%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP594-1 : TPTP v9.3.1. Released v2.6.0.
% 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 07:30:26 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 54 ( 54 unt; 0 def)
% Number of atoms : 54 ( 53 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 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 : 170 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : inverse(double_divide(double_divide(VAR_0,VAR_1),inverse(double_divide(VAR_0,inverse(double_divide(VAR_2,VAR_1)))))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(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_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_3,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_343,plain,
multiply(inverse(double_divide(b2,inverse(b2))),a2) != a2,
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4,plain,
inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2,
inference(paramod,[status(thm)],[c_2,c_343]) ).
cnf(c_5,plain,
inverse(double_divide(double_divide(A,inverse(double_divide(B,inverse(double_divide(C,D))))),inverse(double_divide(A,C)))) = double_divide(B,D),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
inverse(double_divide(double_divide(double_divide(A,B),inverse(double_divide(C,B))),C)) = A,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_7,plain,
inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),inverse(double_divide(A,double_divide(D,E))))) = double_divide(B,inverse(double_divide(D,inverse(double_divide(C,E))))),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_9,plain,
inverse(double_divide(double_divide(A,B),inverse(double_divide(A,C)))) = double_divide(double_divide(C,D),inverse(double_divide(B,D))),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_344,plain,
A = double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),B)),C),
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_16,plain,
double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),B)),C) = A,
inference(copy,[status(thm)],[c_344]) ).
cnf(c_19,plain,
double_divide(double_divide(inverse(double_divide(A,B)),C),inverse(double_divide(B,C))) = A,
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_35,plain,
double_divide(double_divide(A,B),inverse(double_divide(inverse(double_divide(inverse(double_divide(double_divide(C,D),A)),D)),B))) = C,
inference(paramod,[status(thm)],[c_9,c_6]) ).
cnf(c_41,plain,
double_divide(double_divide(A,B),inverse(double_divide(C,B))) = double_divide(double_divide(A,D),inverse(double_divide(C,D))),
inference(paramod,[status(thm)],[c_9,c_9]) ).
cnf(c_59,plain,
inverse(double_divide(double_divide(A,inverse(double_divide(B,inverse(double_divide(C,D))))),B)) = double_divide(inverse(double_divide(A,C)),D),
inference(paramod,[status(thm)],[c_19,c_6]) ).
cnf(c_345,plain,
inverse(double_divide(double_divide(A,inverse(double_divide(double_divide(B,C),inverse(double_divide(D,C))))),inverse(double_divide(A,D)))) = double_divide(double_divide(B,E),E),
inference(paramod,[status(thm)],[c_41,c_5]) ).
cnf(c_76,plain,
double_divide(double_divide(A,B),B) = double_divide(double_divide(A,C),C),
inference(paramod,[status(thm)],[c_5,c_345]) ).
cnf(c_84,plain,
inverse(double_divide(double_divide(A,B),inverse(double_divide(A,B)))) = double_divide(double_divide(C,D),inverse(double_divide(C,D))),
inference(paramod,[status(thm)],[c_41,c_9]) ).
cnf(c_106,plain,
inverse(double_divide(double_divide(A,B),B)) = double_divide(double_divide(C,D),inverse(double_divide(inverse(double_divide(A,C)),D))),
inference(paramod,[status(thm)],[c_76,c_9]) ).
cnf(c_149,plain,
inverse(double_divide(double_divide(A,B),B)) = double_divide(A,inverse(double_divide(C,inverse(double_divide(double_divide(C,D),D))))),
inference(paramod,[status(thm)],[c_76,c_7]) ).
cnf(c_176,plain,
inverse(double_divide(double_divide(A,inverse(B)),inverse(double_divide(A,double_divide(C,D))))) = double_divide(inverse(double_divide(double_divide(B,inverse(double_divide(E,F))),E)),inverse(double_divide(C,inverse(double_divide(F,D))))),
inference(paramod,[status(thm)],[c_16,c_7]) ).
cnf(c_346,plain,
inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),inverse(double_divide(A,double_divide(double_divide(D,E),inverse(double_divide(D,E))))))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_84,c_1]) ).
cnf(c_181,plain,
double_divide(A,inverse(double_divide(double_divide(B,C),inverse(double_divide(D,inverse(double_divide(B,C))))))) = double_divide(A,D),
inference(paramod,[status(thm)],[c_7,c_346]) ).
cnf(c_347,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,B)))),inverse(double_divide(double_divide(C,D),inverse(double_divide(E,inverse(double_divide(C,D)))))))) = E,
inference(paramod,[status(thm)],[c_84,c_1]) ).
cnf(c_183,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,B)))),C)) = C,
inference(paramod,[status(thm)],[c_181,c_347]) ).
cnf(c_348,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,B)))),inverse(double_divide(double_divide(C,inverse(double_divide(D,E))),D)))) = double_divide(C,E),
inference(paramod,[status(thm)],[c_84,c_5]) ).
cnf(c_191,plain,
inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),B)) = double_divide(A,C),
inference(paramod,[status(thm)],[c_183,c_348]) ).
cnf(c_349,plain,
inverse(double_divide(double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,B)))),inverse(double_divide(C,inverse(double_divide(D,E))))),C)) = double_divide(D,E),
inference(paramod,[status(thm)],[c_84,c_6]) ).
