%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP504-1 : 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 07:30:04 AM UTC 2026
% Result : Unsatisfiable 20.89s 3.09s
% Output : CNFRefutation 20.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 3
% Syntax : Number of formulae : 121 ( 121 unt; 0 def)
% Number of atoms : 121 ( 120 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 16 ( 16 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 16 ( 3 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 : 506 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : double_divide(double_divide(VAR_0,inverse(double_divide(VAR_1,VAR_2))),double_divide(inverse(VAR_1),inverse(double_divide(VAR_3,double_divide(VAR_0,VAR_3))))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(A,inverse(double_divide(B,C))),double_divide(inverse(B),inverse(double_divide(D,double_divide(A,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_3,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c_3,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_6578,plain,
multiply(inverse(double_divide(b3,a3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_6579,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_6578]) ).
cnf(c_6580,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,inverse(double_divide(c3,b3))),
inference(paramod,[status(thm)],[c_2,c_6579]) ).
cnf(c_6581,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(paramod,[status(thm)],[c_2,c_6580]) ).
cnf(c_4,plain,
inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(copy,[status(thm)],[c_6581]) ).
cnf(c_6582,plain,
double_divide(double_divide(A,inverse(B)),double_divide(inverse(double_divide(C,inverse(double_divide(D,B)))),inverse(double_divide(E,double_divide(A,E))))) = double_divide(inverse(D),inverse(double_divide(F,double_divide(C,F)))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
double_divide(inverse(A),inverse(double_divide(B,double_divide(C,B)))) = double_divide(double_divide(D,inverse(E)),double_divide(inverse(double_divide(C,inverse(double_divide(A,E)))),inverse(double_divide(F,double_divide(D,F))))),
inference(copy,[status(thm)],[c_6582]) ).
cnf(c_6,plain,
double_divide(double_divide(double_divide(A,inverse(double_divide(B,C))),inverse(double_divide(D,E))),double_divide(inverse(D),inverse(double_divide(double_divide(inverse(B),inverse(double_divide(F,double_divide(A,F)))),C)))) = E,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_8,plain,
double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(double_divide(C,inverse(double_divide(D,B)))),inverse(double_divide(E,double_divide(A,E))))),double_divide(inverse(F),inverse(double_divide(V6,double_divide(inverse(D),V6))))) = double_divide(C,F),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_10,plain,
double_divide(double_divide(A,inverse(double_divide(B,C))),double_divide(double_divide(D,inverse(E)),double_divide(inverse(double_divide(A,inverse(double_divide(B,E)))),inverse(double_divide(F,double_divide(D,F)))))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_12,plain,
double_divide(double_divide(double_divide(A,inverse(B)),inverse(double_divide(C,D))),double_divide(inverse(C),inverse(double_divide(double_divide(inverse(double_divide(E,inverse(double_divide(F,B)))),inverse(double_divide(V6,double_divide(A,V6)))),double_divide(inverse(F),inverse(double_divide(V7,double_divide(E,V7)))))))) = D,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_6583,plain,
double_divide(inverse(A),inverse(double_divide(B,double_divide(C,B)))) = double_divide(double_divide(double_divide(D,inverse(E)),double_divide(inverse(double_divide(F,inverse(double_divide(V6,E)))),inverse(double_divide(V7,double_divide(D,V7))))),double_divide(inverse(double_divide(C,inverse(double_divide(A,double_divide(V8,double_divide(F,V8)))))),inverse(double_divide(V9,double_divide(inverse(V6),V9))))),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_18,plain,
double_divide(inverse(A),inverse(double_divide(B,double_divide(C,B)))) = double_divide(D,double_divide(C,inverse(double_divide(A,double_divide(E,double_divide(D,E)))))),
inference(paramod,[status(thm)],[c_8,c_6583]) ).
cnf(c_26,plain,
double_divide(inverse(A),inverse(double_divide(B,double_divide(C,B)))) = double_divide(inverse(A),inverse(double_divide(D,double_divide(C,D)))),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_6584,plain,
double_divide(double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(C,double_divide(D,C)))))),double_divide(inverse(inverse(B)),inverse(double_divide(E,double_divide(A,E))))) = inverse(double_divide(F,double_divide(D,F))),
inference(paramod,[status(thm)],[c_26,c_1]) ).
