%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG246-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 09:07:16 AM UTC 2026
% Result : Unsatisfiable 71.32s 9.36s
% Output : CNFRefutation 73.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 95
% Number of leaves : 14
% Syntax : Number of clauses : 602 ( 602 unt; 0 nHn; 27 RR)
% Number of literals : 602 ( 601 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 943 ( 68 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
v(tptp1(n(a),n(tptp0(a,b))),n(b)) != n(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
v(A,B) = tptp4(tptp0(tptp0(A,B),B),tptp0(tptp0(B,A),A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
cnf(c3,plain,
v(tptp1(n(X),n(tptp0(X,X2))),n(X2)) = tptp4(tptp0(tptp0(tptp1(n(X),n(tptp0(X,X2))),n(X2)),n(X2)),tptp0(tptp0(n(X2),tptp1(n(X),n(tptp0(X,X2)))),tptp1(n(X),n(tptp0(X,X2))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
tptp1(A2,B2) = tptp1(B2,A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
cnf(c5,plain,
tptp1(X,X2) = tptp1(X2,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
tptp0(tptp1(X,X2),X3) = tptp0(tptp1(X2,X),X3),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
tptp0(tptp1(A2,B2),C) = tptp0(A2,tptp0(B2,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
cnf(c8,plain,
tptp0(tptp1(X3,X2),X) = tptp0(X3,tptp0(X2,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
tptp0(tptp1(X2,X3),X) = tptp0(X3,tptp0(X2,X)),
inference(transitivity,[status(thm)],[c6,c8]) ).
cnf(c10,plain,
tptp0(tptp1(n(X3),n(X2)),X) = tptp0(n(X2),tptp0(n(X3),X)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
n(tptp0(tptp1(n(X3),n(X2)),X)) = n(tptp0(n(X2),tptp0(n(X3),X))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,axiom,
tptp4(A2,B2) = tptp1(A2,tptp0(A2,B2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
cnf(c13,plain,
tptp4(X2,X) = tptp1(X2,tptp0(X2,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
m(tptp4(X2,X)) = m(tptp1(X2,tptp0(X2,X))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
tptp4(m(X2),m(tptp4(X2,X))) = tptp4(m(X2),m(tptp1(X2,tptp0(X2,X)))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,axiom,
m(A2) = tptp0(A2,tptp3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c10) ).
cnf(c17,plain,
m(X) = tptp0(X,tptp3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
tptp0(X2,m(X)) = tptp0(X2,tptp0(X,tptp3)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
tptp0(tptp1(X2,X),tptp3) = tptp0(X2,tptp0(X,tptp3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c20,plain,
tptp0(X2,tptp0(X,tptp3)) = tptp0(tptp1(X2,X),tptp3),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
m(tptp1(X2,X)) = tptp0(tptp1(X2,X),tptp3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c22,plain,
tptp0(tptp1(X2,X),tptp3) = m(tptp1(X2,X)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
tptp0(X2,tptp0(X,tptp3)) = m(tptp1(X2,X)),
inference(transitivity,[status(thm)],[c20,c22]) ).
cnf(c24,plain,
tptp0(X2,m(X)) = m(tptp1(X2,X)),
inference(transitivity,[status(thm)],[c18,c23]) ).
cnf(c25,plain,
m(tptp1(X2,X)) = tptp0(X2,m(X)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
tptp4(m(X2),m(tptp1(X2,X))) = tptp4(m(X2),tptp0(X2,m(X))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
tptp0(tptp1(X2,X3),X) = tptp0(X2,tptp0(X3,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c28,plain,
tptp0(X2,tptp0(X3,X)) = tptp0(tptp1(X2,X3),X),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
tptp1(X2,X) = tptp1(X,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c30,plain,
tptp1(X,X2) = tptp1(X2,X),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
tptp0(tptp1(X2,X3),X) = tptp0(tptp1(X3,X2),X),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
tptp0(tptp1(X3,X2),X) = tptp0(X3,tptp0(X2,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c33,plain,
tptp0(tptp1(X2,X3),X) = tptp0(X3,tptp0(X2,X)),
inference(transitivity,[status(thm)],[c31,c32]) ).
