%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP576-1 : 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 07:30:24 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 74 ( 74 unt; 0 def)
% Number of atoms : 74 ( 73 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 : 8 ( 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 : 97 ( 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(VAR_1,double_divide(VAR_2,VAR_0)),double_divide(VAR_2,identity))),double_divide(identity,identity)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B,
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_75,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_75]) ).
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_76,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_76]) ).
cnf(c_8,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,double_divide(C,B)),double_divide(C,identity))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_77,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(B,double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_11,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = double_divide(identity,double_divide(A,double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_1,c_77]) ).
cnf(c_12,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(A,double_divide(double_divide(identity,double_divide(B,A)),double_divide(B,identity)))),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_78,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(B,identity),double_divide(double_divide(A,identity),double_divide(B,identity))),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_79,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(double_divide(B,identity),double_divide(double_divide(A,identity),double_divide(B,identity))),
inference(paramod,[status(thm)],[c_11,c_78]) ).
cnf(c_15,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(double_divide(B,double_divide(identity,identity)),double_divide(identity,identity))),
inference(copy,[status(thm)],[c_79]) ).
cnf(c_80,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_16,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_11,c_80]) ).
cnf(c_81,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(B,double_divide(double_divide(A,double_divide(C,B)),double_divide(C,identity))),
inference(paramod,[status(thm)],[c_11,c_8]) ).
cnf(c_82,plain,
double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(B,double_divide(double_divide(A,double_divide(C,B)),double_divide(C,identity))),
inference(paramod,[status(thm)],[c_16,c_81]) ).
cnf(c_21,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(copy,[status(thm)],[c_82]) ).
cnf(c_83,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(identity,double_divide(identity,identity)))),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_21,c_12]) ).
cnf(c_84,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_5,c_83]) ).
cnf(c_85,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_11,c_84]) ).
cnf(c_86,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_5,c_85]) ).
cnf(c_87,plain,
double_divide(identity,double_divide(identity,double_divide(identity,identity))) = identity,
inference(paramod,[status(thm)],[c_11,c_86]) ).
cnf(c_22,plain,
double_divide(identity,identity) = identity,
inference(paramod,[status(thm)],[c_5,c_87]) ).
cnf(c_88,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(double_divide(B,identity),double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_22,c_15]) ).
cnf(c_23,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(double_divide(B,identity),identity)),
inference(paramod,[status(thm)],[c_22,c_88]) ).
cnf(c_89,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,double_divide(identity,identity))),
inference(paramod,[status(thm)],[c_22,c_11]) ).
cnf(c_28,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_22,c_89]) ).
cnf(c_90,plain,
double_divide(double_divide(identity,double_divide(double_divide(B,identity),identity)),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_23,c_9]) ).
cnf(c_91,plain,
double_divide(double_divide(identity,double_divide(double_divide(B,identity),identity)),identity) = B,
inference(paramod,[status(thm)],[c_22,c_90]) ).
cnf(c_29,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)) = A,
inference(paramod,[status(thm)],[c_28,c_91]) ).
cnf(c_92,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_5,c_21]) ).
cnf(c_30,plain,
double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_23,c_92]) ).
cnf(c_93,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
inference(paramod,[status(thm)],[c_30,c_29]) ).
cnf(c_31,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(paramod,[status(thm)],[c_30,c_93]) ).
cnf(c_34,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,identity))) = identity,
inference(paramod,[status(thm)],[c_28,c_5]) ).
cnf(c_94,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,identity)),identity)),
inference(paramod,[status(thm)],[c_21,c_28]) ).
cnf(c_95,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),identity)) = double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,identity)),identity)),
inference(paramod,[status(thm)],[c_28,c_94]) ).
cnf(c_96,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,identity)),identity)),
inference(paramod,[status(thm)],[c_28,c_95]) ).
cnf(c_97,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,identity)),identity)),
inference(paramod,[status(thm)],[c_30,c_96]) ).
cnf(c_98,plain,
A = double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,identity)),identity)),
inference(paramod,[status(thm)],[c_31,c_97]) ).
cnf(c_37,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,identity)),identity)) = A,
inference(copy,[status(thm)],[c_98]) ).
cnf(c_99,plain,
double_divide(double_divide(A,identity),double_divide(identity,double_divide(identity,identity))) = double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),
inference(paramod,[status(thm)],[c_34,c_21]) ).
cnf(c_100,plain,
double_divide(double_divide(A,identity),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),
inference(paramod,[status(thm)],[c_22,c_99]) ).
cnf(c_101,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),
inference(paramod,[status(thm)],[c_22,c_100]) ).
cnf(c_102,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),
inference(paramod,[status(thm)],[c_28,c_101]) ).
cnf(c_39,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_31,c_102]) ).
cnf(c_103,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(B,identity)),identity))) = identity,
inference(paramod,[status(thm)],[c_21,c_34]) ).
cnf(c_40,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),A) = identity,
inference(paramod,[status(thm)],[c_37,c_103]) ).
cnf(c_104,plain,
double_divide(identity,A) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_39,c_30]) ).
cnf(c_42,plain,
double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(identity,A),
inference(copy,[status(thm)],[c_104]) ).
cnf(c_44,plain,
double_divide(double_divide(identity,A),A) = identity,
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_50,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_42,c_31]) ).
cnf(c_51,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_50,c_21]) ).
cnf(c_105,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_50,c_42]) ).
cnf(c_52,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(copy,[status(thm)],[c_105]) ).
cnf(c_54,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_52,c_39]) ).
cnf(c_106,plain,
double_divide(identity,double_divide(b,a)) != double_divide(double_divide(a,b),identity),
inference(paramod,[status(thm)],[c_52,c_7]) ).
cnf(c_55,plain,
double_divide(identity,double_divide(b,a)) != double_divide(identity,double_divide(a,b)),
inference(paramod,[status(thm)],[c_52,c_106]) ).
cnf(c_107,plain,
double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(double_divide(identity,double_divide(B,A)),identity),
inference(paramod,[status(thm)],[c_44,c_51]) ).
cnf(c_108,plain,
double_divide(A,B) = double_divide(double_divide(identity,double_divide(B,A)),identity),
inference(paramod,[status(thm)],[c_54,c_107]) ).
cnf(c_109,plain,
double_divide(A,B) = double_divide(identity,double_divide(identity,double_divide(B,A))),
inference(paramod,[status(thm)],[c_52,c_108]) ).
cnf(c_66,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_50,c_109]) ).
cnf(c_110,plain,
double_divide(identity,double_divide(a,b)) != double_divide(identity,double_divide(a,b)),
inference(paramod,[status(thm)],[c_66,c_55]) ).
cnf(c_74,plain,
$false,
inference(copy,[status(thm)],[c_110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP576-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 15:00:50 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 3485447 was started by sandbox on n004,
% 0.14/0.36 % Fri Sep 25 15:00:50 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 33.
% 0.14/0.39 % Level of proof is 15.
% 0.14/0.39 % Maximum clause weight is 96.000.
% 0.14/0.39 % Given clauses 15.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------