%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP442-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n007.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 06:44:04 AM UTC 2025
% Result : Unsatisfiable 64.86s 65.05s
% Output : CNFRefutation 64.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 3 RR)
% Number of literals : 28 ( 27 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 95 ( 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,
inverse(multiply(X,multiply(Y,multiply(multiply(Z,inverse(Z)),inverse(multiply(W,multiply(X,Y))))))) = W,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
inverse(multiply(X,multiply(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,multiply(W,X)))),multiply(multiply(V,inverse(V)),Z)))) = W,
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),Y),multiply(multiply(multiply(Z,inverse(Z)),W),multiply(multiply(V,inverse(V)),U)))) = multiply(multiply(U2,inverse(U2)),inverse(multiply(Y,multiply(W,U)))),
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(Y,multiply(inverse(multiply(Z,multiply(W,multiply(multiply(V,inverse(V)),Y)))),Z)))) = W,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
multiply(multiply(X,inverse(X)),Y) = multiply(multiply(Z,inverse(Z)),Y),
inference(equational,[status(thm)],[c2,c3,c4]) ).
cnf(c6,plain,
multiply(X,inverse(X)) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c9,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(inverse(multiply(Y,multiply(Z,W))),multiply(Y,Z)))) = W,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c10,plain,
inverse(multiply(inverse(multiply(X,multiply(Y,multiply(multiply(Z,inverse(Z)),W)))),multiply(X,Y))) = W,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c12,plain,
inverse(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,Y))) = inverse(multiply(inverse(multiply(W,multiply(V,Z))),multiply(W,V))),
inference(equational,[status(thm)],[c9,c10]) ).
cnf(c13,plain,
inverse(multiply(inverse(multiply(X,multiply(Y,inverse(Y)))),multiply(X,Z))) = inverse(multiply(inverse(multiply(W,multiply(V,inverse(Z)))),multiply(W,V))),
inference(equational,[status(thm)],[c6,c12]) ).
cnf(c14,plain,
inverse(multiply(X,multiply(Y,inverse(Y)))) = inverse(multiply(X,multiply(Z,inverse(Z)))),
inference(equational,[status(thm)],[c1,c9,c13]) ).
cnf(c18,plain,
inverse(multiply(inverse(multiply(X,multiply(inverse(X),Y))),multiply(Z,inverse(Z)))) = inverse(multiply(inverse(multiply(W,multiply(V,Y))),multiply(W,V))),
inference(equational,[status(thm)],[c6,c12]) ).
cnf(c19,plain,
inverse(multiply(X,multiply(inverse(X),Y))) = inverse(multiply(Z,multiply(inverse(Z),Y))),
inference(equational,[status(thm)],[c1,c9,c18]) ).
cnf(c20,plain,
inverse(multiply(X,multiply(inverse(X),inverse(inverse(Y))))) = inverse(multiply(Y,multiply(Z,inverse(Z)))),
inference(equational,[status(thm)],[c14,c19]) ).
cnf(c44,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(inverse(multiply(Y,multiply(Z,inverse(Z)))),multiply(Y,W)))) = inverse(W),
inference(equational,[status(thm)],[c6,c9]) ).
cnf(c55,plain,
multiply(multiply(inverse(multiply(X,multiply(Y,multiply(multiply(Z,inverse(Z)),W)))),multiply(X,Y)),W) = multiply(V,inverse(V)),
inference(equational,[status(thm)],[c6,c10]) ).
cnf(c56,plain,
inverse(multiply(X,inverse(X))) = inverse(multiply(Y,multiply(inverse(Y),inverse(multiply(Z,inverse(Z)))))),
inference(equational,[status(thm)],[c10,c20,c55]) ).
cnf(c95,plain,
inverse(multiply(inverse(X),multiply(Y,multiply(multiply(Z,inverse(Z)),inverse(multiply(W,multiply(inverse(W),Y))))))) = X,
inference(equational,[status(thm)],[c2,c9,c18]) ).
cnf(c103,plain,
multiply(X,multiply(inverse(X),inverse(multiply(Y,inverse(Y))))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c56,c95]) ).
cnf(c104,plain,
multiply(inverse(X),inverse(multiply(Y,inverse(Y)))) = inverse(X),
inference(equational,[status(thm)],[c9,c44,c103]) ).
cnf(c105,plain,
multiply(X,inverse(multiply(Y,inverse(Y)))) = X,
inference(equational,[status(thm)],[c1,c104]) ).
cnf(c106,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,Y)) = multiply(inverse(multiply(W,multiply(V,Z))),multiply(W,V)),
inference(equational,[status(thm)],[c12,c95]) ).
cnf(c111,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Y)) = multiply(inverse(multiply(Z,W)),multiply(Z,W)),
inference(equational,[status(thm)],[c105,c106]) ).
cnf(c112,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(Y,Z)),multiply(Y,Z)),
inference(equational,[status(thm)],[c105,c111]) ).
cnf(c113,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c105,c112]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c113]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP442-1 : TPTP v9.0.0. Released v2.6.0.
% 0.11/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n007.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 08:28:04 EDT 2025
% 0.11/0.32 % CPUTime :
% 64.86/65.05 % SZS status Unsatisfiable
% 64.86/65.05 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------