%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP472-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 06:44:08 AM UTC 2025
% Result : Unsatisfiable 0.87s 1.06s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c1,axiom,
multiply(X,Y) = divide(X,inverse(Y)),
file('theBenchmark.p',multiply) ).
cnf(c2,axiom,
divide(divide(inverse(divide(X,Y)),divide(divide(Z,W),X)),divide(W,Z)) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
divide(divide(inverse(divide(divide(X,Y),Z)),W),divide(divide(divide(Y,X),V),inverse(divide(V,W)))) = Z,
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
divide(divide(inverse(X),divide(divide(Y,Z),divide(inverse(divide(W,X)),divide(divide(V,U),W)))),divide(Z,Y)) = divide(U,V),
inference(equational,[status(thm)],[c2]) ).
cnf(c5,plain,
divide(divide(inverse(X),divide(divide(Y,Z),divide(inverse(divide(divide(W,V),X)),U))),divide(Z,Y)) = divide(divide(divide(V,W),U2),inverse(divide(U2,U))),
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c6,plain,
divide(divide(divide(X,Y),Z),inverse(divide(Z,divide(divide(W,V),divide(Y,X))))) = divide(V,W),
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c10,plain,
divide(inverse(divide(X,divide(divide(Y,Z),divide(W,V)))),divide(divide(V,W),X)) = divide(Y,Z),
inference(equational,[status(thm)],[c6]) ).
cnf(c11,plain,
divide(inverse(divide(X,divide(Y,divide(Z,W)))),divide(divide(W,Z),X)) = Y,
inference(equational,[status(thm)],[c3,c10]) ).
cnf(c12,plain,
divide(inverse(divide(X,Y)),divide(divide(Z,divide(W,V)),X)) = inverse(divide(Z,divide(Y,divide(V,W)))),
inference(equational,[status(thm)],[c11]) ).
cnf(c13,plain,
inverse(divide(X,divide(divide(Y,divide(divide(Z,W),X)),divide(W,Z)))) = Y,
inference(equational,[status(thm)],[c11,c12]) ).
cnf(c18,plain,
divide(divide(divide(X,Y),Z),inverse(divide(Z,divide(W,divide(Y,X))))) = divide(divide(V,U),divide(inverse(divide(U2,W)),divide(divide(U,V),U2))),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c19,plain,
divide(divide(X,Y),divide(inverse(divide(Z,divide(W,V))),divide(divide(Y,X),Z))) = divide(V,W),
inference(equational,[status(thm)],[c6,c18]) ).
cnf(c20,plain,
divide(divide(inverse(divide(X,Y)),divide(Y,X)),divide(Z,W)) = divide(W,Z),
inference(equational,[status(thm)],[c4,c19]) ).
cnf(c21,plain,
divide(divide(X,Y),divide(inverse(divide(Z,W)),divide(W,Z))) = divide(X,Y),
inference(equational,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
divide(inverse(divide(X,Y)),divide(Y,X)) = divide(divide(Z,W),inverse(divide(W,Z))),
inference(equational,[status(thm)],[c20,c21]) ).
cnf(c23,plain,
divide(X,divide(inverse(divide(Y,Z)),divide(Z,Y))) = X,
inference(equational,[status(thm)],[c2,c21]) ).
cnf(c26,plain,
divide(inverse(X),divide(divide(Y,Z),X)) = inverse(divide(Y,Z)),
inference(equational,[status(thm)],[c11,c23]) ).
cnf(c27,plain,
inverse(inverse(divide(X,Y))) = inverse(divide(Y,X)),
inference(equational,[status(thm)],[c22,c23,c26]) ).
cnf(c29,plain,
inverse(inverse(inverse(divide(X,Y)))) = inverse(divide(X,Y)),
inference(equational,[status(thm)],[c27]) ).
cnf(c30,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c13,c29]) ).
cnf(c31,plain,
divide(X,Y) = inverse(divide(Y,X)),
inference(equational,[status(thm)],[c27,c30]) ).
cnf(c36,plain,
divide(X,divide(divide(Y,Z),inverse(divide(Z,Y)))) = X,
inference(equational,[status(thm)],[c22,c23]) ).
cnf(c37,plain,
divide(inverse(divide(X,Y)),divide(Z,X)) = inverse(divide(Z,Y)),
inference(equational,[status(thm)],[c12,c23,c36]) ).
cnf(c38,plain,
divide(X,divide(Y,Y)) = X,
inference(equational,[status(thm)],[c23,c31,c37]) ).
cnf(c39,plain,
divide(divide(X,X),Y) = inverse(Y),
inference(equational,[status(thm)],[c27,c30,c38]) ).
cnf(c40,plain,
divide(X,X) = divide(Y,Y),
inference(equational,[status(thm)],[c31,c38,c39]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c1,c40]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP472-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Jul 14 08:29:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.87/1.06 % SZS status Unsatisfiable
% 0.87/1.06 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------