%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP104-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 07:27:20 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 3
% Syntax : Number of formulae : 106 ( 83 unt; 0 def)
% Number of atoms : 167 ( 166 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 163 ( 102 ~; 61 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 170 ( 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,axiom,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('theBenchmark.p',prove_these_axioms) ).
cnf(c_3,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(clausify,[status(thm)],[prove_these_axioms]) ).
cnf(c_159,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| inverse(double_divide(a1,inverse(a1))) != multiply(inverse(b1),b1) ),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_160,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_159]) ).
cnf(c_161,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(double_divide(b2,inverse(b2))),a2) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_160]) ).
cnf(c_162,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_161]) ).
cnf(c_163,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(inverse(double_divide(b3,a3)),c3) != multiply(a3,multiply(b3,c3))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_162]) ).
cnf(c_164,plain,
( multiply(a4,b4) != multiply(b4,a4)
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,multiply(b3,c3))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_163]) ).
cnf(c_165,plain,
( multiply(a4,b4) != multiply(b4,a4)
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,inverse(double_divide(c3,b3)))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_164]) ).
cnf(c_166,plain,
( multiply(a4,b4) != multiply(b4,a4)
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_165]) ).
cnf(c_167,plain,
( inverse(double_divide(b4,a4)) != multiply(b4,a4)
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_166]) ).
cnf(c_168,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(paramod,[status(thm)],[c_2,c_167]) ).
cnf(c_169,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))) ),
inference(copy,[status(thm)],[c_168]) ).
cnf(c_4,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))) ),
inference(copy,[status(thm)],[c_169]) ).
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_170,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_170]) ).
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_171,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_171]) ).
cnf(c_172,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_173,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_172]) ).
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_173]) ).
cnf(c_174,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_175,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_174]) ).
cnf(c_19,plain,
double_divide(A,inverse(double_divide(inverse(B),inverse(A)))) = B,
inference(paramod,[status(thm)],[c_16,c_175]) ).
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_26,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,inverse(A)))) = double_divide(C,inverse(B)),
inference(paramod,[status(thm)],[c_10,c_20]) ).
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_176,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_176]) ).
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_177,plain,
multiply(inverse(A),inverse(B)) = inverse(double_divide(inverse(A),inverse(B))),
inference(paramod,[status(thm)],[c_36,c_2]) ).
cnf(c_42,plain,
inverse(double_divide(inverse(A),inverse(B))) = inverse(double_divide(inverse(B),inverse(A))),
inference(paramod,[status(thm)],[c_2,c_177]) ).
cnf(c_45,plain,
double_divide(inverse(double_divide(A,B)),inverse(C)) = double_divide(A,inverse(double_divide(inverse(C),B))),
inference(paramod,[status(thm)],[c_36,c_20]) ).
cnf(c_178,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(C,inverse(A))),inverse(B)))) = double_divide(C,inverse(B)),
inference(paramod,[status(thm)],[c_45,c_26]) ).
cnf(c_47,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(C),inverse(A)))))) = double_divide(B,inverse(C)),
inference(paramod,[status(thm)],[c_45,c_178]) ).
cnf(c_179,plain,
double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(inverse(C),inverse(D))))),B) = double_divide(inverse(double_divide(inverse(D),inverse(C))),inverse(A)),
inference(paramod,[status(thm)],[c_42,c_13]) ).
cnf(c_180,plain,
double_divide(inverse(double_divide(inverse(C),inverse(D))),inverse(A)) = double_divide(inverse(double_divide(inverse(D),inverse(C))),inverse(A)),
inference(paramod,[status(thm)],[c_13,c_179]) ).
cnf(c_181,plain,
double_divide(inverse(C),inverse(double_divide(inverse(A),inverse(D)))) = double_divide(inverse(double_divide(inverse(D),inverse(C))),inverse(A)),
inference(paramod,[status(thm)],[c_45,c_180]) ).
cnf(c_60,plain,
double_divide(inverse(A),inverse(double_divide(inverse(B),inverse(C)))) = double_divide(inverse(C),inverse(double_divide(inverse(B),inverse(A)))),
inference(paramod,[status(thm)],[c_45,c_181]) ).
cnf(c_64,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_41,c_19]) ).
cnf(c_182,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_182]) ).
cnf(c_183,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,inverse(A)))) = double_divide(inverse(B),inverse(inverse(C))),
inference(paramod,[status(thm)],[c_41,c_13]) ).
