%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP588-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 07:30:26 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 41 unt; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(VAR_0,inverse(double_divide(inverse(double_divide(double_divide(VAR_0,VAR_1),inverse(VAR_2))),VAR_1))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = inverse(double_divide(VAR_1,VAR_0)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(clausify,[status(thm)],[multiply]) ).
fof(prove_these_axioms_4,axiom,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c_3,plain,
multiply(a,b) != multiply(b,a),
inference(clausify,[status(thm)],[prove_these_axioms_4]) ).
cnf(c_94,plain,
inverse(double_divide(b,a)) != multiply(b,a),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4,plain,
inverse(double_divide(b,a)) != inverse(double_divide(a,b)),
inference(paramod,[status(thm)],[c_2,c_94]) ).
cnf(c_5,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,inverse(C))),inverse(double_divide(inverse(double_divide(double_divide(A,D),inverse(B))),D))))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_95,plain,
double_divide(A,inverse(double_divide(inverse(B),C))) = double_divide(inverse(double_divide(double_divide(double_divide(A,C),D),inverse(B))),D),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
double_divide(inverse(double_divide(double_divide(double_divide(A,B),C),inverse(D))),C) = double_divide(A,inverse(double_divide(inverse(D),B))),
inference(copy,[status(thm)],[c_95]) ).
cnf(c_7,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,inverse(C))),inverse(double_divide(inverse(double_divide(D,inverse(B))),inverse(double_divide(inverse(double_divide(double_divide(A,E),inverse(D))),E))))))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_10,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(A)) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_96,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(double_divide(double_divide(B,C),inverse(A))),C),
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_13,plain,
double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B) = double_divide(inverse(C),inverse(A)),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_97,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(double_divide(C,inverse(A))),inverse(double_divide(inverse(double_divide(double_divide(B,D),inverse(C))),D))),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_98,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(double_divide(C,inverse(A))),inverse(double_divide(inverse(C),inverse(B)))),
inference(paramod,[status(thm)],[c_13,c_97]) ).
cnf(c_16,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(inverse(A),inverse(C)))) = double_divide(inverse(B),inverse(C)),
inference(copy,[status(thm)],[c_98]) ).
cnf(c_99,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,inverse(C))),inverse(double_divide(inverse(double_divide(D,inverse(B))),inverse(double_divide(inverse(D),inverse(A)))))))) = C,
inference(paramod,[status(thm)],[c_13,c_7]) ).
cnf(c_100,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,inverse(C))),inverse(double_divide(inverse(B),inverse(A)))))) = C,
inference(paramod,[status(thm)],[c_16,c_99]) ).
cnf(c_19,plain,
double_divide(A,inverse(double_divide(inverse(B),inverse(A)))) = B,
inference(paramod,[status(thm)],[c_16,c_100]) ).
cnf(c_20,plain,
double_divide(inverse(A),inverse(double_divide(B,C))) = double_divide(B,inverse(double_divide(inverse(A),C))),
inference(paramod,[status(thm)],[c_13,c_6]) ).
cnf(c_26,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,inverse(A)))) = double_divide(C,inverse(B)),
inference(paramod,[status(thm)],[c_10,c_20]) ).
cnf(c_29,plain,
double_divide(inverse(A),inverse(double_divide(B,inverse(B)))) = A,
inference(paramod,[status(thm)],[c_20,c_19]) ).
cnf(c_101,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(B),inverse(double_divide(inverse(A),inverse(double_divide(C,inverse(C)))))),
inference(paramod,[status(thm)],[c_29,c_20]) ).
cnf(c_36,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(B),inverse(A)),
inference(paramod,[status(thm)],[c_29,c_101]) ).
cnf(c_41,plain,
double_divide(inverse(A),inverse(double_divide(A,inverse(B)))) = B,
inference(paramod,[status(thm)],[c_36,c_10]) ).
cnf(c_45,plain,
double_divide(inverse(double_divide(A,B)),inverse(C)) = double_divide(A,inverse(double_divide(inverse(C),B))),
inference(paramod,[status(thm)],[c_36,c_20]) ).
cnf(c_102,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(C,inverse(A))),inverse(B)))) = double_divide(C,inverse(B)),
inference(paramod,[status(thm)],[c_45,c_26]) ).
cnf(c_47,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(C),inverse(A)))))) = double_divide(B,inverse(C)),
inference(paramod,[status(thm)],[c_45,c_102]) ).
cnf(c_64,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_41,c_19]) ).
cnf(c_103,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,inverse(A)))) = double_divide(inverse(B),inverse(inverse(C))),
inference(paramod,[status(thm)],[c_41,c_13]) ).
cnf(c_104,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(C,inverse(A))),inverse(B)))) = double_divide(inverse(B),inverse(inverse(C))),
inference(paramod,[status(thm)],[c_45,c_103]) ).
cnf(c_105,plain,
double_divide(A,inverse(double_divide(C,inverse(double_divide(inverse(B),inverse(A)))))) = double_divide(inverse(B),inverse(inverse(C))),
inference(paramod,[status(thm)],[c_45,c_104]) ).
cnf(c_106,plain,
double_divide(C,inverse(B)) = double_divide(inverse(B),inverse(inverse(C))),
inference(paramod,[status(thm)],[c_47,c_105]) ).
cnf(c_107,plain,
double_divide(C,inverse(B)) = double_divide(inverse(B),C),
inference(paramod,[status(thm)],[c_64,c_106]) ).
cnf(c_69,plain,
double_divide(inverse(A),B) = double_divide(B,inverse(A)),
inference(copy,[status(thm)],[c_107]) ).
cnf(c_108,plain,
double_divide(A,B) = double_divide(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_64,c_69]) ).
cnf(c_89,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_64,c_108]) ).
cnf(c_109,plain,
inverse(double_divide(a,b)) != inverse(double_divide(a,b)),
inference(paramod,[status(thm)],[c_89,c_4]) ).
cnf(c_93,plain,
$false,
inference(copy,[status(thm)],[c_109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP588-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n010.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 15:01:31 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 1043408 was started by sandbox on n010,
% 0.16/0.43 % Fri Sep 25 15:01:31 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 0.16/0.48
% 0.16/0.48 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.16/0.48
% 0.16/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.48
% 0.16/0.48 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.16/0.48 % Length of proof is 22.
% 0.16/0.48 % Level of proof is 12.
% 0.16/0.48 % Maximum clause weight is 88.000.
% 0.16/0.48 % Given clauses 15.
% 0.16/0.48
% 0.16/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------