%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : TOP049-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 02:33:47 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.37s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 14
% Syntax : Number of clauses : 287 ( 287 unt; 0 nHn; 270 RR)
% Number of literals : 287 ( 286 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 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 : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
product(X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle) ).
cnf(c3,plain,
product(a2,a2) = a2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
a2 = product(a2,a2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
a7 = product(a6,a1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
product(a7,a2) = product(product(a6,a1),a2),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
a3 = product(a1,a2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c8,plain,
product(product(X2,a2),a3) = product(product(X2,a2),product(a1,a2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
product(product(X2,Y),Z) = product(product(X2,Z),product(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_02) ).
cnf(c10,plain,
product(product(X2,a1),a2) = product(product(X2,a2),product(a1,a2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
product(product(X2,a2),product(a1,a2)) = product(product(X2,a1),a2),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
product(product(X2,a2),a3) = product(product(X2,a1),a2),
inference(transitivity,[status(thm)],[c8,c11]) ).
cnf(c13,plain,
product(product(a6,a2),a3) = product(product(a6,a1),a2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
product(product(a6,a1),a2) = product(product(a6,a2),a3),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,axiom,
a2 = product(a3,a4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c16,plain,
product(a2,a3) = product(product(a3,a4),a3),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
product(product(X2,X3),X2) = product(product(X2,X2),product(X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c18,plain,
product(product(X3,X3),product(X2,X3)) = product(X3,product(X2,X3)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c19,plain,
product(product(X3,X2),X3) = product(X3,product(X2,X3)),
inference(transitivity,[status(thm)],[c17,c18]) ).
cnf(c20,plain,
product(product(a3,a4),a3) = product(a3,product(a4,a3)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,axiom,
a4 = product(a10,a3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c22,plain,
product(a4,a3) = product(product(a10,a3),a3),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,axiom,
product(product(X2,Y2),Y2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_01) ).
cnf(c24,plain,
product(product(a10,a3),a3) = a10,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
product(a4,a3) = a10,
inference(transitivity,[status(thm)],[c22,c24]) ).
cnf(c26,plain,
product(a3,product(a4,a3)) = product(a3,a10),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
product(product(a3,a4),a3) = product(a3,a10),
inference(transitivity,[status(thm)],[c20,c26]) ).
cnf(c28,plain,
product(a2,a3) = product(a3,a10),
inference(transitivity,[status(thm)],[c16,c27]) ).
cnf(c29,plain,
product(a3,a10) = product(a2,a3),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,axiom,
a5 = product(a2,a10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c31,plain,
product(a5,a10) = product(product(a2,a10),a10),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
product(product(a2,a10),a10) = a2,
inference(substitution,[status(thm)],[c23]) ).
cnf(c33,plain,
product(a5,a10) = a2,
inference(transitivity,[status(thm)],[c31,c32]) ).
cnf(c34,plain,
a2 = product(a5,a10),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
product(a2,a3) = product(product(a5,a10),a3),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
product(product(X2,a3),a4) = product(product(X2,a3),product(a10,a3)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c37,plain,
product(product(X2,a10),a3) = product(product(X2,a3),product(a10,a3)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c38,plain,
product(product(X2,a3),product(a10,a3)) = product(product(X2,a10),a3),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
product(product(X2,a3),a4) = product(product(X2,a10),a3),
inference(transitivity,[status(thm)],[c36,c38]) ).
cnf(c40,plain,
product(product(a5,a3),a4) = product(product(a5,a10),a3),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
product(product(a5,a10),a3) = product(product(a5,a3),a4),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
product(product(a5,X2),a4) = product(product(a5,a4),product(X2,a4)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c43,axiom,
a6 = product(a5,a4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c44,plain,
product(a5,a4) = a6,
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
product(product(a5,a4),product(X2,a4)) = product(a6,product(X2,a4)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
product(product(a5,X2),a4) = product(a6,product(X2,a4)),
inference(transitivity,[status(thm)],[c42,c45]) ).
cnf(c47,plain,
product(product(a5,a3),a4) = product(a6,product(a3,a4)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
product(a3,a4) = a2,
inference(symmetry,[status(thm)],[c15]) ).
