%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP604-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 3
% Syntax : Number of formulae : 111 ( 111 unt; 0 def)
% Number of atoms : 111 ( 110 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 10 ( 3 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 : 394 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : inverse(double_divide(inverse(double_divide(VAR_0,inverse(double_divide(VAR_1,double_divide(VAR_0,VAR_2))))),VAR_2)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(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_4,axiom,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c_3,plain,
multiply(a,b) != multiply(b,a),
inference(clausify,[status(thm)],[prove_these_axioms_4]) ).
cnf(c_319,plain,
inverse(double_divide(b,a)) != multiply(b,a),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4,plain,
inverse(double_divide(b,a)) != inverse(double_divide(a,b)),
inference(paramod,[status(thm)],[c_2,c_319]) ).
cnf(c_320,plain,
inverse(double_divide(inverse(double_divide(A,B)),C)) = inverse(double_divide(D,inverse(double_divide(B,double_divide(D,double_divide(A,C)))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(A,double_divide(C,D)))))) = inverse(double_divide(inverse(double_divide(C,B)),D)),
inference(copy,[status(thm)],[c_320]) ).
cnf(c_6,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_7,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(C,inverse(double_divide(A,double_divide(C,D))))),B))) = D,
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_11,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_6,c_6]) ).
cnf(c_14,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(inverse(double_divide(D,C)),double_divide(D,A)),
inference(paramod,[status(thm)],[c_11,c_6]) ).
cnf(c_321,plain,
inverse(double_divide(A,double_divide(B,C))) = double_divide(inverse(double_divide(D,B)),double_divide(D,inverse(double_divide(E,inverse(double_divide(A,double_divide(E,C))))))),
inference(paramod,[status(thm)],[c_1,c_14]) ).
cnf(c_21,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(C,inverse(double_divide(D,double_divide(C,E))))))) = inverse(double_divide(D,double_divide(B,E))),
inference(copy,[status(thm)],[c_321]) ).
cnf(c_31,plain,
inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(A,B)),double_divide(A,C)),D)),double_divide(inverse(double_divide(C,E)),D))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_14,c_6]) ).
cnf(c_32,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_14,c_6]) ).
cnf(c_42,plain,
inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),double_divide(A,C))))) = B,
inference(paramod,[status(thm)],[c_14,c_11]) ).
cnf(c_55,plain,
inverse(double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,B)))) = inverse(double_divide(A,C)),
inference(paramod,[status(thm)],[c_32,c_1]) ).
cnf(c_60,plain,
inverse(double_divide(inverse(double_divide(inverse(A),B)),double_divide(inverse(double_divide(C,D)),B))) = double_divide(C,inverse(double_divide(D,A))),
inference(paramod,[status(thm)],[c_32,c_6]) ).
cnf(c_61,plain,
inverse(double_divide(inverse(A),double_divide(B,double_divide(B,inverse(double_divide(C,A)))))) = C,
inference(paramod,[status(thm)],[c_32,c_6]) ).
cnf(c_66,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(inverse(double_divide(B,C)),A)),D))) = double_divide(B,inverse(double_divide(C,D))),
inference(paramod,[status(thm)],[c_32,c_11]) ).
cnf(c_68,plain,
inverse(double_divide(inverse(A),double_divide(B,double_divide(C,inverse(double_divide(D,A)))))) = double_divide(inverse(double_divide(E,B)),double_divide(E,inverse(double_divide(C,D)))),
inference(paramod,[status(thm)],[c_32,c_14]) ).
cnf(c_71,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),D)),double_divide(E,D))) = double_divide(inverse(double_divide(inverse(double_divide(A,B)),E)),C),
inference(paramod,[status(thm)],[c_32,c_14]) ).
cnf(c_322,plain,
inverse(double_divide(A,inverse(double_divide(B,C)))) = inverse(double_divide(inverse(double_divide(D,inverse(double_divide(A,double_divide(D,inverse(C)))))),B)),
inference(paramod,[status(thm)],[c_1,c_55]) ).
cnf(c_79,plain,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,inverse(C)))))),D)) = inverse(double_divide(B,inverse(double_divide(D,C)))),
inference(copy,[status(thm)],[c_322]) ).
cnf(c_323,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(inverse(double_divide(A,inverse(D))),C))) = inverse(double_divide(B,D)),
inference(paramod,[status(thm)],[c_55,c_6]) ).
