%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP201-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n013.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 61.24s 61.41s
% Output : CNFRefutation 61.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of clauses : 65 ( 65 unt; 0 nHn; 3 RR)
% Number of literals : 65 ( 64 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 : 132 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
file('theBenchmark.p',prove_moufang3) ).
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(c12,plain,
left_inverse(right_inverse(X)) = X,
inference(equational,[status(thm)],[c3,c9,c11]) ).
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(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(multiply(X,Y),Z),Y) = multiply(X,multiply(Y,multiply(Z,Y))),
file('theBenchmark.p',moufang2) ).
cnf(c22,plain,
multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)),
inference(equational,[status(thm)],[c1,c2,c21]) ).
cnf(c23,plain,
multiply(multiply(X,Y),X) = multiply(X,multiply(Y,X)),
inference(equational,[status(thm)],[c1,c21]) ).
cnf(c24,plain,
multiply(X,multiply(right_inverse(X),X)) = X,
inference(equational,[status(thm)],[c1,c3,c23]) ).
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(c36,plain,
multiply(right_division(X,Y),multiply(Y,Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c7,c22]) ).
cnf(c43,plain,
multiply(X,multiply(left_division(X,Y),X)) = multiply(Y,X),
inference(equational,[status(thm)],[c13,c23]) ).
cnf(c44,plain,
multiply(left_division(X,Y),X) = left_division(X,multiply(Y,X)),
inference(equational,[status(thm)],[c15,c43]) ).
cnf(c46,plain,
multiply(left_inverse(X),multiply(X,multiply(Y,X))) = multiply(Y,X),
inference(equational,[status(thm)],[c1,c5,c21]) ).
cnf(c47,plain,
multiply(left_inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c7,c46]) ).
cnf(c48,plain,
left_division(left_inverse(X),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c15,c47]) ).
cnf(c49,plain,
multiply(left_inverse(X),Y) = left_division(X,Y),
inference(equational,[status(thm)],[c13,c47]) ).
cnf(c50,plain,
right_division(X,multiply(Y,X)) = left_inverse(Y),
inference(equational,[status(thm)],[c9,c47]) ).
cnf(c51,plain,
left_inverse(right_division(X,Y)) = right_division(Y,X),
inference(equational,[status(thm)],[c7,c50]) ).
cnf(c52,plain,
right_division(left_division(X,Y),Y) = left_inverse(X),
inference(equational,[status(thm)],[c13,c50]) ).
cnf(c53,plain,
multiply(left_division(X,Y),Y) = left_division(X,multiply(Y,Y)),
inference(equational,[status(thm)],[c22,c49]) ).
cnf(c54,plain,
multiply(right_division(X,Y),Z) = left_division(right_division(Y,X),Z),
inference(equational,[status(thm)],[c48,c51]) ).
cnf(c56,plain,
right_division(multiply(X,Y),multiply(Y,Y)) = right_division(X,Y),
inference(equational,[status(thm)],[c9,c36]) ).
cnf(c57,plain,
right_division(right_division(X,Y),Y) = right_division(X,multiply(Y,Y)),
inference(equational,[status(thm)],[c7,c56]) ).
cnf(c58,plain,
right_division(multiply(X,X),Y) = right_division(X,right_division(Y,X)),
inference(equational,[status(thm)],[c51,c57]) ).
cnf(c62,plain,
multiply(multiply(X,multiply(Y,X)),Y) = multiply(X,multiply(Y,multiply(X,Y))),
inference(equational,[status(thm)],[c21,c23]) ).
cnf(c63,plain,
multiply(multiply(X,Y),left_division(Y,X)) = multiply(X,X),
inference(equational,[status(thm)],[c13,c43,c53,c62]) ).
cnf(c64,plain,
right_division(X,left_inverse(Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c9,c52,c58,c63]) ).
cnf(c65,plain,
multiply(X,left_inverse(Y)) = right_division(X,Y),
inference(equational,[status(thm)],[c12,c26,c64]) ).
cnf(c66,plain,
right_division(left_inverse(X),Y) = left_inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c51,c64]) ).
cnf(c67,plain,
left_inverse(left_division(X,Y)) = left_division(Y,X),
inference(equational,[status(thm)],[c49,c64,c66]) ).
cnf(c68,plain,
left_division(multiply(X,Y),X) = left_inverse(Y),
inference(equational,[status(thm)],[c19,c64]) ).
cnf(c70,plain,
left_division(X,left_inverse(Y)) = left_inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c47,c68]) ).
