%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP456-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 07:29:45 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 4
% Syntax : Number of formulae : 73 ( 73 unt; 0 def)
% Number of atoms : 73 ( 72 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 127 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(identity,divide(VAR_0,divide(VAR_1,divide(divide(divide(VAR_0,VAR_0),VAR_0),VAR_2)))),VAR_2) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(identity,divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = divide(VAR_0,divide(identity,VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,divide(identity,B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(identity,axiom,
! [VAR_0] : identity = divide(VAR_0,VAR_0),
file('theBenchmark.p',identity) ).
cnf(c_4,plain,
identity = divide(A,A),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_5,plain,
divide(A,A) = identity,
inference(copy,[status(thm)],[c_4]) ).
fof(prove_these_axioms_3,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c_6,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_83,plain,
multiply(divide(a3,divide(identity,b3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_84,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_83]) ).
cnf(c_85,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != multiply(a3,divide(b3,divide(identity,c3))),
inference(paramod,[status(thm)],[c_2,c_84]) ).
cnf(c_7,plain,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(paramod,[status(thm)],[c_2,c_85]) ).
cnf(c_8,plain,
divide(divide(identity,divide(A,divide(B,divide(divide(identity,A),C)))),C) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_9,plain,
divide(divide(identity,divide(identity,divide(A,divide(identity,B)))),B) = A,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_12,plain,
divide(divide(identity,divide(divide(A,divide(B,divide(divide(identity,A),C))),divide(D,B))),C) = D,
inference(paramod,[status(thm)],[c_8,c_8]) ).
cnf(c_14,plain,
divide(divide(identity,divide(identity,divide(A,identity))),identity) = A,
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_16,plain,
divide(divide(identity,divide(A,B)),C) = divide(identity,divide(identity,divide(B,divide(identity,divide(divide(identity,A),C))))),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_86,plain,
divide(divide(identity,divide(identity,A)),B) = divide(identity,divide(C,divide(A,divide(divide(identity,C),divide(identity,B))))),
inference(paramod,[status(thm)],[c_8,c_9]) ).
cnf(c_87,plain,
divide(identity,divide(identity,divide(A,divide(identity,divide(divide(identity,identity),B))))) = divide(identity,divide(C,divide(A,divide(divide(identity,C),divide(identity,B))))),
inference(paramod,[status(thm)],[c_16,c_86]) ).
cnf(c_17,plain,
divide(identity,divide(identity,divide(A,divide(identity,divide(identity,B))))) = divide(identity,divide(C,divide(A,divide(divide(identity,C),divide(identity,B))))),
inference(paramod,[status(thm)],[c_5,c_87]) ).
cnf(c_88,plain,
divide(identity,divide(identity,divide(divide(A,identity),divide(identity,divide(divide(identity,identity),identity))))) = A,
inference(paramod,[status(thm)],[c_16,c_14]) ).
cnf(c_89,plain,
divide(identity,divide(identity,divide(divide(A,identity),divide(identity,divide(identity,identity))))) = A,
inference(paramod,[status(thm)],[c_5,c_88]) ).
cnf(c_90,plain,
divide(identity,divide(identity,divide(divide(A,identity),divide(identity,identity)))) = A,
inference(paramod,[status(thm)],[c_5,c_89]) ).
cnf(c_19,plain,
divide(identity,divide(identity,divide(divide(A,identity),identity))) = A,
inference(paramod,[status(thm)],[c_5,c_90]) ).
cnf(c_91,plain,
divide(identity,divide(identity,divide(divide(D,B),divide(identity,divide(divide(identity,divide(A,divide(B,divide(divide(identity,A),C)))),C))))) = D,
inference(paramod,[status(thm)],[c_16,c_12]) ).
cnf(c_21,plain,
divide(identity,divide(identity,divide(divide(A,B),divide(identity,divide(identity,divide(identity,divide(divide(B,divide(divide(identity,C),D)),divide(identity,divide(divide(identity,C),D))))))))) = A,
inference(paramod,[status(thm)],[c_16,c_91]) ).
cnf(c_24,plain,
divide(identity,divide(identity,divide(divide(A,divide(divide(identity,B),C)),divide(identity,divide(divide(identity,B),C))))) = A,
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_25,plain,
divide(identity,divide(identity,divide(divide(A,B),divide(identity,B)))) = A,
inference(paramod,[status(thm)],[c_24,c_21]) ).
cnf(c_26,plain,
divide(identity,divide(identity,divide(identity,divide(identity,A)))) = A,
inference(paramod,[status(thm)],[c_5,c_25]) ).
