%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : TOP053-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 02:33:48 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.15s
% Output : CNFRefutation 0.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 104
% Number of leaves : 19
% Syntax : Number of clauses : 373 ( 373 unt; 0 nHn; 349 RR)
% Number of literals : 373 ( 372 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 : 17 ( 17 usr; 15 con; 0-14 aty)
% Number of variables : 30 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) != tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
product(product(X,Y),Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_01) ).
cnf(c3,plain,
product(product(a3,a8),a8) = a3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
a3 = product(product(a3,a8),a8),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
product(a7,a3) = a8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
a8 = product(a7,a3),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
product(a3,a8) = product(a3,product(a7,a3)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
product(product(X2,Y2),Z) = product(product(X2,Z),product(Y2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutory_quandle_02) ).
cnf(c9,plain,
product(product(X3,X2),X3) = product(product(X3,X3),product(X2,X3)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,axiom,
product(X2,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c11,plain,
product(product(X3,X3),product(X2,X3)) = product(X3,product(X2,X3)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
product(product(X3,X2),X3) = product(X3,product(X2,X3)),
inference(transitivity,[status(thm)],[c9,c11]) ).
cnf(c13,plain,
product(product(a3,a7),a3) = product(a3,product(a7,a3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
product(a3,product(a7,a3)) = product(product(a3,a7),a3),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,axiom,
product(a3,a4) = a5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c16,plain,
a5 = product(a3,a4),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
product(a5,a4) = product(product(a3,a4),a4),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
product(product(a3,a4),a4) = a3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
product(a5,a4) = a3,
inference(transitivity,[status(thm)],[c17,c18]) ).
cnf(c20,plain,
a3 = product(a5,a4),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
product(a3,a7) = product(product(a5,a4),a7),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,axiom,
product(a4,a7) = a11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c23,plain,
a11 = product(a4,a7),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
product(product(X2,a7),a11) = product(product(X2,a7),product(a4,a7)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
product(product(X2,a4),a7) = product(product(X2,a7),product(a4,a7)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c26,plain,
product(product(X2,a7),product(a4,a7)) = product(product(X2,a4),a7),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
product(product(X2,a7),a11) = product(product(X2,a4),a7),
inference(transitivity,[status(thm)],[c24,c26]) ).
cnf(c28,plain,
product(product(a5,a7),a11) = product(product(a5,a4),a7),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
product(product(a5,a4),a7) = product(product(a5,a7),a11),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,axiom,
product(a6,a7) = a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c31,plain,
a2 = product(a6,a7),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
product(a7,a2) = product(a7,product(a6,a7)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
product(product(a7,a6),a7) = product(a7,product(a6,a7)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c34,plain,
product(a7,product(a6,a7)) = product(product(a7,a6),a7),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,axiom,
product(a5,a6) = a7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c36,plain,
a7 = product(a5,a6),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
product(a7,a6) = product(product(a5,a6),a6),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
product(product(a5,a6),a6) = a5,
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
product(a7,a6) = a5,
inference(transitivity,[status(thm)],[c37,c38]) ).
cnf(c40,plain,
product(product(a7,a6),a7) = product(a5,a7),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
product(a7,product(a6,a7)) = product(a5,a7),
inference(transitivity,[status(thm)],[c34,c40]) ).
cnf(c42,plain,
product(a7,a2) = product(a5,a7),
inference(transitivity,[status(thm)],[c32,c41]) ).
cnf(c43,plain,
product(a5,a7) = product(a7,a2),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,axiom,
product(a9,a1) = a10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c45,plain,
a10 = product(a9,a1),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
product(a10,a2) = product(product(a9,a1),a2),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,axiom,
product(a1,a2) = a3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c48,plain,
a3 = product(a1,a2),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
product(product(X2,a2),a3) = product(product(X2,a2),product(a1,a2)),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
product(product(X2,a1),a2) = product(product(X2,a2),product(a1,a2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c51,plain,
product(product(X2,a2),product(a1,a2)) = product(product(X2,a1),a2),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
product(product(X2,a2),a3) = product(product(X2,a1),a2),
inference(transitivity,[status(thm)],[c49,c51]) ).
cnf(c53,plain,
product(product(a9,a2),a3) = product(product(a9,a1),a2),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
product(product(a9,a1),a2) = product(product(a9,a2),a3),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,axiom,
product(a8,a2) = a9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c56,plain,
a9 = product(a8,a2),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
product(a9,a2) = product(product(a8,a2),a2),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
product(product(a8,a2),a2) = a8,
inference(substitution,[status(thm)],[c2]) ).
cnf(c59,plain,
product(a9,a2) = a8,
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
product(product(a9,a2),a3) = product(a8,a3),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
a8 = product(a7,a3),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c62,plain,
product(a8,a3) = product(product(a7,a3),a3),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
product(product(a7,a3),a3) = a7,
inference(substitution,[status(thm)],[c2]) ).
cnf(c64,plain,
product(a8,a3) = a7,
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
product(product(a9,a2),a3) = a7,
inference(transitivity,[status(thm)],[c60,c64]) ).
cnf(c66,plain,
product(product(a9,a1),a2) = a7,
inference(transitivity,[status(thm)],[c54,c65]) ).
cnf(c67,plain,
product(a10,a2) = a7,
inference(transitivity,[status(thm)],[c46,c66]) ).
