)),inverse(multiply(E,C)))))),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_21,plain,
inverse(multiply(A,inverse(multiply(multiply(B,multiply(A,C)),inverse(multiply(B,D)))))) = multiply(multiply(C,E),inverse(multiply(D,E))),
inference(copy,[status(thm)],[c_187]) ).
cnf(c_188,plain,
A = inverse(multiply(B,multiply(C,inverse(multiply(multiply(B,C),A))))),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_23,plain,
inverse(multiply(A,multiply(B,inverse(multiply(multiply(A,B),C))))) = C,
inference(copy,[status(thm)],[c_188]) ).
cnf(c_189,plain,
multiply(A,inverse(multiply(multiply(B,A),inverse(C)))) = inverse(multiply(multiply(D,B),inverse(multiply(D,C)))),
inference(paramod,[status(thm)],[c_4,c_4]) ).
cnf(c_27,plain,
inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(D,inverse(multiply(multiply(B,D),inverse(C)))),
inference(copy,[status(thm)],[c_189]) ).
cnf(c_28,plain,
multiply(multiply(multiply(A,B),multiply(C,inverse(multiply(multiply(A,C),D)))),D) = B,
inference(paramod,[status(thm)],[c_23,c_1]) ).
cnf(c_190,plain,
inverse(multiply(A,multiply(B,inverse(C)))) = inverse(multiply(multiply(D,multiply(A,B)),inverse(multiply(D,C)))),
inference(paramod,[status(thm)],[c_4,c_23]) ).
cnf(c_37,plain,
inverse(multiply(multiply(A,multiply(B,C)),inverse(multiply(A,D)))) = inverse(multiply(B,multiply(C,inverse(D)))),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_40,plain,
inverse(multiply(A,inverse(multiply(A,multiply(B,inverse(C)))))) = multiply(multiply(B,D),inverse(multiply(C,D))),
inference(paramod,[status(thm)],[c_37,c_21]) ).
cnf(c_41,plain,
multiply(A,inverse(multiply(B,inverse(multiply(B,multiply(C,inverse(A))))))) = C,
inference(paramod,[status(thm)],[c_37,c_16]) ).
cnf(c_52,plain,
multiply(A,inverse(multiply(multiply(B,A),C))) = inverse(multiply(B,C)),
inference(paramod,[status(thm)],[c_1,c_11]) ).
cnf(c_191,plain,
multiply(multiply(inverse(multiply(A,B)),C),inverse(multiply(inverse(multiply(A,B)),C))) = inverse(multiply(D,inverse(D))),
inference(paramod,[status(thm)],[c_11,c_3]) ).
cnf(c_55,plain,
inverse(multiply(A,inverse(A))) = multiply(multiply(inverse(multiply(B,C)),D),inverse(multiply(inverse(multiply(B,C)),D))),
inference(copy,[status(thm)],[c_191]) ).
cnf(c_192,plain,
multiply(A,inverse(B)) = inverse(multiply(multiply(C,B),inverse(multiply(C,A)))),
inference(paramod,[status(thm)],[c_4,c_11]) ).
cnf(c_62,plain,
inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(C,inverse(B)),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_75,plain,
multiply(multiply(multiply(A,B),inverse(multiply(A,C))),C) = B,
inference(paramod,[status(thm)],[c_52,c_28]) ).
cnf(c_193,plain,
multiply(C,inverse(B)) = multiply(D,inverse(multiply(multiply(B,D),inverse(C)))),
inference(paramod,[status(thm)],[c_62,c_27]) ).
cnf(c_194,plain,
multiply(C,inverse(B)) = inverse(multiply(B,inverse(C))),
inference(paramod,[status(thm)],[c_52,c_193]) ).
cnf(c_76,plain,
inverse(multiply(A,inverse(B))) = multiply(B,inverse(A)),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_195,plain,
inverse(multiply(A,inverse(multiply(A,C)))) = C,
inference(paramod,[status(thm)],[c_52,c_23]) ).
cnf(c_77,plain,
multiply(multiply(A,B),inverse(A)) = B,
inference(paramod,[status(thm)],[c_76,c_195]) ).
cnf(c_100,plain,
inverse(multiply(A,B)) = multiply(multiply(multiply(multiply(C,D),inverse(multiply(C,A))),E),inverse(multiply(multiply(D,B),E))),
inference(paramod,[status(thm)],[c_76,c_20]) ).