cnf(c34,plain,
tptp0(X2,tptp0(X3,X)) = tptp0(X3,tptp0(X2,X)),
inference(transitivity,[status(thm)],[c28,c33]) ).
cnf(c35,plain,
tptp1(X3,tptp0(X2,tptp0(X3,X))) = tptp1(X3,tptp0(X3,tptp0(X2,X))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
tptp4(X3,tptp0(X2,X)) = tptp1(X3,tptp0(X3,tptp0(X2,X))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c37,plain,
tptp1(X3,tptp0(X3,tptp0(X2,X))) = tptp4(X3,tptp0(X2,X)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
tptp1(X3,tptp0(X2,tptp0(X3,X))) = tptp4(X3,tptp0(X2,X)),
inference(transitivity,[status(thm)],[c35,c37]) ).
cnf(c39,plain,
tptp1(m(X2),tptp0(X2,tptp0(m(X2),X))) = tptp4(m(X2),tptp0(X2,X)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
tptp4(m(X2),tptp0(X2,X)) = tptp1(m(X2),tptp0(X2,tptp0(m(X2),X))),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
tptp0(tptp1(X2,m(X2)),X) = tptp0(X2,tptp0(m(X2),X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c42,plain,
tptp0(X2,tptp0(m(X2),X)) = tptp0(tptp1(X2,m(X2)),X),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
m(X) = tptp0(X,tptp3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c44,plain,
tptp1(X,m(X)) = tptp1(X,tptp0(X,tptp3)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
tptp4(X,tptp3) = tptp1(X,tptp0(X,tptp3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c46,plain,
tptp1(X,tptp0(X,tptp3)) = tptp4(X,tptp3),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
tptp4(X,X2) = tptp1(X,tptp0(X,X2)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c48,axiom,
tptp1(A2,tptp0(A2,B2)) = tptp1(B2,tptp0(B2,A2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
cnf(c49,plain,
tptp1(X2,tptp0(X2,X)) = tptp1(X,tptp0(X,X2)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
tptp1(X,tptp0(X,X2)) = tptp1(X2,tptp0(X2,X)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
tptp4(X2,X) = tptp1(X2,tptp0(X2,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c52,plain,
tptp1(X2,tptp0(X2,X)) = tptp4(X2,X),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
tptp1(X,tptp0(X,X2)) = tptp4(X2,X),
inference(transitivity,[status(thm)],[c50,c52]) ).
cnf(c54,plain,
tptp4(X,X2) = tptp4(X2,X),
inference(transitivity,[status(thm)],[c47,c53]) ).
cnf(c55,plain,
tptp4(X,tptp3) = tptp4(tptp3,X),
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
tptp4(tptp3,X) = tptp1(tptp3,tptp0(tptp3,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c57,axiom,
tptp0(tptp3,A2) = tptp5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
cnf(c58,plain,
tptp0(tptp3,X) = tptp5,
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
tptp1(tptp3,tptp0(tptp3,X)) = tptp1(tptp3,tptp5),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
tptp1(tptp5,X) = tptp1(X,tptp5),
inference(substitution,[status(thm)],[c4]) ).
cnf(c61,plain,
tptp1(X,tptp5) = tptp1(tptp5,X),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,axiom,
tptp1(tptp5,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
cnf(c63,plain,
tptp1(tptp5,X) = X,
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
tptp1(X,tptp5) = X,
inference(transitivity,[status(thm)],[c61,c63]) ).
cnf(c65,plain,
tptp1(tptp3,tptp5) = tptp3,
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
tptp1(tptp3,tptp0(tptp3,X)) = tptp3,
inference(transitivity,[status(thm)],[c59,c65]) ).
cnf(c67,plain,
tptp4(tptp3,X) = tptp3,
inference(transitivity,[status(thm)],[c56,c66]) ).
