%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP606-1 : 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 : n026.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 07:30:28 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.60s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 44 unt; 0 def)
% Number of atoms : 44 ( 43 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 99 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(inverse(double_divide(VAR_0,inverse(double_divide(inverse(VAR_1),double_divide(VAR_0,VAR_2))))),VAR_2) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = B,
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_89,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_89]) ).
cnf(c_5,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),inverse(double_divide(inverse(D),B)))),C) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_90,plain,
double_divide(inverse(double_divide(A,inverse(B))),C) = double_divide(D,inverse(double_divide(inverse(B),double_divide(D,double_divide(A,C))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
double_divide(A,inverse(double_divide(inverse(B),double_divide(A,double_divide(C,D))))) = double_divide(inverse(double_divide(C,inverse(B))),D),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_7,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),inverse(double_divide(inverse(D),B)))),inverse(double_divide(inverse(E),D)))),C) = E,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_10,plain,
double_divide(inverse(A),inverse(double_divide(inverse(B),A))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_91,plain,
double_divide(inverse(A),inverse(B)) = double_divide(C,inverse(double_divide(inverse(B),double_divide(C,A)))),
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_13,plain,
double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C)))) = double_divide(inverse(C),inverse(B)),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_92,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(double_divide(C,inverse(double_divide(inverse(D),double_divide(C,A))))),inverse(double_divide(inverse(B),D))),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_93,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(double_divide(inverse(A),inverse(D))),inverse(double_divide(inverse(B),D))),
inference(paramod,[status(thm)],[c_13,c_92]) ).
cnf(c_16,plain,
double_divide(inverse(double_divide(inverse(A),inverse(B))),inverse(double_divide(inverse(C),B))) = double_divide(inverse(A),inverse(C)),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_94,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(C),inverse(B))),inverse(double_divide(inverse(D),B)))),inverse(double_divide(inverse(E),D)))),C) = E,
inference(paramod,[status(thm)],[c_13,c_7]) ).
cnf(c_95,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(C),inverse(D))),inverse(double_divide(inverse(E),D)))),C) = E,
inference(paramod,[status(thm)],[c_16,c_94]) ).
cnf(c_19,plain,
double_divide(inverse(double_divide(inverse(A),inverse(B))),A) = B,
inference(paramod,[status(thm)],[c_16,c_95]) ).
cnf(c_96,plain,
double_divide(inverse(double_divide(C,D)),inverse(B)) = double_divide(inverse(double_divide(C,inverse(B))),D),
inference(paramod,[status(thm)],[c_13,c_6]) ).
cnf(c_20,plain,
double_divide(inverse(double_divide(A,inverse(B))),C) = double_divide(inverse(double_divide(A,C)),inverse(B)),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_27,plain,
double_divide(inverse(double_divide(inverse(A),A)),inverse(B)) = B,
inference(paramod,[status(thm)],[c_20,c_19]) ).
cnf(c_33,plain,
double_divide(inverse(inverse(A)),inverse(A)) = double_divide(inverse(B),B),
inference(paramod,[status(thm)],[c_27,c_10]) ).
cnf(c_97,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(A),A)),inverse(B))),inverse(C)) = double_divide(inverse(C),inverse(B)),
inference(paramod,[status(thm)],[c_27,c_20]) ).
cnf(c_36,plain,
double_divide(inverse(A),inverse(B)) = double_divide(inverse(B),inverse(A)),
inference(paramod,[status(thm)],[c_27,c_97]) ).
cnf(c_38,plain,
double_divide(inverse(A),inverse(inverse(A))) = double_divide(inverse(B),B),
inference(paramod,[status(thm)],[c_36,c_33]) ).
cnf(c_50,plain,
double_divide(inverse(A),inverse(double_divide(inverse(B),B))) = A,
inference(paramod,[status(thm)],[c_36,c_27]) ).
cnf(c_98,plain,
double_divide(inverse(inverse(inverse(A))),inverse(double_divide(inverse(B),B))) = A,
inference(paramod,[status(thm)],[c_38,c_10]) ).
cnf(c_65,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_50,c_98]) ).
cnf(c_99,plain,
double_divide(A,inverse(double_divide(inverse(B),inverse(inverse(B))))) = double_divide(inverse(C),inverse(double_divide(A,C))),
inference(paramod,[status(thm)],[c_38,c_13]) ).
cnf(c_100,plain,
double_divide(A,inverse(double_divide(inverse(B),B))) = double_divide(inverse(C),inverse(double_divide(A,C))),
inference(paramod,[status(thm)],[c_65,c_99]) ).
cnf(c_69,plain,
double_divide(inverse(A),inverse(double_divide(B,A))) = double_divide(B,inverse(double_divide(inverse(C),C))),
inference(copy,[status(thm)],[c_100]) ).
cnf(c_81,plain,
double_divide(inverse(A),inverse(double_divide(B,A))) = inverse(B),
inference(paramod,[status(thm)],[c_65,c_10]) ).
cnf(c_101,plain,
double_divide(A,inverse(B)) = double_divide(inverse(B),inverse(inverse(A))),
inference(paramod,[status(thm)],[c_65,c_36]) ).
cnf(c_102,plain,
double_divide(A,inverse(B)) = double_divide(inverse(B),A),
inference(paramod,[status(thm)],[c_65,c_101]) ).
cnf(c_82,plain,
double_divide(inverse(A),B) = double_divide(B,inverse(A)),
inference(copy,[status(thm)],[c_102]) ).
cnf(c_103,plain,
inverse(B) = double_divide(B,inverse(double_divide(inverse(C),C))),
inference(paramod,[status(thm)],[c_81,c_69]) ).
cnf(c_104,plain,
inverse(B) = double_divide(B,inverse(double_divide(C,inverse(C)))),
inference(paramod,[status(thm)],[c_82,c_103]) ).
cnf(c_85,plain,
double_divide(A,inverse(double_divide(B,inverse(B)))) = inverse(A),
inference(copy,[status(thm)],[c_104]) ).
cnf(c_105,plain,
inverse(inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_85,c_4]) ).
cnf(c_106,plain,
a2 != a2,
inference(paramod,[status(thm)],[c_65,c_105]) ).
cnf(c_88,plain,
$false,
inference(copy,[status(thm)],[c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP606-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n026.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Fri Sep 25 15:04:41 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.57 % Process 2832389 was started by sandbox2 on n026,
% 0.09/0.57 % Fri Sep 25 15:04:41 2026
% 0.09/0.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.58
% 0.09/0.58 % From the command line: assign(max_seconds, 300).
% 0.14/0.60
% 0.14/0.60 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.14/0.60
% 0.14/0.60 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.60
% 0.14/0.60 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.60 % Length of proof is 23.
% 0.14/0.60 % Level of proof is 12.
% 0.14/0.60 % Maximum clause weight is 85.000.
% 0.14/0.60 % Given clauses 13.
% 0.14/0.60
% 0.14/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------