cnf(c_84,plain,
double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C)))) = inverse(double_divide(C,B)),
inference(paramod,[status(thm)],[c_60,c_323]) ).
cnf(c_86,plain,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),D)) = inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,D)),C)))),
inference(paramod,[status(thm)],[c_6,c_55]) ).
cnf(c_92,plain,
double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(A,inverse(C))),inverse(double_divide(inverse(double_divide(B,C)),D)))) = D,
inference(paramod,[status(thm)],[c_55,c_32]) ).
cnf(c_97,plain,
inverse(inverse(double_divide(A,double_divide(B,A)))) = B,
inference(paramod,[status(thm)],[c_84,c_42]) ).
cnf(c_324,plain,
inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,D)),double_divide(A,inverse(C)))))) = inverse(double_divide(B,inverse(double_divide(D,C)))),
inference(paramod,[status(thm)],[c_86,c_79]) ).
cnf(c_98,plain,
inverse(inverse(double_divide(inverse(A),double_divide(B,C)))) = inverse(double_divide(B,inverse(double_divide(C,A)))),
inference(paramod,[status(thm)],[c_84,c_324]) ).
cnf(c_118,plain,
inverse(double_divide(inverse(double_divide(inverse(A),double_divide(B,C))),double_divide(inverse(inverse(double_divide(C,A))),double_divide(B,D)))) = D,
inference(paramod,[status(thm)],[c_84,c_11]) ).
cnf(c_119,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),inverse(double_divide(C,D))))) = inverse(double_divide(inverse(D),double_divide(B,C))),
inference(paramod,[status(thm)],[c_84,c_11]) ).
cnf(c_325,plain,
double_divide(inverse(double_divide(A,inverse(B))),C) = inverse(double_divide(double_divide(A,C),B)),
inference(paramod,[status(thm)],[c_11,c_84]) ).
cnf(c_121,plain,
inverse(double_divide(double_divide(A,B),C)) = double_divide(inverse(double_divide(A,inverse(C))),B),
inference(copy,[status(thm)],[c_325]) ).
cnf(c_326,plain,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(C,D))))),inverse(double_divide(D,B)))) = double_divide(inverse(double_divide(E,C)),double_divide(E,A)),
inference(paramod,[status(thm)],[c_84,c_14]) ).
cnf(c_327,plain,
inverse(double_divide(A,inverse(double_divide(inverse(double_divide(inverse(B),inverse(double_divide(D,B)))),double_divide(C,D))))) = double_divide(inverse(double_divide(E,C)),double_divide(E,A)),
inference(paramod,[status(thm)],[c_86,c_326]) ).
cnf(c_123,plain,
inverse(double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(inverse(double_divide(C,double_divide(D,C))),B)))))) = double_divide(inverse(double_divide(E,D)),double_divide(E,A)),
inference(paramod,[status(thm)],[c_86,c_327]) ).
cnf(c_125,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(A),double_divide(B,C))),D)),double_divide(E,D))) = double_divide(inverse(double_divide(B,E)),inverse(double_divide(C,A))),
inference(paramod,[status(thm)],[c_84,c_14]) ).
cnf(c_328,plain,
double_divide(A,inverse(inverse(double_divide(inverse(double_divide(B,C)),double_divide(D,C))))) = inverse(double_divide(B,double_divide(A,D))),
inference(paramod,[status(thm)],[c_14,c_84]) ).
cnf(c_129,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(C,double_divide(D,C)))))) = inverse(double_divide(D,double_divide(A,B))),
inference(paramod,[status(thm)],[c_98,c_328]) ).
cnf(c_132,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,B))) = double_divide(A,C),
inference(paramod,[status(thm)],[c_84,c_32]) ).
cnf(c_329,plain,
double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(C),D))) = inverse(double_divide(double_divide(A,inverse(double_divide(B,D))),C)),
inference(paramod,[status(thm)],[c_32,c_84]) ).
cnf(c_330,plain,
double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(C),D))) = double_divide(inverse(double_divide(A,inverse(C))),inverse(double_divide(B,D))),
inference(paramod,[status(thm)],[c_121,c_329]) ).
cnf(c_133,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,D))) = double_divide(inverse(double_divide(A,C)),inverse(double_divide(inverse(B),D))),
inference(copy,[status(thm)],[c_330]) ).