cnf(c68,plain,
tptp4(X,tptp3) = tptp3,
inference(transitivity,[status(thm)],[c55,c67]) ).
cnf(c69,plain,
tptp1(X,tptp0(X,tptp3)) = tptp3,
inference(transitivity,[status(thm)],[c46,c68]) ).
cnf(c70,plain,
tptp1(X,m(X)) = tptp3,
inference(transitivity,[status(thm)],[c44,c69]) ).
cnf(c71,plain,
tptp0(tptp1(X2,m(X2)),X) = tptp0(tptp3,X),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
tptp0(tptp3,X) = tptp5,
inference(substitution,[status(thm)],[c57]) ).
cnf(c73,plain,
tptp0(tptp1(X2,m(X2)),X) = tptp5,
inference(transitivity,[status(thm)],[c71,c72]) ).
cnf(c74,plain,
tptp0(X2,tptp0(m(X2),X)) = tptp5,
inference(transitivity,[status(thm)],[c42,c73]) ).
cnf(c75,plain,
tptp1(m(X2),tptp0(X2,tptp0(m(X2),X))) = tptp1(m(X2),tptp5),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
tptp1(m(X),tptp5) = m(X),
inference(substitution,[status(thm)],[c64]) ).
cnf(c77,plain,
tptp1(m(X2),tptp0(X2,tptp0(m(X2),X))) = m(X2),
inference(transitivity,[status(thm)],[c75,c76]) ).
cnf(c78,plain,
tptp4(m(X2),tptp0(X2,X)) = m(X2),
inference(transitivity,[status(thm)],[c40,c77]) ).
cnf(c79,plain,
tptp4(m(X2),tptp0(X2,m(X))) = m(X2),
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
tptp4(m(X2),m(tptp1(X2,X))) = m(X2),
inference(transitivity,[status(thm)],[c26,c79]) ).
cnf(c81,plain,
tptp4(m(X2),m(tptp1(X2,tptp0(X2,X)))) = m(X2),
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
tptp4(m(X2),m(tptp4(X2,X))) = m(X2),
inference(transitivity,[status(thm)],[c15,c81]) ).
cnf(c83,plain,
tptp4(m(m(n(X))),m(tptp4(m(n(X)),tptp2(X)))) = m(m(n(X))),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
m(m(n(X))) = tptp4(m(m(n(X))),m(tptp4(m(n(X)),tptp2(X)))),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
tptp4(m(n(X)),tptp2(X)) = tptp4(tptp2(X),m(n(X))),
inference(substitution,[status(thm)],[c54]) ).
cnf(c86,plain,
tptp1(X2,X) = tptp1(X,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c87,plain,
tptp1(X,X2) = tptp1(X2,X),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
m(tptp1(X,X2)) = m(tptp1(X2,X)),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
tptp1(X2,m(tptp1(X,X2))) = tptp1(X2,m(tptp1(X2,X))),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
m(tptp1(X2,X)) = tptp0(X2,m(X)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c91,plain,
tptp1(X2,m(tptp1(X2,X))) = tptp1(X2,tptp0(X2,m(X))),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
tptp4(X2,m(X)) = tptp1(X2,tptp0(X2,m(X))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c93,plain,
tptp1(X2,tptp0(X2,m(X))) = tptp4(X2,m(X)),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
tptp1(X2,m(tptp1(X2,X))) = tptp4(X2,m(X)),
inference(transitivity,[status(thm)],[c91,c93]) ).
cnf(c95,plain,
tptp1(X2,m(tptp1(X,X2))) = tptp4(X2,m(X)),
inference(transitivity,[status(thm)],[c89,c94]) ).
cnf(c96,plain,
tptp1(tptp2(X),m(tptp1(n(X),tptp2(X)))) = tptp4(tptp2(X),m(n(X))),
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
tptp4(tptp2(X),m(n(X))) = tptp1(tptp2(X),m(tptp1(n(X),tptp2(X)))),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
tptp1(tptp2(X),n(X)) = tptp1(n(X),tptp2(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c99,plain,
tptp1(n(X),tptp2(X)) = tptp1(tptp2(X),n(X)),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,axiom,
n(A2) = m(tptp2(A2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c11) ).