cnf(c_184,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(C,inverse(A))),inverse(B)))) = double_divide(inverse(B),inverse(inverse(C))),
inference(paramod,[status(thm)],[c_45,c_183]) ).
cnf(c_185,plain,
double_divide(A,inverse(double_divide(C,inverse(double_divide(inverse(B),inverse(A)))))) = double_divide(inverse(B),inverse(inverse(C))),
inference(paramod,[status(thm)],[c_45,c_184]) ).
cnf(c_186,plain,
double_divide(C,inverse(B)) = double_divide(inverse(B),inverse(inverse(C))),
inference(paramod,[status(thm)],[c_47,c_185]) ).
cnf(c_187,plain,
double_divide(C,inverse(B)) = double_divide(inverse(B),C),
inference(paramod,[status(thm)],[c_64,c_186]) ).
cnf(c_69,plain,
double_divide(inverse(A),B) = double_divide(B,inverse(A)),
inference(copy,[status(thm)],[c_187]) ).
cnf(c_188,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(a3,inverse(double_divide(c3,b3)))) != inverse(double_divide(c3,inverse(double_divide(b3,a3))))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))) ),
inference(paramod,[status(thm)],[c_69,c_4]) ).
cnf(c_76,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(a3,inverse(double_divide(c3,b3))))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))) ),
inference(copy,[status(thm)],[c_188]) ).
cnf(c_189,plain,
multiply(inverse(A),A) = inverse(double_divide(B,inverse(B))),
inference(paramod,[status(thm)],[c_67,c_2]) ).
cnf(c_77,plain,
inverse(double_divide(A,inverse(A))) = inverse(double_divide(B,inverse(B))),
inference(paramod,[status(thm)],[c_2,c_189]) ).
cnf(c_190,plain,
double_divide(inverse(A),inverse(double_divide(B,inverse(inverse(A))))) = double_divide(B,inverse(double_divide(C,inverse(C)))),
inference(paramod,[status(thm)],[c_67,c_20]) ).
cnf(c_78,plain,
double_divide(inverse(A),inverse(double_divide(B,A))) = double_divide(B,inverse(double_divide(C,inverse(C)))),
inference(paramod,[status(thm)],[c_64,c_190]) ).
cnf(c_80,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(a3,inverse(double_divide(c3,b3))))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ),
inference(resolve,[status(thm)],[c_77,c_76]) ).
cnf(c_89,plain,
double_divide(A,inverse(double_divide(B,inverse(B)))) = inverse(A),
inference(paramod,[status(thm)],[c_64,c_29]) ).
cnf(c_90,plain,
double_divide(inverse(A),inverse(double_divide(A,B))) = inverse(B),
inference(paramod,[status(thm)],[c_64,c_41]) ).
cnf(c_191,plain,
double_divide(A,B) = double_divide(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_64,c_69]) ).
cnf(c_91,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_64,c_191]) ).
cnf(c_192,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(a3,inverse(double_divide(c3,b3))))
| inverse(inverse(a2)) != a2 ),
inference(paramod,[status(thm)],[c_89,c_80]) ).
cnf(c_193,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(a3,inverse(double_divide(c3,b3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_64,c_192]) ).
cnf(c_194,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(a3,inverse(double_divide(c3,b3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_91,c_193]) ).
cnf(c_195,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_91,c_194]) ).
cnf(c_196,plain,
( inverse(double_divide(a4,b4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_91,c_195]) ).
cnf(c_197,plain,
( inverse(double_divide(a4,b4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))) ),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_92,plain,
inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(copy,[status(thm)],[c_197]) ).
cnf(c_93,plain,
double_divide(inverse(A),inverse(double_divide(B,A))) = inverse(B),
inference(paramod,[status(thm)],[c_89,c_78]) ).
cnf(c_198,plain,
double_divide(inverse(inverse(double_divide(A,B))),inverse(inverse(B))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_90,c_93]) ).
cnf(c_199,plain,
double_divide(double_divide(A,B),inverse(inverse(B))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_64,c_198]) ).
cnf(c_200,plain,
double_divide(double_divide(A,B),B) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_64,c_199]) ).
cnf(c_201,plain,
double_divide(B,double_divide(A,B)) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_91,c_200]) ).
cnf(c_109,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_64,c_201]) ).
cnf(c_202,plain,
double_divide(inverse(A),inverse(B)) = inverse(double_divide(B,A)),
inference(paramod,[status(thm)],[c_109,c_90]) ).
cnf(c_112,plain,
inverse(double_divide(A,B)) = double_divide(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_202]) ).