cnf(c_331,plain,
double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(C,D))))) = inverse(double_divide(inverse(double_divide(inverse(D),double_divide(A,C))),B)),
inference(paramod,[status(thm)],[c_84,c_84]) ).
cnf(c_137,plain,
inverse(double_divide(inverse(double_divide(inverse(A),double_divide(B,C))),D)) = double_divide(B,inverse(double_divide(inverse(D),inverse(double_divide(C,A))))),
inference(copy,[status(thm)],[c_331]) ).
cnf(c_332,plain,
inverse(double_divide(double_divide(inverse(double_divide(A,inverse(D))),inverse(double_divide(B,C))),double_divide(E,D))) = double_divide(inverse(double_divide(inverse(double_divide(A,B)),E)),C),
inference(paramod,[status(thm)],[c_121,c_71]) ).
cnf(c_333,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,inverse(D))),inverse(double_divide(E,D)))),inverse(double_divide(B,C))) = double_divide(inverse(double_divide(inverse(double_divide(A,B)),E)),C),
inference(paramod,[status(thm)],[c_121,c_332]) ).
cnf(c_334,plain,
double_divide(inverse(double_divide(A,E)),inverse(double_divide(B,C))) = double_divide(inverse(double_divide(inverse(double_divide(A,B)),E)),C),
inference(paramod,[status(thm)],[c_132,c_333]) ).
cnf(c_143,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),D) = double_divide(inverse(double_divide(A,C)),inverse(double_divide(B,D))),
inference(copy,[status(thm)],[c_334]) ).
cnf(c_335,plain,
inverse(double_divide(double_divide(inverse(double_divide(inverse(double_divide(A,B)),inverse(D))),double_divide(A,C)),double_divide(inverse(double_divide(C,E)),D))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_121,c_31]) ).
cnf(c_336,plain,
inverse(double_divide(double_divide(inverse(double_divide(A,inverse(D))),inverse(double_divide(B,double_divide(A,C)))),double_divide(inverse(double_divide(C,E)),D))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_143,c_335]) ).
cnf(c_337,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,inverse(D))),inverse(double_divide(inverse(double_divide(C,E)),D)))),inverse(double_divide(B,double_divide(A,C)))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_121,c_336]) ).
cnf(c_149,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),inverse(double_divide(D,double_divide(A,B)))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_132,c_337]) ).
cnf(c_338,plain,
inverse(double_divide(double_divide(B,inverse(double_divide(inverse(D),inverse(double_divide(C,A))))),double_divide(E,D))) = double_divide(inverse(double_divide(B,E)),inverse(double_divide(C,A))),
inference(paramod,[status(thm)],[c_137,c_125]) ).
cnf(c_157,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),inverse(double_divide(inverse(C),inverse(double_divide(D,E))))) = double_divide(inverse(double_divide(A,B)),inverse(double_divide(D,E))),
inference(paramod,[status(thm)],[c_121,c_338]) ).
cnf(c_339,plain,
double_divide(B,inverse(double_divide(inverse(double_divide(inverse(inverse(double_divide(C,A))),double_divide(B,D))),inverse(double_divide(C,A))))) = D,
inference(paramod,[status(thm)],[c_137,c_118]) ).
cnf(c_158,plain,
double_divide(A,double_divide(A,inverse(double_divide(inverse(inverse(double_divide(B,C))),inverse(double_divide(D,inverse(double_divide(B,C)))))))) = D,
inference(paramod,[status(thm)],[c_137,c_339]) ).
cnf(c_340,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),inverse(double_divide(C,D))))) = double_divide(B,inverse(double_divide(C,D))),
inference(paramod,[status(thm)],[c_143,c_66]) ).
cnf(c_164,plain,
inverse(double_divide(inverse(A),double_divide(B,C))) = double_divide(B,inverse(double_divide(C,A))),
inference(paramod,[status(thm)],[c_119,c_340]) ).
cnf(c_341,plain,
inverse(double_divide(double_divide(B,inverse(double_divide(C,A))),D)) = double_divide(B,inverse(double_divide(inverse(D),inverse(double_divide(C,A))))),
inference(paramod,[status(thm)],[c_164,c_137]) ).
cnf(c_176,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,D))) = double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(C,D))))),
inference(paramod,[status(thm)],[c_121,c_341]) ).