cnf(c_196,plain,
multiply(A,multiply(multiply(B,multiply(C,inverse(A))),inverse(B))) = C,
inference(paramod,[status(thm)],[c_76,c_41]) ).
cnf(c_103,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(paramod,[status(thm)],[c_77,c_196]) ).
cnf(c_197,plain,
multiply(multiply(A,multiply(B,inverse(C))),inverse(A)) = multiply(multiply(B,D),inverse(multiply(C,D))),
inference(paramod,[status(thm)],[c_76,c_40]) ).
cnf(c_198,plain,
multiply(B,inverse(C)) = multiply(multiply(B,D),inverse(multiply(C,D))),
inference(paramod,[status(thm)],[c_77,c_197]) ).
cnf(c_104,plain,
multiply(multiply(A,B),inverse(multiply(C,B))) = multiply(A,inverse(C)),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_105,plain,
multiply(multiply(A,B),inverse(multiply(A,C))) = multiply(B,inverse(C)),
inference(paramod,[status(thm)],[c_76,c_62]) ).
cnf(c_199,plain,
multiply(A,inverse(A)) = multiply(multiply(inverse(multiply(B,C)),D),inverse(multiply(inverse(multiply(B,C)),D))),
inference(paramod,[status(thm)],[c_76,c_55]) ).
cnf(c_106,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(paramod,[status(thm)],[c_105,c_199]) ).
cnf(c_200,plain,
inverse(multiply(A,B)) = multiply(multiply(multiply(D,inverse(A)),E),inverse(multiply(multiply(D,B),E))),
inference(paramod,[status(thm)],[c_105,c_100]) ).
cnf(c_201,plain,
inverse(multiply(A,B)) = multiply(multiply(D,inverse(A)),inverse(multiply(D,B))),
inference(paramod,[status(thm)],[c_104,c_200]) ).
cnf(c_109,plain,
inverse(multiply(A,B)) = multiply(inverse(A),inverse(B)),
inference(paramod,[status(thm)],[c_105,c_201]) ).
cnf(c_123,plain,
multiply(multiply(multiply(A,B),multiply(inverse(A),inverse(C))),C) = B,
inference(paramod,[status(thm)],[c_109,c_75]) ).
cnf(c_127,plain,
multiply(multiply(A,B),multiply(inverse(A),inverse(C))) = multiply(B,inverse(C)),
inference(paramod,[status(thm)],[c_109,c_105]) ).
cnf(c_151,plain,
multiply(multiply(A,inverse(B)),B) = A,
inference(paramod,[status(thm)],[c_127,c_123]) ).
cnf(c_159,plain,
multiply(A,B) = multiply(B,A),
inference(paramod,[status(thm)],[c_77,c_151]) ).
cnf(c_202,plain,
multiply(multiply(b2,inverse(b2)),a2) != a2,
inference(paramod,[status(thm)],[c_159,c_2]) ).
cnf(c_179,plain,
multiply(a2,multiply(b2,inverse(b2))) != a2,
inference(paramod,[status(thm)],[c_159,c_202]) ).
cnf(c_184,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_106,c_103]) ).
cnf(c_185,plain,
$false,
inference(resolve,[status(thm)],[c_184,c_179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP510-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.58 % Computer : n004.cluster.edu
% 0.10/10.58 % Model : x86_64 x86_64
% 0.10/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.58 % Memory : 8046.5625MB
% 0.10/10.58 % OS : Linux 6.8.0-71-generic
% 0.10/10.58 % CPULimit : 300
% 0.10/10.58 % WCLimit : 300
% 0.10/10.58 % DateTime : Fri Sep 25 14:57:49 UTC 2026
% 0.10/10.58 % CPUTime :
% 0.10/10.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.58 % Process 3477814 was started by sandbox2 on n004,
% 0.10/10.58 % Fri Sep 25 14:57:49 2026
% 0.10/10.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/10.59
% 0.10/10.59 % From the command line: assign(max_seconds, 300).
% 0.14/10.61
% 0.14/10.61 % SZS status Unsatisfiable for theBenchmark
% 0.14/10.61
% 0.14/10.61 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/10.61 % Length of proof is 33.
% 0.14/10.61 % Level of proof is 12.
% 0.14/10.61 % Maximum clause weight is 23.000.
% 0.14/10.61 % Given clauses 13.
% 0.14/10.61
% 0.14/10.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------