cnf(c68,plain,
a7 = product(a10,a2),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
product(a7,a2) = product(product(a10,a2),a2),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
product(product(a10,a2),a2) = a10,
inference(substitution,[status(thm)],[c2]) ).
cnf(c71,plain,
product(a7,a2) = a10,
inference(transitivity,[status(thm)],[c69,c70]) ).
cnf(c72,plain,
product(a5,a7) = a10,
inference(transitivity,[status(thm)],[c43,c71]) ).
cnf(c73,plain,
product(product(a5,a7),a11) = product(a10,a11),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,axiom,
product(a10,a11) = a12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c75,plain,
product(product(a5,a7),a11) = a12,
inference(transitivity,[status(thm)],[c73,c74]) ).
cnf(c76,plain,
product(product(a5,a4),a7) = a12,
inference(transitivity,[status(thm)],[c29,c75]) ).
cnf(c77,plain,
product(a3,a7) = a12,
inference(transitivity,[status(thm)],[c21,c76]) ).
cnf(c78,plain,
product(product(a3,a7),a3) = product(a12,a3),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,axiom,
product(a12,a3) = a13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c80,plain,
product(product(a3,a7),a3) = a13,
inference(transitivity,[status(thm)],[c78,c79]) ).
cnf(c81,plain,
product(a3,product(a7,a3)) = a13,
inference(transitivity,[status(thm)],[c14,c80]) ).
cnf(c82,plain,
product(a3,a8) = a13,
inference(transitivity,[status(thm)],[c7,c81]) ).
cnf(c83,plain,
product(product(a3,a8),a8) = product(a13,a8),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,axiom,
product(a13,a8) = a6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c85,plain,
product(product(a3,a8),a8) = a6,
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
a3 = a6,
inference(transitivity,[status(thm)],[c4,c85]) ).
cnf(c87,plain,
tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) = tuple(a1,a2,a6,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
a8 = product(a7,a3),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c89,plain,
product(a7,a3) = product(a7,a6),
inference(congruence,[status(thm)],[c86]) ).
cnf(c90,plain,
product(a7,a3) = a5,
inference(transitivity,[status(thm)],[c89,c39]) ).
cnf(c91,plain,
a8 = a5,
inference(transitivity,[status(thm)],[c88,c90]) ).
cnf(c92,plain,
tuple(a1,a2,a6,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) = tuple(a1,a2,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
a2 = product(a6,a7),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c94,plain,
a6 = a3,
inference(symmetry,[status(thm)],[c86]) ).
cnf(c95,plain,
product(a6,a7) = product(a3,a7),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
product(a6,a7) = a12,
inference(transitivity,[status(thm)],[c95,c77]) ).
cnf(c97,plain,
a2 = a12,
inference(transitivity,[status(thm)],[c93,c96]) ).
cnf(c98,plain,
tuple(a1,a2,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14) = tuple(a1,a12,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
product(a12,a12) = a12,
inference(substitution,[status(thm)],[c10]) ).
cnf(c100,plain,
a12 = product(a12,a12),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
a12 = a2,
inference(symmetry,[status(thm)],[c97]) ).
cnf(c102,plain,
product(a12,a12) = product(a2,a12),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,axiom,
product(a2,a12) = a14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c104,plain,
product(a12,a12) = a14,
inference(transitivity,[status(thm)],[c102,c103]) ).
cnf(c105,plain,
a12 = a14,
inference(transitivity,[status(thm)],[c100,c104]) ).
cnf(c106,plain,
tuple(a1,a12,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14) = tuple(a1,a14,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
tuple(a1,a14,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14) = tuple(a1,a14,a6,a4,a5,a6,a7,a5,a9,a10,a11,a14,a13,a14),
inference(congruence,[status(thm)],[c105]) ).
cnf(c108,plain,
product(a6,a6) = a6,
inference(substitution,[status(thm)],[c10]) ).
cnf(c109,plain,
a6 = product(a6,a6),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
a6 = a3,
inference(symmetry,[status(thm)],[c86]) ).
cnf(c111,plain,
product(a6,a6) = product(a6,a3),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
product(a7,a7) = a7,
inference(substitution,[status(thm)],[c10]) ).
cnf(c113,plain,
a7 = product(a7,a7),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
product(a14,a7) = product(a14,product(a7,a7)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
product(product(a6,X2),a7) = product(product(a6,a7),product(X2,a7)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c116,plain,
product(product(a6,a7),product(X2,a7)) = product(a2,product(X2,a7)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c117,plain,
product(a2,product(X2,a7)) = product(a12,product(X2,a7)),
inference(congruence,[status(thm)],[c97]) ).
cnf(c118,plain,
product(a12,product(X2,a7)) = product(a14,product(X2,a7)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c119,plain,
product(a2,product(X2,a7)) = product(a14,product(X2,a7)),
inference(transitivity,[status(thm)],[c117,c118]) ).
cnf(c120,plain,
product(product(a6,a7),product(X2,a7)) = product(a14,product(X2,a7)),
inference(transitivity,[status(thm)],[c116,c119]) ).
cnf(c121,plain,
product(product(a6,X2),a7) = product(a14,product(X2,a7)),
inference(transitivity,[status(thm)],[c115,c120]) ).
cnf(c122,plain,
product(product(a6,a7),a7) = product(a14,product(a7,a7)),
inference(substitution,[status(thm)],[c121]) ).