cnf(c_27,plain,
inverse(double_divide(A,double_divide(B,A))) = inverse(double_divide(C,double_divide(B,C))),
inference(paramod,[status(thm)],[c_1,c_6584]) ).
cnf(c_63,plain,
double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),A)),inverse(double_divide(D,double_divide(inverse(B),D)))) = C,
inference(paramod,[status(thm)],[c_18,c_1]) ).
cnf(c_138,plain,
double_divide(double_divide(inverse(A),inverse(double_divide(double_divide(double_divide(B,inverse(double_divide(A,C))),B),D))),C) = D,
inference(paramod,[status(thm)],[c_63,c_1]) ).
cnf(c_6585,plain,
inverse(double_divide(A,B)) = inverse(double_divide(C,double_divide(double_divide(inverse(D),inverse(double_divide(double_divide(double_divide(E,inverse(double_divide(D,A))),E),B))),C))),
inference(paramod,[status(thm)],[c_138,c_27]) ).
cnf(c_192,plain,
inverse(double_divide(A,double_divide(double_divide(inverse(B),inverse(double_divide(double_divide(double_divide(C,inverse(double_divide(B,D))),C),E))),A))) = inverse(double_divide(D,E)),
inference(copy,[status(thm)],[c_6585]) ).
cnf(c_6586,plain,
double_divide(inverse(A),inverse(double_divide(B,double_divide(double_divide(inverse(C),inverse(double_divide(double_divide(double_divide(D,inverse(double_divide(C,inverse(double_divide(A,double_divide(E,double_divide(F,E))))))),D),V6))),B)))) = double_divide(F,V6),
inference(paramod,[status(thm)],[c_138,c_18]) ).
cnf(c_199,plain,
double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(C,B)))),D))) = double_divide(C,D),
inference(paramod,[status(thm)],[c_192,c_6586]) ).
cnf(c_6587,plain,
double_divide(A,double_divide(inverse(B),inverse(double_divide(double_divide(inverse(double_divide(double_divide(C,inverse(double_divide(D,inverse(double_divide(B,E))))),C)),inverse(double_divide(F,double_divide(inverse(D),F)))),A)))) = E,
inference(paramod,[status(thm)],[c_138,c_6]) ).
cnf(c_208,plain,
double_divide(A,double_divide(inverse(B),inverse(double_divide(inverse(double_divide(B,C)),A)))) = C,
inference(paramod,[status(thm)],[c_63,c_6587]) ).
cnf(c_221,plain,
double_divide(double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(B,inverse(B)))),A)),inverse(double_divide(C,D))),C) = D,
inference(paramod,[status(thm)],[c_138,c_138]) ).
cnf(c_234,plain,
double_divide(A,double_divide(inverse(B),inverse(double_divide(inverse(double_divide(C,double_divide(D,C))),A)))) = double_divide(D,B),
inference(paramod,[status(thm)],[c_27,c_208]) ).
cnf(c_273,plain,
double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(double_divide(C,double_divide(B,C))),D))) = double_divide(A,D),
inference(paramod,[status(thm)],[c_27,c_199]) ).
cnf(c_298,plain,
double_divide(A,double_divide(B,A)) = double_divide(C,double_divide(B,C)),
inference(paramod,[status(thm)],[c_199,c_208]) ).
cnf(c_6588,plain,
double_divide(A,B) = double_divide(C,double_divide(double_divide(inverse(D),inverse(double_divide(double_divide(double_divide(E,inverse(double_divide(D,A))),E),B))),C)),
inference(paramod,[status(thm)],[c_138,c_298]) ).
cnf(c_426,plain,
double_divide(A,double_divide(double_divide(inverse(B),inverse(double_divide(double_divide(double_divide(C,inverse(double_divide(B,D))),C),E))),A)) = double_divide(D,E),
inference(copy,[status(thm)],[c_6588]) ).
cnf(c_6589,plain,
inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(A,double_divide(inverse(inverse(double_divide(b3,a3))),inverse(double_divide(inverse(double_divide(B,double_divide(c3,B))),A))))),
inference(paramod,[status(thm)],[c_234,c_4]) ).
cnf(c_786,plain,
inverse(double_divide(A,double_divide(inverse(inverse(double_divide(b3,a3))),inverse(double_divide(inverse(double_divide(B,double_divide(c3,B))),A))))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(copy,[status(thm)],[c_6589]) ).