cnf(c101,plain,
n(X) = m(tptp2(X)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
tptp1(tptp2(X),n(X)) = tptp1(tptp2(X),m(tptp2(X))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
tptp1(tptp2(X),m(tptp2(X))) = tptp3,
inference(substitution,[status(thm)],[c70]) ).
cnf(c104,plain,
tptp1(tptp2(X),n(X)) = tptp3,
inference(transitivity,[status(thm)],[c102,c103]) ).
cnf(c105,plain,
tptp1(n(X),tptp2(X)) = tptp3,
inference(transitivity,[status(thm)],[c99,c104]) ).
cnf(c106,plain,
m(tptp1(n(X),tptp2(X))) = m(tptp3),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
tptp1(tptp2(X),m(tptp1(n(X),tptp2(X)))) = tptp1(tptp2(X),m(tptp3)),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
m(tptp3) = tptp0(tptp3,tptp3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c109,plain,
tptp0(tptp3,tptp3) = tptp5,
inference(substitution,[status(thm)],[c57]) ).
cnf(c110,plain,
m(tptp3) = tptp5,
inference(transitivity,[status(thm)],[c108,c109]) ).
cnf(c111,plain,
tptp1(tptp2(X),m(tptp3)) = tptp1(tptp2(X),tptp5),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
tptp1(tptp2(X),tptp5) = tptp2(X),
inference(substitution,[status(thm)],[c64]) ).
cnf(c113,plain,
tptp1(tptp2(X),m(tptp3)) = tptp2(X),
inference(transitivity,[status(thm)],[c111,c112]) ).
cnf(c114,plain,
tptp1(tptp2(X),m(tptp1(n(X),tptp2(X)))) = tptp2(X),
inference(transitivity,[status(thm)],[c107,c113]) ).
cnf(c115,plain,
tptp4(tptp2(X),m(n(X))) = tptp2(X),
inference(transitivity,[status(thm)],[c97,c114]) ).
cnf(c116,plain,
tptp4(m(n(X)),tptp2(X)) = tptp2(X),
inference(transitivity,[status(thm)],[c85,c115]) ).
cnf(c117,plain,
m(tptp4(m(n(X)),tptp2(X))) = m(tptp2(X)),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
tptp4(m(m(n(X))),m(tptp4(m(n(X)),tptp2(X)))) = tptp4(m(m(n(X))),m(tptp2(X))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
n(X) = m(tptp2(X)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c120,plain,
m(tptp2(X)) = n(X),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
tptp4(m(m(n(X))),m(tptp2(X))) = tptp4(m(m(n(X))),n(X)),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
tptp4(n(X),m(m(n(X)))) = tptp4(m(m(n(X))),n(X)),
inference(substitution,[status(thm)],[c54]) ).
cnf(c123,plain,
tptp4(m(m(n(X))),n(X)) = tptp4(n(X),m(m(n(X)))),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
m(m(X)) = tptp0(m(X),tptp3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c125,plain,
tptp4(X,m(m(X))) = tptp4(X,tptp0(m(X),tptp3)),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
tptp4(X2,tptp0(m(X2),X)) = tptp1(X2,tptp0(X2,tptp0(m(X2),X))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c127,plain,
tptp1(X2,tptp0(X2,tptp0(m(X2),X))) = tptp1(X2,tptp5),
inference(congruence,[status(thm)],[c74]) ).
cnf(c128,plain,
tptp1(X2,tptp0(X2,tptp0(m(X2),X))) = X2,
inference(transitivity,[status(thm)],[c127,c64]) ).
cnf(c129,plain,
tptp4(X2,tptp0(m(X2),X)) = X2,
inference(transitivity,[status(thm)],[c126,c128]) ).
cnf(c130,plain,
tptp4(X,tptp0(m(X),tptp3)) = X,
inference(substitution,[status(thm)],[c129]) ).