cnf(c_191,plain,
double_divide(A,double_divide(A,inverse(double_divide(B,C)))) = inverse(double_divide(B,C)),
inference(paramod,[status(thm)],[c_164,c_84]) ).
cnf(c_342,plain,
double_divide(B,inverse(double_divide(double_divide(C,inverse(double_divide(D,A))),A))) = double_divide(inverse(double_divide(E,B)),double_divide(E,inverse(double_divide(C,D)))),
inference(paramod,[status(thm)],[c_164,c_68]) ).
cnf(c_343,plain,
double_divide(B,double_divide(inverse(double_divide(C,inverse(A))),inverse(double_divide(D,A)))) = double_divide(inverse(double_divide(E,B)),double_divide(E,inverse(double_divide(C,D)))),
inference(paramod,[status(thm)],[c_121,c_342]) ).
cnf(c_344,plain,
double_divide(B,double_divide(C,D)) = double_divide(inverse(double_divide(E,B)),double_divide(E,inverse(double_divide(C,D)))),
inference(paramod,[status(thm)],[c_132,c_343]) ).
cnf(c_193,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(C,D)))) = double_divide(B,double_divide(C,D)),
inference(copy,[status(thm)],[c_344]) ).
cnf(c_194,plain,
inverse(double_divide(inverse(A),inverse(double_divide(B,A)))) = B,
inference(paramod,[status(thm)],[c_191,c_61]) ).
cnf(c_345,plain,
double_divide(C,inverse(double_divide(B,double_divide(A,B)))) = double_divide(inverse(double_divide(D,C)),double_divide(D,A)),
inference(paramod,[status(thm)],[c_164,c_14]) ).
cnf(c_202,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,C)) = double_divide(B,inverse(double_divide(D,double_divide(C,D)))),
inference(copy,[status(thm)],[c_345]) ).
cnf(c_346,plain,
double_divide(inverse(double_divide(C,inverse(double_divide(A,double_divide(C,D))))),inverse(double_divide(B,double_divide(A,B)))) = D,
inference(paramod,[status(thm)],[c_164,c_7]) ).
cnf(c_347,plain,
double_divide(C,inverse(double_divide(inverse(double_divide(A,double_divide(C,D))),inverse(double_divide(B,double_divide(A,B)))))) = D,
inference(paramod,[status(thm)],[c_176,c_346]) ).
cnf(c_203,plain,
inverse(double_divide(A,double_divide(B,inverse(double_divide(A,double_divide(B,C)))))) = C,
inference(paramod,[status(thm)],[c_129,c_347]) ).
cnf(c_205,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),inverse(double_divide(inverse(C),inverse(double_divide(D,E))))))) = double_divide(inverse(double_divide(A,B)),inverse(double_divide(D,E))),
inference(paramod,[status(thm)],[c_176,c_157]) ).
cnf(c_207,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),inverse(double_divide(D,double_divide(A,B)))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_176,c_149]) ).
cnf(c_348,plain,
double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(C,D))))) = double_divide(inverse(double_divide(A,C)),inverse(double_divide(inverse(B),D))),
inference(paramod,[status(thm)],[c_176,c_133]) ).
cnf(c_211,plain,
double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(C),D))) = double_divide(A,inverse(double_divide(inverse(C),inverse(double_divide(B,D))))),
inference(copy,[status(thm)],[c_348]) ).
cnf(c_349,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),inverse(double_divide(inverse(C),D)))))) = D,
inference(paramod,[status(thm)],[c_211,c_92]) ).
cnf(c_350,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(C),inverse(double_divide(C,D)))))))) = D,
inference(paramod,[status(thm)],[c_211,c_349]) ).
cnf(c_213,plain,
inverse(double_divide(inverse(A),inverse(double_divide(A,B)))) = B,
inference(paramod,[status(thm)],[c_32,c_350]) ).
cnf(c_216,plain,
double_divide(A,double_divide(B,inverse(double_divide(C,double_divide(B,D))))) = inverse(double_divide(C,double_divide(A,D))),
inference(paramod,[status(thm)],[c_193,c_21]) ).
cnf(c_218,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_194,c_158]) ).
cnf(c_223,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(C,B))))) = double_divide(inverse(double_divide(D,C)),double_divide(D,A)),
inference(paramod,[status(thm)],[c_194,c_123]) ).