cnf(c72,plain,
multiply(X,right_division(Y,Z)) = right_division(X,right_division(Z,Y)),
inference(equational,[status(thm)],[c51,c64]) ).
cnf(c74,plain,
right_division(left_division(X,Y),X) = left_division(X,right_division(Y,X)),
inference(equational,[status(thm)],[c23,c49,c65]) ).
cnf(c83,plain,
right_division(X,left_division(X,multiply(Y,X))) = left_division(Y,X),
inference(equational,[status(thm)],[c44,c50,c67]) ).
cnf(c85,plain,
right_division(X,left_division(X,Y)) = left_division(right_division(Y,X),X),
inference(equational,[status(thm)],[c7,c83]) ).
cnf(c87,plain,
multiply(left_division(X,Y),Z) = left_division(left_division(Y,X),Z),
inference(equational,[status(thm)],[c9,c54,c74,c83]) ).
cnf(c88,plain,
multiply(X,left_division(Y,Z)) = right_division(X,left_division(Z,Y)),
inference(equational,[status(thm)],[c9,c72,c74,c83]) ).
cnf(c89,plain,
right_division(X,multiply(X,multiply(Y,X))) = left_inverse(multiply(X,Y)),
inference(equational,[status(thm)],[c23,c50]) ).
cnf(c97,plain,
left_division(right_division(X,Y),multiply(X,multiply(Z,X))) = multiply(multiply(Y,Z),X),
inference(equational,[status(thm)],[c7,c21,c54]) ).
cnf(c98,plain,
left_division(left_division(X,left_division(Y,Z)),Y) = left_division(Z,multiply(Y,multiply(X,Y))),
inference(equational,[status(thm)],[c20,c87,c97]) ).
cnf(c99,plain,
left_division(right_division(right_division(X,Y),Z),X) = left_division(right_division(X,Z),multiply(X,Y)),
inference(equational,[status(thm)],[c7,c54,c72,c97]) ).
cnf(c101,plain,
right_division(multiply(X,multiply(Y,multiply(Z,Y))),Y) = multiply(multiply(X,Y),Z),
inference(equational,[status(thm)],[c9,c21]) ).
cnf(c102,plain,
right_division(multiply(X,multiply(Y,Z)),Y) = right_division(multiply(X,Y),right_division(Y,Z)),
inference(equational,[status(thm)],[c7,c72,c101]) ).
cnf(c170,plain,
left_division(right_division(multiply(X,Y),Z),X) = left_division(right_division(X,Z),right_division(X,Y)),
inference(equational,[status(thm)],[c64,c65,c99]) ).
cnf(c182,plain,
right_division(X,left_division(Y,multiply(X,multiply(Z,X)))) = left_division(Z,left_division(X,Y)),
inference(equational,[status(thm)],[c20,c98]) ).
cnf(c183,plain,
right_division(X,left_division(Y,multiply(Z,X))) = left_division(left_division(X,Z),left_division(X,Y)),
inference(equational,[status(thm)],[c43,c182]) ).
cnf(c186,plain,
right_division(multiply(X,Y),left_division(Z,Y)) = right_division(Y,left_division(Z,left_division(X,Y))),
inference(equational,[status(thm)],[c48,c49,c70,c88,c183]) ).
cnf(c188,plain,
right_division(X,left_division(right_division(Y,X),left_division(Z,X))) = right_division(multiply(Z,Y),X),
inference(equational,[status(thm)],[c13,c85,c102,c186]) ).
cnf(c189,plain,
right_division(left_division(right_division(X,Y),Z),Y) = right_division(Y,left_division(right_division(Z,Y),X)),
inference(equational,[status(thm)],[c19,c54,c188]) ).
cnf(c191,plain,
right_division(multiply(multiply(X,Y),Z),X) = right_division(X,right_division(right_division(X,Z),Y)),
inference(equational,[status(thm)],[c50,c51,c70,c72,c97,c170,c189]) ).
cnf(c221,plain,
multiply(multiply(X,multiply(Y,X)),Z) = multiply(X,multiply(Y,multiply(X,Z))),
inference(equational,[status(thm)],[c23,c64,c66,c89,c101,c191]) ).
cnf(g1,plain,
multiply(multiply(multiply(a,b),a),c) = multiply(a,multiply(b,multiply(a,c))),
inference(equational,[status(thm)],[c23,c221]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP201-1 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:16:49 EDT 2025
% 0.11/0.32 % CPUTime :
% 61.24/61.41 % SZS status Unsatisfiable
% 61.24/61.41 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------