cnf(c131,plain,
tptp4(X,m(m(X))) = X,
inference(transitivity,[status(thm)],[c125,c130]) ).
cnf(c132,plain,
tptp4(n(X),m(m(n(X)))) = n(X),
inference(substitution,[status(thm)],[c131]) ).
cnf(c133,plain,
tptp4(m(m(n(X))),n(X)) = n(X),
inference(transitivity,[status(thm)],[c123,c132]) ).
cnf(c134,plain,
tptp4(m(m(n(X))),m(tptp2(X))) = n(X),
inference(transitivity,[status(thm)],[c121,c133]) ).
cnf(c135,plain,
tptp4(m(m(n(X))),m(tptp4(m(n(X)),tptp2(X)))) = n(X),
inference(transitivity,[status(thm)],[c118,c134]) ).
cnf(c136,plain,
m(m(n(X))) = n(X),
inference(transitivity,[status(thm)],[c84,c135]) ).
cnf(c137,plain,
n(X) = m(m(n(X))),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
tptp0(n(X2),X) = tptp0(m(m(n(X2))),X),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
n(tptp0(n(X2),X)) = n(tptp0(m(m(n(X2))),X)),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
m(X) = tptp0(X,tptp3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c141,plain,
tptp2(m(X)) = tptp2(tptp0(X,tptp3)),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
tptp4(m(m(X)),tptp2(m(X))) = tptp4(m(m(X)),tptp2(tptp0(X,tptp3))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
tptp1(tptp5,tptp2(tptp5)) = tptp2(tptp5),
inference(substitution,[status(thm)],[c62]) ).
cnf(c144,plain,
tptp2(tptp5) = tptp1(tptp5,tptp2(tptp5)),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
tptp0(tptp3,tptp2(tptp5)) = tptp5,
inference(substitution,[status(thm)],[c57]) ).
cnf(c146,plain,
tptp5 = tptp0(tptp3,tptp2(tptp5)),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
n(tptp5) = n(tptp0(tptp3,tptp2(tptp5))),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,axiom,
tptp2(tptp2(A2)) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c12) ).
cnf(c149,plain,
tptp2(tptp2(X)) = X,
inference(substitution,[status(thm)],[c148]) ).
cnf(c150,plain,
X = tptp2(tptp2(X)),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
tptp0(X,tptp2(X2)) = tptp0(tptp2(tptp2(X)),tptp2(X2)),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
n(tptp0(X,tptp2(X2))) = n(tptp0(tptp2(tptp2(X)),tptp2(X2))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,axiom,
n(tptp0(A2,B2)) = n(tptp0(tptp2(B2),tptp2(A2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c13) ).
cnf(c154,plain,
n(tptp0(X2,tptp2(X))) = n(tptp0(tptp2(tptp2(X)),tptp2(X2))),
inference(substitution,[status(thm)],[c153]) ).
cnf(c155,plain,
n(tptp0(tptp2(tptp2(X)),tptp2(X2))) = n(tptp0(X2,tptp2(X))),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
n(tptp0(X,tptp2(X2))) = n(tptp0(X2,tptp2(X))),
inference(transitivity,[status(thm)],[c152,c155]) ).
cnf(c157,plain,
n(tptp0(X,tptp2(tptp5))) = n(tptp0(tptp5,tptp2(X))),
inference(substitution,[status(thm)],[c156]) ).
cnf(c158,plain,
tptp1(tptp5,tptp0(tptp5,X)) = tptp0(tptp5,X),
inference(substitution,[status(thm)],[c62]) ).
cnf(c159,plain,
tptp0(tptp5,X) = tptp1(tptp5,tptp0(tptp5,X)),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
tptp4(tptp5,X) = tptp1(tptp5,tptp0(tptp5,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c161,plain,
tptp1(tptp5,tptp0(tptp5,X)) = tptp4(tptp5,X),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
tptp4(X,tptp5) = tptp4(tptp5,X),
inference(substitution,[status(thm)],[c54]) ).