cnf(c_203,plain,
inverse(double_divide(c3,double_divide(inverse(b3),inverse(a3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_112,c_92]) ).
cnf(c_204,plain,
inverse(double_divide(c3,double_divide(inverse(a3),inverse(b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_91,c_203]) ).
cnf(c_205,plain,
double_divide(inverse(double_divide(inverse(a3),inverse(b3))),inverse(c3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_112,c_204]) ).
cnf(c_206,plain,
double_divide(double_divide(inverse(inverse(b3)),inverse(inverse(a3))),inverse(c3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_112,c_205]) ).
cnf(c_207,plain,
double_divide(double_divide(b3,inverse(inverse(a3))),inverse(c3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_64,c_206]) ).
cnf(c_208,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_64,c_207]) ).
cnf(c_209,plain,
double_divide(double_divide(a3,b3),inverse(c3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_91,c_208]) ).
cnf(c_210,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_91,c_209]) ).
cnf(c_211,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != inverse(double_divide(a3,double_divide(inverse(c3),inverse(b3)))),
inference(paramod,[status(thm)],[c_112,c_210]) ).
cnf(c_212,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != inverse(double_divide(a3,double_divide(inverse(b3),inverse(c3)))),
inference(paramod,[status(thm)],[c_91,c_211]) ).
cnf(c_213,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(double_divide(inverse(b3),inverse(c3))),inverse(a3)),
inference(paramod,[status(thm)],[c_112,c_212]) ).
cnf(c_214,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(double_divide(inverse(inverse(c3)),inverse(inverse(b3))),inverse(a3)),
inference(paramod,[status(thm)],[c_112,c_213]) ).
cnf(c_215,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(double_divide(c3,inverse(inverse(b3))),inverse(a3)),
inference(paramod,[status(thm)],[c_64,c_214]) ).
cnf(c_216,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(double_divide(c3,b3),inverse(a3)),
inference(paramod,[status(thm)],[c_64,c_215]) ).
cnf(c_217,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(double_divide(b3,c3),inverse(a3)),
inference(paramod,[status(thm)],[c_91,c_216]) ).
cnf(c_122,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_91,c_217]) ).
cnf(c_218,plain,
double_divide(inverse(A),double_divide(inverse(inverse(C)),inverse(inverse(B)))) = double_divide(inverse(C),inverse(double_divide(inverse(B),inverse(A)))),
inference(paramod,[status(thm)],[c_112,c_60]) ).
cnf(c_219,plain,
double_divide(inverse(A),double_divide(C,inverse(inverse(B)))) = double_divide(inverse(C),inverse(double_divide(inverse(B),inverse(A)))),
inference(paramod,[status(thm)],[c_64,c_218]) ).
cnf(c_220,plain,
double_divide(inverse(A),double_divide(C,B)) = double_divide(inverse(C),inverse(double_divide(inverse(B),inverse(A)))),
inference(paramod,[status(thm)],[c_64,c_219]) ).
cnf(c_221,plain,
double_divide(inverse(A),double_divide(C,B)) = double_divide(inverse(C),double_divide(inverse(inverse(A)),inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_112,c_220]) ).
cnf(c_222,plain,
double_divide(inverse(A),double_divide(C,B)) = double_divide(inverse(C),double_divide(A,inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_64,c_221]) ).
cnf(c_135,plain,
double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(B),double_divide(A,C)),
inference(paramod,[status(thm)],[c_64,c_222]) ).
cnf(c_157,plain,
double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(C),double_divide(A,B)),
inference(paramod,[status(thm)],[c_91,c_135]) ).
cnf(c_223,plain,
double_divide(inverse(a3),double_divide(b3,c3)) != double_divide(inverse(c3),double_divide(a3,b3)),
inference(copy,[status(thm)],[c_122]) ).
cnf(c_158,plain,
$false,
inference(resolve,[status(thm)],[c_157,c_223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP104-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.41 % Computer : n005.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Fri Sep 25 14:22:02 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.41 % Process 3685178 was started by sandbox2 on n005,
% 0.17/0.41 % Fri Sep 25 14:22:02 2026
% 0.17/0.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.42
% 0.17/0.42 % From the command line: assign(max_seconds, 300).
% 0.17/0.49
% 0.17/0.49 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 0.17/0.49
% 0.17/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.49
% 0.17/0.49 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.17/0.49 % Length of proof is 38.
% 0.17/0.49 % Level of proof is 17.
% 0.17/0.49 % Maximum clause weight is 88.000.
% 0.17/0.49 % Given clauses 28.
% 0.17/0.49
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------