%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP202-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 60.27s 60.63s
% Output : CNFRefutation 60.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% 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 : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
file('theBenchmark.p',prove_moufang1) ).
cnf(c1,axiom,
multiply(identity,X) = X,
file('theBenchmark.p',left_identity) ).
cnf(c2,axiom,
multiply(X,identity) = X,
file('theBenchmark.p',right_identity) ).
cnf(c3,axiom,
multiply(X,right_inverse(X)) = identity,
file('theBenchmark.p',right_inverse) ).
cnf(c5,axiom,
multiply(left_inverse(X),X) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c9,axiom,
right_division(multiply(X,Y),Y) = X,
file('theBenchmark.p',right_division_multiply) ).
cnf(c11,plain,
right_division(identity,X) = left_inverse(X),
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c13,axiom,
multiply(X,left_division(X,Y)) = Y,
file('theBenchmark.p',multiply_left_division) ).
cnf(c15,axiom,
left_division(X,multiply(X,Y)) = Y,
file('theBenchmark.p',left_division_multiply) ).
cnf(c16,plain,
left_division(X,X) = identity,
inference(equational,[status(thm)],[c2,c15]) ).
cnf(c21,axiom,
multiply(multiply(multiply(X,Y),X),Z) = multiply(X,multiply(Y,multiply(X,Z))),
file('theBenchmark.p',moufang3) ).
cnf(c22,plain,
multiply(multiply(X,Y),X) = multiply(X,multiply(Y,X)),
inference(equational,[status(thm)],[c2,c21]) ).
cnf(c24,plain,
multiply(X,multiply(right_inverse(X),X)) = X,
inference(equational,[status(thm)],[c1,c3,c22]) ).
cnf(c25,plain,
multiply(right_inverse(X),X) = identity,
inference(equational,[status(thm)],[c15,c16,c24]) ).
cnf(c26,plain,
right_inverse(X) = left_inverse(X),
inference(equational,[status(thm)],[c9,c11,c25]) ).
cnf(c42,plain,
multiply(X,multiply(left_inverse(X),multiply(X,Y))) = multiply(X,Y),
inference(equational,[status(thm)],[c1,c3,c21,c26]) ).
cnf(c43,plain,
multiply(left_inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c15,c42]) ).
cnf(c45,plain,
multiply(left_inverse(X),Y) = left_division(X,Y),
inference(equational,[status(thm)],[c13,c43]) ).
cnf(c83,plain,
multiply(X,multiply(left_division(X,Y),multiply(X,Z))) = multiply(multiply(Y,X),Z),
inference(equational,[status(thm)],[c13,c21]) ).
cnf(c84,plain,
multiply(multiply(X,Y),left_inverse(Y)) = X,
inference(equational,[status(thm)],[c2,c3,c13,c26,c83]) ).
cnf(c85,plain,
right_division(X,left_inverse(Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c9,c84]) ).
cnf(c87,plain,
left_division(multiply(X,Y),X) = left_inverse(Y),
inference(equational,[status(thm)],[c43,c45,c84]) ).
cnf(c89,plain,
left_division(X,left_inverse(Y)) = left_inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c43,c87]) ).
cnf(c113,plain,
right_division(multiply(X,multiply(Y,multiply(X,Z))),Z) = multiply(X,multiply(Y,X)),
inference(equational,[status(thm)],[c9,c21,c22]) ).
cnf(c128,plain,
right_division(multiply(X,multiply(Y,Z)),left_division(X,Z)) = multiply(X,multiply(Y,X)),
inference(equational,[status(thm)],[c13,c113]) ).
cnf(c129,plain,
multiply(multiply(X,Y),multiply(Z,X)) = multiply(X,multiply(multiply(Y,Z),X)),
inference(equational,[status(thm)],[c84,c85,c89,c128]) ).
cnf(g1,plain,
multiply(multiply(a,multiply(b,c)),a) = multiply(multiply(a,b),multiply(c,a)),
inference(equational,[status(thm)],[c22,c129]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP202-1 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n006.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 08:16:34 EDT 2025
% 0.12/0.32 % CPUTime :
% 60.27/60.63 % SZS status Unsatisfiable
% 60.27/60.63 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------