cnf(c123,plain,
product(a14,product(a7,a7)) = product(product(a6,a7),a7),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
product(product(a6,a7),a7) = product(a2,a7),
inference(congruence,[status(thm)],[c30]) ).
cnf(c125,plain,
a2 = product(a6,a7),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c126,plain,
product(a2,a7) = product(product(a6,a7),a7),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
product(product(a6,a7),a7) = a6,
inference(substitution,[status(thm)],[c2]) ).
cnf(c128,plain,
product(a2,a7) = a6,
inference(transitivity,[status(thm)],[c126,c127]) ).
cnf(c129,plain,
product(product(a6,a7),a7) = a6,
inference(transitivity,[status(thm)],[c124,c128]) ).
cnf(c130,plain,
product(a14,product(a7,a7)) = a6,
inference(transitivity,[status(thm)],[c123,c129]) ).
cnf(c131,plain,
product(a14,a7) = a6,
inference(transitivity,[status(thm)],[c114,c130]) ).
cnf(c132,plain,
a6 = product(a14,a7),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
product(a6,a3) = product(product(a14,a7),a3),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
product(product(a14,X2),a3) = product(product(a14,a3),product(X2,a3)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c135,axiom,
product(a14,a3) = a15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c136,plain,
product(product(a14,a3),product(X2,a3)) = product(a15,product(X2,a3)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
product(product(a14,X2),a3) = product(a15,product(X2,a3)),
inference(transitivity,[status(thm)],[c134,c136]) ).
cnf(c138,plain,
product(product(a14,a7),a3) = product(a15,product(a7,a3)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
product(a15,product(a7,a3)) = product(a15,a8),
inference(congruence,[status(thm)],[c5]) ).
cnf(c140,axiom,
product(a15,a8) = a4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c141,plain,
product(a15,product(a7,a3)) = a4,
inference(transitivity,[status(thm)],[c139,c140]) ).
cnf(c142,plain,
product(product(a14,a7),a3) = a4,
inference(transitivity,[status(thm)],[c138,c141]) ).
cnf(c143,plain,
product(a6,a3) = a4,
inference(transitivity,[status(thm)],[c133,c142]) ).
cnf(c144,plain,
product(a6,a6) = a4,
inference(transitivity,[status(thm)],[c111,c143]) ).
cnf(c145,plain,
a6 = a4,
inference(transitivity,[status(thm)],[c109,c144]) ).
cnf(c146,plain,
tuple(a1,a14,a6,a4,a5,a6,a7,a5,a9,a10,a11,a14,a13,a14) = tuple(a1,a14,a4,a4,a5,a6,a7,a5,a9,a10,a11,a14,a13,a14),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
tuple(a1,a14,a4,a4,a5,a6,a7,a5,a9,a10,a11,a14,a13,a14) = tuple(a1,a14,a4,a4,a5,a4,a7,a5,a9,a10,a11,a14,a13,a14),
inference(congruence,[status(thm)],[c145]) ).
cnf(c148,plain,
a11 = product(a4,a7),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c149,plain,
a4 = a6,
inference(symmetry,[status(thm)],[c145]) ).
cnf(c150,plain,
product(a4,a7) = product(a6,a7),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
a2 = a14,
inference(transitivity,[status(thm)],[c97,c105]) ).
cnf(c152,plain,
product(a6,a7) = a14,
inference(transitivity,[status(thm)],[c30,c151]) ).
cnf(c153,plain,
product(a4,a7) = a14,
inference(transitivity,[status(thm)],[c150,c152]) ).
cnf(c154,plain,
a11 = a14,
inference(transitivity,[status(thm)],[c148,c153]) ).
cnf(c155,plain,
tuple(a1,a14,a4,a4,a5,a4,a7,a5,a9,a10,a11,a14,a13,a14) = tuple(a1,a14,a4,a4,a5,a4,a7,a5,a9,a10,a14,a14,a13,a14),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
a6 = product(a13,a8),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c157,plain,
product(a6,a8) = product(product(a13,a8),a8),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
product(product(a13,a8),a8) = a13,
inference(substitution,[status(thm)],[c2]) ).
cnf(c159,plain,
product(a6,a8) = a13,
inference(transitivity,[status(thm)],[c157,c158]) ).
cnf(c160,plain,
a13 = product(a6,a8),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
product(a6,a8) = product(a4,a8),
inference(congruence,[status(thm)],[c145]) ).
cnf(c162,plain,
a4 = product(a15,a8),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c163,plain,
product(a4,a8) = product(product(a15,a8),a8),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
product(product(a15,a8),a8) = a15,
inference(substitution,[status(thm)],[c2]) ).
cnf(c165,plain,
product(a4,a8) = a15,
inference(transitivity,[status(thm)],[c163,c164]) ).
cnf(c166,plain,
product(a6,a8) = a15,
inference(transitivity,[status(thm)],[c161,c165]) ).
cnf(c167,plain,
a13 = a15,
inference(transitivity,[status(thm)],[c160,c166]) ).
cnf(c168,plain,
tuple(a1,a14,a4,a4,a5,a4,a7,a5,a9,a10,a14,a14,a13,a14) = tuple(a1,a14,a4,a4,a5,a4,a7,a5,a9,a10,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
a4 = a6,
inference(symmetry,[status(thm)],[c145]) ).