cnf(c_351,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(C),inverse(double_divide(C,inverse(double_divide(D,E))))))))) = double_divide(inverse(double_divide(A,B)),inverse(double_divide(D,E))),
inference(paramod,[status(thm)],[c_211,c_205]) ).
cnf(c_352,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(D,E))))) = double_divide(inverse(double_divide(A,B)),inverse(double_divide(D,E))),
inference(paramod,[status(thm)],[c_213,c_351]) ).
cnf(c_227,plain,
double_divide(inverse(double_divide(A,B)),inverse(double_divide(C,D))) = double_divide(A,inverse(double_divide(B,inverse(double_divide(C,D))))),
inference(copy,[status(thm)],[c_352]) ).
cnf(c_353,plain,
inverse(inverse(double_divide(A,double_divide(A,C)))) = C,
inference(paramod,[status(thm)],[c_216,c_203]) ).
cnf(c_229,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_218,c_353]) ).
cnf(c_246,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(C,inverse(double_divide(D,double_divide(A,B)))))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_227,c_207]) ).
cnf(c_267,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_229,c_97]) ).
cnf(c_354,plain,
inverse(double_divide(A,inverse(C))) = double_divide(inverse(double_divide(D,C)),double_divide(D,A)),
inference(paramod,[status(thm)],[c_267,c_223]) ).
cnf(c_279,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,C)) = inverse(double_divide(C,inverse(B))),
inference(copy,[status(thm)],[c_354]) ).
cnf(c_355,plain,
inverse(double_divide(C,inverse(B))) = double_divide(B,inverse(double_divide(D,double_divide(C,D)))),
inference(paramod,[status(thm)],[c_279,c_202]) ).
cnf(c_280,plain,
inverse(double_divide(A,inverse(B))) = double_divide(B,inverse(A)),
inference(paramod,[status(thm)],[c_267,c_355]) ).
cnf(c_356,plain,
double_divide(A,inverse(double_divide(B,inverse(D)))) = inverse(double_divide(D,double_divide(A,B))),
inference(paramod,[status(thm)],[c_267,c_129]) ).
cnf(c_357,plain,
double_divide(A,double_divide(D,inverse(B))) = inverse(double_divide(D,double_divide(A,B))),
inference(paramod,[status(thm)],[c_280,c_356]) ).
cnf(c_285,plain,
inverse(double_divide(A,double_divide(B,C))) = double_divide(B,double_divide(A,inverse(C))),
inference(copy,[status(thm)],[c_357]) ).
cnf(c_358,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(C,double_divide(A,double_divide(D,inverse(B)))))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_285,c_246]) ).
cnf(c_359,plain,
double_divide(A,inverse(double_divide(B,double_divide(A,double_divide(C,inverse(double_divide(D,inverse(B)))))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_285,c_358]) ).
cnf(c_360,plain,
double_divide(A,inverse(double_divide(B,double_divide(A,double_divide(C,double_divide(B,inverse(D))))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_280,c_359]) ).
cnf(c_361,plain,
double_divide(A,double_divide(A,double_divide(B,inverse(double_divide(C,double_divide(B,inverse(D))))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_285,c_360]) ).
cnf(c_362,plain,
double_divide(A,double_divide(A,double_divide(B,double_divide(B,double_divide(C,inverse(inverse(D))))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_285,c_361]) ).
cnf(c_363,plain,
double_divide(A,double_divide(A,double_divide(B,double_divide(B,double_divide(C,D))))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_229,c_362]) ).
cnf(c_364,plain,
double_divide(A,double_divide(A,double_divide(C,D))) = double_divide(D,C),
inference(paramod,[status(thm)],[c_218,c_363]) ).
cnf(c_291,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_218,c_364]) ).
cnf(c_365,plain,
inverse(double_divide(a,b)) != inverse(double_divide(a,b)),
inference(paramod,[status(thm)],[c_291,c_4]) ).
cnf(c_318,plain,
$false,
inference(copy,[status(thm)],[c_365]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP604-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 15:01:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3488200 was started by sandbox on n004,
% 0.10/0.37 % Fri Sep 25 15:01:51 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.44
% 0.10/0.44 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.10/0.44
% 0.10/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.44
% 0.10/0.44 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.10/0.44 % Length of proof is 61.
% 0.10/0.44 % Level of proof is 20.
% 0.10/0.44 % Maximum clause weight is 85.000.
% 0.10/0.44 % Given clauses 10.
% 0.10/0.44
% 0.10/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------