%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP610-1 : 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 : n003.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 07:30:29 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.55s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 40 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 134 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : inverse(double_divide(inverse(double_divide(inverse(double_divide(VAR_0,VAR_1)),VAR_2)),double_divide(VAR_0,VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,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_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_381,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_381]) ).
cnf(c_5,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(inverse(double_divide(C,A)),D)),B))) = double_divide(C,D),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_7,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(inverse(double_divide(D,E)),C))) = double_divide(inverse(double_divide(inverse(double_divide(A,D)),B)),E),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_10,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_1,c_5]) ).
cnf(c_382,plain,
A = double_divide(B,inverse(double_divide(C,double_divide(inverse(double_divide(B,C)),A)))),
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_16,plain,
double_divide(A,inverse(double_divide(B,double_divide(inverse(double_divide(A,B)),C)))) = C,
inference(copy,[status(thm)],[c_382]) ).
cnf(c_19,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_10,c_1]) ).
cnf(c_41,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,C)) = double_divide(inverse(double_divide(D,B)),double_divide(D,C)),
inference(paramod,[status(thm)],[c_10,c_10]) ).
cnf(c_60,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_19,c_6]) ).
cnf(c_84,plain,
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_41,c_10]) ).
cnf(c_178,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(inverse(D),C))) = double_divide(inverse(double_divide(inverse(double_divide(A,E)),B)),inverse(double_divide(F,double_divide(inverse(double_divide(E,F)),D)))),
inference(paramod,[status(thm)],[c_16,c_7]) ).
cnf(c_383,plain,
inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(A,B)),double_divide(A,B)),C)),double_divide(inverse(double_divide(D,E)),C))) = double_divide(D,E),
inference(paramod,[status(thm)],[c_84,c_1]) ).
cnf(c_182,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,B))),D) = double_divide(C,D),
inference(paramod,[status(thm)],[c_7,c_383]) ).
cnf(c_384,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,B))),inverse(double_divide(inverse(double_divide(D,E)),double_divide(D,E))))) = C,
inference(paramod,[status(thm)],[c_84,c_1]) ).
cnf(c_186,plain,
inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),double_divide(B,C))))) = A,
inference(paramod,[status(thm)],[c_182,c_384]) ).
cnf(c_385,plain,
inverse(double_divide(inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),C))),inverse(double_divide(inverse(double_divide(D,E)),double_divide(D,E))))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_84,c_5]) ).
cnf(c_193,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),C))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_186,c_385]) ).
cnf(c_386,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(inverse(double_divide(B,C)),A)),inverse(double_divide(inverse(double_divide(D,E)),double_divide(D,E)))))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_84,c_6]) ).
cnf(c_199,plain,
double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(double_divide(C,D)),double_divide(C,D)))) = double_divide(A,B),
inference(paramod,[status(thm)],[c_193,c_386]) ).
cnf(c_387,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(D,C))) = double_divide(inverse(double_divide(inverse(double_divide(A,B)),D)),inverse(double_divide(inverse(double_divide(E,F)),double_divide(E,F)))),
inference(paramod,[status(thm)],[c_84,c_10]) ).
cnf(c_208,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(D,C))) = double_divide(inverse(double_divide(A,B)),D),
inference(paramod,[status(thm)],[c_199,c_387]) ).
cnf(c_388,plain,
double_divide(inverse(double_divide(A,B)),inverse(D)) = double_divide(inverse(double_divide(inverse(double_divide(A,E)),B)),inverse(double_divide(F,double_divide(inverse(double_divide(E,F)),D)))),
inference(paramod,[status(thm)],[c_208,c_178]) ).
cnf(c_389,plain,
double_divide(inverse(double_divide(A,B)),inverse(D)) = double_divide(inverse(double_divide(inverse(double_divide(A,E)),B)),double_divide(E,D)),
inference(paramod,[status(thm)],[c_193,c_388]) ).
cnf(c_246,plain,
double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(B,D)) = double_divide(inverse(double_divide(A,C)),inverse(D)),
inference(copy,[status(thm)],[c_389]) ).
cnf(c_262,plain,
double_divide(inverse(double_divide(A,B)),C) = double_divide(A,inverse(double_divide(B,C))),
inference(paramod,[status(thm)],[c_193,c_60]) ).
cnf(c_390,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),double_divide(B,D)) = double_divide(inverse(double_divide(A,C)),inverse(D)),
inference(paramod,[status(thm)],[c_262,c_246]) ).
cnf(c_391,plain,
double_divide(A,inverse(double_divide(inverse(double_divide(B,C)),double_divide(B,D)))) = double_divide(inverse(double_divide(A,C)),inverse(D)),
inference(paramod,[status(thm)],[c_262,c_390]) ).
cnf(c_392,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(C,double_divide(B,D)))))) = double_divide(inverse(double_divide(A,C)),inverse(D)),
inference(paramod,[status(thm)],[c_262,c_391]) ).
cnf(c_356,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(C,double_divide(B,D)))))) = double_divide(A,inverse(double_divide(C,inverse(D)))),
inference(paramod,[status(thm)],[c_262,c_392]) ).
cnf(c_393,plain,
inverse(double_divide(A,inverse(double_divide(B,inverse(double_divide(C,double_divide(B,C))))))) = A,
inference(paramod,[status(thm)],[c_262,c_186]) ).
cnf(c_379,plain,
inverse(double_divide(A,inverse(double_divide(B,inverse(B))))) = A,
inference(paramod,[status(thm)],[c_356,c_393]) ).
cnf(c_380,plain,
$false,
inference(resolve,[status(thm)],[c_379,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP610-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n003.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 15:03:37 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 477367 was started by sandbox on n003,
% 0.18/0.44 % Fri Sep 25 15:03:37 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.22/0.55
% 0.22/0.55 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.22/0.55
% 0.22/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.55
% 0.22/0.55 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.22/0.55 % Length of proof is 24.
% 0.22/0.55 % Level of proof is 13.
% 0.22/0.55 % Maximum clause weight is 80.000.
% 0.22/0.55 % Given clauses 13.
% 0.22/0.55
% 0.22/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------