cnf(c170,plain,
product(a5,a4) = product(a5,a6),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
product(a5,a4) = a7,
inference(transitivity,[status(thm)],[c170,c35]) ).
cnf(c172,plain,
a7 = product(a5,a4),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
a3 = a4,
inference(transitivity,[status(thm)],[c86,c145]) ).
cnf(c174,plain,
product(a5,a4) = a4,
inference(transitivity,[status(thm)],[c19,c173]) ).
cnf(c175,plain,
a7 = a4,
inference(transitivity,[status(thm)],[c172,c174]) ).
cnf(c176,plain,
tuple(a1,a14,a4,a4,a5,a4,a7,a5,a9,a10,a14,a14,a15,a14) = tuple(a1,a14,a4,a4,a5,a4,a4,a5,a9,a10,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
a12 = product(a10,a11),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c178,plain,
product(a12,a11) = product(product(a10,a11),a11),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
product(product(a10,a11),a11) = a10,
inference(substitution,[status(thm)],[c2]) ).
cnf(c180,plain,
product(a12,a11) = a10,
inference(transitivity,[status(thm)],[c178,c179]) ).
cnf(c181,plain,
a10 = product(a12,a11),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
product(a12,a11) = product(a12,a14),
inference(congruence,[status(thm)],[c154]) ).
cnf(c183,plain,
product(a12,a14) = product(a14,a14),
inference(congruence,[status(thm)],[c105]) ).
cnf(c184,plain,
product(a14,a14) = a14,
inference(substitution,[status(thm)],[c10]) ).
cnf(c185,plain,
product(a12,a14) = a14,
inference(transitivity,[status(thm)],[c183,c184]) ).
cnf(c186,plain,
product(a12,a11) = a14,
inference(transitivity,[status(thm)],[c182,c185]) ).
cnf(c187,plain,
a10 = a14,
inference(transitivity,[status(thm)],[c181,c186]) ).
cnf(c188,plain,
tuple(a1,a14,a4,a4,a5,a4,a4,a5,a9,a10,a14,a14,a15,a14) = tuple(a1,a14,a4,a4,a5,a4,a4,a5,a9,a14,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
product(a4,a4) = a4,
inference(substitution,[status(thm)],[c10]) ).
cnf(c190,plain,
a4 = product(a4,a4),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
a4 = a7,
inference(symmetry,[status(thm)],[c175]) ).
cnf(c192,plain,
product(a4,a4) = product(a4,a7),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
product(a4,a7) = a14,
inference(transitivity,[status(thm)],[c22,c154]) ).
cnf(c194,plain,
product(a4,a4) = a14,
inference(transitivity,[status(thm)],[c192,c193]) ).
cnf(c195,plain,
a4 = a14,
inference(transitivity,[status(thm)],[c190,c194]) ).
cnf(c196,plain,
tuple(a1,a14,a4,a4,a5,a4,a4,a5,a9,a14,a14,a14,a15,a14) = tuple(a1,a14,a14,a4,a5,a4,a4,a5,a9,a14,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
tuple(a1,a14,a14,a4,a5,a4,a4,a5,a9,a14,a14,a14,a15,a14) = tuple(a1,a14,a14,a14,a5,a4,a4,a5,a9,a14,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c195]) ).
cnf(c198,plain,
tuple(a1,a14,a14,a14,a5,a4,a4,a5,a9,a14,a14,a14,a15,a14) = tuple(a1,a14,a14,a14,a5,a14,a4,a5,a9,a14,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c195]) ).
cnf(c199,plain,
tuple(a1,a14,a14,a14,a5,a14,a4,a5,a9,a14,a14,a14,a15,a14) = tuple(a1,a14,a14,a14,a5,a14,a14,a5,a9,a14,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c195]) ).
cnf(c200,plain,
a5 = a8,
inference(symmetry,[status(thm)],[c91]) ).
cnf(c201,plain,
a8 = product(a7,a3),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c202,plain,
product(a7,a3) = product(a4,a3),
inference(congruence,[status(thm)],[c175]) ).
cnf(c203,plain,
product(a4,a3) = product(a14,a3),
inference(congruence,[status(thm)],[c195]) ).
cnf(c204,plain,
product(a4,a3) = a15,
inference(transitivity,[status(thm)],[c203,c135]) ).
cnf(c205,plain,
product(a7,a3) = a15,
inference(transitivity,[status(thm)],[c202,c204]) ).
cnf(c206,plain,
a8 = a15,
inference(transitivity,[status(thm)],[c201,c205]) ).
cnf(c207,plain,
a5 = a15,
inference(transitivity,[status(thm)],[c200,c206]) ).
cnf(c208,plain,
tuple(a1,a14,a14,a14,a5,a14,a14,a5,a9,a14,a14,a14,a15,a14) = tuple(a1,a14,a14,a14,a15,a14,a14,a5,a9,a14,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
tuple(a1,a14,a14,a14,a15,a14,a14,a5,a9,a14,a14,a14,a15,a14) = tuple(a1,a14,a14,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c207]) ).
cnf(c210,plain,
product(a14,a14) = a14,
inference(substitution,[status(thm)],[c10]) ).
cnf(c211,plain,
a14 = product(a14,a14),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
a14 = a4,
inference(symmetry,[status(thm)],[c195]) ).
cnf(c213,plain,
product(a14,a14) = product(a14,a4),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
a4 = a6,
inference(symmetry,[status(thm)],[c145]) ).