cnf(c49,plain,
product(a6,product(a3,a4)) = product(a6,a2),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
product(product(a5,a3),a4) = product(a6,a2),
inference(transitivity,[status(thm)],[c47,c49]) ).
cnf(c51,plain,
product(product(a5,a10),a3) = product(a6,a2),
inference(transitivity,[status(thm)],[c41,c50]) ).
cnf(c52,plain,
product(a2,a3) = product(a6,a2),
inference(transitivity,[status(thm)],[c35,c51]) ).
cnf(c53,plain,
product(a3,a10) = product(a6,a2),
inference(transitivity,[status(thm)],[c29,c52]) ).
cnf(c54,plain,
product(a6,a2) = product(a3,a10),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
product(product(a6,a2),a3) = product(product(a3,a10),a3),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
product(product(a3,a10),a3) = product(a3,product(a10,a3)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c57,plain,
product(a10,a3) = a4,
inference(symmetry,[status(thm)],[c21]) ).
cnf(c58,plain,
product(a3,product(a10,a3)) = product(a3,a4),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
product(a3,a4) = a2,
inference(symmetry,[status(thm)],[c15]) ).
cnf(c60,plain,
product(a3,product(a10,a3)) = a2,
inference(transitivity,[status(thm)],[c58,c59]) ).
cnf(c61,plain,
product(product(a3,a10),a3) = a2,
inference(transitivity,[status(thm)],[c56,c60]) ).
cnf(c62,plain,
product(product(a6,a2),a3) = a2,
inference(transitivity,[status(thm)],[c55,c61]) ).
cnf(c63,plain,
product(product(a6,a1),a2) = a2,
inference(transitivity,[status(thm)],[c14,c62]) ).
cnf(c64,plain,
product(a7,a2) = a2,
inference(transitivity,[status(thm)],[c6,c63]) ).
cnf(c65,plain,
a2 = product(a7,a2),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
product(a2,a2) = product(product(a7,a2),a2),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
product(product(a7,a2),a2) = a7,
inference(substitution,[status(thm)],[c23]) ).
cnf(c68,plain,
product(a2,a2) = a7,
inference(transitivity,[status(thm)],[c66,c67]) ).
cnf(c69,plain,
a2 = a7,
inference(transitivity,[status(thm)],[c4,c68]) ).
cnf(c70,plain,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) = tuple(a1,a9,a8,a6,a7,a7,a3,a4,a5),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
product(a1,a2) = product(a1,a7),
inference(congruence,[status(thm)],[c69]) ).
cnf(c72,axiom,
a1 = product(a9,a7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c73,plain,
product(a1,a7) = product(product(a9,a7),a7),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
product(product(a9,a7),a7) = a9,
inference(substitution,[status(thm)],[c23]) ).
cnf(c75,plain,
product(a1,a7) = a9,
inference(transitivity,[status(thm)],[c73,c74]) ).
cnf(c76,plain,
product(a1,a2) = a9,
inference(transitivity,[status(thm)],[c71,c75]) ).
cnf(c77,plain,
a3 = a9,
inference(transitivity,[status(thm)],[c7,c76]) ).
cnf(c78,plain,
tuple(a1,a9,a8,a6,a7,a7,a3,a4,a5) = tuple(a1,a9,a8,a6,a7,a7,a9,a4,a5),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
product(a10,a3) = product(a10,a9),
inference(congruence,[status(thm)],[c77]) ).
cnf(c80,axiom,
a10 = product(a8,a9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c81,plain,
product(a10,a9) = product(product(a8,a9),a9),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
product(product(a8,a9),a9) = a8,
inference(substitution,[status(thm)],[c23]) ).
cnf(c83,plain,
product(a10,a9) = a8,
inference(transitivity,[status(thm)],[c81,c82]) ).
cnf(c84,plain,
product(a10,a3) = a8,
inference(transitivity,[status(thm)],[c79,c83]) ).
cnf(c85,plain,
a4 = a8,
inference(transitivity,[status(thm)],[c21,c84]) ).
