%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP616-1 : 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 : n014.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 07:30:30 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.49s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% 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 : 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 : 66 ( 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_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_177,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_177]) ).
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_178,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_178]) ).
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_179,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_179]) ).
cnf(c_45,plain,
double_divide(inverse(A),A) = double_divide(inverse(B),B),
inference(paramod,[status(thm)],[c_14,c_32]) ).
cnf(c_180,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_180]) ).
cnf(c_181,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_182,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_181]) ).
cnf(c_64,plain,
double_divide(inverse(A),double_divide(B,inverse(A))) = B,
inference(paramod,[status(thm)],[c_14,c_182]) ).
cnf(c_183,plain,
double_divide(inverse(double_divide(inverse(A),double_divide(inverse(double_divide(inverse(inverse(B)),inverse(inverse(C)))),inverse(A)))),B) = C,
inference(paramod,[status(thm)],[c_13,c_13]) ).
cnf(c_184,plain,
double_divide(inverse(double_divide(inverse(A),double_divide(inverse(double_divide(B,inverse(inverse(C)))),inverse(A)))),B) = C,
inference(paramod,[status(thm)],[c_60,c_183]) ).
cnf(c_185,plain,
double_divide(inverse(double_divide(inverse(A),double_divide(inverse(double_divide(B,C)),inverse(A)))),B) = C,
inference(paramod,[status(thm)],[c_60,c_184]) ).
cnf(c_186,plain,
double_divide(inverse(inverse(double_divide(B,C))),B) = C,
inference(paramod,[status(thm)],[c_64,c_185]) ).
cnf(c_68,plain,
double_divide(double_divide(A,B),A) = B,
inference(paramod,[status(thm)],[c_60,c_186]) ).
cnf(c_187,plain,
double_divide(A,double_divide(inverse(inverse(A)),B)) = B,
inference(paramod,[status(thm)],[c_60,c_32]) ).
cnf(c_104,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_60,c_187]) ).
cnf(c_127,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_104,c_68]) ).
cnf(c_188,plain,
inverse(double_divide(a,b)) != inverse(double_divide(a,b)),
inference(paramod,[status(thm)],[c_127,c_4]) ).
cnf(c_176,plain,
$false,
inference(copy,[status(thm)],[c_188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP616-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n014.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 15:02:47 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 525785 was started by sandbox on n014,
% 0.17/0.45 % Fri Sep 25 15:02:47 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.22/0.49
% 0.22/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.49
% 0.22/0.49 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.22/0.49 % Length of proof is 18.
% 0.22/0.49 % Level of proof is 10.
% 0.22/0.49 % Maximum clause weight is 81.000.
% 0.22/0.49 % Given clauses 20.
% 0.22/0.49
% 0.22/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------