cnf(c_92,plain,
divide(identity,divide(identity,A)) = divide(divide(A,identity),identity),
inference(paramod,[status(thm)],[c_19,c_26]) ).
cnf(c_31,plain,
divide(divide(A,identity),identity) = divide(identity,divide(identity,A)),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_93,plain,
divide(identity,divide(identity,A)) = divide(divide(A,B),divide(identity,B)),
inference(paramod,[status(thm)],[c_25,c_26]) ).
cnf(c_34,plain,
divide(divide(A,B),divide(identity,B)) = divide(identity,divide(identity,A)),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_94,plain,
divide(divide(identity,divide(identity,divide(A,divide(identity,divide(divide(identity,B),identity))))),identity) = divide(identity,divide(identity,divide(identity,divide(B,A)))),
inference(paramod,[status(thm)],[c_16,c_31]) ).
cnf(c_95,plain,
divide(identity,divide(identity,divide(divide(A,divide(identity,divide(divide(identity,B),identity))),divide(identity,divide(divide(identity,identity),identity))))) = divide(identity,divide(identity,divide(identity,divide(B,A)))),
inference(paramod,[status(thm)],[c_16,c_94]) ).
cnf(c_96,plain,
divide(identity,divide(identity,divide(divide(A,divide(identity,divide(divide(identity,B),identity))),divide(identity,divide(identity,identity))))) = divide(identity,divide(identity,divide(identity,divide(B,A)))),
inference(paramod,[status(thm)],[c_5,c_95]) ).
cnf(c_97,plain,
divide(identity,divide(identity,divide(divide(A,divide(identity,divide(divide(identity,B),identity))),divide(identity,identity)))) = divide(identity,divide(identity,divide(identity,divide(B,A)))),
inference(paramod,[status(thm)],[c_5,c_96]) ).
cnf(c_37,plain,
divide(identity,divide(identity,divide(divide(A,divide(identity,divide(divide(identity,B),identity))),identity))) = divide(identity,divide(identity,divide(identity,divide(B,A)))),
inference(paramod,[status(thm)],[c_5,c_97]) ).
cnf(c_98,plain,
divide(divide(identity,divide(identity,divide(identity,A))),B) = divide(identity,divide(identity,divide(identity,divide(identity,divide(divide(identity,divide(A,identity)),B))))),
inference(paramod,[status(thm)],[c_31,c_16]) ).
cnf(c_99,plain,
divide(identity,divide(identity,divide(divide(identity,A),divide(identity,divide(divide(identity,identity),B))))) = divide(identity,divide(identity,divide(identity,divide(identity,divide(divide(identity,divide(A,identity)),B))))),
inference(paramod,[status(thm)],[c_16,c_98]) ).
cnf(c_100,plain,
divide(identity,divide(identity,divide(divide(identity,A),divide(identity,divide(identity,B))))) = divide(identity,divide(identity,divide(identity,divide(identity,divide(divide(identity,divide(A,identity)),B))))),
inference(paramod,[status(thm)],[c_5,c_99]) ).
cnf(c_101,plain,
divide(identity,divide(identity,divide(divide(identity,A),divide(identity,divide(identity,B))))) = divide(identity,divide(identity,divide(identity,divide(identity,divide(identity,divide(identity,divide(identity,divide(identity,divide(divide(identity,A),B))))))))),
inference(paramod,[status(thm)],[c_16,c_100]) ).
cnf(c_102,plain,
divide(identity,divide(identity,divide(divide(identity,A),divide(identity,divide(identity,B))))) = divide(identity,divide(identity,divide(identity,divide(identity,divide(divide(identity,A),B))))),
inference(paramod,[status(thm)],[c_26,c_101]) ).
cnf(c_38,plain,
divide(identity,divide(identity,divide(divide(identity,A),divide(identity,divide(identity,B))))) = divide(divide(identity,A),B),
inference(paramod,[status(thm)],[c_26,c_102]) ).
cnf(c_40,plain,
divide(divide(A,divide(identity,divide(identity,divide(identity,B)))),B) = divide(identity,divide(identity,A)),
inference(paramod,[status(thm)],[c_26,c_34]) ).
cnf(c_103,plain,
divide(divide(divide(identity,divide(identity,divide(identity,A))),B),divide(identity,B)) = divide(identity,A),
inference(paramod,[status(thm)],[c_26,c_34]) ).
cnf(c_104,plain,
divide(divide(identity,divide(identity,divide(divide(identity,A),divide(identity,divide(divide(identity,identity),B))))),divide(identity,B)) = divide(identity,A),
inference(paramod,[status(thm)],[c_16,c_103]) ).