cnf(c215,plain,
product(a14,a4) = product(a14,a6),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
a14 = a4,
inference(symmetry,[status(thm)],[c195]) ).
cnf(c217,plain,
product(a14,a6) = product(a4,a6),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
a4 = a7,
inference(symmetry,[status(thm)],[c175]) ).
cnf(c219,plain,
product(a4,a6) = product(a7,a6),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
product(a7,a6) = a15,
inference(transitivity,[status(thm)],[c39,c207]) ).
cnf(c221,plain,
product(a4,a6) = a15,
inference(transitivity,[status(thm)],[c219,c220]) ).
cnf(c222,plain,
product(a14,a6) = a15,
inference(transitivity,[status(thm)],[c217,c221]) ).
cnf(c223,plain,
product(a14,a4) = a15,
inference(transitivity,[status(thm)],[c215,c222]) ).
cnf(c224,plain,
product(a14,a14) = a15,
inference(transitivity,[status(thm)],[c213,c223]) ).
cnf(c225,plain,
a14 = a15,
inference(transitivity,[status(thm)],[c211,c224]) ).
cnf(c226,plain,
tuple(a1,a14,a14,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14) = tuple(a1,a15,a14,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
tuple(a1,a15,a14,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14) = tuple(a1,a15,a15,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c225]) ).
cnf(c228,plain,
tuple(a1,a15,a15,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14) = tuple(a1,a15,a15,a15,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c225]) ).
cnf(c229,plain,
tuple(a1,a15,a15,a15,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14) = tuple(a1,a15,a15,a15,a15,a15,a14,a15,a9,a14,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c225]) ).
cnf(c230,plain,
tuple(a1,a15,a15,a15,a15,a15,a14,a15,a9,a14,a14,a14,a15,a14) = tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a14,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c225]) ).
cnf(c231,plain,
tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a14,a14,a14,a15,a14) = tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a15,a14,a14,a15,a14),
inference(congruence,[status(thm)],[c225]) ).
cnf(c232,plain,
tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a15,a14,a14,a15,a14) = tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a14,a15,a14),
inference(congruence,[status(thm)],[c225]) ).
cnf(c233,plain,
tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a14,a15,a14) = tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a14),
inference(congruence,[status(thm)],[c225]) ).
cnf(c234,plain,
tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a14) = tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15),
inference(congruence,[status(thm)],[c225]) ).
cnf(c235,axiom,
product(a11,a10) = a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c236,plain,
a1 = product(a11,a10),
inference(symmetry,[status(thm)],[c235]) ).
cnf(c237,plain,
product(a11,a10) = product(a11,a14),
inference(congruence,[status(thm)],[c187]) ).
cnf(c238,plain,
product(a11,a14) = product(a14,a14),
inference(congruence,[status(thm)],[c154]) ).
cnf(c239,plain,
product(a14,a14) = a14,
inference(substitution,[status(thm)],[c10]) ).
cnf(c240,plain,
product(a14,a14) = a15,
inference(transitivity,[status(thm)],[c239,c225]) ).
cnf(c241,plain,
product(a11,a14) = a15,
inference(transitivity,[status(thm)],[c238,c240]) ).
cnf(c242,plain,
product(a11,a10) = a15,
inference(transitivity,[status(thm)],[c237,c241]) ).
cnf(c243,plain,
a1 = a15,
inference(transitivity,[status(thm)],[c236,c242]) ).
cnf(c244,plain,
tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15) = tuple(a15,a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
a12 = product(a10,a11),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c246,plain,
product(a12,a10) = product(product(a10,a11),a10),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
product(product(a10,a11),a10) = product(a10,product(a11,a10)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c248,plain,
product(a10,product(a11,a10)) = product(a10,a1),
inference(congruence,[status(thm)],[c235]) ).
cnf(c249,plain,
a10 = product(a9,a1),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c250,plain,
product(a10,a1) = product(product(a9,a1),a1),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
product(product(a9,a1),a1) = a9,
inference(substitution,[status(thm)],[c2]) ).
cnf(c252,plain,
product(a10,a1) = a9,
inference(transitivity,[status(thm)],[c250,c251]) ).
cnf(c253,plain,
product(a10,product(a11,a10)) = a9,
inference(transitivity,[status(thm)],[c248,c252]) ).
cnf(c254,plain,
product(product(a10,a11),a10) = a9,
inference(transitivity,[status(thm)],[c247,c253]) ).
cnf(c255,plain,
product(a12,a10) = a9,
inference(transitivity,[status(thm)],[c246,c254]) ).
cnf(c256,plain,
a9 = product(a12,a10),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c257,plain,
product(a12,a10) = product(a12,a14),
inference(congruence,[status(thm)],[c187]) ).
cnf(c258,plain,
product(a12,a14) = product(a14,a14),
inference(congruence,[status(thm)],[c105]) ).
cnf(c259,plain,
product(a14,a14) = a14,
inference(substitution,[status(thm)],[c10]) ).
cnf(c260,plain,
product(a14,a14) = a15,
inference(transitivity,[status(thm)],[c259,c225]) ).
cnf(c261,plain,
product(a12,a14) = a15,
inference(transitivity,[status(thm)],[c258,c260]) ).
cnf(c262,plain,
product(a12,a10) = a15,
inference(transitivity,[status(thm)],[c257,c261]) ).
