%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP443-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.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 65.19s 65.42s
% Output : CNFRefutation 65.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of clauses : 57 ( 57 unt; 0 nHn; 3 RR)
% Number of literals : 57 ( 56 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 : 190 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
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(c7,plain,
multiply(X,inverse(X)) = multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,inverse(Z)))),
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c8,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(Z,inverse(Z)),W)))) = inverse(multiply(X,multiply(Y,multiply(multiply(V,inverse(V)),W)))),
inference(equational,[status(thm)],[c2,c4]) ).
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(c16,plain,
inverse(multiply(inverse(multiply(X,multiply(Y,multiply(Z,inverse(Z))))),multiply(X,Y))) = inverse(multiply(W,inverse(W))),
inference(equational,[status(thm)],[c6,c10]) ).
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(c26,plain,
inverse(multiply(X,multiply(multiply(Y,inverse(Y)),multiply(multiply(Z,inverse(Z)),W)))) = inverse(multiply(X,multiply(multiply(V,inverse(V)),multiply(multiply(U,inverse(U)),W)))),
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c27,plain,
inverse(multiply(X,multiply(multiply(Y,inverse(Y)),Z))) = inverse(multiply(X,multiply(multiply(W,inverse(W)),Z))),
inference(equational,[status(thm)],[c4,c26]) ).
cnf(c29,plain,
inverse(multiply(multiply(X,inverse(X)),multiply(multiply(Y,inverse(Y)),Z))) = inverse(multiply(multiply(W,inverse(W)),multiply(multiply(V,inverse(V)),Z))),
inference(equational,[status(thm)],[c5,c27]) ).
cnf(c30,plain,
inverse(multiply(multiply(X,inverse(X)),Y)) = inverse(multiply(multiply(Z,inverse(Z)),Y)),
inference(equational,[status(thm)],[c9,c29]) ).
cnf(c31,plain,
inverse(multiply(X,inverse(X))) = inverse(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,inverse(Z))))),
inference(equational,[status(thm)],[c6,c30]) ).
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(c46,plain,
multiply(multiply(X,multiply(inverse(X),Y)),inverse(multiply(Z,multiply(inverse(Z),Y)))) = multiply(multiply(W,inverse(W)),inverse(multiply(V,inverse(V)))),
inference(equational,[status(thm)],[c7,c19]) ).
cnf(c49,plain,
inverse(multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y))))) = inverse(multiply(multiply(Z,inverse(Z)),inverse(multiply(W,inverse(W))))),
inference(equational,[status(thm)],[c31,c46]) ).
cnf(c52,plain,
multiply(multiply(X,multiply(Y,inverse(Y))),inverse(multiply(X,multiply(Z,inverse(Z))))) = multiply(multiply(W,inverse(W)),inverse(multiply(V,inverse(V)))),
inference(equational,[status(thm)],[c7,c14]) ).
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(c57,plain,
inverse(multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y))))) = inverse(multiply(Z,multiply(inverse(Z),inverse(multiply(W,inverse(W)))))),
inference(equational,[status(thm)],[c52,c56]) ).
cnf(c58,plain,
inverse(multiply(X,multiply(inverse(X),inverse(multiply(Y,inverse(Y)))))) = inverse(multiply(Z,multiply(inverse(Z),inverse(multiply(W,inverse(W)))))),
inference(equational,[status(thm)],[c49,c57]) ).
cnf(c81,plain,
inverse(multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y))))) = inverse(multiply(inverse(multiply(Z,multiply(W,multiply(V,inverse(V))))),multiply(Z,W))),
inference(equational,[status(thm)],[c16,c46]) ).
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(c96,plain,
multiply(X,multiply(inverse(X),Y)) = multiply(Z,multiply(inverse(Z),Y)),
inference(equational,[status(thm)],[c19,c95]) ).
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(c108,plain,
multiply(X,multiply(Y,multiply(inverse(Y),Z))) = multiply(W,multiply(inverse(W),multiply(inverse(inverse(X)),Z))),
inference(equational,[status(thm)],[c96]) ).
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(c114,plain,
multiply(inverse(X),X) = inverse(inverse(multiply(Y,inverse(Y)))),
inference(equational,[status(thm)],[c105,c113]) ).
cnf(c118,plain,
multiply(inverse(multiply(X,inverse(X))),multiply(Y,inverse(Y))) = inverse(inverse(multiply(Z,inverse(Z)))),
inference(equational,[status(thm)],[c56,c105,c106,c114]) ).
cnf(c119,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(Y,inverse(Y))),multiply(Z,inverse(Z))),
inference(equational,[status(thm)],[c9,c16,c114,c118]) ).
cnf(c120,plain,
multiply(inverse(multiply(X,multiply(inverse(Y),Y))),X) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c55,c105,c119]) ).
cnf(c121,plain,
inverse(multiply(X,inverse(X))) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c58,c104,c120]) ).
cnf(c122,plain,
inverse(multiply(X,inverse(X))) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c104,c119,c121]) ).
cnf(c123,plain,
multiply(inverse(X),X) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c105,c120,c122]) ).
cnf(c124,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c9,c44,c123]) ).
cnf(c125,plain,
multiply(X,multiply(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c105,c121]) ).
cnf(c128,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c96,c124,c125]) ).
cnf(c129,plain,
multiply(multiply(X,inverse(X)),Y) = Y,
inference(equational,[status(thm)],[c44,c124,c125]) ).
cnf(c131,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c81,c105,c122]) ).
cnf(c132,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference(equational,[status(thm)],[c108,c124,c128,c129,c131]) ).
cnf(g1,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(equational,[status(thm)],[c132]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP443-1 : TPTP v9.0.0. Released v2.6.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n016.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
% 0.11/0.33 % CPUTime :
% 65.19/65.42 % SZS status Unsatisfiable
% 65.19/65.42 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------