%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP468-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 06:44:07 AM UTC 2025
% Result : Unsatisfiable 0.67s 0.92s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 3 RR)
% Number of literals : 29 ( 28 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c1,axiom,
multiply(X,Y) = divide(X,inverse(Y)),
file('theBenchmark.p',multiply) ).
cnf(c2,axiom,
divide(divide(X,X),divide(Y,divide(divide(Z,divide(W,Y)),inverse(W)))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
divide(divide(X,X),divide(divide(divide(Y,divide(Z,W)),inverse(Z)),divide(Y,inverse(W)))) = divide(V,V),
inference(equational,[status(thm)],[c2]) ).
cnf(c5,plain,
divide(divide(X,X),divide(divide(Y,inverse(Z)),divide(divide(W,W),inverse(divide(divide(Y,divide(V,Z)),inverse(V)))))) = divide(U,U),
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c6,plain,
divide(X,X) = divide(divide(divide(Y,divide(Z,W)),inverse(Z)),divide(Y,inverse(W))),
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,plain,
divide(divide(X,X),divide(Y,Y)) = divide(Z,Z),
inference(equational,[status(thm)],[c3,c6]) ).
cnf(c8,plain,
divide(divide(divide(X,X),divide(Y,Y)),divide(Z,Z)) = divide(W,W),
inference(equational,[status(thm)],[c7]) ).
cnf(c9,plain,
divide(X,X) = divide(Y,Y),
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c10,plain,
divide(divide(X,X),divide(divide(Y,Y),divide(Z,Z))) = divide(W,W),
inference(equational,[status(thm)],[c7]) ).
cnf(c16,plain,
divide(divide(X,X),divide(Y,divide(divide(Z,Z),inverse(W)))) = divide(W,Y),
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c18,plain,
divide(divide(X,X),divide(inverse(Y),divide(divide(Z,Z),inverse(W)))) = divide(divide(W,divide(V,Y)),inverse(V)),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c19,plain,
divide(divide(X,divide(Y,Z)),inverse(Y)) = divide(X,inverse(Z)),
inference(equational,[status(thm)],[c2,c18]) ).
cnf(c20,plain,
divide(divide(X,X),inverse(Y)) = divide(divide(Z,Z),inverse(Y)),
inference(equational,[status(thm)],[c7,c19]) ).
cnf(c21,plain,
divide(divide(X,X),inverse(Y)) = divide(divide(Y,Z),inverse(Z)),
inference(equational,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
divide(divide(X,Y),inverse(Y)) = divide(divide(X,Z),inverse(Z)),
inference(equational,[status(thm)],[c19,c21]) ).
cnf(c39,plain,
divide(divide(X,X),divide(Y,divide(Z,inverse(Y)))) = Z,
inference(equational,[status(thm)],[c2,c19]) ).
cnf(c40,plain,
inverse(divide(X,X)) = divide(Y,Y),
inference(equational,[status(thm)],[c10,c39]) ).
cnf(c41,plain,
divide(X,divide(Y,Y)) = X,
inference(equational,[status(thm)],[c2,c39]) ).
cnf(c42,plain,
divide(divide(X,X),Y) = inverse(Y),
inference(equational,[status(thm)],[c39,c41]) ).
cnf(c45,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference(equational,[status(thm)],[c16,c41,c42]) ).
cnf(c46,plain,
divide(X,inverse(divide(Y,Y))) = X,
inference(equational,[status(thm)],[c2,c39,c40]) ).
cnf(c47,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c39,c42,c46]) ).
cnf(c48,plain,
inverse(divide(X,Y)) = divide(Y,X),
inference(equational,[status(thm)],[c18,c19,c42,c47]) ).
cnf(c49,plain,
inverse(divide(inverse(X),divide(Y,X))) = Y,
inference(equational,[status(thm)],[c22,c41,c46,c48]) ).
cnf(c51,plain,
divide(inverse(X),divide(Y,X)) = inverse(Y),
inference(equational,[status(thm)],[c45,c47,c49]) ).
cnf(c58,plain,
divide(divide(X,inverse(Y)),Z) = divide(X,inverse(divide(Y,Z))),
inference(equational,[status(thm)],[c19,c47,c51]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c1,c58]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP468-1 : TPTP v9.0.0. Released v2.6.0.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:29:19 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.67/0.92 % SZS status Unsatisfiable
% 0.67/0.92 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------