cnf(c263,plain,
a9 = a15,
inference(transitivity,[status(thm)],[c256,c262]) ).
cnf(c264,plain,
tuple(a15,a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15) = tuple(a15,a15,a15,a15,a15,a15,a15,a15,a15,a15,a15,a15,a15,a15),
inference(congruence,[status(thm)],[c263]) ).
cnf(c265,plain,
a15 = a9,
inference(symmetry,[status(thm)],[c263]) ).
cnf(c266,plain,
tuple(a15,a15,a15,a15,a15,a15,a15,a15,a15,a15,a15,a15,a15,a15) = tuple(a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15,a15),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
a15 = a14,
inference(symmetry,[status(thm)],[c225]) ).
cnf(c268,plain,
tuple(a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15,a15) = tuple(a14,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15,a15),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
a15 = a14,
inference(symmetry,[status(thm)],[c225]) ).
cnf(c270,plain,
tuple(a14,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15,a15) = tuple(a14,a14,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15,a15),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
a15 = a14,
inference(symmetry,[status(thm)],[c225]) ).
cnf(c272,plain,
tuple(a14,a14,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15,a15) = tuple(a14,a14,a14,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15,a15),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
a15 = a14,
inference(symmetry,[status(thm)],[c225]) ).
cnf(c274,plain,
tuple(a14,a14,a14,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15,a15) = tuple(a14,a14,a14,a15,a14,a15,a15,a9,a15,a15,a15,a15,a15,a15),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
a15 = a14,
inference(symmetry,[status(thm)],[c225]) ).
cnf(c276,plain,
tuple(a14,a14,a14,a15,a14,a15,a15,a9,a15,a15,a15,a15,a15,a15) = tuple(a14,a14,a14,a15,a14,a14,a15,a9,a15,a15,a15,a15,a15,a15),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
a15 = a14,
inference(symmetry,[status(thm)],[c225]) ).
cnf(c278,plain,
tuple(a14,a14,a14,a15,a14,a14,a15,a9,a15,a15,a15,a15,a15,a15) = tuple(a14,a14,a14,a15,a14,a14,a15,a9,a14,a15,a15,a15,a15,a15),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
a15 = a14,
inference(symmetry,[status(thm)],[c225]) ).
cnf(c280,plain,
tuple(a14,a14,a14,a15,a14,a14,a15,a9,a14,a15,a15,a15,a15,a15) = tuple(a14,a14,a14,a15,a14,a14,a15,a9,a14,a14,a15,a15,a15,a15),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
a15 = a14,
inference(symmetry,[status(thm)],[c225]) ).
cnf(c282,plain,
tuple(a14,a14,a14,a15,a14,a14,a15,a9,a14,a14,a15,a15,a15,a15) = tuple(a14,a14,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a15,a15),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
a15 = a14,
inference(symmetry,[status(thm)],[c225]) ).
cnf(c284,plain,
tuple(a14,a14,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a15,a15) = tuple(a14,a14,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14,a15),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
a15 = a5,
inference(symmetry,[status(thm)],[c207]) ).
cnf(c286,plain,
tuple(a14,a14,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14,a15) = tuple(a14,a14,a14,a5,a14,a14,a15,a9,a14,a14,a14,a15,a14,a15),
inference(congruence,[status(thm)],[c285]) ).
cnf(c287,plain,
a15 = a5,
inference(symmetry,[status(thm)],[c207]) ).
cnf(c288,plain,
tuple(a14,a14,a14,a5,a14,a14,a15,a9,a14,a14,a14,a15,a14,a15) = tuple(a14,a14,a14,a5,a14,a14,a5,a9,a14,a14,a14,a15,a14,a15),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
a14 = a4,
inference(symmetry,[status(thm)],[c195]) ).
cnf(c290,plain,
tuple(a14,a14,a14,a5,a14,a14,a5,a9,a14,a14,a14,a15,a14,a15) = tuple(a14,a4,a14,a5,a14,a14,a5,a9,a14,a14,a14,a15,a14,a15),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
a14 = a4,
inference(symmetry,[status(thm)],[c195]) ).
cnf(c292,plain,
tuple(a14,a4,a14,a5,a14,a14,a5,a9,a14,a14,a14,a15,a14,a15) = tuple(a14,a4,a4,a5,a14,a14,a5,a9,a14,a14,a14,a15,a14,a15),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
a14 = a4,
inference(symmetry,[status(thm)],[c195]) ).
cnf(c294,plain,
tuple(a14,a4,a4,a5,a14,a14,a5,a9,a14,a14,a14,a15,a14,a15) = tuple(a14,a4,a4,a5,a4,a14,a5,a9,a14,a14,a14,a15,a14,a15),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
a14 = a4,
inference(symmetry,[status(thm)],[c195]) ).
cnf(c296,plain,
tuple(a14,a4,a4,a5,a4,a14,a5,a9,a14,a14,a14,a15,a14,a15) = tuple(a14,a4,a4,a5,a4,a4,a5,a9,a14,a14,a14,a15,a14,a15),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
a14 = a10,
inference(symmetry,[status(thm)],[c187]) ).
cnf(c298,plain,
tuple(a14,a4,a4,a5,a4,a4,a5,a9,a14,a14,a14,a15,a14,a15) = tuple(a14,a4,a4,a5,a4,a4,a5,a9,a10,a14,a14,a15,a14,a15),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
a4 = a7,
inference(symmetry,[status(thm)],[c175]) ).
