%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP203-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n010.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 06:43:46 AM UTC 2025
% Result : Unsatisfiable 61.43s 61.70s
% Output : CNFRefutation 61.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 3 RR)
% Number of literals : 32 ( 31 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))),
file('theBenchmark.p',prove_moufang2) ).
cnf(c1,axiom,
multiply(identity,X) = X,
file('theBenchmark.p',left_identity) ).
cnf(c2,axiom,
multiply(left_inverse(X),X) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c3,axiom,
multiply(multiply(multiply(X,Y),X),Z) = multiply(X,multiply(Y,multiply(X,Z))),
file('theBenchmark.p',moufang3) ).
cnf(c4,plain,
multiply(multiply(X,identity),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c6,plain,
multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)),
inference(equational,[status(thm)],[c1,c3,c4]) ).
cnf(c12,plain,
multiply(left_inverse(X),multiply(X,multiply(left_inverse(X),Y))) = multiply(left_inverse(X),Y),
inference(equational,[status(thm)],[c1,c2,c3]) ).
cnf(c13,plain,
multiply(left_inverse(X),multiply(X,identity)) = identity,
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c14,plain,
multiply(multiply(X,multiply(Y,multiply(X,identity))),Z) = multiply(X,multiply(Y,multiply(X,Z))),
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c15,plain,
multiply(X,multiply(left_inverse(X),multiply(X,Y))) = multiply(X,Y),
inference(equational,[status(thm)],[c4,c13,c14]) ).
cnf(c16,plain,
multiply(left_inverse(X),multiply(left_inverse(left_inverse(X)),identity)) = identity,
inference(equational,[status(thm)],[c2,c15]) ).
cnf(c23,plain,
multiply(X,multiply(multiply(Y,multiply(X,identity)),multiply(X,Z))) = multiply(multiply(X,multiply(Y,multiply(X,X))),Z),
inference(equational,[status(thm)],[c3,c14]) ).
cnf(c24,plain,
multiply(multiply(X,multiply(Y,multiply(Y,multiply(X,identity)))),Z) = multiply(X,multiply(Y,multiply(Y,multiply(X,Z)))),
inference(equational,[status(thm)],[c6,c14]) ).
cnf(c26,plain,
multiply(X,multiply(left_inverse(X),multiply(left_inverse(X),multiply(X,Y)))) = multiply(multiply(X,multiply(left_inverse(X),identity)),Y),
inference(equational,[status(thm)],[c13,c24]) ).
cnf(c27,plain,
multiply(left_inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c1,c12,c16,c26]) ).
cnf(c28,plain,
multiply(left_inverse(left_inverse(X)),identity) = X,
inference(equational,[status(thm)],[c2,c27]) ).
cnf(c29,plain,
multiply(X,multiply(left_inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c1,c12,c16,c26]) ).
cnf(c30,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c2,c29]) ).
cnf(c31,plain,
left_inverse(left_inverse(X)) = X,
inference(equational,[status(thm)],[c28,c30]) ).
cnf(c33,plain,
multiply(multiply(X,Y),X) = multiply(X,multiply(Y,X)),
inference(equational,[status(thm)],[c3,c30]) ).
cnf(c34,plain,
multiply(multiply(X,multiply(Y,X)),Z) = multiply(X,multiply(Y,multiply(X,Z))),
inference(equational,[status(thm)],[c14,c30]) ).
cnf(c35,plain,
multiply(X,multiply(multiply(Y,X),X)) = multiply(X,multiply(Y,multiply(X,X))),
inference(equational,[status(thm)],[c23,c30]) ).
cnf(c36,plain,
multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)),
inference(equational,[status(thm)],[c27,c35]) ).
cnf(c40,plain,
multiply(X,multiply(multiply(left_inverse(X),Y),X)) = multiply(Y,X),
inference(equational,[status(thm)],[c29,c33]) ).
cnf(c41,plain,
multiply(multiply(X,left_inverse(Y)),Y) = X,
inference(equational,[status(thm)],[c2,c29,c30,c34,c40]) ).
cnf(c59,plain,
multiply(multiply(X,multiply(X,left_inverse(Y))),Y) = multiply(X,X),
inference(equational,[status(thm)],[c2,c24,c29,c30,c40]) ).
cnf(c60,plain,
multiply(multiply(X,Y),multiply(X,Y)) = multiply(X,multiply(Y,multiply(X,Y))),
inference(equational,[status(thm)],[c31,c33,c34,c41,c59]) ).
cnf(c63,plain,
multiply(X,multiply(multiply(left_inverse(X),Y),multiply(X,Z))) = multiply(multiply(Y,X),Z),
inference(equational,[status(thm)],[c3,c29]) ).
cnf(c95,plain,
multiply(multiply(X,multiply(Y,multiply(X,Z))),Z) = multiply(X,multiply(Y,multiply(X,multiply(Z,Z)))),
inference(equational,[status(thm)],[c3,c33,c34,c36]) ).
cnf(c96,plain,
multiply(multiply(multiply(X,Y),Z),Y) = multiply(X,multiply(Y,multiply(Z,Y))),
inference(equational,[status(thm)],[c27,c29,c60,c63,c95]) ).
cnf(g1,plain,
multiply(multiply(multiply(a,b),c),b) = multiply(a,multiply(b,multiply(c,b))),
inference(equational,[status(thm)],[c96]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP203-1 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.32 % Computer : n010.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon Jul 14 08:16:49 EDT 2025
% 0.13/0.32 % CPUTime :
% 61.43/61.70 % SZS status Unsatisfiable
% 61.43/61.70 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------