%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP586-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% 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 : 7 ( 7 ~; 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 : 74 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(VAR_0,inverse(double_divide(inverse(double_divide(double_divide(VAR_0,VAR_1),inverse(VAR_2))),VAR_1))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),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_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_3,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_93,plain,
multiply(inverse(double_divide(b2,inverse(b2))),a2) != a2,
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4,plain,
inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2,
inference(paramod,[status(thm)],[c_2,c_93]) ).
cnf(c_5,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,inverse(C))),inverse(double_divide(inverse(double_divide(double_divide(A,D),inverse(B))),D))))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_94,plain,
double_divide(A,inverse(double_divide(inverse(B),C))) = double_divide(inverse(double_divide(double_divide(double_divide(A,C),D),inverse(B))),D),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
double_divide(inverse(double_divide(double_divide(double_divide(A,B),C),inverse(D))),C) = double_divide(A,inverse(double_divide(inverse(D),B))),
inference(copy,[status(thm)],[c_94]) ).
cnf(c_7,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,inverse(C))),inverse(double_divide(inverse(double_divide(D,inverse(B))),inverse(double_divide(inverse(double_divide(double_divide(A,E),inverse(D))),E))))))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_10,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(A)) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_95,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(double_divide(double_divide(B,C),inverse(A))),C),
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_13,plain,
double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B) = double_divide(inverse(C),inverse(A)),
inference(copy,[status(thm)],[c_95]) ).
cnf(c_96,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(double_divide(C,inverse(A))),inverse(double_divide(inverse(double_divide(double_divide(B,D),inverse(C))),D))),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_97,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(double_divide(C,inverse(A))),inverse(double_divide(inverse(C),inverse(B)))),
inference(paramod,[status(thm)],[c_13,c_96]) ).
cnf(c_16,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(inverse(A),inverse(C)))) = double_divide(inverse(B),inverse(C)),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_98,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,inverse(C))),inverse(double_divide(inverse(double_divide(D,inverse(B))),inverse(double_divide(inverse(D),inverse(A)))))))) = C,
inference(paramod,[status(thm)],[c_13,c_7]) ).
cnf(c_99,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,inverse(C))),inverse(double_divide(inverse(B),inverse(A)))))) = C,
inference(paramod,[status(thm)],[c_16,c_98]) ).
cnf(c_19,plain,
double_divide(A,inverse(double_divide(inverse(B),inverse(A)))) = B,
inference(paramod,[status(thm)],[c_16,c_99]) ).
cnf(c_20,plain,
double_divide(inverse(A),inverse(double_divide(B,C))) = double_divide(B,inverse(double_divide(inverse(A),C))),
inference(paramod,[status(thm)],[c_13,c_6]) ).
cnf(c_29,plain,
double_divide(inverse(A),inverse(double_divide(B,inverse(B)))) = A,
inference(paramod,[status(thm)],[c_20,c_19]) ).
cnf(c_100,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(B),inverse(double_divide(inverse(A),inverse(double_divide(C,inverse(C)))))),
inference(paramod,[status(thm)],[c_29,c_20]) ).
cnf(c_36,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(B),inverse(A)),
inference(paramod,[status(thm)],[c_29,c_100]) ).
cnf(c_41,plain,
double_divide(inverse(A),inverse(double_divide(A,inverse(B)))) = B,
inference(paramod,[status(thm)],[c_36,c_10]) ).
cnf(c_64,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_41,c_19]) ).
cnf(c_101,plain,
double_divide(inverse(inverse(A)),inverse(A)) = double_divide(B,inverse(B)),
inference(paramod,[status(thm)],[c_29,c_41]) ).
cnf(c_67,plain,
double_divide(A,inverse(A)) = double_divide(B,inverse(B)),
inference(paramod,[status(thm)],[c_64,c_101]) ).
cnf(c_77,plain,
inverse(double_divide(a2,inverse(double_divide(A,inverse(A))))) != a2,
inference(paramod,[status(thm)],[c_67,c_4]) ).
cnf(c_88,plain,
double_divide(A,inverse(double_divide(B,inverse(B)))) = inverse(A),
inference(paramod,[status(thm)],[c_64,c_29]) ).
cnf(c_102,plain,
inverse(inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_88,c_77]) ).
cnf(c_103,plain,
a2 != a2,
inference(paramod,[status(thm)],[c_64,c_102]) ).
cnf(c_92,plain,
$false,
inference(copy,[status(thm)],[c_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP586-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 15:00:37 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 690088 was started by sandbox on n013,
% 0.10/0.36 % Fri Sep 25 15:00:37 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.13/0.39
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.39 % Length of proof is 20.
% 0.13/0.39 % Level of proof is 12.
% 0.13/0.39 % Maximum clause weight is 88.000.
% 0.13/0.39 % Given clauses 15.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------