%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP614-1 : 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 : n026.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 07:30:29 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 11 ( 3 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 : 60 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(inverse(double_divide(inverse(double_divide(VAR_0,inverse(VAR_1))),VAR_2)),double_divide(VAR_0,VAR_2)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),double_divide(A,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_115,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_115]) ).
cnf(c_5,plain,
double_divide(inverse(A),double_divide(inverse(double_divide(B,inverse(A))),double_divide(B,inverse(C)))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),inverse(D))),double_divide(A,C))),B) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_116,plain,
double_divide(inverse(double_divide(inverse(A),double_divide(inverse(double_divide(inverse(double_divide(B,inverse(inverse(C)))),D)),double_divide(B,D)))),A) = C,
inference(paramod,[status(thm)],[c_6,c_6]) ).
cnf(c_11,plain,
double_divide(inverse(double_divide(inverse(A),inverse(B))),A) = B,
inference(paramod,[status(thm)],[c_1,c_116]) ).
cnf(c_13,plain,
double_divide(inverse(double_divide(inverse(A),B)),double_divide(inverse(double_divide(inverse(inverse(C)),inverse(A))),B)) = C,
inference(paramod,[status(thm)],[c_11,c_1]) ).
cnf(c_14,plain,
double_divide(inverse(A),double_divide(inverse(B),B)) = A,
inference(paramod,[status(thm)],[c_11,c_1]) ).
cnf(c_29,plain,
double_divide(inverse(double_divide(inverse(A),A)),inverse(B)) = B,
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_117,plain,
double_divide(inverse(A),double_divide(inverse(A),double_divide(inverse(double_divide(inverse(B),B)),inverse(C)))) = C,
inference(paramod,[status(thm)],[c_29,c_5]) ).
cnf(c_32,plain,
double_divide(inverse(A),double_divide(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_29,c_117]) ).
cnf(c_45,plain,
double_divide(inverse(A),A) = double_divide(inverse(B),B),
inference(paramod,[status(thm)],[c_14,c_32]) ).
cnf(c_58,plain,
double_divide(inverse(A),double_divide(inverse(double_divide(inverse(inverse(B)),inverse(double_divide(inverse(C),C)))),inverse(A))) = B,
inference(paramod,[status(thm)],[c_29,c_13]) ).
cnf(c_118,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_13,c_32]) ).
cnf(c_60,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_118]) ).
cnf(c_119,plain,
double_divide(inverse(double_divide(inverse(A),double_divide(inverse(inverse(B)),inverse(A)))),double_divide(inverse(C),C)) = B,
inference(paramod,[status(thm)],[c_45,c_13]) ).
cnf(c_120,plain,
double_divide(inverse(double_divide(inverse(A),double_divide(B,inverse(A)))),double_divide(inverse(C),C)) = B,
inference(paramod,[status(thm)],[c_60,c_119]) ).
cnf(c_64,plain,
double_divide(inverse(A),double_divide(B,inverse(A))) = B,
inference(paramod,[status(thm)],[c_14,c_120]) ).
cnf(c_121,plain,
double_divide(inverse(A),double_divide(inverse(double_divide(B,inverse(double_divide(inverse(C),C)))),inverse(A))) = B,
inference(paramod,[status(thm)],[c_60,c_58]) ).
cnf(c_70,plain,
inverse(double_divide(A,inverse(double_divide(inverse(B),B)))) = A,
inference(paramod,[status(thm)],[c_64,c_121]) ).
cnf(c_122,plain,
double_divide(A,inverse(A)) = double_divide(inverse(B),B),
inference(paramod,[status(thm)],[c_60,c_45]) ).
cnf(c_105,plain,
double_divide(inverse(A),A) = double_divide(B,inverse(B)),
inference(copy,[status(thm)],[c_122]) ).
cnf(c_123,plain,
inverse(double_divide(a2,inverse(double_divide(inverse(A),A)))) != a2,
inference(paramod,[status(thm)],[c_105,c_4]) ).
cnf(c_124,plain,
a2 != a2,
inference(paramod,[status(thm)],[c_70,c_123]) ).
cnf(c_114,plain,
$false,
inference(copy,[status(thm)],[c_124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP614-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 15:04:55 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.35 % Process 2833316 was started by sandbox on n026,
% 0.12/0.35 % Fri Sep 25 15:04:55 2026
% 0.12/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.38
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.38
% 0.12/0.38 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.12/0.38 % Length of proof is 18.
% 0.12/0.38 % Level of proof is 9.
% 0.12/0.38 % Maximum clause weight is 81.000.
% 0.12/0.38 % Given clauses 17.
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------