%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP447-1 : 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 : n019.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 07:29:44 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 53 ( 53 unt; 0 def)
% Number of atoms : 53 ( 52 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 : 7 ( 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 : 108 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(VAR_0,divide(divide(divide(divide(VAR_0,VAR_0),VAR_1),VAR_2),divide(divide(divide(VAR_0,VAR_0),VAR_0),VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(A,divide(divide(divide(divide(A,A),B),C),divide(divide(divide(A,A),A),C))) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,VAR_1) = divide(VAR_0,divide(divide(VAR_2,VAR_2),VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(inverse,axiom,
! [VAR_0,VAR_1] : inverse(VAR_0) = divide(divide(VAR_1,VAR_1),VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_3,plain,
inverse(A) = divide(divide(B,B),A),
inference(clausify,[status(thm)],[inverse]) ).
cnf(c_4,plain,
divide(divide(A,A),B) = inverse(B),
inference(copy,[status(thm)],[c_3]) ).
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_5,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_6,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_103,plain,
divide(A,divide(divide(inverse(B),C),divide(divide(divide(A,A),A),C))) = B,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_7,plain,
divide(A,divide(divide(inverse(B),C),divide(inverse(A),C))) = B,
inference(paramod,[status(thm)],[c_4,c_103]) ).
cnf(c_104,plain,
multiply(divide(a3,inverse(b3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_105,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_6,c_104]) ).
cnf(c_106,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,divide(b3,inverse(c3))),
inference(paramod,[status(thm)],[c_6,c_105]) ).
cnf(c_8,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_6,c_106]) ).
cnf(c_9,plain,
divide(inverse(divide(A,A)),B) = inverse(B),
inference(paramod,[status(thm)],[c_4,c_4]) ).
cnf(c_107,plain,
A = inverse(divide(divide(inverse(A),B),divide(inverse(divide(C,C)),B))),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_108,plain,
A = inverse(divide(divide(inverse(A),B),inverse(B))),
inference(paramod,[status(thm)],[c_9,c_107]) ).
cnf(c_10,plain,
inverse(divide(divide(inverse(A),B),inverse(B))) = A,
inference(copy,[status(thm)],[c_108]) ).
cnf(c_16,plain,
inverse(divide(inverse(A),inverse(A))) = divide(B,B),
inference(paramod,[status(thm)],[c_9,c_10]) ).
cnf(c_109,plain,
multiply(A,divide(inverse(B),inverse(B))) = divide(A,divide(C,C)),
inference(paramod,[status(thm)],[c_16,c_6]) ).
cnf(c_19,plain,
divide(A,inverse(divide(inverse(B),inverse(B)))) = divide(A,divide(C,C)),
inference(paramod,[status(thm)],[c_6,c_109]) ).
cnf(c_21,plain,
divide(A,inverse(divide(inverse(B),inverse(B)))) = A,
inference(paramod,[status(thm)],[c_16,c_7]) ).
cnf(c_110,plain,
inverse(divide(A,inverse(divide(divide(inverse(A),B),inverse(B))))) = divide(C,C),
inference(paramod,[status(thm)],[c_10,c_16]) ).
cnf(c_24,plain,
inverse(divide(A,A)) = divide(B,B),
inference(paramod,[status(thm)],[c_10,c_110]) ).
cnf(c_26,plain,
divide(A,A) = divide(B,B),
inference(paramod,[status(thm)],[c_16,c_16]) ).
cnf(c_111,plain,
A = divide(A,divide(C,C)),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_27,plain,
divide(A,divide(B,B)) = A,
inference(copy,[status(thm)],[c_111]) ).
cnf(c_112,plain,
divide(A,divide(divide(inverse(B),inverse(A)),divide(C,C))) = B,
inference(paramod,[status(thm)],[c_26,c_7]) ).
cnf(c_28,plain,
divide(A,divide(inverse(B),inverse(A))) = B,
inference(paramod,[status(thm)],[c_27,c_112]) ).
cnf(c_113,plain,
inverse(divide(divide(inverse(A),divide(B,B)),divide(C,C))) = A,
inference(paramod,[status(thm)],[c_24,c_10]) ).
cnf(c_114,plain,
inverse(divide(inverse(A),divide(C,C))) = A,
inference(paramod,[status(thm)],[c_27,c_113]) ).
cnf(c_32,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_27,c_114]) ).
cnf(c_33,plain,
divide(A,divide(divide(B,C),divide(inverse(A),C))) = inverse(B),
inference(paramod,[status(thm)],[c_32,c_7]) ).
cnf(c_35,plain,
inverse(divide(divide(A,B),inverse(B))) = inverse(A),
inference(paramod,[status(thm)],[c_32,c_10]) ).
cnf(c_44,plain,
divide(A,divide(B,inverse(A))) = inverse(B),
inference(paramod,[status(thm)],[c_32,c_28]) ).
cnf(c_47,plain,
divide(inverse(A),divide(B,A)) = inverse(B),
inference(paramod,[status(thm)],[c_32,c_44]) ).
cnf(c_115,plain,
divide(inverse(divide(A,B)),inverse(A)) = inverse(inverse(B)),
inference(paramod,[status(thm)],[c_47,c_47]) ).
cnf(c_49,plain,
divide(inverse(divide(A,B)),inverse(A)) = B,
inference(paramod,[status(thm)],[c_32,c_115]) ).
cnf(c_50,plain,
divide(inverse(A),divide(divide(B,C),divide(A,C))) = inverse(B),
inference(paramod,[status(thm)],[c_32,c_33]) ).
cnf(c_116,plain,
inverse(inverse(A)) = divide(divide(A,B),inverse(B)),
inference(paramod,[status(thm)],[c_35,c_32]) ).
cnf(c_117,plain,
A = divide(divide(A,B),inverse(B)),
inference(paramod,[status(thm)],[c_32,c_116]) ).
cnf(c_53,plain,
divide(divide(A,B),inverse(B)) = A,
inference(copy,[status(thm)],[c_117]) ).
cnf(c_118,plain,
divide(A,B) = inverse(divide(B,A)),
inference(paramod,[status(thm)],[c_53,c_44]) ).
cnf(c_57,plain,
inverse(divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_118]) ).
cnf(c_62,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3)),
inference(paramod,[status(thm)],[c_57,c_8]) ).
cnf(c_119,plain,
divide(inverse(inverse(A)),inverse(inverse(B))) = divide(divide(A,C),divide(B,C)),
inference(paramod,[status(thm)],[c_50,c_49]) ).
cnf(c_120,plain,
divide(A,inverse(inverse(B))) = divide(divide(A,C),divide(B,C)),
inference(paramod,[status(thm)],[c_32,c_119]) ).
cnf(c_121,plain,
divide(A,B) = divide(divide(A,C),divide(B,C)),
inference(paramod,[status(thm)],[c_32,c_120]) ).
cnf(c_85,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(copy,[status(thm)],[c_121]) ).
cnf(c_101,plain,
divide(divide(A,inverse(B)),C) = divide(A,divide(C,B)),
inference(paramod,[status(thm)],[c_53,c_85]) ).
cnf(c_102,plain,
$false,
inference(resolve,[status(thm)],[c_101,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP447-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n019.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 14:55:03 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 3035263 was started by sandbox2 on n019,
% 0.07/0.35 % Fri Sep 25 14:55:03 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.41
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.41
% 0.13/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/0.41 % Length of proof is 30.
% 0.13/0.41 % Level of proof is 13.
% 0.13/0.41 % Maximum clause weight is 45.000.
% 0.13/0.41 % Given clauses 33.
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------