%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP200-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n008.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 62.23s 62.54s
% Output : CNFRefutation 62.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 3 RR)
% Number of literals : 52 ( 51 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 : 95 ( 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(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(c7,axiom,
multiply(right_division(X,Y),Y) = X,
file('theBenchmark.p',multiply_right_division) ).
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(c17,plain,
left_division(X,identity) = right_inverse(X),
inference(equational,[status(thm)],[c3,c15]) ).
cnf(c18,plain,
right_inverse(left_inverse(X)) = X,
inference(equational,[status(thm)],[c5,c15,c17]) ).
cnf(c19,plain,
left_division(right_division(X,Y),X) = Y,
inference(equational,[status(thm)],[c7,c15]) ).
cnf(c20,plain,
right_division(X,left_division(Y,X)) = Y,
inference(equational,[status(thm)],[c9,c13]) ).
cnf(c21,axiom,
multiply(multiply(X,multiply(Y,Z)),X) = multiply(multiply(X,Y),multiply(Z,X)),
file('theBenchmark.p',moufang1) ).
cnf(c22,plain,
multiply(multiply(X,Y),X) = multiply(X,multiply(Y,X)),
inference(equational,[status(thm)],[c1,c2,c21]) ).
cnf(c23,plain,
multiply(X,multiply(right_inverse(X),X)) = X,
inference(equational,[status(thm)],[c1,c3,c22]) ).
cnf(c24,plain,
multiply(right_inverse(X),X) = identity,
inference(equational,[status(thm)],[c15,c16,c23]) ).
cnf(c25,plain,
right_inverse(X) = left_inverse(X),
inference(equational,[status(thm)],[c9,c11,c24]) ).
cnf(c26,plain,
left_inverse(left_inverse(X)) = X,
inference(equational,[status(thm)],[c18,c25]) ).
cnf(c28,plain,
multiply(X,multiply(left_division(X,Y),X)) = multiply(Y,X),
inference(equational,[status(thm)],[c13,c22]) ).
cnf(c30,plain,
multiply(left_division(X,Y),X) = left_division(X,multiply(Y,X)),
inference(equational,[status(thm)],[c15,c28]) ).
cnf(c34,plain,
right_division(multiply(X,multiply(Y,X)),X) = multiply(X,Y),
inference(equational,[status(thm)],[c9,c22]) ).
cnf(c35,plain,
multiply(X,right_division(Y,X)) = right_division(multiply(X,Y),X),
inference(equational,[status(thm)],[c7,c34]) ).
cnf(c46,plain,
multiply(multiply(X,Y),multiply(Z,X)) = multiply(X,multiply(multiply(Y,Z),X)),
inference(equational,[status(thm)],[c21,c22]) ).
cnf(c52,plain,
right_division(left_division(X,multiply(Y,X)),X) = left_division(X,Y),
inference(equational,[status(thm)],[c9,c30]) ).
cnf(c53,plain,
right_division(left_division(X,Y),X) = left_division(X,right_division(Y,X)),
inference(equational,[status(thm)],[c7,c52]) ).
cnf(c54,plain,
left_division(X,right_division(multiply(X,Y),X)) = right_division(Y,X),
inference(equational,[status(thm)],[c15,c35]) ).
cnf(c60,plain,
multiply(X,multiply(multiply(Y,left_inverse(X)),X)) = multiply(X,Y),
inference(equational,[status(thm)],[c2,c5,c46]) ).
cnf(c61,plain,
multiply(X,left_inverse(Y)) = right_division(X,Y),
inference(equational,[status(thm)],[c9,c54,c60]) ).
cnf(c62,plain,
right_division(X,left_inverse(Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c26,c61]) ).
cnf(c63,plain,
left_division(X,right_division(X,Y)) = left_inverse(Y),
inference(equational,[status(thm)],[c15,c61]) ).
cnf(c64,plain,
left_inverse(left_division(X,Y)) = left_division(Y,X),
inference(equational,[status(thm)],[c20,c63]) ).
cnf(c70,plain,
multiply(X,multiply(multiply(left_inverse(X),Y),X)) = multiply(Y,X),
inference(equational,[status(thm)],[c1,c3,c25,c46]) ).
cnf(c71,plain,
multiply(left_inverse(X),Y) = left_division(X,Y),
inference(equational,[status(thm)],[c9,c54,c70]) ).
cnf(c72,plain,
left_division(left_inverse(X),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c26,c71]) ).
cnf(c73,plain,
right_division(left_inverse(X),Y) = left_division(X,left_inverse(Y)),
inference(equational,[status(thm)],[c61,c71]) ).
cnf(c74,plain,
right_division(left_division(X,Y),Y) = left_inverse(X),
inference(equational,[status(thm)],[c9,c71]) ).
cnf(c75,plain,
left_inverse(right_division(X,Y)) = right_division(Y,X),
inference(equational,[status(thm)],[c19,c74]) ).
cnf(c76,plain,
right_division(X,multiply(Y,X)) = left_inverse(Y),
inference(equational,[status(thm)],[c15,c74]) ).
cnf(c79,plain,
left_division(X,left_inverse(Y)) = left_inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c63,c76]) ).
cnf(c97,plain,
multiply(X,left_division(Y,Z)) = right_division(X,left_division(Z,Y)),
inference(equational,[status(thm)],[c61,c64]) ).
cnf(c99,plain,
multiply(right_division(X,Y),Z) = left_division(right_division(Y,X),Z),
inference(equational,[status(thm)],[c72,c75]) ).
cnf(c100,plain,
multiply(X,right_division(Y,Z)) = right_division(X,right_division(Z,Y)),
inference(equational,[status(thm)],[c61,c75]) ).
cnf(c102,plain,
right_division(X,left_division(X,Y)) = left_division(right_division(Y,X),X),
inference(equational,[status(thm)],[c53,c64,c75]) ).
cnf(c127,plain,
left_division(right_division(right_division(right_division(X,Y),Z),X),X) = multiply(multiply(X,Z),Y),
inference(equational,[status(thm)],[c7,c46,c97,c99,c100,c102]) ).
cnf(c179,plain,
left_division(right_division(left_division(right_division(X,Y),Z),X),Y) = left_division(right_division(Z,X),X),
inference(equational,[status(thm)],[c20,c97,c99,c127]) ).
cnf(c180,plain,
right_division(left_division(right_division(X,Y),Z),X) = right_division(Y,left_division(right_division(Z,X),X)),
inference(equational,[status(thm)],[c20,c179]) ).
cnf(c221,plain,
multiply(multiply(multiply(X,Y),Z),Y) = multiply(X,multiply(Y,multiply(Z,Y))),
inference(equational,[status(thm)],[c62,c72,c73,c79,c180]) ).
cnf(g1,plain,
multiply(multiply(multiply(a,b),c),b) = multiply(a,multiply(b,multiply(c,b))),
inference(equational,[status(thm)],[c221]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP200-1 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:16:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 62.23/62.54 % SZS status Unsatisfiable
% 62.23/62.54 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------