cnf(c_196,plain,
double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,B)))),inverse(double_divide(C,D))) = double_divide(C,D),
inference(paramod,[status(thm)],[c_191,c_349]) ).
cnf(c_350,plain,
inverse(double_divide(double_divide(A,B),inverse(double_divide(A,double_divide(C,D))))) = double_divide(inverse(double_divide(double_divide(E,F),inverse(double_divide(E,F)))),inverse(double_divide(B,inverse(double_divide(C,D))))),
inference(paramod,[status(thm)],[c_84,c_9]) ).
cnf(c_205,plain,
inverse(double_divide(double_divide(A,B),inverse(double_divide(A,double_divide(C,D))))) = double_divide(B,inverse(double_divide(C,D))),
inference(paramod,[status(thm)],[c_196,c_350]) ).
cnf(c_351,plain,
double_divide(inverse(B),inverse(double_divide(C,D))) = double_divide(inverse(double_divide(double_divide(B,inverse(double_divide(E,F))),E)),inverse(double_divide(C,inverse(double_divide(F,D))))),
inference(paramod,[status(thm)],[c_205,c_176]) ).
cnf(c_352,plain,
double_divide(inverse(B),inverse(double_divide(C,D))) = double_divide(double_divide(B,F),inverse(double_divide(C,inverse(double_divide(F,D))))),
inference(paramod,[status(thm)],[c_191,c_351]) ).
cnf(c_247,plain,
double_divide(double_divide(A,B),inverse(double_divide(C,inverse(double_divide(B,D))))) = double_divide(inverse(A),inverse(double_divide(C,D))),
inference(copy,[status(thm)],[c_352]) ).
cnf(c_353,plain,
double_divide(A,inverse(double_divide(C,D))) = double_divide(inverse(double_divide(A,C)),D),
inference(paramod,[status(thm)],[c_191,c_59]) ).
cnf(c_261,plain,
double_divide(inverse(double_divide(A,B)),C) = double_divide(A,inverse(double_divide(B,C))),
inference(copy,[status(thm)],[c_353]) ).
cnf(c_264,plain,
double_divide(double_divide(A,B),B) = A,
inference(paramod,[status(thm)],[c_191,c_16]) ).
cnf(c_354,plain,
inverse(A) = double_divide(double_divide(C,D),inverse(double_divide(inverse(double_divide(A,C)),D))),
inference(paramod,[status(thm)],[c_264,c_106]) ).
cnf(c_355,plain,
inverse(A) = double_divide(double_divide(C,D),inverse(double_divide(A,inverse(double_divide(C,D))))),
inference(paramod,[status(thm)],[c_261,c_354]) ).
cnf(c_266,plain,
double_divide(double_divide(A,B),inverse(double_divide(C,inverse(double_divide(A,B))))) = inverse(C),
inference(copy,[status(thm)],[c_355]) ).
cnf(c_356,plain,
double_divide(double_divide(A,B),inverse(double_divide(inverse(double_divide(double_divide(C,D),inverse(double_divide(A,D)))),B))) = C,
inference(paramod,[status(thm)],[c_261,c_35]) ).
cnf(c_357,plain,
double_divide(double_divide(A,B),inverse(double_divide(double_divide(C,D),inverse(double_divide(inverse(double_divide(A,D)),B))))) = C,
inference(paramod,[status(thm)],[c_261,c_356]) ).
cnf(c_358,plain,
double_divide(double_divide(A,B),inverse(double_divide(double_divide(C,D),inverse(double_divide(A,inverse(double_divide(D,B))))))) = C,
inference(paramod,[status(thm)],[c_261,c_357]) ).
cnf(c_359,plain,
double_divide(double_divide(A,B),inverse(double_divide(inverse(C),inverse(double_divide(A,B))))) = C,
inference(paramod,[status(thm)],[c_247,c_358]) ).
cnf(c_272,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_266,c_359]) ).
cnf(c_360,plain,
inverse(A) = double_divide(A,inverse(double_divide(C,inverse(double_divide(double_divide(C,D),D))))),
inference(paramod,[status(thm)],[c_264,c_149]) ).
cnf(c_361,plain,
inverse(A) = double_divide(A,inverse(double_divide(C,inverse(C)))),
inference(paramod,[status(thm)],[c_264,c_360]) ).
cnf(c_326,plain,
double_divide(A,inverse(double_divide(B,inverse(B)))) = inverse(A),
inference(copy,[status(thm)],[c_361]) ).
cnf(c_362,plain,
inverse(inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_326,c_4]) ).
cnf(c_363,plain,
a2 != a2,
inference(paramod,[status(thm)],[c_272,c_362]) ).
cnf(c_342,plain,
$false,
inference(copy,[status(thm)],[c_363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP594-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.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 15:01:33 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 3777974 was started by sandbox2 on n005,
% 0.10/0.37 % Fri Sep 25 15:01:33 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.42
% 0.10/0.42 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.10/0.42
% 0.10/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.42
% 0.10/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.10/0.42 % Length of proof is 30.
% 0.10/0.42 % Level of proof is 12.
% 0.10/0.42 % Maximum clause weight is 80.000.
% 0.10/0.42 % Given clauses 13.
% 0.10/0.42
% 0.10/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------