cnf(c86,plain,
tuple(a1,a9,a8,a6,a7,a7,a9,a4,a5) = tuple(a1,a9,a8,a6,a7,a7,a9,a8,a5),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,axiom,
a8 = product(a7,a4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c88,plain,
a7 = a2,
inference(symmetry,[status(thm)],[c69]) ).
cnf(c89,plain,
product(a7,a4) = product(a2,a4),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
product(a2,a4) = product(product(a3,a4),a4),
inference(congruence,[status(thm)],[c15]) ).
cnf(c91,plain,
product(product(a3,a4),a4) = a3,
inference(substitution,[status(thm)],[c23]) ).
cnf(c92,plain,
product(a2,a4) = a3,
inference(transitivity,[status(thm)],[c90,c91]) ).
cnf(c93,plain,
product(a2,a4) = a9,
inference(transitivity,[status(thm)],[c92,c77]) ).
cnf(c94,plain,
product(a7,a4) = a9,
inference(transitivity,[status(thm)],[c89,c93]) ).
cnf(c95,plain,
a8 = a9,
inference(transitivity,[status(thm)],[c87,c94]) ).
cnf(c96,plain,
tuple(a1,a9,a8,a6,a7,a7,a9,a8,a5) = tuple(a1,a9,a9,a6,a7,a7,a9,a8,a5),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
tuple(a1,a9,a9,a6,a7,a7,a9,a8,a5) = tuple(a1,a9,a9,a6,a7,a7,a9,a9,a5),
inference(congruence,[status(thm)],[c95]) ).
cnf(c98,plain,
a9 = a8,
inference(symmetry,[status(thm)],[c95]) ).
cnf(c99,plain,
product(a7,a4) = product(a7,a8),
inference(congruence,[status(thm)],[c85]) ).
cnf(c100,plain,
product(a8,a4) = product(product(a7,a4),a4),
inference(congruence,[status(thm)],[c87]) ).
cnf(c101,plain,
product(product(a7,a4),a4) = a7,
inference(substitution,[status(thm)],[c23]) ).
cnf(c102,plain,
product(a8,a4) = a7,
inference(transitivity,[status(thm)],[c100,c101]) ).
cnf(c103,plain,
a7 = product(a8,a4),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
product(a7,a8) = product(product(a8,a4),a8),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
product(product(a8,a4),a8) = product(a8,product(a4,a8)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c106,axiom,
a9 = product(a4,a8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c107,plain,
product(a4,a8) = a9,
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
product(a8,product(a4,a8)) = product(a8,a9),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
product(a8,a9) = a10,
inference(symmetry,[status(thm)],[c80]) ).
cnf(c110,plain,
product(a8,product(a4,a8)) = a10,
inference(transitivity,[status(thm)],[c108,c109]) ).
cnf(c111,plain,
product(product(a8,a4),a8) = a10,
inference(transitivity,[status(thm)],[c105,c110]) ).
cnf(c112,plain,
product(a7,a8) = a10,
inference(transitivity,[status(thm)],[c104,c111]) ).
cnf(c113,plain,
product(a7,a4) = a10,
inference(transitivity,[status(thm)],[c99,c112]) ).
cnf(c114,plain,
a8 = a10,
inference(transitivity,[status(thm)],[c87,c113]) ).
cnf(c115,plain,
a9 = a10,
inference(transitivity,[status(thm)],[c98,c114]) ).
cnf(c116,plain,
tuple(a1,a9,a9,a6,a7,a7,a9,a9,a5) = tuple(a1,a10,a9,a6,a7,a7,a9,a9,a5),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
tuple(a1,a10,a9,a6,a7,a7,a9,a9,a5) = tuple(a1,a10,a10,a6,a7,a7,a9,a9,a5),
inference(congruence,[status(thm)],[c115]) ).
cnf(c118,plain,
tuple(a1,a10,a10,a6,a7,a7,a9,a9,a5) = tuple(a1,a10,a10,a6,a7,a7,a10,a9,a5),
inference(congruence,[status(thm)],[c115]) ).
cnf(c119,plain,
tuple(a1,a10,a10,a6,a7,a7,a10,a9,a5) = tuple(a1,a10,a10,a6,a7,a7,a10,a10,a5),
inference(congruence,[status(thm)],[c115]) ).