cnf(c_1488,plain,
double_divide(double_divide(double_divide(A,inverse(double_divide(B,inverse(B)))),C),inverse(double_divide(D,double_divide(A,D)))) = C,
inference(paramod,[status(thm)],[c_273,c_221]) ).
cnf(c_6590,plain,
double_divide(double_divide(inverse(A),inverse(B)),inverse(A)) = inverse(double_divide(C,double_divide(B,C))),
inference(paramod,[status(thm)],[c_1488,c_138]) ).
cnf(c_1531,plain,
inverse(double_divide(A,double_divide(B,A))) = double_divide(double_divide(inverse(C),inverse(B)),inverse(C)),
inference(copy,[status(thm)],[c_6590]) ).
cnf(c_6591,plain,
double_divide(double_divide(A,B),inverse(double_divide(C,double_divide(double_divide(inverse(D),inverse(double_divide(double_divide(double_divide(E,inverse(double_divide(D,inverse(double_divide(F,inverse(F)))))),E),A))),C)))) = B,
inference(paramod,[status(thm)],[c_138,c_1488]) ).
cnf(c_1532,plain,
double_divide(double_divide(A,B),inverse(double_divide(inverse(double_divide(C,inverse(C))),A))) = B,
inference(paramod,[status(thm)],[c_426,c_6591]) ).
cnf(c_1655,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,inverse(A))),B)),C) = double_divide(D,double_divide(double_divide(B,C),D)),
inference(paramod,[status(thm)],[c_1532,c_298]) ).
cnf(c_1656,plain,
double_divide(double_divide(A,double_divide(B,A)),inverse(double_divide(inverse(double_divide(C,inverse(C))),D))) = double_divide(B,D),
inference(paramod,[status(thm)],[c_298,c_1532]) ).
cnf(c_1705,plain,
double_divide(double_divide(A,B),inverse(double_divide(C,double_divide(double_divide(inverse(inverse(double_divide(D,inverse(D)))),A),C)))) = B,
inference(paramod,[status(thm)],[c_1532,c_1488]) ).
cnf(c_1711,plain,
double_divide(double_divide(A,B),inverse(double_divide(inverse(inverse(double_divide(C,inverse(C)))),A))) = B,
inference(paramod,[status(thm)],[c_1532,c_1532]) ).
cnf(c_6592,plain,
multiply(inverse(A),double_divide(inverse(A),inverse(B))) = inverse(inverse(double_divide(C,double_divide(B,C)))),
inference(paramod,[status(thm)],[c_1531,c_2]) ).
cnf(c_6593,plain,
inverse(double_divide(double_divide(inverse(A),inverse(B)),inverse(A))) = inverse(inverse(double_divide(C,double_divide(B,C)))),
inference(paramod,[status(thm)],[c_2,c_6592]) ).
cnf(c_2051,plain,
inverse(inverse(double_divide(A,double_divide(B,A)))) = inverse(double_divide(double_divide(inverse(C),inverse(B)),inverse(C))),
inference(copy,[status(thm)],[c_6593]) ).
cnf(c_2189,plain,
inverse(double_divide(A,double_divide(inverse(inverse(double_divide(b3,a3))),inverse(double_divide(double_divide(double_divide(inverse(B),inverse(c3)),inverse(B)),A))))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(paramod,[status(thm)],[c_1531,c_786]) ).
cnf(c_2349,plain,
double_divide(double_divide(double_divide(A,B),inverse(double_divide(inverse(inverse(double_divide(C,inverse(C)))),D))),double_divide(double_divide(E,inverse(A)),double_divide(inverse(B),inverse(double_divide(F,double_divide(E,F)))))) = D,
inference(paramod,[status(thm)],[c_1711,c_10]) ).
cnf(c_2583,plain,
inverse(inverse(double_divide(A,double_divide(B,A)))) = inverse(inverse(double_divide(C,double_divide(B,C)))),
inference(paramod,[status(thm)],[c_1531,c_2051]) ).
cnf(c_3033,plain,
inverse(double_divide(double_divide(inverse(A),inverse(double_divide(B,double_divide(double_divide(inverse(double_divide(A,C)),inverse(c3)),B)))),double_divide(inverse(inverse(double_divide(b3,a3))),inverse(C)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(paramod,[status(thm)],[c_1,c_2189]) ).
