%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : TOP049-1 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n015.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 08:44:17 AM UTC 2025
% Result : Unsatisfiable 5.93s 6.11s
% Output : CNFRefutation 5.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 62 ( 62 unt; 0 nHn; 41 RR)
% Number of literals : 62 ( 61 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 : 12 ( 12 usr; 10 con; 0-9 aty)
% Number of variables : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
file('theBenchmark.p',goal) ).
cnf(c1,axiom,
product(X,X) = X,
file('theBenchmark.p',involutory_quandle) ).
cnf(c2,axiom,
a1 = product(a9,a7),
file('theBenchmark.p',knot) ).
cnf(c3,axiom,
a3 = product(a1,a2),
file('theBenchmark.p',knot_03) ).
cnf(c4,plain,
product(product(a9,a7),a2) = a3,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,axiom,
a2 = product(a3,a4),
file('theBenchmark.p',knot_04) ).
cnf(c6,axiom,
a5 = product(a2,a10),
file('theBenchmark.p',knot_05) ).
cnf(c7,plain,
a5 = product(product(a3,a4),a10),
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c8,axiom,
a6 = product(a5,a4),
file('theBenchmark.p',knot_06) ).
cnf(c9,plain,
a6 = product(product(product(a3,a4),a10),a4),
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c12,axiom,
a8 = product(a7,a4),
file('theBenchmark.p',knot_08) ).
cnf(c13,axiom,
a10 = product(a8,a9),
file('theBenchmark.p',knot_09) ).
cnf(c14,plain,
a10 = product(product(a7,a4),a9),
inference(equational,[status(thm)],[c12,c13]) ).
cnf(c15,axiom,
a4 = product(a10,a3),
file('theBenchmark.p',knot_10) ).
cnf(c16,plain,
product(product(product(a7,a4),a9),a3) = a4,
inference(equational,[status(thm)],[c14,c15]) ).
cnf(c17,axiom,
a9 = product(a4,a8),
file('theBenchmark.p',knot_11) ).
cnf(c18,plain,
a9 = product(a4,product(a7,a4)),
inference(equational,[status(thm)],[c12,c17]) ).
cnf(c19,axiom,
product(product(X,Y),Y) = X,
file('theBenchmark.p',involutory_quandle_01) ).
cnf(c20,axiom,
product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)),
file('theBenchmark.p',involutory_quandle_02) ).
cnf(c21,plain,
product(product(X,Y),X) = product(X,product(Y,X)),
inference(equational,[status(thm)],[c1,c20]) ).
cnf(c22,plain,
product(product(product(a4,product(a3,a4)),product(a7,product(a3,a4))),product(product(a7,product(a3,a4)),product(product(a4,product(a3,a4)),product(a7,product(a3,a4))))) = a3,
inference(equational,[status(thm)],[c4,c5,c18,c20,c21]) ).
cnf(c23,plain,
product(product(product(X,Y),Z),Y) = product(X,product(Z,Y)),
inference(equational,[status(thm)],[c19,c20]) ).
cnf(c24,plain,
product(product(X,Y),product(Y,product(X,Y))) = product(X,product(X,Y)),
inference(equational,[status(thm)],[c20,c21,c23]) ).
cnf(c25,plain,
product(a4,product(a4,a7)) = product(a3,product(a3,a4)),
inference(equational,[status(thm)],[c4,c5,c18,c19,c20,c21,c24]) ).
cnf(c26,plain,
product(product(X,Y),product(Y,product(Z,Y))) = product(product(X,Z),product(Z,Y)),
inference(equational,[status(thm)],[c20,c21,c23]) ).
cnf(c27,plain,
product(product(product(X,Y),Z),product(Y,Z)) = product(X,Z),
inference(equational,[status(thm)],[c19,c20]) ).
cnf(c28,plain,
product(product(a4,X),product(a3,X)) = product(product(a7,product(a7,a4)),X),
inference(equational,[status(thm)],[c16,c18,c24,c27]) ).
cnf(c29,plain,
product(a7,product(a7,a4)) = product(a4,a3),
inference(equational,[status(thm)],[c19,c23,c28]) ).
cnf(c30,plain,
product(product(a4,a3),product(a7,a4)) = a7,
inference(equational,[status(thm)],[c19,c29]) ).
cnf(c31,plain,
product(product(X,Y),product(Y,X)) = product(X,product(X,product(Y,X))),
inference(equational,[status(thm)],[c1,c26]) ).
cnf(c32,plain,
product(a4,product(a4,product(a7,a4))) = product(a3,product(a4,a3)),
inference(equational,[status(thm)],[c19,c20,c21,c25]) ).
cnf(c37,plain,
product(product(product(X,Y),product(Z,Y)),W) = product(product(product(X,Z),W),product(Y,W)),
inference(equational,[status(thm)],[c20]) ).
cnf(c38,plain,
product(product(product(X,Y),Z),product(X,Z)) = product(product(X,product(Y,X)),Z),
inference(equational,[status(thm)],[c1,c37]) ).
cnf(c41,plain,
product(product(product(X,Y),Z),X) = product(product(X,product(Y,X)),product(Z,X)),
inference(equational,[status(thm)],[c20,c21]) ).
cnf(c43,plain,
product(a7,a4) = product(product(a4,product(a3,a4)),a7),
inference(equational,[status(thm)],[c19,c30,c41]) ).
cnf(c44,plain,
product(a7,product(a4,a7)) = product(a4,product(a3,a4)),
inference(equational,[status(thm)],[c19,c21,c43]) ).