cnf(c120,plain,
a7 = a2,
inference(symmetry,[status(thm)],[c69]) ).
cnf(c121,plain,
product(a3,a4) = product(a3,a8),
inference(congruence,[status(thm)],[c85]) ).
cnf(c122,plain,
product(a3,a8) = product(a9,a8),
inference(congruence,[status(thm)],[c77]) ).
cnf(c123,plain,
product(a9,a8) = product(product(a4,a8),a8),
inference(congruence,[status(thm)],[c106]) ).
cnf(c124,plain,
product(product(a4,a8),a8) = a4,
inference(substitution,[status(thm)],[c23]) ).
cnf(c125,plain,
product(a9,a8) = a4,
inference(transitivity,[status(thm)],[c123,c124]) ).
cnf(c126,plain,
a8 = a10,
inference(transitivity,[status(thm)],[c95,c115]) ).
cnf(c127,plain,
a4 = a10,
inference(transitivity,[status(thm)],[c85,c126]) ).
cnf(c128,plain,
product(a9,a8) = a10,
inference(transitivity,[status(thm)],[c125,c127]) ).
cnf(c129,plain,
product(a3,a8) = a10,
inference(transitivity,[status(thm)],[c122,c128]) ).
cnf(c130,plain,
product(a3,a4) = a10,
inference(transitivity,[status(thm)],[c121,c129]) ).
cnf(c131,plain,
a2 = a10,
inference(transitivity,[status(thm)],[c15,c130]) ).
cnf(c132,plain,
a7 = a10,
inference(transitivity,[status(thm)],[c120,c131]) ).
cnf(c133,plain,
tuple(a1,a10,a10,a6,a7,a7,a10,a10,a5) = tuple(a1,a10,a10,a6,a10,a7,a10,a10,a5),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
tuple(a1,a10,a10,a6,a10,a7,a10,a10,a5) = tuple(a1,a10,a10,a6,a10,a10,a10,a10,a5),
inference(congruence,[status(thm)],[c132]) ).
cnf(c135,plain,
product(a10,a10) = a10,
inference(substitution,[status(thm)],[c2]) ).
cnf(c136,plain,
a10 = product(a10,a10),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
a10 = a7,
inference(symmetry,[status(thm)],[c132]) ).
cnf(c138,plain,
product(a10,a10) = product(a10,a7),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
product(a10,a8) = product(product(a8,a9),a8),
inference(congruence,[status(thm)],[c80]) ).
cnf(c140,plain,
product(product(a8,a9),a8) = product(a8,product(a9,a8)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c141,plain,
product(a8,product(a9,a8)) = product(a8,a4),
inference(congruence,[status(thm)],[c125]) ).
cnf(c142,plain,
product(a8,product(a9,a8)) = a7,
inference(transitivity,[status(thm)],[c141,c102]) ).
cnf(c143,plain,
product(product(a8,a9),a8) = a7,
inference(transitivity,[status(thm)],[c140,c142]) ).
cnf(c144,plain,
product(a10,a8) = a7,
inference(transitivity,[status(thm)],[c139,c143]) ).
cnf(c145,plain,
a7 = product(a10,a8),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
product(a10,a7) = product(a10,product(a10,a8)),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
a10 = a7,
inference(symmetry,[status(thm)],[c132]) ).
cnf(c148,plain,
product(a10,product(a10,a8)) = product(a7,product(a10,a8)),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
a7 = a2,
inference(symmetry,[status(thm)],[c69]) ).
cnf(c150,plain,
product(a7,product(a10,a8)) = product(a2,product(a10,a8)),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
a8 = a4,
inference(symmetry,[status(thm)],[c85]) ).
cnf(c152,plain,
product(a10,a8) = product(a10,a4),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
product(a2,product(a10,a8)) = product(a2,product(a10,a4)),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
product(a4,a2) = product(a4,product(a3,a4)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c155,plain,
product(product(a4,a3),a4) = product(a4,product(a3,a4)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c156,plain,
product(a4,product(a3,a4)) = product(product(a4,a3),a4),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
product(product(a4,a3),a4) = product(a10,a4),
inference(congruence,[status(thm)],[c25]) ).