cnf(c_3080,plain,
double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(inverse(double_divide(B,double_divide(C,B))),D))),A)),inverse(double_divide(E,double_divide(inverse(inverse(double_divide(F,double_divide(C,F)))),E)))) = D,
inference(paramod,[status(thm)],[c_2583,c_63]) ).
cnf(c_3531,plain,
double_divide(inverse(double_divide(A,double_divide(inverse(B),inverse(double_divide(inverse(double_divide(C,double_divide(inverse(double_divide(D,inverse(D))),C))),A))))),E) = double_divide(F,double_divide(double_divide(B,E),F)),
inference(paramod,[status(thm)],[c_234,c_1655]) ).
cnf(c_6594,plain,
inverse(double_divide(A,double_divide(B,A))) = double_divide(double_divide(C,double_divide(double_divide(D,inverse(B)),C)),inverse(double_divide(inverse(double_divide(E,inverse(E))),D))),
inference(paramod,[status(thm)],[c_1655,c_1531]) ).
cnf(c_3623,plain,
inverse(double_divide(A,double_divide(B,A))) = double_divide(double_divide(C,inverse(B)),C),
inference(paramod,[status(thm)],[c_1656,c_6594]) ).
cnf(c_6595,plain,
double_divide(double_divide(double_divide(A,inverse(B)),inverse(C)),double_divide(inverse(double_divide(D,C)),inverse(double_divide(double_divide(inverse(double_divide(E,inverse(double_divide(F,B)))),inverse(double_divide(V6,double_divide(A,V6)))),double_divide(inverse(F),inverse(double_divide(V7,double_divide(E,V7)))))))) = inverse(double_divide(inverse(inverse(double_divide(V8,inverse(V8)))),D)),
inference(paramod,[status(thm)],[c_1711,c_12]) ).
cnf(c_3875,plain,
inverse(double_divide(inverse(inverse(double_divide(A,inverse(A)))),B)) = double_divide(double_divide(double_divide(C,inverse(D)),inverse(E)),double_divide(inverse(double_divide(B,E)),inverse(double_divide(double_divide(inverse(double_divide(F,inverse(double_divide(V6,D)))),inverse(double_divide(V7,double_divide(C,V7)))),double_divide(inverse(V6),inverse(double_divide(V8,double_divide(F,V8)))))))),
inference(copy,[status(thm)],[c_6595]) ).
cnf(c_4120,plain,
double_divide(A,inverse(double_divide(B,double_divide(C,B)))) = double_divide(D,double_divide(double_divide(A,inverse(C)),D)),
inference(paramod,[status(thm)],[c_3623,c_298]) ).
cnf(c_4160,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,double_divide(B,A))),C)),double_divide(D,C))) = double_divide(double_divide(E,inverse(inverse(double_divide(D,B)))),E),
inference(paramod,[status(thm)],[c_273,c_3623]) ).
cnf(c_4273,plain,
double_divide(double_divide(A,inverse(B)),A) = double_divide(double_divide(C,inverse(B)),C),
inference(paramod,[status(thm)],[c_3623,c_3623]) ).
cnf(c_6596,plain,
double_divide(double_divide(A,B),inverse(C)) = double_divide(double_divide(D,inverse(double_divide(inverse(double_divide(C,double_divide(E,double_divide(A,E)))),B))),D),
inference(paramod,[status(thm)],[c_199,c_4273]) ).
cnf(c_4310,plain,
double_divide(double_divide(A,inverse(double_divide(inverse(double_divide(B,double_divide(C,double_divide(D,C)))),E))),A) = double_divide(double_divide(D,E),inverse(B)),
inference(copy,[status(thm)],[c_6596]) ).
cnf(c_6597,plain,
double_divide(A,inverse(double_divide(B,double_divide(C,B)))) = double_divide(double_divide(inverse(double_divide(D,inverse(double_divide(E,C)))),inverse(double_divide(F,double_divide(A,F)))),double_divide(inverse(E),inverse(double_divide(V6,double_divide(D,V6))))),
inference(paramod,[status(thm)],[c_5,c_4120]) ).
