%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP600-1 : 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 : n005.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 07:30:27 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 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 : 44 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(double_divide(VAR_0,VAR_1),inverse(double_divide(VAR_0,inverse(double_divide(inverse(VAR_2),VAR_1))))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(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_84,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_84]) ).
cnf(c_5,plain,
double_divide(A,inverse(double_divide(double_divide(B,C),inverse(double_divide(inverse(D),inverse(double_divide(B,inverse(double_divide(inverse(A),C))))))))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_85,plain,
double_divide(A,inverse(double_divide(double_divide(double_divide(B,C),inverse(double_divide(B,inverse(double_divide(inverse(inverse(D)),C))))),inverse(A)))) = D,
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_12,plain,
double_divide(A,inverse(double_divide(inverse(B),inverse(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_85]) ).
cnf(c_15,plain,
double_divide(double_divide(A,inverse(A)),inverse(B)) = B,
inference(paramod,[status(thm)],[c_12,c_1]) ).
cnf(c_23,plain,
double_divide(inverse(A),inverse(double_divide(B,inverse(B)))) = A,
inference(paramod,[status(thm)],[c_15,c_12]) ).
cnf(c_86,plain,
double_divide(A,inverse(double_divide(inverse(A),inverse(double_divide(inverse(B),inverse(double_divide(C,inverse(C)))))))) = B,
inference(paramod,[status(thm)],[c_23,c_1]) ).
cnf(c_24,plain,
double_divide(A,inverse(double_divide(inverse(A),inverse(B)))) = B,
inference(paramod,[status(thm)],[c_23,c_86]) ).
cnf(c_31,plain,
double_divide(double_divide(A,inverse(B)),inverse(B)) = A,
inference(paramod,[status(thm)],[c_24,c_1]) ).
cnf(c_87,plain,
double_divide(double_divide(inverse(inverse(A)),inverse(B)),inverse(B)) = A,
inference(paramod,[status(thm)],[c_24,c_12]) ).
cnf(c_38,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_31,c_87]) ).
cnf(c_88,plain,
double_divide(A,inverse(B)) = double_divide(inverse(B),inverse(inverse(A))),
inference(paramod,[status(thm)],[c_12,c_24]) ).
cnf(c_89,plain,
double_divide(A,inverse(B)) = double_divide(inverse(B),A),
inference(paramod,[status(thm)],[c_38,c_88]) ).
cnf(c_39,plain,
double_divide(inverse(A),B) = double_divide(B,inverse(A)),
inference(copy,[status(thm)],[c_89]) ).
cnf(c_90,plain,
double_divide(A,B) = double_divide(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_38,c_39]) ).
cnf(c_80,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_38,c_90]) ).
cnf(c_91,plain,
inverse(double_divide(a,b)) != inverse(double_divide(a,b)),
inference(paramod,[status(thm)],[c_80,c_4]) ).
cnf(c_83,plain,
$false,
inference(copy,[status(thm)],[c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP600-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n005.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 15:01:17 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3777114 was started by sandbox on n005,
% 0.09/0.35 % Fri Sep 25 15:01:17 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.35
% 0.13/0.35 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 14.
% 0.13/0.38 % Level of proof is 10.
% 0.13/0.38 % Maximum clause weight is 21.000.
% 0.13/0.38 % Given clauses 12.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------