cnf(c163,plain,
tptp4(tptp5,X) = tptp4(X,tptp5),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
tptp1(tptp5,tptp0(tptp5,X)) = tptp4(X,tptp5),
inference(transitivity,[status(thm)],[c161,c163]) ).
cnf(c165,plain,
tptp0(tptp5,X) = tptp4(X,tptp5),
inference(transitivity,[status(thm)],[c159,c164]) ).
cnf(c166,plain,
tptp0(tptp5,tptp2(X)) = tptp4(tptp2(X),tptp5),
inference(substitution,[status(thm)],[c165]) ).
cnf(c167,plain,
n(tptp0(tptp5,tptp2(X))) = n(tptp4(tptp2(X),tptp5)),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
tptp4(X,tptp5) = tptp1(X,tptp0(X,tptp5)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c169,plain,
tptp0(tptp3,m(X)) = tptp5,
inference(substitution,[status(thm)],[c57]) ).
cnf(c170,plain,
tptp5 = tptp0(tptp3,m(X)),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
tptp0(X2,tptp5) = tptp0(X2,tptp0(tptp3,m(X))),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
tptp0(tptp1(X2,tptp3),m(X)) = tptp0(X2,tptp0(tptp3,m(X))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c173,plain,
tptp0(X2,tptp0(tptp3,m(X))) = tptp0(tptp1(X2,tptp3),m(X)),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
m(X) = tptp0(X,tptp3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c175,plain,
v(m(X2),m(X)) = v(m(X2),tptp0(X,tptp3)),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
m(X) = tptp0(X,tptp3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c177,plain,
v(m(X2),tptp0(X,tptp3)) = v(tptp0(X2,tptp3),tptp0(X,tptp3)),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,axiom,
tptp0(tptp1(A2,B2),tptp3) = v(tptp0(A2,tptp3),tptp0(B2,tptp3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
cnf(c179,plain,
tptp0(tptp1(X2,X),tptp3) = v(tptp0(X2,tptp3),tptp0(X,tptp3)),
inference(substitution,[status(thm)],[c178]) ).
cnf(c180,plain,
v(tptp0(X2,tptp3),tptp0(X,tptp3)) = tptp0(tptp1(X2,X),tptp3),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
tptp0(tptp1(X2,X),tptp3) = tptp0(X2,tptp0(X,tptp3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c182,plain,
m(X) = tptp0(X,tptp3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c183,plain,
tptp0(X,tptp3) = m(X),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c184,plain,
tptp0(X2,tptp0(X,tptp3)) = tptp0(X2,m(X)),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
tptp0(tptp1(X2,X),tptp3) = tptp0(X2,m(X)),
inference(transitivity,[status(thm)],[c181,c184]) ).
cnf(c186,plain,
v(tptp0(X2,tptp3),tptp0(X,tptp3)) = tptp0(X2,m(X)),
inference(transitivity,[status(thm)],[c180,c185]) ).
cnf(c187,plain,
v(m(X2),tptp0(X,tptp3)) = tptp0(X2,m(X)),
inference(transitivity,[status(thm)],[c177,c186]) ).
cnf(c188,plain,
v(m(X2),m(X)) = tptp0(X2,m(X)),
inference(transitivity,[status(thm)],[c175,c187]) ).
cnf(c189,plain,
v(m(tptp1(X2,tptp3)),m(X)) = tptp0(tptp1(X2,tptp3),m(X)),
inference(substitution,[status(thm)],[c188]) ).
cnf(c190,plain,
tptp0(tptp1(X2,tptp3),m(X)) = v(m(tptp1(X2,tptp3)),m(X)),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
tptp1(tptp3,X) = tptp1(X,tptp3),
inference(substitution,[status(thm)],[c4]) ).
cnf(c192,plain,
tptp1(X,tptp3) = tptp1(tptp3,X),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
m(tptp1(X,tptp3)) = m(tptp1(tptp3,X)),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
tptp0(tptp3,m(X)) = m(tptp1(tptp3,X)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c195,plain,
m(tptp1(tptp3,X)) = tptp0(tptp3,m(X)),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
tptp0(tptp3,m(X)) = tptp5,
inference(substitution,[status(thm)],[c57]) ).
