%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP601-1 : 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 : n019.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 07:30:27 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 3
% Syntax : Number of formulae : 85 ( 85 unt; 0 def)
% Number of atoms : 85 ( 84 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 10 ( 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 : 275 ( 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_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_313,plain,
inverse(double_divide(a1,inverse(a1))) != multiply(inverse(b1),b1),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_314,plain,
inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))),
inference(paramod,[status(thm)],[c_2,c_313]) ).
cnf(c_4,plain,
inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))),
inference(copy,[status(thm)],[c_314]) ).
cnf(c_315,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_315]) ).
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_316,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_316]) ).
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_50,plain,
inverse(inverse(double_divide(inverse(double_divide(A,B)),double_divide(A,B)))) = double_divide(inverse(double_divide(C,D)),double_divide(C,D)),
inference(paramod,[status(thm)],[c_14,c_14]) ).
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_317,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_317]) ).
cnf(c_318,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_318]) ).
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_97,plain,
inverse(inverse(double_divide(A,double_divide(B,A)))) = B,
inference(paramod,[status(thm)],[c_84,c_42]) ).
cnf(c_319,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_319]) ).
cnf(c_103,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(A,B))))) = double_divide(inverse(double_divide(C,D)),double_divide(C,D)),
inference(paramod,[status(thm)],[c_98,c_50]) ).
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_320,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_320]) ).
cnf(c_321,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_322,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_321]) ).
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_322]) ).
cnf(c_323,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_323]) ).
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_324,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_324]) ).
cnf(c_325,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_326,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_325]) ).
cnf(c_327,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_326]) ).
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_327]) ).
cnf(c_328,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_328]) ).
cnf(c_329,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_329]) ).
cnf(c_330,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_330]) ).
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_331,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_332,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_331]) ).
cnf(c_333,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_332]) ).
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_333]) ).
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_334,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_334]) ).
cnf(c_335,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_336,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_335]) ).
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_336]) ).
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_337,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_337]) ).
cnf(c_267,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_229,c_97]) ).
cnf(c_338,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_338]) ).
cnf(c_339,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_339]) ).
cnf(c_340,plain,
inverse(double_divide(A,inverse(A))) = double_divide(inverse(double_divide(C,D)),double_divide(C,D)),
inference(paramod,[status(thm)],[c_267,c_103]) ).
cnf(c_341,plain,
double_divide(A,inverse(A)) = double_divide(inverse(double_divide(C,D)),double_divide(C,D)),
inference(paramod,[status(thm)],[c_280,c_340]) ).
cnf(c_342,plain,
double_divide(A,inverse(A)) = inverse(double_divide(D,inverse(D))),
inference(paramod,[status(thm)],[c_279,c_341]) ).
cnf(c_286,plain,
double_divide(A,inverse(A)) = double_divide(B,inverse(B)),
inference(paramod,[status(thm)],[c_280,c_342]) ).
cnf(c_343,plain,
double_divide(b1,inverse(b1)) != inverse(double_divide(a1,inverse(a1))),
inference(paramod,[status(thm)],[c_280,c_4]) ).
cnf(c_344,plain,
double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)),
inference(paramod,[status(thm)],[c_280,c_343]) ).
cnf(c_312,plain,
$false,
inference(resolve,[status(thm)],[c_286,c_344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP601-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 15:01:34 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 3047566 was started by sandbox on n019,
% 0.10/0.37 % Fri Sep 25 15:01:34 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % 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 (+ 0.01) seconds.
% 0.10/0.44 % Length of proof is 50.
% 0.10/0.44 % Level of proof is 19.
% 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
%------------------------------------------------------------------------------