%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP592-1 : 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 : n004.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 07:30:26 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.55s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 34 unt; 0 def)
% Number of atoms : 34 ( 33 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 : 63 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(inverse(double_divide(double_divide(VAR_0,VAR_1),inverse(double_divide(VAR_0,inverse(VAR_2))))),VAR_1) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,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_168,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_168]) ).
cnf(c_5,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(B,C),inverse(double_divide(B,inverse(A))))),inverse(D))))),C) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_7,plain,
double_divide(inverse(double_divide(A,inverse(A))),inverse(B)) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_169,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,inverse(B))),inverse(C))))),inverse(A)) = C,
inference(paramod,[status(thm)],[c_7,c_1]) ).
cnf(c_8,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(A)) = B,
inference(paramod,[status(thm)],[c_7,c_169]) ).
cnf(c_20,plain,
double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(B))))) = A,
inference(paramod,[status(thm)],[c_7,c_8]) ).
cnf(c_170,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(A),inverse(B))))),inverse(inverse(double_divide(C,inverse(C))))) = B,
inference(paramod,[status(thm)],[c_20,c_1]) ).
cnf(c_27,plain,
double_divide(A,inverse(double_divide(inverse(A),inverse(B)))) = B,
inference(paramod,[status(thm)],[c_20,c_170]) ).
cnf(c_171,plain,
double_divide(A,inverse(A)) = inverse(double_divide(B,inverse(B))),
inference(paramod,[status(thm)],[c_20,c_7]) ).
cnf(c_32,plain,
inverse(double_divide(A,inverse(A))) = double_divide(B,inverse(B)),
inference(copy,[status(thm)],[c_171]) ).
cnf(c_37,plain,
double_divide(double_divide(A,inverse(A)),inverse(B)) = B,
inference(paramod,[status(thm)],[c_32,c_1]) ).
cnf(c_172,plain,
double_divide(inverse(double_divide(double_divide(A,inverse(A)),inverse(B))),double_divide(C,inverse(C))) = B,
inference(paramod,[status(thm)],[c_32,c_8]) ).
cnf(c_50,plain,
double_divide(inverse(A),double_divide(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_37,c_172]) ).
cnf(c_56,plain,
double_divide(A,inverse(A)) = double_divide(B,inverse(B)),
inference(paramod,[status(thm)],[c_32,c_32]) ).
cnf(c_82,plain,
double_divide(inverse(A),double_divide(double_divide(B,inverse(B)),double_divide(C,inverse(C)))) = A,
inference(paramod,[status(thm)],[c_32,c_50]) ).
cnf(c_90,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(B),inverse(A)),
inference(paramod,[status(thm)],[c_27,c_8]) ).
cnf(c_92,plain,
double_divide(A,double_divide(B,inverse(B))) = inverse(A),
inference(paramod,[status(thm)],[c_32,c_27]) ).
cnf(c_94,plain,
double_divide(A,inverse(double_divide(B,inverse(B)))) = inverse(A),
inference(paramod,[status(thm)],[c_56,c_27]) ).
cnf(c_173,plain,
double_divide(inverse(A),inverse(double_divide(B,inverse(B)))) = A,
inference(paramod,[status(thm)],[c_92,c_82]) ).
cnf(c_109,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_94,c_173]) ).
cnf(c_174,plain,
double_divide(A,inverse(B)) = double_divide(inverse(B),inverse(inverse(A))),
inference(paramod,[status(thm)],[c_109,c_90]) ).
cnf(c_175,plain,
double_divide(A,inverse(B)) = double_divide(inverse(B),A),
inference(paramod,[status(thm)],[c_109,c_174]) ).
cnf(c_147,plain,
double_divide(inverse(A),B) = double_divide(B,inverse(A)),
inference(copy,[status(thm)],[c_175]) ).
cnf(c_176,plain,
double_divide(A,B) = double_divide(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_109,c_147]) ).
cnf(c_162,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_109,c_176]) ).
cnf(c_177,plain,
inverse(double_divide(a,b)) != inverse(double_divide(a,b)),
inference(paramod,[status(thm)],[c_162,c_4]) ).
cnf(c_167,plain,
$false,
inference(copy,[status(thm)],[c_177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP592-1 : 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 : n004.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 15:01:37 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 3487483 was started by sandbox on n004,
% 0.17/0.44 % Fri Sep 25 15:01:37 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.55
% 0.17/0.55 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.17/0.55
% 0.17/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.55
% 0.17/0.55 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.17/0.55 % Length of proof is 21.
% 0.17/0.55 % Level of proof is 12.
% 0.17/0.55 % Maximum clause weight is 81.000.
% 0.17/0.55 % Given clauses 21.
% 0.17/0.55
% 0.17/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------