cnf(c158,plain,
product(a4,product(a3,a4)) = product(a10,a4),
inference(transitivity,[status(thm)],[c156,c157]) ).
cnf(c159,plain,
product(a4,a2) = product(a10,a4),
inference(transitivity,[status(thm)],[c154,c158]) ).
cnf(c160,plain,
product(a10,a4) = product(a4,a2),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
product(a2,product(a10,a4)) = product(a2,product(a4,a2)),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
product(product(a2,a4),a2) = product(a2,product(a4,a2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c163,plain,
product(a2,product(a4,a2)) = product(product(a2,a4),a2),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
product(product(a2,a4),a2) = product(a3,a2),
inference(congruence,[status(thm)],[c92]) ).
cnf(c165,plain,
product(a3,a2) = product(product(a1,a2),a2),
inference(congruence,[status(thm)],[c7]) ).
cnf(c166,plain,
product(product(a1,a2),a2) = a1,
inference(substitution,[status(thm)],[c23]) ).
cnf(c167,plain,
product(a3,a2) = a1,
inference(transitivity,[status(thm)],[c165,c166]) ).
cnf(c168,plain,
product(product(a2,a4),a2) = a1,
inference(transitivity,[status(thm)],[c164,c167]) ).
cnf(c169,plain,
product(a2,product(a4,a2)) = a1,
inference(transitivity,[status(thm)],[c163,c168]) ).
cnf(c170,plain,
product(a2,product(a10,a4)) = a1,
inference(transitivity,[status(thm)],[c161,c169]) ).
cnf(c171,plain,
product(a2,product(a10,a8)) = a1,
inference(transitivity,[status(thm)],[c153,c170]) ).
cnf(c172,plain,
product(a7,product(a10,a8)) = a1,
inference(transitivity,[status(thm)],[c150,c171]) ).
cnf(c173,plain,
product(a10,product(a10,a8)) = a1,
inference(transitivity,[status(thm)],[c148,c172]) ).
cnf(c174,plain,
product(a10,a7) = a1,
inference(transitivity,[status(thm)],[c146,c173]) ).
cnf(c175,plain,
product(a10,a10) = a1,
inference(transitivity,[status(thm)],[c138,c174]) ).
cnf(c176,plain,
a10 = a1,
inference(transitivity,[status(thm)],[c136,c175]) ).
cnf(c177,plain,
tuple(a1,a10,a10,a6,a10,a10,a10,a10,a5) = tuple(a1,a1,a10,a6,a10,a10,a10,a10,a5),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
tuple(a1,a1,a10,a6,a10,a10,a10,a10,a5) = tuple(a1,a1,a1,a6,a10,a10,a10,a10,a5),
inference(congruence,[status(thm)],[c176]) ).
cnf(c179,plain,
tuple(a1,a1,a1,a6,a10,a10,a10,a10,a5) = tuple(a1,a1,a1,a6,a1,a10,a10,a10,a5),
inference(congruence,[status(thm)],[c176]) ).
cnf(c180,plain,
tuple(a1,a1,a1,a6,a1,a10,a10,a10,a5) = tuple(a1,a1,a1,a6,a1,a1,a10,a10,a5),
inference(congruence,[status(thm)],[c176]) ).
cnf(c181,plain,
tuple(a1,a1,a1,a6,a1,a1,a10,a10,a5) = tuple(a1,a1,a1,a6,a1,a1,a1,a10,a5),
inference(congruence,[status(thm)],[c176]) ).
cnf(c182,plain,
tuple(a1,a1,a1,a6,a1,a1,a1,a10,a5) = tuple(a1,a1,a1,a6,a1,a1,a1,a1,a5),
inference(congruence,[status(thm)],[c176]) ).
cnf(c183,plain,
product(a7,a1) = product(product(a6,a1),a1),
inference(congruence,[status(thm)],[c5]) ).
cnf(c184,plain,
product(product(a6,a1),a1) = a6,
inference(substitution,[status(thm)],[c23]) ).
cnf(c185,plain,
product(a7,a1) = a6,
inference(transitivity,[status(thm)],[c183,c184]) ).
cnf(c186,plain,
a6 = product(a7,a1),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
a7 = a2,
inference(symmetry,[status(thm)],[c69]) ).