cnf(c_5285,plain,
double_divide(double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),inverse(double_divide(D,double_divide(E,D)))),double_divide(inverse(B),inverse(double_divide(F,double_divide(A,F))))) = double_divide(E,inverse(double_divide(V6,double_divide(C,V6)))),
inference(copy,[status(thm)],[c_6597]) ).
cnf(c_5388,plain,
double_divide(double_divide(A,inverse(double_divide(B,double_divide(C,B)))),double_divide(D,double_divide(double_divide(inverse(E),inverse(A)),D))) = double_divide(C,E),
inference(paramod,[status(thm)],[c_4120,c_234]) ).
cnf(c_6598,plain,
double_divide(double_divide(A,B),inverse(double_divide(C,double_divide(double_divide(inverse(inverse(double_divide(D,inverse(D)))),A),C)))) = double_divide(E,double_divide(B,E)),
inference(paramod,[status(thm)],[c_1711,c_4120]) ).
cnf(c_6599,plain,
B = double_divide(E,double_divide(B,E)),
inference(paramod,[status(thm)],[c_1705,c_6598]) ).
cnf(c_5492,plain,
double_divide(A,double_divide(B,A)) = B,
inference(copy,[status(thm)],[c_6599]) ).
cnf(c_6600,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,inverse(C)),inverse(D)),A)),double_divide(inverse(E),inverse(double_divide(double_divide(inverse(double_divide(F,inverse(double_divide(V6,C)))),inverse(double_divide(V7,double_divide(B,V7)))),double_divide(inverse(V6),inverse(double_divide(V8,double_divide(F,V8)))))))) = double_divide(D,E),
inference(paramod,[status(thm)],[c_4120,c_12]) ).
cnf(c_6601,plain,
double_divide(double_divide(double_divide(B,inverse(C)),inverse(D)),double_divide(inverse(E),inverse(double_divide(double_divide(inverse(double_divide(F,inverse(double_divide(V6,C)))),inverse(double_divide(V7,double_divide(B,V7)))),double_divide(inverse(V6),inverse(double_divide(V8,double_divide(F,V8)))))))) = double_divide(D,E),
inference(paramod,[status(thm)],[c_5492,c_6600]) ).
cnf(c_6602,plain,
double_divide(double_divide(double_divide(B,inverse(C)),inverse(D)),double_divide(inverse(E),inverse(double_divide(double_divide(inverse(double_divide(F,inverse(double_divide(V6,C)))),inverse(B)),double_divide(inverse(V6),inverse(double_divide(V8,double_divide(F,V8)))))))) = double_divide(D,E),
inference(paramod,[status(thm)],[c_5492,c_6601]) ).
cnf(c_5519,plain,
double_divide(double_divide(double_divide(A,inverse(B)),inverse(C)),double_divide(inverse(D),inverse(double_divide(double_divide(inverse(double_divide(E,inverse(double_divide(F,B)))),inverse(A)),double_divide(inverse(F),inverse(E)))))) = double_divide(C,D),
inference(paramod,[status(thm)],[c_5492,c_6602]) ).
cnf(c_6603,plain,
double_divide(double_divide(double_divide(A,inverse(inverse(double_divide(B,double_divide(C,B))))),inverse(double_divide(D,E))),double_divide(inverse(D),inverse(double_divide(double_divide(inverse(double_divide(F,inverse(double_divide(V6,double_divide(double_divide(V7,inverse(C)),V6))))),inverse(double_divide(V8,double_divide(A,V8)))),double_divide(inverse(V7),inverse(double_divide(V9,double_divide(F,V9)))))))) = E,
inference(paramod,[status(thm)],[c_4120,c_12]) ).
cnf(c_6604,plain,
double_divide(double_divide(double_divide(A,inverse(inverse(C))),inverse(double_divide(D,E))),double_divide(inverse(D),inverse(double_divide(double_divide(inverse(double_divide(F,inverse(double_divide(V6,double_divide(double_divide(V7,inverse(C)),V6))))),inverse(double_divide(V8,double_divide(A,V8)))),double_divide(inverse(V7),inverse(double_divide(V9,double_divide(F,V9)))))))) = E,
inference(paramod,[status(thm)],[c_5492,c_6603]) ).
