%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO070-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n012.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 06:14:51 AM UTC 2025
% Result : Unsatisfiable 70.32s 70.55s
% Output : CNFRefutation 70.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 3 RR)
% Number of literals : 26 ( 25 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 110 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(a,a,b) != a,
file('theBenchmark.p',prove_tba_axioms_4) ).
cnf(c1,axiom,
multiply(multiply(X,inverse(X),Y),inverse(multiply(multiply(Z,W,V),U,multiply(Z,W,U2))),multiply(W,multiply(U2,U,V),Z)) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
multiply(multiply(X,Y,Z),inverse(multiply(multiply(W,V,U),U2,multiply(W,V,U3))),multiply(V,multiply(U3,U2,U),W)) = multiply(Y,multiply(Z,inverse(multiply(X,Y,U4)),U4),X),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(inverse(X),multiply(Y,inverse(multiply(X,inverse(X),Z)),Z),X) = Y,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(multiply(X,inverse(X),Y),inverse(multiply(multiply(Z,inverse(Z),W),inverse(multiply(Z,inverse(Z),W)),multiply(Z,inverse(Z),V))),V) = Y,
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c6,plain,
multiply(multiply(X,Y,Z),inverse(multiply(multiply(W,inverse(W),V),inverse(multiply(W,inverse(W),V)),multiply(W,inverse(W),U))),U) = multiply(Y,multiply(Z,inverse(multiply(X,Y,U2)),U2),X),
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c7,plain,
multiply(multiply(X,Y,Z),inverse(multiply(W,inverse(W),multiply(multiply(W,inverse(W),V),inverse(multiply(W,inverse(W),V)),U))),U) = multiply(Y,multiply(Z,inverse(multiply(X,Y,U2)),U2),X),
inference(equational,[status(thm)],[c3,c6]) ).
cnf(c8,plain,
multiply(multiply(X,inverse(X),Y),inverse(multiply(multiply(Z,W,V),multiply(U,inverse(multiply(V,inverse(V),U2)),U2),multiply(Z,W,inverse(V)))),multiply(W,U,Z)) = Y,
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c21,plain,
multiply(X,inverse(multiply(multiply(Y,Z,W),V,multiply(Y,Z,U))),multiply(Z,multiply(U,V,W),Y)) = multiply(multiply(X,inverse(multiply(U2,inverse(U2),U3)),U3),multiply(U2,inverse(multiply(inverse(U2),multiply(X,inverse(multiply(U2,inverse(U2),U3)),U3),U4)),U4),inverse(U2)),
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c22,plain,
multiply(multiply(X,inverse(multiply(Y,inverse(Y),Z)),Z),multiply(Y,inverse(X),Y),inverse(Y)) = multiply(X,inverse(multiply(multiply(W,V,U),U2,multiply(W,V,U3))),multiply(V,multiply(U3,U2,U),W)),
inference(equational,[status(thm)],[c3,c21]) ).
cnf(c24,plain,
multiply(X,inverse(multiply(multiply(Y,inverse(Y),Z),inverse(multiply(Y,inverse(Y),Z)),multiply(Y,inverse(Y),W))),W) = multiply(multiply(X,inverse(multiply(V,inverse(V),U)),U),multiply(V,inverse(X),V),inverse(V)),
inference(equational,[status(thm)],[c3,c22]) ).
cnf(c51,plain,
multiply(multiply(X,inverse(X),Y),inverse(multiply(Z,inverse(Z),Z)),multiply(Z,inverse(multiply(multiply(W,inverse(W),V),inverse(multiply(W,inverse(W),V)),multiply(W,inverse(W),U))),U)) = Y,
inference(equational,[status(thm)],[c1,c3,c24]) ).
cnf(c63,plain,
multiply(multiply(X,inverse(X),Y),inverse(multiply(Z,inverse(Z),Z)),multiply(Z,inverse(multiply(W,inverse(W),multiply(multiply(W,inverse(W),V),inverse(multiply(W,inverse(W),V)),U))),U)) = Y,
inference(equational,[status(thm)],[c4,c51]) ).
cnf(c82,plain,
multiply(multiply(X,inverse(X),Y),inverse(Z),multiply(inverse(W),multiply(V,inverse(multiply(multiply(V,W,U),multiply(inverse(W),inverse(multiply(U,inverse(U),U2)),U2),multiply(V,W,inverse(U)))),Z),W)) = Y,
inference(equational,[status(thm)],[c1,c8]) ).
cnf(c83,plain,
multiply(multiply(X,inverse(X),Y),inverse(multiply(Z,inverse(Z),multiply(W,inverse(W),V))),multiply(inverse(Z),V,Z)) = Y,
inference(equational,[status(thm)],[c8,c82]) ).
cnf(c84,plain,
multiply(inverse(X),Y,X) = Y,
inference(equational,[status(thm)],[c83]) ).
cnf(c85,plain,
inverse(multiply(X,inverse(X),Y)) = inverse(Y),
inference(equational,[status(thm)],[c3,c84]) ).
cnf(c87,plain,
multiply(X,inverse(Y),Y) = X,
inference(equational,[status(thm)],[c3,c84,c85]) ).
cnf(c88,plain,
multiply(X,inverse(X),Y) = Y,
inference(equational,[status(thm)],[c63,c85,c87]) ).
cnf(c89,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c84,c88]) ).
cnf(c92,plain,
multiply(X,Y,inverse(X)) = Y,
inference(equational,[status(thm)],[c84,c89]) ).
cnf(c94,plain,
multiply(X,Y,multiply(X,Y,Z)) = multiply(Y,Z,X),
inference(equational,[status(thm)],[c7,c87,c88]) ).
cnf(c96,plain,
multiply(X,Y,Y) = Y,
inference(equational,[status(thm)],[c87,c92,c94]) ).
cnf(c98,plain,
multiply(X,X,Y) = X,
inference(equational,[status(thm)],[c94,c96]) ).
cnf(g1,plain,
multiply(a,a,b) = a,
inference(equational,[status(thm)],[c98]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.19 % Problem : BOO070-1 : TPTP v9.0.0. Released v2.6.0.
% 0.07/0.19 % Command : run_Leo-III %s %d THM
% 0.11/0.42 % Computer : n012.cluster.edu
% 0.11/0.42 % Model : x86_64 x86_64
% 0.11/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.42 % Memory : 8042.1875MB
% 0.11/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.42 % CPULimit : 300
% 0.11/0.42 % WCLimit : 300
% 0.11/0.42 % DateTime : Mon Jul 14 04:29:36 EDT 2025
% 0.11/0.42 % CPUTime :
% 70.32/70.55 % SZS status Unsatisfiable
% 70.32/70.55 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------