cnf(c188,plain,
product(a7,a1) = product(a2,a1),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
a1 = a10,
inference(symmetry,[status(thm)],[c176]) ).
cnf(c190,plain,
product(a2,a1) = product(a2,a10),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
product(a2,a10) = a5,
inference(symmetry,[status(thm)],[c30]) ).
cnf(c192,plain,
product(a2,a1) = a5,
inference(transitivity,[status(thm)],[c190,c191]) ).
cnf(c193,plain,
product(a7,a1) = a5,
inference(transitivity,[status(thm)],[c188,c192]) ).
cnf(c194,plain,
a6 = a5,
inference(transitivity,[status(thm)],[c186,c193]) ).
cnf(c195,plain,
tuple(a1,a1,a1,a6,a1,a1,a1,a1,a5) = tuple(a1,a1,a1,a5,a1,a1,a1,a1,a5),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
product(a2,a10) = product(a7,a10),
inference(congruence,[status(thm)],[c69]) ).
cnf(c197,plain,
product(a7,a10) = product(a10,a10),
inference(congruence,[status(thm)],[c132]) ).
cnf(c198,plain,
product(a10,a10) = a10,
inference(substitution,[status(thm)],[c2]) ).
cnf(c199,plain,
product(a10,a10) = a1,
inference(transitivity,[status(thm)],[c198,c176]) ).
cnf(c200,plain,
product(a7,a10) = a1,
inference(transitivity,[status(thm)],[c197,c199]) ).
cnf(c201,plain,
product(a2,a10) = a1,
inference(transitivity,[status(thm)],[c196,c200]) ).
cnf(c202,plain,
a5 = a1,
inference(transitivity,[status(thm)],[c30,c201]) ).
cnf(c203,plain,
tuple(a1,a1,a1,a5,a1,a1,a1,a1,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1),
inference(congruence,[status(thm)],[c202]) ).
cnf(c205,plain,
a1 = a5,
inference(symmetry,[status(thm)],[c202]) ).
cnf(c206,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) = tuple(a1,a1,a1,a1,a1,a1,a1,a5,a1),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
a1 = a5,
inference(symmetry,[status(thm)],[c202]) ).
cnf(c208,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a5,a1) = tuple(a1,a1,a1,a1,a1,a1,a1,a5,a5),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
a5 = a6,
inference(symmetry,[status(thm)],[c194]) ).
cnf(c210,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a5,a5) = tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
a1 = a10,
inference(symmetry,[status(thm)],[c176]) ).
cnf(c212,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) = tuple(a10,a1,a1,a1,a1,a1,a1,a5,a6),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
a1 = a10,
inference(symmetry,[status(thm)],[c176]) ).
cnf(c214,plain,
tuple(a10,a1,a1,a1,a1,a1,a1,a5,a6) = tuple(a10,a10,a1,a1,a1,a1,a1,a5,a6),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
a1 = a10,
inference(symmetry,[status(thm)],[c176]) ).
cnf(c216,plain,
tuple(a10,a10,a1,a1,a1,a1,a1,a5,a6) = tuple(a10,a10,a10,a1,a1,a1,a1,a5,a6),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
a1 = a10,
inference(symmetry,[status(thm)],[c176]) ).
cnf(c218,plain,
tuple(a10,a10,a10,a1,a1,a1,a1,a5,a6) = tuple(a10,a10,a10,a10,a1,a1,a1,a5,a6),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
a1 = a10,
inference(symmetry,[status(thm)],[c176]) ).
cnf(c220,plain,
tuple(a10,a10,a10,a10,a1,a1,a1,a5,a6) = tuple(a10,a10,a10,a10,a10,a1,a1,a5,a6),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
a1 = a10,
inference(symmetry,[status(thm)],[c176]) ).
cnf(c222,plain,
tuple(a10,a10,a10,a10,a10,a1,a1,a5,a6) = tuple(a10,a10,a10,a10,a10,a10,a1,a5,a6),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
a1 = a10,
inference(symmetry,[status(thm)],[c176]) ).