cnf(c300,plain,
tuple(a14,a4,a4,a5,a4,a4,a5,a9,a10,a14,a14,a15,a14,a15) = tuple(a14,a4,a4,a5,a4,a7,a5,a9,a10,a14,a14,a15,a14,a15),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
a15 = a13,
inference(symmetry,[status(thm)],[c167]) ).
cnf(c302,plain,
tuple(a14,a4,a4,a5,a4,a7,a5,a9,a10,a14,a14,a15,a14,a15) = tuple(a14,a4,a4,a5,a4,a7,a5,a9,a10,a14,a14,a13,a14,a15),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
a14 = a11,
inference(symmetry,[status(thm)],[c154]) ).
cnf(c304,plain,
tuple(a14,a4,a4,a5,a4,a7,a5,a9,a10,a14,a14,a13,a14,a15) = tuple(a14,a4,a4,a5,a4,a7,a5,a9,a10,a11,a14,a13,a14,a15),
inference(congruence,[status(thm)],[c303]) ).
cnf(c305,plain,
a4 = a6,
inference(symmetry,[status(thm)],[c145]) ).
cnf(c306,plain,
tuple(a14,a4,a4,a5,a4,a7,a5,a9,a10,a11,a14,a13,a14,a15) = tuple(a14,a6,a4,a5,a4,a7,a5,a9,a10,a11,a14,a13,a14,a15),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
a4 = a6,
inference(symmetry,[status(thm)],[c145]) ).
cnf(c308,plain,
tuple(a14,a6,a4,a5,a4,a7,a5,a9,a10,a11,a14,a13,a14,a15) = tuple(a14,a6,a4,a5,a6,a7,a5,a9,a10,a11,a14,a13,a14,a15),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
a14 = a12,
inference(symmetry,[status(thm)],[c105]) ).
cnf(c310,plain,
tuple(a14,a6,a4,a5,a6,a7,a5,a9,a10,a11,a14,a13,a14,a15) = tuple(a12,a6,a4,a5,a6,a7,a5,a9,a10,a11,a14,a13,a14,a15),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
a14 = a12,
inference(symmetry,[status(thm)],[c105]) ).
cnf(c312,plain,
tuple(a12,a6,a4,a5,a6,a7,a5,a9,a10,a11,a14,a13,a14,a15) = tuple(a12,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14,a15),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
a12 = a2,
inference(symmetry,[status(thm)],[c97]) ).
cnf(c314,plain,
tuple(a12,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14,a15) = tuple(a2,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14,a15),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
a5 = a8,
inference(symmetry,[status(thm)],[c91]) ).
cnf(c316,plain,
tuple(a2,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14,a15) = tuple(a2,a6,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(congruence,[status(thm)],[c315]) ).
cnf(c317,plain,
a6 = a3,
inference(symmetry,[status(thm)],[c86]) ).
cnf(c318,plain,
tuple(a2,a6,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(congruence,[status(thm)],[c317]) ).
cnf(c319,plain,
tuple(a2,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c316,c318]) ).
cnf(c320,plain,
tuple(a12,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c314,c319]) ).
cnf(c321,plain,
tuple(a12,a6,a4,a5,a6,a7,a5,a9,a10,a11,a14,a13,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c312,c320]) ).
cnf(c322,plain,
tuple(a14,a6,a4,a5,a6,a7,a5,a9,a10,a11,a14,a13,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c310,c321]) ).
cnf(c323,plain,
tuple(a14,a6,a4,a5,a4,a7,a5,a9,a10,a11,a14,a13,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c308,c322]) ).
cnf(c324,plain,
tuple(a14,a4,a4,a5,a4,a7,a5,a9,a10,a11,a14,a13,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c306,c323]) ).
cnf(c325,plain,
tuple(a14,a4,a4,a5,a4,a7,a5,a9,a10,a14,a14,a13,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c304,c324]) ).
cnf(c326,plain,
tuple(a14,a4,a4,a5,a4,a7,a5,a9,a10,a14,a14,a15,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c302,c325]) ).
cnf(c327,plain,
tuple(a14,a4,a4,a5,a4,a4,a5,a9,a10,a14,a14,a15,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c300,c326]) ).
cnf(c328,plain,
tuple(a14,a4,a4,a5,a4,a4,a5,a9,a14,a14,a14,a15,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c298,c327]) ).
cnf(c329,plain,
tuple(a14,a4,a4,a5,a4,a14,a5,a9,a14,a14,a14,a15,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c296,c328]) ).
cnf(c330,plain,
tuple(a14,a4,a4,a5,a14,a14,a5,a9,a14,a14,a14,a15,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c294,c329]) ).
cnf(c331,plain,
tuple(a14,a4,a14,a5,a14,a14,a5,a9,a14,a14,a14,a15,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c292,c330]) ).
cnf(c332,plain,
tuple(a14,a14,a14,a5,a14,a14,a5,a9,a14,a14,a14,a15,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c290,c331]) ).
cnf(c333,plain,
tuple(a14,a14,a14,a5,a14,a14,a15,a9,a14,a14,a14,a15,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c288,c332]) ).
cnf(c334,plain,
tuple(a14,a14,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c286,c333]) ).
cnf(c335,plain,
tuple(a14,a14,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a15,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c284,c334]) ).
