%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP437-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 06:44:03 AM UTC 2025
% Result : Unsatisfiable 65.95s 66.11s
% Output : CNFRefutation 65.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 2
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 3 RR)
% Number of literals : 40 ( 39 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 147 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c1,axiom,
multiply(X,inverse(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),inverse(multiply(W,Y))),X))))) = W,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(Z,W))),inverse(V))),multiply(V,multiply(Z,X))))) = W,
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(Z,inverse(W))),multiply(W,multiply(V,X))))) = multiply(U,multiply(multiply(inverse(U),inverse(multiply(Z,V))),inverse(Y))),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(Z,W))),Z))),inverse(Y))) = W,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(Y,Z))),inverse(W))) = multiply(V,multiply(multiply(inverse(V),inverse(multiply(Y,Z))),inverse(W))),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c7,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(Z)),W))),inverse(Y))) = inverse(multiply(V,multiply(U,multiply(multiply(inverse(U),inverse(multiply(Z,V))),W)))),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c8,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(multiply(Z,W),X))),Z)))) = W,
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
multiply(X,multiply(multiply(inverse(X),Y),inverse(Z))) = multiply(W,multiply(multiply(inverse(W),Y),inverse(Z))),
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c10,plain,
multiply(X,multiply(multiply(inverse(X),Y),Z)) = multiply(W,multiply(multiply(inverse(W),Y),Z)),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c11,plain,
inverse(multiply(multiply(X,multiply(Y,inverse(Z))),multiply(Z,multiply(W,V)))) = multiply(multiply(inverse(V),inverse(multiply(Y,W))),inverse(X)),
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c12,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(Y,inverse(multiply(Z,W))),Z))),Y)) = W,
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c18,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(Y,inverse(Z)),W))),Y)) = inverse(multiply(V,multiply(U,multiply(multiply(inverse(U),inverse(multiply(Z,V))),W)))),
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c19,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(multiply(Z,inverse(W)),X))),Z))) = W,
inference(equational,[status(thm)],[c1,c18]) ).
cnf(c22,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(Z,X))),W)))) = multiply(multiply(inverse(W),inverse(multiply(multiply(V,inverse(multiply(U,Z))),U))),V),
inference(equational,[status(thm)],[c8,c12]) ).
cnf(c23,plain,
multiply(multiply(inverse(X),inverse(multiply(multiply(Y,inverse(multiply(Z,multiply(X,W)))),Z))),Y) = W,
inference(equational,[status(thm)],[c8,c22]) ).
cnf(c24,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(Z)),inverse(W)))) = multiply(multiply(X,inverse(multiply(V,multiply(W,Z)))),V),
inference(equational,[status(thm)],[c19,c23]) ).
cnf(c25,plain,
multiply(multiply(X,inverse(multiply(Y,multiply(Z,W)))),Y) = multiply(multiply(X,inverse(multiply(V,multiply(Z,W)))),V),
inference(equational,[status(thm)],[c9,c24]) ).
cnf(c26,plain,
multiply(multiply(X,inverse(multiply(Y,Z))),Y) = multiply(multiply(X,inverse(multiply(W,Z))),W),
inference(equational,[status(thm)],[c2,c11,c12,c25]) ).
cnf(c41,plain,
multiply(inverse(X),inverse(multiply(multiply(Y,inverse(multiply(Z,multiply(X,multiply(W,Y))))),Z))) = W,
inference(equational,[status(thm)],[c1,c24]) ).
cnf(c51,plain,
multiply(multiply(X,inverse(multiply(Y,multiply(multiply(inverse(Y),Z),W)))),V) = multiply(multiply(X,inverse(multiply(U,multiply(multiply(inverse(V),Z),W)))),U),
inference(equational,[status(thm)],[c10,c25]) ).
cnf(c65,plain,
multiply(multiply(X,inverse(multiply(Y,multiply(multiply(inverse(Y),Z),W)))),V) = multiply(multiply(X,inverse(multiply(U,multiply(multiply(inverse(U),Z),W)))),V),
inference(equational,[status(thm)],[c10,c51]) ).
cnf(c66,plain,
multiply(X,inverse(multiply(Y,multiply(multiply(inverse(Y),Z),W)))) = multiply(X,inverse(multiply(V,multiply(multiply(inverse(V),Z),W)))),
inference(equational,[status(thm)],[c41,c65]) ).
cnf(c70,plain,
multiply(X,inverse(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),inverse(multiply(W,Y))),W))))) = X,
inference(equational,[status(thm)],[c1,c26]) ).
cnf(c71,plain,
multiply(multiply(X,inverse(Y)),Y) = multiply(multiply(X,inverse(Z)),Z),
inference(equational,[status(thm)],[c26,c70]) ).
cnf(c72,plain,
multiply(X,multiply(inverse(X),Y)) = multiply(Z,multiply(inverse(Z),Y)),
inference(equational,[status(thm)],[c10,c70]) ).
cnf(c73,plain,
multiply(X,inverse(X)) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c70,c72]) ).
cnf(c74,plain,
multiply(multiply(X,inverse(X)),Y) = multiply(multiply(Y,inverse(Z)),Z),
inference(equational,[status(thm)],[c71,c73]) ).
cnf(c89,plain,
multiply(X,inverse(multiply(Y,multiply(inverse(Y),Z)))) = multiply(X,inverse(multiply(W,multiply(inverse(W),Z)))),
inference(equational,[status(thm)],[c66,c70]) ).
cnf(c90,plain,
multiply(X,inverse(multiply(Y,inverse(Y)))) = multiply(X,inverse(multiply(Z,inverse(Z)))),
inference(equational,[status(thm)],[c70,c89]) ).
cnf(c91,plain,
multiply(X,inverse(multiply(Y,inverse(Y)))) = X,
inference(equational,[status(thm)],[c70,c90]) ).
cnf(c93,plain,
multiply(X,multiply(Y,inverse(Y))) = multiply(multiply(X,inverse(Z)),Z),
inference(equational,[status(thm)],[c71,c91]) ).
cnf(c101,plain,
multiply(multiply(X,inverse(multiply(Y,inverse(Z)))),Y) = multiply(X,Z),
inference(equational,[status(thm)],[c26,c91]) ).
cnf(c114,plain,
multiply(X,multiply(Y,inverse(Y))) = multiply(X,inverse(inverse(multiply(Z,inverse(Z))))),
inference(equational,[status(thm)],[c90,c91,c93]) ).
cnf(c116,plain,
multiply(multiply(inverse(X),inverse(Y)),Y) = inverse(X),
inference(equational,[status(thm)],[c23,c91,c101,c114]) ).
cnf(c117,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference(equational,[status(thm)],[c8,c116]) ).
cnf(c118,plain,
multiply(inverse(X),X) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c74,c116,c117]) ).
cnf(c129,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference(equational,[status(thm)],[c117,c118]) ).
cnf(g1,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(equational,[status(thm)],[c129]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP437-1 : TPTP v9.0.0. Released v2.6.0.
% 0.00/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n004.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 08:27:49 EDT 2025
% 0.12/0.32 % CPUTime :
% 65.95/66.11 % SZS status Unsatisfiable
% 65.95/66.11 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------