cnf(c224,plain,
tuple(a10,a10,a10,a10,a10,a10,a1,a5,a6) = tuple(a10,a10,a10,a10,a10,a10,a10,a5,a6),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
a10 = a7,
inference(symmetry,[status(thm)],[c132]) ).
cnf(c226,plain,
tuple(a10,a10,a10,a10,a10,a10,a10,a5,a6) = tuple(a7,a10,a10,a10,a10,a10,a10,a5,a6),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
a10 = a7,
inference(symmetry,[status(thm)],[c132]) ).
cnf(c228,plain,
tuple(a7,a10,a10,a10,a10,a10,a10,a5,a6) = tuple(a7,a10,a10,a7,a10,a10,a10,a5,a6),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
a10 = a9,
inference(symmetry,[status(thm)],[c115]) ).
cnf(c230,plain,
tuple(a7,a10,a10,a7,a10,a10,a10,a5,a6) = tuple(a7,a10,a9,a7,a10,a10,a10,a5,a6),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
a10 = a9,
inference(symmetry,[status(thm)],[c115]) ).
cnf(c232,plain,
tuple(a7,a10,a9,a7,a10,a10,a10,a5,a6) = tuple(a7,a10,a9,a7,a9,a10,a10,a5,a6),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
a10 = a9,
inference(symmetry,[status(thm)],[c115]) ).
cnf(c234,plain,
tuple(a7,a10,a9,a7,a9,a10,a10,a5,a6) = tuple(a7,a10,a9,a7,a9,a9,a10,a5,a6),
inference(congruence,[status(thm)],[c233]) ).
cnf(c235,plain,
a10 = a9,
inference(symmetry,[status(thm)],[c115]) ).
cnf(c236,plain,
tuple(a7,a10,a9,a7,a9,a9,a10,a5,a6) = tuple(a7,a10,a9,a7,a9,a9,a9,a5,a6),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
a9 = a8,
inference(symmetry,[status(thm)],[c95]) ).
cnf(c238,plain,
tuple(a7,a10,a9,a7,a9,a9,a9,a5,a6) = tuple(a7,a10,a9,a7,a8,a9,a9,a5,a6),
inference(congruence,[status(thm)],[c237]) ).
cnf(c239,plain,
a9 = a8,
inference(symmetry,[status(thm)],[c95]) ).
cnf(c240,plain,
tuple(a7,a10,a9,a7,a8,a9,a9,a5,a6) = tuple(a7,a10,a9,a7,a8,a9,a8,a5,a6),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
a8 = a4,
inference(symmetry,[status(thm)],[c85]) ).
cnf(c242,plain,
tuple(a7,a10,a9,a7,a8,a9,a8,a5,a6) = tuple(a7,a10,a9,a7,a8,a9,a4,a5,a6),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
a9 = a3,
inference(symmetry,[status(thm)],[c77]) ).
cnf(c244,plain,
tuple(a7,a10,a9,a7,a8,a9,a4,a5,a6) = tuple(a7,a10,a9,a7,a8,a3,a4,a5,a6),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
a7 = a2,
inference(symmetry,[status(thm)],[c69]) ).
cnf(c246,plain,
tuple(a7,a10,a9,a7,a8,a3,a4,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
tuple(a7,a10,a9,a7,a8,a9,a4,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c244,c246]) ).
cnf(c248,plain,
tuple(a7,a10,a9,a7,a8,a9,a8,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c242,c247]) ).
cnf(c249,plain,
tuple(a7,a10,a9,a7,a8,a9,a9,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c240,c248]) ).
cnf(c250,plain,
tuple(a7,a10,a9,a7,a9,a9,a9,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c238,c249]) ).
cnf(c251,plain,
tuple(a7,a10,a9,a7,a9,a9,a10,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c236,c250]) ).
cnf(c252,plain,
tuple(a7,a10,a9,a7,a9,a10,a10,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c234,c251]) ).
cnf(c253,plain,
tuple(a7,a10,a9,a7,a10,a10,a10,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c232,c252]) ).
cnf(c254,plain,
tuple(a7,a10,a10,a7,a10,a10,a10,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c230,c253]) ).
cnf(c255,plain,
tuple(a7,a10,a10,a10,a10,a10,a10,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c228,c254]) ).