cnf(c_6605,plain,
double_divide(double_divide(double_divide(A,inverse(inverse(C))),inverse(double_divide(D,E))),double_divide(inverse(D),inverse(double_divide(double_divide(inverse(double_divide(F,inverse(double_divide(V7,inverse(C))))),inverse(double_divide(V8,double_divide(A,V8)))),double_divide(inverse(V7),inverse(double_divide(V9,double_divide(F,V9)))))))) = E,
inference(paramod,[status(thm)],[c_5492,c_6604]) ).
cnf(c_6606,plain,
double_divide(double_divide(double_divide(A,inverse(inverse(C))),inverse(double_divide(D,E))),double_divide(inverse(D),inverse(double_divide(double_divide(inverse(double_divide(F,inverse(double_divide(V7,inverse(C))))),inverse(A)),double_divide(inverse(V7),inverse(double_divide(V9,double_divide(F,V9)))))))) = E,
inference(paramod,[status(thm)],[c_5492,c_6605]) ).
cnf(c_6607,plain,
double_divide(double_divide(double_divide(A,inverse(inverse(C))),inverse(double_divide(D,E))),double_divide(inverse(D),inverse(double_divide(double_divide(inverse(double_divide(F,inverse(double_divide(V7,inverse(C))))),inverse(A)),double_divide(inverse(V7),inverse(F)))))) = E,
inference(paramod,[status(thm)],[c_5492,c_6606]) ).
cnf(c_5520,plain,
double_divide(double_divide(A,B),A) = B,
inference(paramod,[status(thm)],[c_5519,c_6607]) ).
cnf(c_6608,plain,
double_divide(double_divide(A,inverse(C)),double_divide(D,double_divide(double_divide(inverse(E),inverse(A)),D))) = double_divide(C,E),
inference(paramod,[status(thm)],[c_5492,c_5388]) ).
cnf(c_5828,plain,
double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_5492,c_6608]) ).
cnf(c_6609,plain,
double_divide(double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),inverse(E)),double_divide(inverse(B),inverse(double_divide(F,double_divide(A,F))))) = double_divide(E,inverse(double_divide(V6,double_divide(C,V6)))),
inference(paramod,[status(thm)],[c_5492,c_5285]) ).
cnf(c_6610,plain,
double_divide(double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),inverse(E)),double_divide(inverse(B),inverse(A))) = double_divide(E,inverse(double_divide(V6,double_divide(C,V6)))),
inference(paramod,[status(thm)],[c_5492,c_6609]) ).
cnf(c_5852,plain,
double_divide(double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),inverse(D)),double_divide(inverse(B),inverse(A))) = double_divide(D,inverse(C)),
inference(paramod,[status(thm)],[c_5492,c_6610]) ).
cnf(c_6611,plain,
double_divide(double_divide(A,inverse(double_divide(inverse(double_divide(B,D)),E))),A) = double_divide(double_divide(D,E),inverse(B)),
inference(paramod,[status(thm)],[c_5492,c_4310]) ).
cnf(c_6196,plain,
inverse(double_divide(inverse(double_divide(A,B)),C)) = double_divide(double_divide(B,C),inverse(A)),
inference(paramod,[status(thm)],[c_5520,c_6611]) ).
cnf(c_6612,plain,
inverse(double_divide(inverse(double_divide(inverse(B),C)),double_divide(D,C))) = double_divide(double_divide(E,inverse(inverse(double_divide(D,B)))),E),
inference(paramod,[status(thm)],[c_5492,c_4160]) ).
cnf(c_6613,plain,
double_divide(double_divide(C,double_divide(D,C)),inverse(inverse(B))) = double_divide(double_divide(E,inverse(inverse(double_divide(D,B)))),E),
inference(paramod,[status(thm)],[c_6196,c_6612]) ).
cnf(c_6614,plain,
double_divide(D,inverse(inverse(B))) = double_divide(double_divide(E,inverse(inverse(double_divide(D,B)))),E),
inference(paramod,[status(thm)],[c_5492,c_6613]) ).
cnf(c_6615,plain,
double_divide(D,inverse(inverse(B))) = inverse(inverse(double_divide(D,B))),
inference(paramod,[status(thm)],[c_5520,c_6614]) ).
cnf(c_6217,plain,
inverse(inverse(double_divide(A,B))) = double_divide(A,inverse(inverse(B))),
inference(copy,[status(thm)],[c_6615]) ).