cnf(c197,plain,
m(tptp1(tptp3,X)) = tptp5,
inference(transitivity,[status(thm)],[c195,c196]) ).
cnf(c198,plain,
m(tptp1(X,tptp3)) = tptp5,
inference(transitivity,[status(thm)],[c193,c197]) ).
cnf(c199,plain,
v(m(tptp1(X2,tptp3)),m(X)) = v(tptp5,m(X)),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
tptp5 = m(tptp3),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c201,plain,
v(tptp5,m(X)) = v(m(tptp3),m(X)),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
v(m(tptp3),m(X)) = tptp0(tptp3,m(X)),
inference(substitution,[status(thm)],[c188]) ).
cnf(c203,plain,
tptp0(tptp3,m(X)) = tptp5,
inference(substitution,[status(thm)],[c57]) ).
cnf(c204,plain,
v(m(tptp3),m(X)) = tptp5,
inference(transitivity,[status(thm)],[c202,c203]) ).
cnf(c205,plain,
v(tptp5,m(X)) = tptp5,
inference(transitivity,[status(thm)],[c201,c204]) ).
cnf(c206,plain,
v(m(tptp1(X2,tptp3)),m(X)) = tptp5,
inference(transitivity,[status(thm)],[c199,c205]) ).
cnf(c207,plain,
tptp0(tptp1(X2,tptp3),m(X)) = tptp5,
inference(transitivity,[status(thm)],[c190,c206]) ).
cnf(c208,plain,
tptp0(X2,tptp0(tptp3,m(X))) = tptp5,
inference(transitivity,[status(thm)],[c173,c207]) ).
cnf(c209,plain,
tptp0(X,tptp5) = tptp5,
inference(transitivity,[status(thm)],[c171,c208]) ).
cnf(c210,plain,
tptp1(X,tptp0(X,tptp5)) = tptp1(X,tptp5),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
tptp1(X,tptp0(X,tptp5)) = X,
inference(transitivity,[status(thm)],[c210,c64]) ).
cnf(c212,plain,
tptp4(X,tptp5) = X,
inference(transitivity,[status(thm)],[c168,c211]) ).
cnf(c213,plain,
tptp4(tptp2(X),tptp5) = tptp2(X),
inference(substitution,[status(thm)],[c212]) ).
cnf(c214,plain,
n(tptp4(tptp2(X),tptp5)) = n(tptp2(X)),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
n(tptp2(X)) = m(tptp2(tptp2(X))),
inference(substitution,[status(thm)],[c100]) ).
cnf(c216,plain,
tptp2(tptp2(X)) = X,
inference(substitution,[status(thm)],[c148]) ).
cnf(c217,plain,
m(tptp2(tptp2(X))) = m(X),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
n(tptp2(X)) = m(X),
inference(transitivity,[status(thm)],[c215,c217]) ).
cnf(c219,plain,
n(tptp4(tptp2(X),tptp5)) = m(X),
inference(transitivity,[status(thm)],[c214,c218]) ).
cnf(c220,plain,
n(tptp0(tptp5,tptp2(X))) = m(X),
inference(transitivity,[status(thm)],[c167,c219]) ).
cnf(c221,plain,
n(tptp0(X,tptp2(tptp5))) = m(X),
inference(transitivity,[status(thm)],[c157,c220]) ).
cnf(c222,plain,
n(tptp0(tptp3,tptp2(tptp5))) = m(tptp3),
inference(substitution,[status(thm)],[c221]) ).
cnf(c223,plain,
n(tptp0(tptp3,tptp2(tptp5))) = tptp5,
inference(transitivity,[status(thm)],[c222,c110]) ).
cnf(c224,plain,
n(tptp5) = tptp5,
inference(transitivity,[status(thm)],[c147,c223]) ).