cnf(c336,plain,
tuple(a14,a14,a14,a15,a14,a14,a15,a9,a14,a14,a15,a15,a15,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c282,c335]) ).
cnf(c337,plain,
tuple(a14,a14,a14,a15,a14,a14,a15,a9,a14,a15,a15,a15,a15,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c280,c336]) ).
cnf(c338,plain,
tuple(a14,a14,a14,a15,a14,a14,a15,a9,a15,a15,a15,a15,a15,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c278,c337]) ).
cnf(c339,plain,
tuple(a14,a14,a14,a15,a14,a15,a15,a9,a15,a15,a15,a15,a15,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c276,c338]) ).
cnf(c340,plain,
tuple(a14,a14,a14,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c274,c339]) ).
cnf(c341,plain,
tuple(a14,a14,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c272,c340]) ).
cnf(c342,plain,
tuple(a14,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c270,c341]) ).
cnf(c343,plain,
tuple(a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c268,c342]) ).
cnf(c344,plain,
tuple(a15,a15,a15,a15,a15,a15,a15,a15,a15,a15,a15,a15,a15,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c266,c343]) ).
cnf(c345,plain,
tuple(a15,a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c264,c344]) ).
cnf(c346,plain,
tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a15) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c244,c345]) ).
cnf(c347,plain,
tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a15,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c234,c346]) ).
cnf(c348,plain,
tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a15,a15,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c233,c347]) ).
cnf(c349,plain,
tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a15,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c232,c348]) ).
cnf(c350,plain,
tuple(a1,a15,a15,a15,a15,a15,a15,a15,a9,a14,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c231,c349]) ).
cnf(c351,plain,
tuple(a1,a15,a15,a15,a15,a15,a14,a15,a9,a14,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c230,c350]) ).
cnf(c352,plain,
tuple(a1,a15,a15,a15,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c229,c351]) ).
cnf(c353,plain,
tuple(a1,a15,a15,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c228,c352]) ).
cnf(c354,plain,
tuple(a1,a15,a14,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c227,c353]) ).
cnf(c355,plain,
tuple(a1,a14,a14,a14,a15,a14,a14,a15,a9,a14,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c226,c354]) ).
cnf(c356,plain,
tuple(a1,a14,a14,a14,a15,a14,a14,a5,a9,a14,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c209,c355]) ).
cnf(c357,plain,
tuple(a1,a14,a14,a14,a5,a14,a14,a5,a9,a14,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c208,c356]) ).
cnf(c358,plain,
tuple(a1,a14,a14,a14,a5,a14,a4,a5,a9,a14,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c199,c357]) ).
cnf(c359,plain,
tuple(a1,a14,a14,a14,a5,a4,a4,a5,a9,a14,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c198,c358]) ).
cnf(c360,plain,
tuple(a1,a14,a14,a4,a5,a4,a4,a5,a9,a14,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c197,c359]) ).
cnf(c361,plain,
tuple(a1,a14,a4,a4,a5,a4,a4,a5,a9,a14,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c196,c360]) ).
cnf(c362,plain,
tuple(a1,a14,a4,a4,a5,a4,a4,a5,a9,a10,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c188,c361]) ).
cnf(c363,plain,
tuple(a1,a14,a4,a4,a5,a4,a7,a5,a9,a10,a14,a14,a15,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c176,c362]) ).
cnf(c364,plain,
tuple(a1,a14,a4,a4,a5,a4,a7,a5,a9,a10,a14,a14,a13,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c168,c363]) ).
cnf(c365,plain,
tuple(a1,a14,a4,a4,a5,a4,a7,a5,a9,a10,a11,a14,a13,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c155,c364]) ).
cnf(c366,plain,
tuple(a1,a14,a4,a4,a5,a6,a7,a5,a9,a10,a11,a14,a13,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c147,c365]) ).
cnf(c367,plain,
tuple(a1,a14,a6,a4,a5,a6,a7,a5,a9,a10,a11,a14,a13,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c146,c366]) ).
cnf(c368,plain,
tuple(a1,a14,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c107,c367]) ).
cnf(c369,plain,
tuple(a1,a12,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c106,c368]) ).
cnf(c370,plain,
tuple(a1,a2,a6,a4,a5,a6,a7,a5,a9,a10,a11,a12,a13,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c98,c369]) ).
cnf(c371,plain,
tuple(a1,a2,a6,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c92,c370]) ).
cnf(c372,plain,
tuple(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14) = tuple(a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15),
inference(transitivity,[status(thm)],[c87,c371]) ).
cnf(c373,plain,
$false,
inference(resolution,[status(thm)],[c1,c372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : TOP053-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.09 % Computer : n012.cluster.edu
% 0.00/0.09 % Model : x86_64 x86_64
% 0.00/0.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.09 % Memory : 8046.5625MB
% 0.00/0.09 % OS : Linux 6.8.0-71-generic
% 0.00/0.09 % CPULimit : 300
% 0.00/0.09 % WCLimit : 300
% 0.00/0.09 % DateTime : Mon Sep 28 19:07:34 UTC 2026
% 0.00/0.09 % CPUTime :
% 0.00/0.10 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.15 Command-line arguments: --no-flatten-goal
% 0.08/0.15
% 0.08/0.15 % SZS status Unsatisfiable
% 0.08/0.15
% 0.08/0.16 % SZS output start CNFRefutation
% See solution above
% 0.96/0.27
% 0.96/0.27 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------