%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP580-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 07:30:25 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 63 ( 63 unt; 0 def)
% Number of atoms : 63 ( 62 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 : 6 ( 2 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 : 82 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(double_divide(VAR_0,double_divide(double_divide(double_divide(VAR_1,VAR_0),VAR_2),double_divide(VAR_1,identity))),double_divide(identity,identity)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = double_divide(double_divide(VAR_1,VAR_0),identity),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = double_divide(double_divide(B,A),identity),
inference(clausify,[status(thm)],[multiply]) ).
fof(inverse,axiom,
! [VAR_0] : inverse(VAR_0) = double_divide(VAR_0,identity),
file('theBenchmark.p',inverse) ).
cnf(c_3,plain,
inverse(A) = double_divide(A,identity),
inference(clausify,[status(thm)],[inverse]) ).
fof(identity,axiom,
! [VAR_0] : identity = double_divide(VAR_0,inverse(VAR_0)),
file('theBenchmark.p',identity) ).
cnf(c_4,plain,
identity = double_divide(A,inverse(A)),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_81,plain,
identity = double_divide(A,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_5,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(copy,[status(thm)],[c_81]) ).
fof(prove_these_axioms_4,axiom,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c_6,plain,
multiply(a,b) != multiply(b,a),
inference(clausify,[status(thm)],[prove_these_axioms_4]) ).
cnf(c_82,plain,
double_divide(double_divide(b,a),identity) != multiply(b,a),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_7,plain,
double_divide(double_divide(b,a),identity) != double_divide(double_divide(a,b),identity),
inference(paramod,[status(thm)],[c_2,c_82]) ).
cnf(c_8,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(A,B),C),double_divide(A,identity)),double_divide(C,double_divide(B,identity))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_83,plain,
double_divide(double_divide(A,B),double_divide(identity,identity)) = double_divide(double_divide(double_divide(C,double_divide(identity,A)),B),double_divide(C,identity)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
double_divide(double_divide(double_divide(A,double_divide(identity,B)),C),double_divide(A,identity)) = double_divide(double_divide(B,C),double_divide(identity,identity)),
inference(copy,[status(thm)],[c_83]) ).
cnf(c_10,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,B),double_divide(A,identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(B,A),identity),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_20,plain,
double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_23,plain,
double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_20]) ).
cnf(c_84,plain,
double_divide(double_divide(A,B),double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity)) = double_divide(double_divide(identity,B),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_20,c_9]) ).
cnf(c_24,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = double_divide(double_divide(B,A),double_divide(double_divide(double_divide(double_divide(identity,B),identity),identity),identity)),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_85,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_23,c_1]) ).
cnf(c_25,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_85]) ).
cnf(c_86,plain,
double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),identity)),double_divide(double_divide(identity,identity),double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_23,c_8]) ).
cnf(c_87,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_86]) ).
cnf(c_88,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_25,c_87]) ).
cnf(c_89,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_88]) ).
cnf(c_90,plain,
identity = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_89]) ).
cnf(c_26,plain,
double_divide(identity,identity) = identity,
inference(copy,[status(thm)],[c_90]) ).
cnf(c_29,plain,
double_divide(double_divide(identity,A),identity) = double_divide(double_divide(B,A),double_divide(double_divide(double_divide(double_divide(identity,B),identity),identity),identity)),
inference(paramod,[status(thm)],[c_26,c_24]) ).
cnf(c_32,plain,
double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity) = A,
inference(paramod,[status(thm)],[c_26,c_20]) ).
cnf(c_41,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),identity) = double_divide(double_divide(B,A),identity),
inference(paramod,[status(thm)],[c_26,c_11]) ).
cnf(c_46,plain,
double_divide(double_divide(identity,A),identity) = double_divide(double_divide(B,A),B),
inference(paramod,[status(thm)],[c_32,c_29]) ).
cnf(c_91,plain,
double_divide(identity,identity) = double_divide(double_divide(A,double_divide(identity,identity)),A),
inference(paramod,[status(thm)],[c_5,c_46]) ).
cnf(c_92,plain,
identity = double_divide(double_divide(A,double_divide(identity,identity)),A),
inference(paramod,[status(thm)],[c_26,c_91]) ).