cnf(c_105,plain,
divide(divide(identity,divide(identity,divide(divide(identity,A),divide(identity,divide(identity,B))))),divide(identity,B)) = divide(identity,A),
inference(paramod,[status(thm)],[c_5,c_104]) ).
cnf(c_106,plain,
divide(divide(divide(identity,A),B),divide(identity,B)) = divide(identity,A),
inference(paramod,[status(thm)],[c_38,c_105]) ).
cnf(c_41,plain,
divide(identity,divide(identity,divide(identity,A))) = divide(identity,A),
inference(paramod,[status(thm)],[c_34,c_106]) ).
cnf(c_47,plain,
divide(divide(A,divide(identity,B)),B) = divide(identity,divide(identity,A)),
inference(paramod,[status(thm)],[c_41,c_40]) ).
cnf(c_49,plain,
divide(identity,divide(identity,divide(divide(A,divide(identity,divide(divide(identity,B),identity))),identity))) = divide(identity,divide(B,A)),
inference(paramod,[status(thm)],[c_41,c_37]) ).
cnf(c_51,plain,
divide(identity,divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_41,c_26]) ).
cnf(c_107,plain,
divide(identity,divide(identity,divide(A,B))) = divide(identity,divide(C,divide(A,divide(divide(identity,C),divide(identity,B))))),
inference(paramod,[status(thm)],[c_51,c_17]) ).
cnf(c_108,plain,
divide(A,B) = divide(identity,divide(C,divide(A,divide(divide(identity,C),divide(identity,B))))),
inference(paramod,[status(thm)],[c_51,c_107]) ).
cnf(c_52,plain,
divide(identity,divide(A,divide(B,divide(divide(identity,A),divide(identity,C))))) = divide(B,C),
inference(copy,[status(thm)],[c_108]) ).
cnf(c_54,plain,
divide(divide(A,divide(identity,divide(divide(identity,B),identity))),identity) = divide(identity,divide(B,A)),
inference(paramod,[status(thm)],[c_51,c_49]) ).
cnf(c_56,plain,
divide(divide(A,divide(identity,B)),B) = A,
inference(paramod,[status(thm)],[c_51,c_47]) ).
cnf(c_64,plain,
divide(divide(identity,divide(A,B)),C) = divide(B,divide(identity,divide(divide(identity,A),C))),
inference(paramod,[status(thm)],[c_51,c_16]) ).
cnf(c_109,plain,
divide(identity,divide(A,identity)) = divide(divide(divide(identity,A),divide(identity,B)),B),
inference(paramod,[status(thm)],[c_5,c_52]) ).
cnf(c_67,plain,
divide(identity,divide(A,identity)) = divide(identity,A),
inference(paramod,[status(thm)],[c_56,c_109]) ).
cnf(c_110,plain,
divide(divide(A,divide(identity,divide(identity,B))),identity) = divide(identity,divide(B,A)),
inference(paramod,[status(thm)],[c_67,c_54]) ).
cnf(c_75,plain,
divide(divide(A,B),identity) = divide(identity,divide(B,A)),
inference(paramod,[status(thm)],[c_51,c_110]) ).
cnf(c_111,plain,
divide(identity,divide(identity,A)) = divide(A,identity),
inference(paramod,[status(thm)],[c_67,c_51]) ).
cnf(c_112,plain,
A = divide(A,identity),
inference(paramod,[status(thm)],[c_51,c_111]) ).
cnf(c_77,plain,
divide(A,identity) = A,
inference(copy,[status(thm)],[c_112]) ).
cnf(c_113,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(paramod,[status(thm)],[c_77,c_75]) ).
cnf(c_79,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_113]) ).
cnf(c_114,plain,
divide(divide(identity,divide(divide(identity,b3),a3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(paramod,[status(thm)],[c_79,c_7]) ).
cnf(c_115,plain,
divide(a3,divide(identity,divide(divide(identity,divide(identity,b3)),divide(identity,c3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(paramod,[status(thm)],[c_64,c_114]) ).
cnf(c_116,plain,
divide(a3,divide(identity,divide(b3,divide(identity,c3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(paramod,[status(thm)],[c_51,c_115]) ).
cnf(c_82,plain,
$false,
inference(copy,[status(thm)],[c_116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP456-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n004.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 14:55:07 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 3465755 was started by sandbox2 on n004,
% 0.17/0.44 % Fri Sep 25 14:55:07 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.46
% 0.17/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.46
% 0.17/0.46 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.46 % Length of proof is 35.
% 0.17/0.46 % Level of proof is 16.
% 0.17/0.46 % Maximum clause weight is 31.000.
% 0.17/0.46 % Given clauses 20.
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------