cnf(c_6616,plain,
inverse(double_divide(double_divide(A,inverse(inverse(inverse(A)))),B)) = double_divide(double_divide(double_divide(C,inverse(D)),inverse(E)),double_divide(inverse(double_divide(B,E)),inverse(double_divide(double_divide(inverse(double_divide(F,inverse(double_divide(V6,D)))),inverse(double_divide(V7,double_divide(C,V7)))),double_divide(inverse(V6),inverse(double_divide(V8,double_divide(F,V8)))))))),
inference(paramod,[status(thm)],[c_6217,c_3875]) ).
cnf(c_6617,plain,
inverse(double_divide(double_divide(A,inverse(inverse(inverse(A)))),B)) = double_divide(double_divide(double_divide(C,inverse(D)),inverse(E)),double_divide(inverse(double_divide(B,E)),inverse(double_divide(double_divide(inverse(double_divide(F,inverse(double_divide(V6,D)))),inverse(C)),double_divide(inverse(V6),inverse(double_divide(V8,double_divide(F,V8)))))))),
inference(paramod,[status(thm)],[c_5492,c_6616]) ).
cnf(c_6618,plain,
inverse(double_divide(double_divide(A,inverse(inverse(inverse(A)))),B)) = double_divide(double_divide(double_divide(C,inverse(D)),inverse(E)),double_divide(inverse(double_divide(B,E)),inverse(double_divide(double_divide(inverse(double_divide(F,inverse(double_divide(V6,D)))),inverse(C)),double_divide(inverse(V6),inverse(F)))))),
inference(paramod,[status(thm)],[c_5492,c_6617]) ).
cnf(c_6619,plain,
inverse(double_divide(double_divide(A,inverse(inverse(inverse(A)))),B)) = double_divide(double_divide(double_divide(C,inverse(D)),inverse(E)),double_divide(inverse(double_divide(B,E)),inverse(double_divide(C,inverse(D))))),
inference(paramod,[status(thm)],[c_5852,c_6618]) ).
cnf(c_6620,plain,
inverse(double_divide(double_divide(A,inverse(inverse(inverse(A)))),B)) = double_divide(E,double_divide(B,E)),
inference(paramod,[status(thm)],[c_5828,c_6619]) ).
cnf(c_6295,plain,
inverse(double_divide(double_divide(A,inverse(inverse(inverse(A)))),B)) = B,
inference(paramod,[status(thm)],[c_5492,c_6620]) ).
cnf(c_6621,plain,
double_divide(inverse(double_divide(A,double_divide(inverse(B),inverse(double_divide(inverse(inverse(double_divide(D,inverse(D)))),A))))),E) = double_divide(F,double_divide(double_divide(B,E),F)),
inference(paramod,[status(thm)],[c_5492,c_3531]) ).
cnf(c_6622,plain,
double_divide(inverse(double_divide(A,double_divide(inverse(B),inverse(double_divide(double_divide(D,inverse(inverse(inverse(D)))),A))))),E) = double_divide(F,double_divide(double_divide(B,E),F)),
inference(paramod,[status(thm)],[c_6217,c_6621]) ).
cnf(c_6623,plain,
double_divide(inverse(double_divide(A,double_divide(inverse(B),A))),E) = double_divide(F,double_divide(double_divide(B,E),F)),
inference(paramod,[status(thm)],[c_6295,c_6622]) ).
cnf(c_6624,plain,
double_divide(inverse(inverse(B)),E) = double_divide(F,double_divide(double_divide(B,E),F)),
inference(paramod,[status(thm)],[c_5492,c_6623]) ).
cnf(c_6401,plain,
double_divide(inverse(inverse(A)),B) = double_divide(A,B),
inference(paramod,[status(thm)],[c_5492,c_6624]) ).
cnf(c_6625,plain,
double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(inverse(C),D))),A)),inverse(double_divide(E,double_divide(inverse(inverse(double_divide(F,double_divide(C,F)))),E)))) = D,
inference(paramod,[status(thm)],[c_5492,c_3080]) ).
cnf(c_6626,plain,
double_divide(inverse(inverse(double_divide(inverse(C),D))),inverse(double_divide(E,double_divide(inverse(inverse(double_divide(F,double_divide(C,F)))),E)))) = D,
inference(paramod,[status(thm)],[c_5520,c_6625]) ).