cnf(c_93,plain,
identity = double_divide(double_divide(A,identity),A),
inference(paramod,[status(thm)],[c_26,c_92]) ).
cnf(c_49,plain,
double_divide(double_divide(A,identity),A) = identity,
inference(copy,[status(thm)],[c_93]) ).
cnf(c_51,plain,
double_divide(double_divide(A,B),A) = double_divide(double_divide(C,B),C),
inference(paramod,[status(thm)],[c_46,c_46]) ).
cnf(c_94,plain,
double_divide(identity,A) = double_divide(double_divide(B,double_divide(A,identity)),B),
inference(paramod,[status(thm)],[c_5,c_51]) ).
cnf(c_55,plain,
double_divide(double_divide(A,double_divide(B,identity)),A) = double_divide(identity,B),
inference(copy,[status(thm)],[c_94]) ).
cnf(c_95,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(double_divide(B,A),B),
inference(paramod,[status(thm)],[c_49,c_51]) ).
cnf(c_56,plain,
double_divide(double_divide(A,B),A) = double_divide(identity,double_divide(B,identity)),
inference(copy,[status(thm)],[c_95]) ).
cnf(c_96,plain,
double_divide(double_divide(double_divide(A,B),A),double_divide(C,B)) = double_divide(double_divide(D,C),D),
inference(paramod,[status(thm)],[c_51,c_51]) ).
cnf(c_97,plain,
double_divide(double_divide(identity,double_divide(B,identity)),double_divide(C,B)) = double_divide(double_divide(D,C),D),
inference(paramod,[status(thm)],[c_56,c_96]) ).
cnf(c_57,plain,
double_divide(double_divide(identity,double_divide(A,identity)),double_divide(B,A)) = double_divide(identity,double_divide(B,identity)),
inference(paramod,[status(thm)],[c_56,c_97]) ).
cnf(c_58,plain,
double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_56,c_55]) ).
cnf(c_98,plain,
double_divide(double_divide(double_divide(identity,double_divide(A,identity)),identity),identity) = A,
inference(paramod,[status(thm)],[c_56,c_32]) ).
cnf(c_99,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),identity) = A,
inference(paramod,[status(thm)],[c_56,c_98]) ).
cnf(c_100,plain,
double_divide(double_divide(identity,A),identity) = A,
inference(paramod,[status(thm)],[c_58,c_99]) ).
cnf(c_62,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_56,c_100]) ).
cnf(c_101,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_62,c_58]) ).
cnf(c_66,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(copy,[status(thm)],[c_101]) ).
cnf(c_102,plain,
double_divide(A,double_divide(B,A)) = double_divide(identity,double_divide(B,identity)),
inference(paramod,[status(thm)],[c_62,c_57]) ).
cnf(c_67,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_62,c_102]) ).
cnf(c_103,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(B,A),identity),
inference(paramod,[status(thm)],[c_67,c_41]) ).
cnf(c_104,plain,
double_divide(identity,double_divide(A,B)) = double_divide(double_divide(B,A),identity),
inference(paramod,[status(thm)],[c_66,c_103]) ).
cnf(c_69,plain,
double_divide(identity,double_divide(A,B)) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_66,c_104]) ).
cnf(c_105,plain,
double_divide(identity,double_divide(b,a)) != double_divide(double_divide(a,b),identity),
inference(paramod,[status(thm)],[c_66,c_7]) ).
cnf(c_106,plain,
double_divide(identity,double_divide(a,b)) != double_divide(double_divide(a,b),identity),
inference(paramod,[status(thm)],[c_69,c_105]) ).
cnf(c_107,plain,
double_divide(identity,double_divide(a,b)) != double_divide(identity,double_divide(a,b)),
inference(paramod,[status(thm)],[c_66,c_106]) ).
cnf(c_80,plain,
$false,
inference(copy,[status(thm)],[c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP580-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 15:06:40 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3623098 was started by sandbox2 on n001,
% 0.10/0.36 % Fri Sep 25 15:06:40 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 31.
% 0.10/0.38 % Level of proof is 15.
% 0.10/0.38 % Maximum clause weight is 93.000.
% 0.10/0.38 % Given clauses 14.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------