%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : TOP051-1 : 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 41.72s 41.86s
% Output : CNFRefutation 41.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 24 RR)
% Number of literals : 43 ( 42 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-10 aty)
% Number of variables : 49 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
file('theBenchmark.p',goal) ).
cnf(c1,axiom,
product(X,X) = X,
file('theBenchmark.p',involutory_quandle) ).
cnf(c2,axiom,
product(a1,a6) = a2,
file('theBenchmark.p',knot) ).
cnf(c3,plain,
a2 = product(a1,a6),
inference(equational,[status(thm)],[c2]) ).
cnf(c4,axiom,
product(a2,a7) = a3,
file('theBenchmark.p',knot_03) ).
cnf(c5,plain,
a3 = product(product(a1,a6),a7),
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c6,axiom,
product(a3,a1) = a4,
file('theBenchmark.p',knot_04) ).
cnf(c7,plain,
a4 = product(product(product(a1,a6),a7),a1),
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c8,axiom,
product(a4,a10) = a5,
file('theBenchmark.p',knot_05) ).
cnf(c9,plain,
a5 = product(product(product(product(a1,a6),a7),a1),a10),
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c10,axiom,
product(a5,a9) = a6,
file('theBenchmark.p',knot_06) ).
cnf(c11,plain,
product(product(product(product(product(a1,a6),a7),a1),a10),a9) = a6,
inference(equational,[status(thm)],[c9,c10]) ).
cnf(c12,axiom,
product(a6,a2) = a7,
file('theBenchmark.p',knot_07) ).
cnf(c13,plain,
a7 = product(a6,product(a1,a6)),
inference(equational,[status(thm)],[c3,c12]) ).
cnf(c14,axiom,
product(a7,a3) = a8,
file('theBenchmark.p',knot_08) ).
cnf(c15,plain,
a8 = product(product(a6,product(a1,a6)),product(product(a1,a6),product(a6,product(a1,a6)))),
inference(equational,[status(thm)],[c5,c13,c14]) ).
cnf(c16,axiom,
product(a8,a6) = a9,
file('theBenchmark.p',knot_09) ).
cnf(c17,plain,
a9 = product(product(product(a6,product(a1,a6)),product(product(a1,a6),product(a6,product(a1,a6)))),a6),
inference(equational,[status(thm)],[c15,c16]) ).
cnf(c18,axiom,
product(a9,a4) = a10,
file('theBenchmark.p',knot_10) ).
cnf(c19,plain,
a10 = product(product(product(product(a6,product(a1,a6)),product(product(a1,a6),product(a6,product(a1,a6)))),a6),product(product(product(a1,a6),product(a6,product(a1,a6))),a1)),
inference(equational,[status(thm)],[c7,c13,c17,c18]) ).
cnf(c20,axiom,
product(a10,a5) = a11,
file('theBenchmark.p',knot_11) ).
cnf(c21,plain,
a11 = product(product(product(product(product(a6,product(a1,a6)),product(product(a1,a6),product(a6,product(a1,a6)))),a6),product(product(product(a1,a6),product(a6,product(a1,a6))),a1)),product(product(product(product(a1,a6),product(a6,product(a1,a6))),a1),product(product(product(product(a6,product(a1,a6)),product(product(a1,a6),product(a6,product(a1,a6)))),a6),product(product(product(a1,a6),product(a6,product(a1,a6))),a1)))),
inference(equational,[status(thm)],[c9,c13,c19,c20]) ).
cnf(c22,axiom,
product(product(X,Y),Y) = X,
file('theBenchmark.p',involutory_quandle_01) ).
cnf(c23,axiom,
product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)),
file('theBenchmark.p',involutory_quandle_02) ).
cnf(c24,plain,
product(product(X,Y),X) = product(X,product(Y,X)),
inference(equational,[status(thm)],[c1,c23]) ).
cnf(c25,plain,
product(product(product(X,Y),Z),Y) = product(X,product(Z,Y)),
inference(equational,[status(thm)],[c22,c23]) ).
cnf(c26,plain,
product(product(X,Y),product(Y,product(X,Y))) = product(X,product(X,Y)),
inference(equational,[status(thm)],[c23,c24,c25]) ).
cnf(c27,plain,
product(product(X,Y),product(Y,product(Z,Y))) = product(product(X,Z),product(Z,Y)),
inference(equational,[status(thm)],[c23,c24,c25]) ).
cnf(c28,plain,
product(product(product(X,Y),Z),product(Y,Z)) = product(X,Z),
inference(equational,[status(thm)],[c22,c23]) ).
cnf(c29,plain,
product(product(X,Y),product(Y,X)) = product(X,product(X,product(Y,X))),
inference(equational,[status(thm)],[c1,c27]) ).
cnf(c30,plain,
product(product(product(X,Y),Z),product(Z,product(Y,Z))) = product(X,product(Y,Z)),
inference(equational,[status(thm)],[c23,c24,c25]) ).
cnf(c31,plain,
product(product(product(X,Y),product(Z,Y)),W) = product(product(product(X,Z),W),product(Y,W)),
inference(equational,[status(thm)],[c23]) ).
cnf(c33,plain,
product(product(product(X,Y),Z),product(X,Z)) = product(product(X,product(Y,X)),Z),
inference(equational,[status(thm)],[c1,c31]) ).
cnf(c37,plain,
product(product(X,product(Y,X)),product(X,Y)) = product(product(X,Y),product(X,product(X,Y))),
inference(equational,[status(thm)],[c24]) ).
cnf(c41,plain,
product(product(X,Y),product(X,product(X,Y))) = product(X,product(Y,product(X,Y))),
inference(equational,[status(thm)],[c23,c24,c25,c26,c33]) ).
cnf(c43,plain,
product(product(X,Y),product(Z,product(Z,Y))) = product(product(X,Z),product(Y,product(Z,Y))),
inference(equational,[status(thm)],[c26,c28,c30]) ).
cnf(c44,plain,
product(product(X,Y),product(X,product(Y,X))) = product(X,product(Y,product(Y,X))),
inference(equational,[status(thm)],[c1,c43]) ).
cnf(c48,plain,
product(product(X,Y),product(product(Z,Y),product(W,Y))) = product(product(X,product(Z,W)),Y),
inference(equational,[status(thm)],[c23]) ).
cnf(c55,plain,
product(product(X,Y),product(Y,product(Y,product(X,Y)))) = product(X,product(X,product(X,Y))),
inference(equational,[status(thm)],[c1,c23,c24,c25,c26,c44,c48]) ).
cnf(c89,plain,
product(product(X,product(Y,Z)),product(Y,product(Z,Y))) = product(product(X,Y),product(Y,product(Y,product(Z,Y)))),
inference(equational,[status(thm)],[c24,c27]) ).
cnf(c178,plain,
a6 = a1,
inference(equational,[status(thm)],[c11,c13,c17,c19,c22,c23,c24,c26,c29,c41,c43,c44]) ).
cnf(g1,plain,
tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8) = tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
inference(equational,[status(thm)],[c1,c3,c5,c7,c9,c13,c15,c17,c19,c21,c22,c23,c26,c27,c29,c37,c41,c43,c55,c89,c178]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : TOP051-1 : TPTP v9.0.0. Released v8.1.0.
% 0.05/0.10 % Command : run_Leo-III %s %d THM
% 0.09/0.30 % Computer : n015.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Jul 14 23:31:19 EDT 2025
% 0.09/0.30 % CPUTime :
% 41.72/41.86 % SZS status Unsatisfiable
% 41.72/41.86 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------