cnf(c256,plain,
tuple(a10,a10,a10,a10,a10,a10,a10,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c226,c255]) ).
cnf(c257,plain,
tuple(a10,a10,a10,a10,a10,a10,a1,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c224,c256]) ).
cnf(c258,plain,
tuple(a10,a10,a10,a10,a10,a1,a1,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c222,c257]) ).
cnf(c259,plain,
tuple(a10,a10,a10,a10,a1,a1,a1,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c220,c258]) ).
cnf(c260,plain,
tuple(a10,a10,a10,a1,a1,a1,a1,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c218,c259]) ).
cnf(c261,plain,
tuple(a10,a10,a1,a1,a1,a1,a1,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c216,c260]) ).
cnf(c262,plain,
tuple(a10,a1,a1,a1,a1,a1,a1,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c214,c261]) ).
cnf(c263,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a5,a6) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c212,c262]) ).
cnf(c264,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a5,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c210,c263]) ).
cnf(c265,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a5,a1) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c208,c264]) ).
cnf(c266,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c206,c265]) ).
cnf(c267,plain,
tuple(a1,a1,a1,a1,a1,a1,a1,a1,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c204,c266]) ).
cnf(c268,plain,
tuple(a1,a1,a1,a5,a1,a1,a1,a1,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c203,c267]) ).
cnf(c269,plain,
tuple(a1,a1,a1,a6,a1,a1,a1,a1,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c195,c268]) ).
cnf(c270,plain,
tuple(a1,a1,a1,a6,a1,a1,a1,a10,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c182,c269]) ).
cnf(c271,plain,
tuple(a1,a1,a1,a6,a1,a1,a10,a10,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c181,c270]) ).
cnf(c272,plain,
tuple(a1,a1,a1,a6,a1,a10,a10,a10,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c180,c271]) ).
cnf(c273,plain,
tuple(a1,a1,a1,a6,a10,a10,a10,a10,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c179,c272]) ).
cnf(c274,plain,
tuple(a1,a1,a10,a6,a10,a10,a10,a10,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c178,c273]) ).
cnf(c275,plain,
tuple(a1,a10,a10,a6,a10,a10,a10,a10,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c177,c274]) ).
cnf(c276,plain,
tuple(a1,a10,a10,a6,a10,a7,a10,a10,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c134,c275]) ).
cnf(c277,plain,
tuple(a1,a10,a10,a6,a7,a7,a10,a10,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c133,c276]) ).
cnf(c278,plain,
tuple(a1,a10,a10,a6,a7,a7,a10,a9,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c119,c277]) ).
cnf(c279,plain,
tuple(a1,a10,a10,a6,a7,a7,a9,a9,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c118,c278]) ).
cnf(c280,plain,
tuple(a1,a10,a9,a6,a7,a7,a9,a9,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c117,c279]) ).
cnf(c281,plain,
tuple(a1,a9,a9,a6,a7,a7,a9,a9,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c116,c280]) ).
cnf(c282,plain,
tuple(a1,a9,a9,a6,a7,a7,a9,a8,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c97,c281]) ).
cnf(c283,plain,
tuple(a1,a9,a8,a6,a7,a7,a9,a8,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c96,c282]) ).
cnf(c284,plain,
tuple(a1,a9,a8,a6,a7,a7,a9,a4,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c86,c283]) ).
cnf(c285,plain,
tuple(a1,a9,a8,a6,a7,a7,a3,a4,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c78,c284]) ).
cnf(c286,plain,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) = tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(transitivity,[status(thm)],[c70,c285]) ).
cnf(c287,plain,
$false,
inference(resolution,[status(thm)],[c1,c286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : TOP049-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25 % Computer : n015.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8046.5625MB
% 0.08/0.25 % OS : Linux 6.8.0-71-generic
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Mon Sep 28 19:10:46 UTC 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.37 Command-line arguments: --no-flatten-goal
% 0.23/0.37
% 0.23/0.37 % SZS status Unsatisfiable
% 0.23/0.37
% 0.23/0.40 % SZS output start CNFRefutation
% See solution above
% 0.71/0.59
% 0.71/0.59 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------