%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP603-1 : 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 : n007.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 07:30:28 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 22 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : inverse(double_divide(inverse(double_divide(VAR_0,inverse(double_divide(VAR_1,double_divide(VAR_0,VAR_2))))),VAR_2)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)) = B,
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_3,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c_3,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_210,plain,
multiply(inverse(double_divide(b3,a3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_211,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_210]) ).
cnf(c_212,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,inverse(double_divide(c3,b3))),
inference(paramod,[status(thm)],[c_2,c_211]) ).
cnf(c_213,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(paramod,[status(thm)],[c_2,c_212]) ).
cnf(c_4,plain,
inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(copy,[status(thm)],[c_213]) ).
cnf(c_5,plain,
inverse(double_divide(inverse(double_divide(A,B)),C)) = inverse(double_divide(D,inverse(double_divide(B,double_divide(D,double_divide(A,C)))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_8,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_10,plain,
inverse(double_divide(A,inverse(double_divide(b3,double_divide(A,double_divide(c3,a3)))))) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_23,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_8,c_8]) ).
cnf(c_29,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(inverse(double_divide(D,C)),double_divide(D,A)),
inference(paramod,[status(thm)],[c_23,c_8]) ).
cnf(c_56,plain,
inverse(double_divide(inverse(double_divide(c3,A)),inverse(double_divide(b3,inverse(double_divide(inverse(double_divide(a3,B)),double_divide(A,B))))))) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_29,c_10]) ).
cnf(c_58,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_29,c_8]) ).
cnf(c_81,plain,
inverse(double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,B)))) = inverse(double_divide(A,C)),
inference(paramod,[status(thm)],[c_58,c_1]) ).
cnf(c_134,plain,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,inverse(double_divide(C,D)))))),inverse(D))) = inverse(double_divide(A,inverse(double_divide(B,C)))),
inference(paramod,[status(thm)],[c_58,c_81]) ).
cnf(c_208,plain,
inverse(double_divide(inverse(double_divide(c3,inverse(double_divide(A,inverse(double_divide(a3,double_divide(A,B))))))),inverse(double_divide(b3,B)))) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_23,c_56]) ).
cnf(c_209,plain,
$false,
inference(resolve,[status(thm)],[c_208,c_134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP603-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n007.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 14:59:54 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 1296645 was started by sandbox on n007,
% 0.08/0.35 % Fri Sep 25 14:59:54 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.11/0.40
% 0.11/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.40
% 0.11/0.40 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.11/0.40 % Length of proof is 15.
% 0.11/0.40 % Level of proof is 8.
% 0.11/0.40 % Maximum clause weight is 81.000.
% 0.11/0.40 % Given clauses 18.
% 0.11/0.40
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------