%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP602-1 : 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 : n013.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 0.14s 5.64s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 33 unt; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 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 : 78 ( 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_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_3,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_249,plain,
multiply(inverse(double_divide(b2,inverse(b2))),a2) != a2,
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4,plain,
inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2,
inference(paramod,[status(thm)],[c_2,c_249]) ).
cnf(c_250,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_5,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(A,double_divide(C,D)))))) = inverse(double_divide(inverse(double_divide(C,B)),D)),
inference(copy,[status(thm)],[c_250]) ).
cnf(c_6,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_11,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_6,c_6]) ).
cnf(c_14,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_11,c_6]) ).
cnf(c_32,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_14,c_6]) ).
cnf(c_42,plain,
inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),double_divide(A,C))))) = B,
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_55,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_32,c_1]) ).
cnf(c_60,plain,
inverse(double_divide(inverse(double_divide(inverse(A),B)),double_divide(inverse(double_divide(C,D)),B))) = double_divide(C,inverse(double_divide(D,A))),
inference(paramod,[status(thm)],[c_32,c_6]) ).
cnf(c_251,plain,
inverse(double_divide(A,inverse(double_divide(B,C)))) = inverse(double_divide(inverse(double_divide(D,inverse(double_divide(A,double_divide(D,inverse(C)))))),B)),
inference(paramod,[status(thm)],[c_1,c_55]) ).
cnf(c_108,plain,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,inverse(C)))))),D)) = inverse(double_divide(B,inverse(double_divide(D,C)))),
inference(copy,[status(thm)],[c_251]) ).
cnf(c_252,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(inverse(double_divide(A,inverse(D))),C))) = inverse(double_divide(B,D)),
inference(paramod,[status(thm)],[c_55,c_6]) ).
cnf(c_113,plain,
double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C)))) = inverse(double_divide(C,B)),
inference(paramod,[status(thm)],[c_60,c_252]) ).
cnf(c_115,plain,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),D)) = inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,D)),C)))),
inference(paramod,[status(thm)],[c_6,c_55]) ).
cnf(c_127,plain,
inverse(inverse(double_divide(A,double_divide(B,A)))) = B,
inference(paramod,[status(thm)],[c_113,c_42]) ).
cnf(c_253,plain,
inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,D)),double_divide(A,inverse(C)))))) = inverse(double_divide(B,inverse(double_divide(D,C)))),
inference(paramod,[status(thm)],[c_115,c_108]) ).
cnf(c_129,plain,
inverse(inverse(double_divide(inverse(A),double_divide(B,C)))) = inverse(double_divide(B,inverse(double_divide(C,A)))),
inference(paramod,[status(thm)],[c_113,c_253]) ).
cnf(c_171,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_32,c_127]) ).
cnf(c_254,plain,
double_divide(inverse(A),double_divide(B,C)) = inverse(double_divide(B,inverse(double_divide(C,A)))),
inference(paramod,[status(thm)],[c_171,c_129]) ).
cnf(c_186,plain,
inverse(double_divide(A,inverse(double_divide(B,C)))) = double_divide(inverse(C),double_divide(A,B)),
inference(copy,[status(thm)],[c_254]) ).
cnf(c_187,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_171,c_127]) ).
cnf(c_255,plain,
double_divide(inverse(inverse(b2)),double_divide(a2,b2)) != a2,
inference(paramod,[status(thm)],[c_186,c_4]) ).
cnf(c_256,plain,
double_divide(b2,double_divide(a2,b2)) != a2,
inference(paramod,[status(thm)],[c_171,c_255]) ).
cnf(c_257,plain,
a2 != a2,
inference(paramod,[status(thm)],[c_187,c_256]) ).
cnf(c_248,plain,
$false,
inference(copy,[status(thm)],[c_257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP602-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.59 % Computer : n013.cluster.edu
% 0.11/5.59 % Model : x86_64 x86_64
% 0.11/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59 % Memory : 8046.5625MB
% 0.11/5.59 % OS : Linux 6.8.0-71-generic
% 0.11/5.59 % CPULimit : 300
% 0.11/5.59 % WCLimit : 300
% 0.11/5.59 % DateTime : Fri Sep 25 15:00:58 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.59 % Process 691229 was started by sandbox on n013,
% 0.11/5.59 % Fri Sep 25 15:00:58 2026
% 0.11/5.59 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.59
% 0.11/5.59 % From the command line: assign(max_seconds, 300).
% 0.14/5.64
% 0.14/5.64 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.14/5.64
% 0.14/5.64 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.64
% 0.14/5.64 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.14/5.64 % Length of proof is 21.
% 0.14/5.64 % Level of proof is 11.
% 0.14/5.64 % Maximum clause weight is 68.000.
% 0.14/5.64 % Given clauses 12.
% 0.14/5.64
% 0.14/5.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------