%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP499-1 : 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 : n016.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 07:29:53 AM UTC 2026
% Result : Unsatisfiable 1.10s 0.59s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 12 ( 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 : 148 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : double_divide(inverse(VAR_0),inverse(double_divide(inverse(double_divide(VAR_0,double_divide(VAR_1,VAR_2))),double_divide(VAR_3,double_divide(VAR_1,VAR_3))))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(B,C))),double_divide(D,double_divide(B,D))))) = 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_1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c_3,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausify,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_389,plain,
inverse(double_divide(a1,inverse(a1))) != multiply(inverse(b1),b1),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_390,plain,
inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))),
inference(paramod,[status(thm)],[c_2,c_389]) ).
cnf(c_4,plain,
inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))),
inference(copy,[status(thm)],[c_390]) ).
cnf(c_5,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(D),C))))) = inverse(double_divide(inverse(double_divide(D,double_divide(E,B))),double_divide(F,double_divide(E,F)))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(inverse(A),C)))),double_divide(D,double_divide(B,D)))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_7,plain,
double_divide(inverse(A),double_divide(inverse(B),inverse(double_divide(inverse(double_divide(B,C)),double_divide(D,double_divide(inverse(A),D)))))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,double_divide(inverse(A),C))))),inverse(double_divide(C,double_divide(D,double_divide(E,D))))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_391,plain,
double_divide(inverse(A),double_divide(inverse(inverse(double_divide(B,double_divide(C,double_divide(inverse(B),D))))),inverse(double_divide(D,double_divide(E,double_divide(inverse(A),E)))))) = double_divide(F,double_divide(C,F)),
inference(paramod,[status(thm)],[c_6,c_7]) ).
cnf(c_14,plain,
double_divide(inverse(A),double_divide(B,inverse(A))) = double_divide(C,double_divide(B,C)),
inference(paramod,[status(thm)],[c_11,c_391]) ).
cnf(c_392,plain,
double_divide(A,double_divide(B,inverse(double_divide(inverse(double_divide(C,double_divide(D,double_divide(inverse(C),A)))),double_divide(E,double_divide(D,E)))))) = double_divide(F,double_divide(B,F)),
inference(paramod,[status(thm)],[c_6,c_14]) ).
cnf(c_30,plain,
double_divide(A,double_divide(B,A)) = double_divide(C,double_divide(B,C)),
inference(paramod,[status(thm)],[c_6,c_392]) ).
cnf(c_33,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(C,B)))),double_divide(D,double_divide(E,D))))) = double_divide(C,E),
inference(paramod,[status(thm)],[c_30,c_1]) ).
cnf(c_34,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(B,double_divide(C,B))),double_divide(D,double_divide(C,D))))) = A,
inference(paramod,[status(thm)],[c_30,c_1]) ).
cnf(c_40,plain,
double_divide(double_divide(A,B),double_divide(C,double_divide(A,C))) = double_divide(D,double_divide(B,D)),
inference(paramod,[status(thm)],[c_30,c_30]) ).
cnf(c_393,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(C,B)))),double_divide(D,double_divide(inverse(E),D))))) = inverse(double_divide(inverse(double_divide(E,double_divide(F,double_divide(V6,F)))),double_divide(V7,double_divide(double_divide(C,V6),V7)))),
inference(paramod,[status(thm)],[c_40,c_5]) ).
cnf(c_394,plain,
double_divide(C,inverse(E)) = inverse(double_divide(inverse(double_divide(E,double_divide(F,double_divide(V6,F)))),double_divide(V7,double_divide(double_divide(C,V6),V7)))),
inference(paramod,[status(thm)],[c_33,c_393]) ).
cnf(c_49,plain,
inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(C,B)))),double_divide(D,double_divide(double_divide(E,C),D)))) = double_divide(E,inverse(A)),
inference(copy,[status(thm)],[c_394]) ).
cnf(c_395,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(double_divide(B,double_divide(C,B)),double_divide(D,double_divide(E,D)))),double_divide(F,double_divide(double_divide(C,E),F))))) = A,
inference(paramod,[status(thm)],[c_40,c_34]) ).
cnf(c_91,plain,
double_divide(inverse(A),double_divide(B,inverse(double_divide(C,double_divide(B,C))))) = A,
inference(paramod,[status(thm)],[c_49,c_395]) ).
cnf(c_100,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(B),C)))) = inverse(double_divide(D,double_divide(inverse(A),D))),
inference(paramod,[status(thm)],[c_91,c_6]) ).