cnf(c46,plain,
product(a7,product(a4,product(a3,a4))) = product(product(a4,a3),a7),
inference(equational,[status(thm)],[c21,c24,c30,c44]) ).
cnf(c48,plain,
product(product(product(product(X,Y),Z),W),Y) = product(product(X,product(Z,Y)),product(W,Y)),
inference(equational,[status(thm)],[c20,c23]) ).
cnf(c49,plain,
product(product(product(X,product(Y,Z)),W),Z) = product(product(product(X,Z),Y),product(W,Z)),
inference(equational,[status(thm)],[c23]) ).
cnf(c52,plain,
product(product(a4,X),product(product(a4,a7),X)) = product(product(a3,product(a3,a4)),X),
inference(equational,[status(thm)],[c20,c25]) ).
cnf(c53,plain,
product(product(X,Y),product(X,product(X,Y))) = product(X,product(Y,product(X,Y))),
inference(equational,[status(thm)],[c20,c21,c23,c24,c38]) ).
cnf(c54,plain,
product(product(product(X,Y),Z),product(Z,Y)) = product(X,product(Y,product(Z,Y))),
inference(equational,[status(thm)],[c19,c26]) ).
cnf(c55,plain,
product(product(a4,a3),product(product(a4,product(a4,product(a3,a4))),product(a7,product(a3,a4)))) = a3,
inference(equational,[status(thm)],[c4,c5,c18,c19,c20,c21,c31,c43,c46,c49]) ).
cnf(c59,plain,
product(product(a4,product(a4,product(a3,a4))),product(product(a4,a3),a7)) = product(a3,product(a3,a4)),
inference(equational,[status(thm)],[c19,c20,c22,c23,c44,c46,c48]) ).
cnf(c66,plain,
product(product(X,product(X,Y)),product(Y,X)) = product(X,product(Y,product(Y,X))),
inference(equational,[status(thm)],[c19,c21,c24,c54]) ).
cnf(c67,plain,
product(a7,product(a3,product(a3,a4))) = product(product(a4,a3),product(a4,a7)),
inference(equational,[status(thm)],[c25,c29,c66]) ).
cnf(c74,plain,
product(a4,product(product(a4,product(a3,a4)),a7)) = product(product(a3,product(a3,a4)),a7),
inference(equational,[status(thm)],[c19,c21,c43,c52]) ).
cnf(c85,plain,
product(product(product(a3,product(a3,a4)),a7),product(a3,product(product(a4,product(a3,a4)),a7))) = a7,
inference(equational,[status(thm)],[c19,c28,c43,c74]) ).
cnf(c86,plain,
product(product(a3,product(a4,a3)),product(product(a3,product(a3,a4)),a7)) = a4,
inference(equational,[status(thm)],[c19,c32,c43,c74]) ).
cnf(c88,plain,
product(product(a4,product(a3,product(a3,a4))),product(product(a4,a3),product(a4,a7))) = product(a4,product(a4,product(a3,a4))),
inference(equational,[status(thm)],[c20,c25,c44,c53,c67]) ).
cnf(c90,plain,
product(product(a3,product(a4,a3)),product(a4,a7)) = product(a4,product(a3,product(a3,a4))),
inference(equational,[status(thm)],[c19,c21,c25,c31,c32]) ).
cnf(c91,plain,
product(a3,product(a4,a7)) = product(a4,product(a4,product(a3,a4))),
inference(equational,[status(thm)],[c27,c88,c90]) ).
cnf(c96,plain,
product(product(product(X,Y),Z),product(W,Z)) = product(product(product(X,W),Z),product(product(Y,W),Z)),
inference(equational,[status(thm)],[c20,c37]) ).
cnf(c110,plain,
product(product(product(a3,product(a3,a4)),X),product(a4,a7)) = product(a4,product(X,product(a4,a7))),
inference(equational,[status(thm)],[c23,c25]) ).
cnf(c111,plain,
product(product(a3,product(a4,a3)),a7) = product(a4,product(a4,product(a3,a4))),
inference(equational,[status(thm)],[c19,c38,c44,c96,c110]) ).
cnf(c112,plain,
product(a3,a7) = product(a3,product(a3,a4)),
inference(equational,[status(thm)],[c27,c59,c111]) ).
cnf(c113,plain,
product(product(a3,product(a3,a4)),a7) = a3,
inference(equational,[status(thm)],[c19,c112]) ).
cnf(c114,plain,
product(a3,a4) = a4,
inference(equational,[status(thm)],[c19,c21,c86,c113]) ).
cnf(c115,plain,
a7 = a4,
inference(equational,[status(thm)],[c1,c21,c25,c43,c85,c91,c114]) ).
cnf(c116,plain,
a4 = a3,
inference(equational,[status(thm)],[c1,c21,c25,c43,c55,c114]) ).
cnf(g1,plain,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(equational,[status(thm)],[c1,c2,c5,c7,c9,c12,c14,c18,c19,c20,c21,c24,c25,c26,c29,c43,c44,c74,c113,c114,c115,c116]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : TOP049-1 : TPTP v9.0.0. Released v8.1.0.
% 0.02/0.10 % Command : run_Leo-III %s %d THM
% 0.10/0.30 % Computer : n015.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Jul 14 23:31:04 EDT 2025
% 0.10/0.30 % CPUTime :
% 5.93/6.11 % SZS status Unsatisfiable
% 5.93/6.11 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------