cnf(c_6627,plain,
double_divide(double_divide(inverse(C),inverse(inverse(D))),inverse(double_divide(E,double_divide(inverse(inverse(double_divide(F,double_divide(C,F)))),E)))) = D,
inference(paramod,[status(thm)],[c_6217,c_6626]) ).
cnf(c_6628,plain,
double_divide(double_divide(inverse(C),inverse(inverse(D))),inverse(double_divide(E,double_divide(inverse(inverse(C)),E)))) = D,
inference(paramod,[status(thm)],[c_5492,c_6627]) ).
cnf(c_6629,plain,
double_divide(double_divide(inverse(C),inverse(inverse(D))),inverse(double_divide(E,double_divide(C,E)))) = D,
inference(paramod,[status(thm)],[c_6401,c_6628]) ).
cnf(c_6630,plain,
double_divide(double_divide(inverse(C),inverse(inverse(D))),inverse(C)) = D,
inference(paramod,[status(thm)],[c_5492,c_6629]) ).
cnf(c_6460,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_5520,c_6630]) ).
cnf(c_6631,plain,
inverse(double_divide(double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,C)),inverse(c3)))),double_divide(inverse(inverse(double_divide(b3,a3))),inverse(C)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(paramod,[status(thm)],[c_5492,c_3033]) ).
cnf(c_6632,plain,
inverse(double_divide(double_divide(inverse(A),double_divide(double_divide(C,inverse(c3)),inverse(A))),double_divide(inverse(inverse(double_divide(b3,a3))),inverse(C)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(paramod,[status(thm)],[c_6196,c_6631]) ).
cnf(c_6633,plain,
inverse(double_divide(double_divide(C,inverse(c3)),double_divide(inverse(inverse(double_divide(b3,a3))),inverse(C)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(paramod,[status(thm)],[c_5492,c_6632]) ).
cnf(c_6634,plain,
inverse(double_divide(double_divide(C,inverse(c3)),double_divide(double_divide(b3,a3),inverse(C)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(paramod,[status(thm)],[c_6460,c_6633]) ).
cnf(c_6470,plain,
inverse(double_divide(double_divide(A,inverse(c3)),double_divide(double_divide(b3,a3),inverse(A)))) != double_divide(double_divide(b3,a3),inverse(c3)),
inference(paramod,[status(thm)],[c_6196,c_6634]) ).
cnf(c_6635,plain,
double_divide(double_divide(double_divide(A,B),inverse(double_divide(double_divide(C,inverse(C)),D))),double_divide(double_divide(E,inverse(A)),double_divide(inverse(B),inverse(double_divide(F,double_divide(E,F)))))) = D,
inference(paramod,[status(thm)],[c_6460,c_2349]) ).
cnf(c_6636,plain,
double_divide(double_divide(double_divide(A,B),inverse(double_divide(double_divide(C,inverse(C)),D))),double_divide(double_divide(E,inverse(A)),double_divide(inverse(B),inverse(E)))) = D,
inference(paramod,[status(thm)],[c_5492,c_6635]) ).
cnf(c_6637,plain,
double_divide(double_divide(double_divide(A,B),inverse(double_divide(double_divide(C,inverse(C)),D))),double_divide(A,B)) = D,
inference(paramod,[status(thm)],[c_5828,c_6636]) ).
cnf(c_6576,plain,
inverse(double_divide(double_divide(A,inverse(A)),B)) = B,
inference(paramod,[status(thm)],[c_5520,c_6637]) ).
cnf(c_6577,plain,
$false,
inference(resolve,[status(thm)],[c_6576,c_6470]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP504-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 15:02:02 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 2689037 was started by sandbox on n016,
% 0.09/0.35 % Fri Sep 25 15:02:02 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 20.89/3.09
% 20.89/3.09 % SZS status Unsatisfiable for theBenchmark
% 20.89/3.09
% 20.89/3.09 % Proof 1 at 2.37 (+ 0.32) seconds.
% 20.89/3.09 % Length of proof is 58.
% 20.89/3.09 % Level of proof is 23.
% 20.89/3.09 % Maximum clause weight is 48.000.
% 20.89/3.09 % Given clauses 65.
% 20.89/3.09
% 20.89/3.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------