cnf(c_103,plain,
double_divide(double_divide(A,inverse(double_divide(B,double_divide(A,B)))),C) = double_divide(D,double_divide(inverse(C),D)),
inference(paramod,[status(thm)],[c_91,c_30]) ).
cnf(c_396,plain,
double_divide(inverse(double_divide(A,double_divide(inverse(B),A))),inverse(double_divide(inverse(double_divide(C,double_divide(D,C))),double_divide(E,double_divide(D,E))))) = double_divide(inverse(double_divide(B,F)),double_divide(V6,double_divide(inverse(F),V6))),
inference(paramod,[status(thm)],[c_100,c_34]) ).
cnf(c_397,plain,
double_divide(A,double_divide(inverse(B),A)) = double_divide(inverse(double_divide(B,F)),double_divide(V6,double_divide(inverse(F),V6))),
inference(paramod,[status(thm)],[c_34,c_396]) ).
cnf(c_162,plain,
double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(B),C))) = double_divide(D,double_divide(inverse(A),D)),
inference(copy,[status(thm)],[c_397]) ).
cnf(c_398,plain,
double_divide(inverse(inverse(double_divide(A,double_divide(B,double_divide(inverse(A),C))))),inverse(double_divide(C,double_divide(D,double_divide(inverse(double_divide(E,double_divide(F,inverse(double_divide(V6,double_divide(F,V6)))))),D))))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_103,c_11]) ).
cnf(c_178,plain,
double_divide(A,inverse(double_divide(B,double_divide(C,inverse(double_divide(D,double_divide(C,D))))))) = double_divide(A,B),
inference(paramod,[status(thm)],[c_11,c_398]) ).
cnf(c_399,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(inverse(C),B)))),double_divide(D,double_divide(inverse(double_divide(C,E)),D))))) = double_divide(F,double_divide(inverse(E),F)),
inference(paramod,[status(thm)],[c_162,c_1]) ).
cnf(c_181,plain,
double_divide(inverse(A),inverse(double_divide(A,B))) = double_divide(C,double_divide(inverse(B),C)),
inference(paramod,[status(thm)],[c_33,c_399]) ).
cnf(c_330,plain,
double_divide(inverse(A),inverse(double_divide(A,B))) = double_divide(inverse(C),inverse(double_divide(C,B))),
inference(paramod,[status(thm)],[c_181,c_181]) ).
cnf(c_400,plain,
double_divide(inverse(inverse(A)),inverse(A)) = double_divide(inverse(B),inverse(double_divide(B,double_divide(C,inverse(double_divide(D,double_divide(C,D))))))),
inference(paramod,[status(thm)],[c_91,c_330]) ).
cnf(c_339,plain,
double_divide(inverse(inverse(A)),inverse(A)) = double_divide(inverse(B),B),
inference(paramod,[status(thm)],[c_178,c_400]) ).
cnf(c_376,plain,
double_divide(inverse(A),A) = double_divide(B,inverse(B)),
inference(paramod,[status(thm)],[c_339,c_11]) ).
cnf(c_401,plain,
multiply(A,inverse(A)) = inverse(double_divide(B,inverse(B))),
inference(paramod,[status(thm)],[c_376,c_2]) ).
cnf(c_387,plain,
inverse(double_divide(inverse(A),A)) = inverse(double_divide(B,inverse(B))),
inference(paramod,[status(thm)],[c_2,c_401]) ).
cnf(c_402,plain,
inverse(double_divide(inverse(A),A)) != inverse(double_divide(a1,inverse(a1))),
inference(paramod,[status(thm)],[c_376,c_4]) ).
cnf(c_388,plain,
$false,
inference(resolve,[status(thm)],[c_387,c_402]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP499-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n016.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 15:02:16 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 2689505 was started by sandbox on n016,
% 0.16/0.42 % Fri Sep 25 15:02:16 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 1.10/0.59
% 1.10/0.59 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 1.10/0.59
% 1.10/0.59 % SZS status Unsatisfiable for theBenchmark
% 1.10/0.59
% 1.10/0.59 % Proof 1 at 0.11 (+ 0.03) seconds.
% 1.10/0.59 % Length of proof is 25.
% 1.10/0.59 % Level of proof is 16.
% 1.10/0.59 % Maximum clause weight is 89.000.
% 1.10/0.59 % Given clauses 23.
% 1.10/0.59
% 1.10/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------