%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP087-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 07:27:18 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 2
% Syntax : Number of formulae : 51 ( 36 unt; 0 def)
% Number of atoms : 91 ( 90 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 96 ( 56 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,multiply(multiply(inverse(multiply(VAR_0,VAR_1)),VAR_2),VAR_1)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_these_axioms,axiom,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('theBenchmark.p',prove_these_axioms) ).
cnf(c_2,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(clausify,[status(thm)],[prove_these_axioms]) ).
cnf(c_86,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_3,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(copy,[status(thm)],[c_86]) ).
cnf(c_4,plain,
multiply(A,multiply(multiply(inverse(B),C),multiply(multiply(inverse(multiply(A,D)),B),D))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_87,plain,
multiply(A,multiply(B,C)) = multiply(multiply(inverse(multiply(inverse(multiply(A,C)),D)),B),D),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
multiply(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D),C) = multiply(A,multiply(D,B)),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_9,plain,
multiply(multiply(inverse(A),B),A) = B,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_88,plain,
multiply(A,multiply(B,multiply(multiply(inverse(multiply(A,C)),D),C))) = multiply(multiply(inverse(E),B),multiply(multiply(inverse(multiply(inverse(D),F)),E),F)),
inference(paramod,[status(thm)],[c_4,c_4]) ).
cnf(c_10,plain,
multiply(multiply(inverse(A),B),multiply(multiply(inverse(multiply(inverse(C),D)),A),D)) = multiply(E,multiply(B,multiply(multiply(inverse(multiply(E,F)),C),F))),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_89,plain,
multiply(A,B) = multiply(multiply(inverse(multiply(inverse(B),C)),A),C),
inference(paramod,[status(thm)],[c_1,c_9]) ).
cnf(c_14,plain,
multiply(multiply(inverse(multiply(inverse(A),B)),C),B) = multiply(C,A),
inference(copy,[status(thm)],[c_89]) ).
cnf(c_90,plain,
multiply(A,B) = multiply(multiply(inverse(C),A),multiply(multiply(inverse(multiply(inverse(B),D)),C),D)),
inference(paramod,[status(thm)],[c_4,c_9]) ).
cnf(c_91,plain,
multiply(A,B) = multiply(multiply(inverse(C),A),multiply(C,B)),
inference(paramod,[status(thm)],[c_14,c_90]) ).
cnf(c_16,plain,
multiply(multiply(inverse(A),B),multiply(A,C)) = multiply(B,C),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_92,plain,
multiply(multiply(inverse(A),B),multiply(A,C)) = multiply(E,multiply(B,multiply(multiply(inverse(multiply(E,F)),C),F))),
inference(paramod,[status(thm)],[c_14,c_10]) ).
cnf(c_93,plain,
multiply(B,C) = multiply(E,multiply(B,multiply(multiply(inverse(multiply(E,F)),C),F))),
inference(paramod,[status(thm)],[c_16,c_92]) ).
cnf(c_17,plain,
multiply(A,multiply(B,multiply(multiply(inverse(multiply(A,C)),D),C))) = multiply(B,D),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_18,plain,
multiply(A,multiply(B,C)) = multiply(B,multiply(A,C)),
inference(paramod,[status(thm)],[c_14,c_5]) ).
cnf(c_19,plain,
multiply(A,multiply(multiply(inverse(A),B),C)) = multiply(B,C),
inference(paramod,[status(thm)],[c_18,c_16]) ).
cnf(c_27,plain,
multiply(A,multiply(multiply(inverse(multiply(B,C)),D),multiply(multiply(inverse(A),B),C))) = D,
inference(paramod,[status(thm)],[c_19,c_1]) ).
cnf(c_94,plain,
multiply(A,multiply(B,C)) = multiply(multiply(multiply(inverse(multiply(inverse(A),D)),B),D),C),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_95,plain,
multiply(A,multiply(B,C)) = multiply(multiply(B,A),C),
inference(paramod,[status(thm)],[c_14,c_94]) ).
cnf(c_29,plain,
multiply(multiply(A,B),C) = multiply(B,multiply(A,C)),
inference(copy,[status(thm)],[c_95]) ).
cnf(c_33,plain,
multiply(A,B) = multiply(B,A),
inference(paramod,[status(thm)],[c_9,c_19]) ).
cnf(c_96,plain,
multiply(A,multiply(multiply(inverse(multiply(B,C)),D),multiply(B,multiply(inverse(A),C)))) = D,
inference(paramod,[status(thm)],[c_29,c_27]) ).
cnf(c_97,plain,
multiply(A,multiply(B,multiply(multiply(inverse(multiply(B,C)),D),multiply(inverse(A),C)))) = D,
inference(paramod,[status(thm)],[c_18,c_96]) ).
cnf(c_41,plain,
multiply(A,multiply(B,multiply(C,multiply(inverse(multiply(B,D)),multiply(inverse(A),D))))) = C,
inference(paramod,[status(thm)],[c_29,c_97]) ).
cnf(c_47,plain,
multiply(A,multiply(B,multiply(C,multiply(inverse(multiply(A,C)),D)))) = multiply(B,D),
inference(paramod,[status(thm)],[c_33,c_17]) ).
cnf(c_51,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_33,c_9]) ).
cnf(c_98,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(b1,inverse(b1)) != multiply(inverse(a1),a1) ),
inference(paramod,[status(thm)],[c_33,c_3]) ).
cnf(c_99,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_33,c_98]) ).
cnf(c_100,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(b2,inverse(b2)),a2) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_33,c_99]) ).
cnf(c_101,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_33,c_100]) ).
cnf(c_102,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_33,c_101]) ).
cnf(c_103,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_18,c_102]) ).
cnf(c_104,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_33,c_103]) ).
cnf(c_105,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_33,c_104]) ).
cnf(c_106,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(copy,[status(thm)],[c_105]) ).
cnf(c_53,plain,
( multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(copy,[status(thm)],[c_106]) ).
cnf(c_57,plain,
multiply(A,multiply(B,C)) = multiply(C,multiply(A,B)),
inference(paramod,[status(thm)],[c_33,c_18]) ).
cnf(c_107,plain,
multiply(A,multiply(B,multiply(C,multiply(D,multiply(inverse(multiply(B,D)),inverse(A)))))) = C,
inference(paramod,[status(thm)],[c_57,c_41]) ).
cnf(c_58,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(paramod,[status(thm)],[c_47,c_107]) ).
cnf(c_108,plain,
A = multiply(A,multiply(B,inverse(B))),
inference(paramod,[status(thm)],[c_58,c_18]) ).
cnf(c_80,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(copy,[status(thm)],[c_108]) ).
cnf(c_109,plain,
( a2 != a2
| multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)) ),
inference(paramod,[status(thm)],[c_80,c_53]) ).
cnf(c_83,plain,
multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)),
inference(copy,[status(thm)],[c_109]) ).
cnf(c_84,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(paramod,[status(thm)],[c_80,c_51]) ).
cnf(c_85,plain,
$false,
inference(resolve,[status(thm)],[c_84,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP087-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 14:24:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3483886 was started by sandbox2 on n002,
% 0.08/0.36 % Fri Sep 25 14:24:19 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 25.
% 0.14/0.39 % Level of proof is 11.
% 0.14/0.39 % Maximum clause weight is 35.000.
% 0.14/0.39 % Given clauses 12.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------