%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP515-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 07:30:16 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,multiply(multiply(VAR_1,VAR_2),inverse(multiply(VAR_0,VAR_2)))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(A,multiply(multiply(B,C),inverse(multiply(A,C)))) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_these_axioms_3,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c_2,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_3,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(multiply(B,C),inverse(multiply(D,C))))))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_8,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_82,plain,
multiply(A,multiply(B,inverse(multiply(A,multiply(C,inverse(C)))))) = B,
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_9,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(paramod,[status(thm)],[c_8,c_82]) ).
cnf(c_14,plain,
multiply(multiply(A,B),multiply(C,inverse(multiply(C,B)))) = A,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_21,plain,
multiply(multiply(A,B),multiply(C,inverse(A))) = multiply(C,B),
inference(paramod,[status(thm)],[c_14,c_3]) ).
cnf(c_83,plain,
multiply(A,multiply(B,inverse(C))) = multiply(B,multiply(multiply(A,D),inverse(multiply(C,D)))),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_31,plain,
multiply(A,multiply(multiply(B,C),inverse(multiply(D,C)))) = multiply(B,multiply(A,inverse(D))),
inference(copy,[status(thm)],[c_83]) ).
cnf(c_84,plain,
multiply(A,multiply(B,inverse(C))) = multiply(B,multiply(D,inverse(multiply(C,multiply(multiply(D,E),inverse(multiply(A,E))))))),
inference(paramod,[status(thm)],[c_3,c_21]) ).
cnf(c_85,plain,
multiply(A,multiply(B,inverse(C))) = multiply(B,multiply(D,inverse(multiply(D,multiply(C,inverse(A)))))),
inference(paramod,[status(thm)],[c_31,c_84]) ).
cnf(c_35,plain,
multiply(A,multiply(B,inverse(multiply(B,multiply(C,inverse(D)))))) = multiply(D,multiply(A,inverse(C))),
inference(copy,[status(thm)],[c_85]) ).
cnf(c_36,plain,
multiply(A,multiply(B,inverse(C))) = multiply(B,multiply(A,inverse(C))),
inference(paramod,[status(thm)],[c_9,c_21]) ).
cnf(c_86,plain,
multiply(multiply(A,B),multiply(C,inverse(multiply(C,multiply(A,inverse(D)))))) = multiply(D,B),
inference(paramod,[status(thm)],[c_21,c_14]) ).
cnf(c_37,plain,
multiply(A,multiply(multiply(B,C),inverse(B))) = multiply(A,C),
inference(paramod,[status(thm)],[c_35,c_86]) ).
cnf(c_40,plain,
multiply(multiply(A,B),C) = multiply(multiply(A,C),B),
inference(paramod,[status(thm)],[c_37,c_21]) ).
cnf(c_43,plain,
multiply(A,multiply(multiply(B,inverse(A)),C)) = multiply(B,C),
inference(paramod,[status(thm)],[c_40,c_9]) ).
cnf(c_58,plain,
multiply(A,inverse(multiply(A,inverse(B)))) = B,
inference(paramod,[status(thm)],[c_43,c_8]) ).
cnf(c_87,plain,
multiply(A,multiply(B,inverse(C))) = multiply(A,inverse(multiply(C,inverse(B)))),
inference(paramod,[status(thm)],[c_58,c_37]) ).
cnf(c_67,plain,
multiply(A,inverse(multiply(B,inverse(C)))) = multiply(A,multiply(C,inverse(B))),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_88,plain,
multiply(A,B) = multiply(C,multiply(A,inverse(multiply(C,inverse(B))))),
inference(paramod,[status(thm)],[c_58,c_36]) ).
cnf(c_89,plain,
multiply(A,B) = multiply(C,multiply(A,multiply(B,inverse(C)))),
inference(paramod,[status(thm)],[c_67,c_88]) ).
cnf(c_69,plain,
multiply(A,multiply(B,multiply(C,inverse(A)))) = multiply(B,C),
inference(copy,[status(thm)],[c_89]) ).
cnf(c_90,plain,
multiply(A,B) = multiply(C,inverse(multiply(multiply(C,inverse(A)),inverse(B)))),
inference(paramod,[status(thm)],[c_58,c_43]) ).
cnf(c_91,plain,
multiply(A,B) = multiply(C,multiply(B,inverse(multiply(C,inverse(A))))),
inference(paramod,[status(thm)],[c_67,c_90]) ).
cnf(c_92,plain,
multiply(A,B) = multiply(C,multiply(B,multiply(A,inverse(C)))),
inference(paramod,[status(thm)],[c_67,c_91]) ).
cnf(c_71,plain,
multiply(A,B) = multiply(B,A),
inference(paramod,[status(thm)],[c_69,c_92]) ).
cnf(c_75,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_71,c_2]) ).
cnf(c_93,plain,
multiply(A,multiply(B,C)) = multiply(multiply(B,A),C),
inference(paramod,[status(thm)],[c_71,c_40]) ).
cnf(c_79,plain,
multiply(multiply(A,B),C) = multiply(B,multiply(A,C)),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_94,plain,
multiply(multiply(A,B),C) = multiply(multiply(C,A),B),
inference(paramod,[status(thm)],[c_71,c_40]) ).
cnf(c_95,plain,
multiply(B,multiply(A,C)) = multiply(multiply(C,A),B),
inference(paramod,[status(thm)],[c_79,c_94]) ).
cnf(c_96,plain,
multiply(B,multiply(A,C)) = multiply(A,multiply(C,B)),
inference(paramod,[status(thm)],[c_79,c_95]) ).
cnf(c_80,plain,
multiply(A,multiply(B,C)) = multiply(C,multiply(A,B)),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_97,plain,
multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3)),
inference(copy,[status(thm)],[c_75]) ).
cnf(c_81,plain,
$false,
inference(resolve,[status(thm)],[c_80,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP515-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n011.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 14:58:13 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 2298908 was started by sandbox on n011,
% 0.16/0.42 % Fri Sep 25 14:58:13 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.46
% 0.16/0.46 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.16/0.46
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.46
% 0.16/0.46 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.16/0.46 % Length of proof is 21.
% 0.16/0.46 % Level of proof is 17.
% 0.16/0.46 % Maximum clause weight is 72.000.
% 0.16/0.46 % Given clauses 15.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------