cnf(c225,plain,
tptp5 = n(tptp5),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
tptp1(tptp5,tptp2(tptp5)) = tptp1(n(tptp5),tptp2(tptp5)),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
tptp1(n(tptp5),tptp2(tptp5)) = tptp3,
inference(substitution,[status(thm)],[c105]) ).
cnf(c228,plain,
tptp1(tptp5,tptp2(tptp5)) = tptp3,
inference(transitivity,[status(thm)],[c226,c227]) ).
cnf(c229,plain,
tptp2(tptp5) = tptp3,
inference(transitivity,[status(thm)],[c144,c228]) ).
cnf(c230,plain,
tptp3 = tptp2(tptp5),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c231,plain,
tptp0(X,tptp3) = tptp0(X,tptp2(tptp5)),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
tptp2(tptp0(X,tptp3)) = tptp2(tptp0(X,tptp2(tptp5))),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
tptp4(m(m(X)),tptp2(tptp0(X,tptp3))) = tptp4(m(m(X)),tptp2(tptp0(X,tptp2(tptp5)))),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
m(X) = n(tptp0(X,tptp2(tptp5))),
inference(symmetry,[status(thm)],[c221]) ).
cnf(c235,plain,
m(m(X)) = m(n(tptp0(X,tptp2(tptp5)))),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
tptp4(m(m(X)),tptp2(tptp0(X,tptp2(tptp5)))) = tptp4(m(n(tptp0(X,tptp2(tptp5)))),tptp2(tptp0(X,tptp2(tptp5)))),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
tptp4(m(n(tptp0(X,tptp2(tptp5)))),tptp2(tptp0(X,tptp2(tptp5)))) = tptp2(tptp0(X,tptp2(tptp5))),
inference(substitution,[status(thm)],[c116]) ).
cnf(c238,plain,
tptp0(X,tptp2(tptp5)) = tptp0(X,tptp3),
inference(congruence,[status(thm)],[c229]) ).
cnf(c239,plain,
tptp2(tptp0(X,tptp2(tptp5))) = tptp2(tptp0(X,tptp3)),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
m(X) = tptp0(X,tptp3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c241,plain,
tptp0(X,tptp3) = m(X),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
tptp2(tptp0(X,tptp3)) = tptp2(m(X)),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
tptp2(tptp0(X,tptp2(tptp5))) = tptp2(m(X)),
inference(transitivity,[status(thm)],[c239,c242]) ).
cnf(c244,plain,
tptp4(m(n(tptp0(X,tptp2(tptp5)))),tptp2(tptp0(X,tptp2(tptp5)))) = tptp2(m(X)),
inference(transitivity,[status(thm)],[c237,c243]) ).
cnf(c245,plain,
tptp4(m(m(X)),tptp2(tptp0(X,tptp2(tptp5)))) = tptp2(m(X)),
inference(transitivity,[status(thm)],[c236,c244]) ).
cnf(c246,plain,
tptp4(m(m(X)),tptp2(tptp0(X,tptp3))) = tptp2(m(X)),
inference(transitivity,[status(thm)],[c233,c245]) ).
cnf(c247,plain,
tptp4(m(m(X)),tptp2(m(X))) = tptp2(m(X)),
inference(transitivity,[status(thm)],[c142,c246]) ).
cnf(c248,plain,
tptp2(m(X)) = tptp4(m(m(X)),tptp2(m(X))),
inference(symmetry,[status(thm)],[c247]) ).
cnf(c249,plain,
m(X) = n(tptp2(X)),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c250,plain,
m(m(X)) = m(n(tptp2(X))),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
m(m(m(X))) = m(m(n(tptp2(X)))),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
m(m(n(tptp2(X)))) = n(tptp2(X)),
inference(substitution,[status(thm)],[c136]) ).
cnf(c253,plain,
m(m(n(tptp2(X)))) = m(X),
inference(transitivity,[status(thm)],[c252,c218]) ).
cnf(c254,plain,
m(m(m(X))) = m(X),
inference(transitivity,[status(thm)],[c251,c253]) ).
cnf(c255,plain,
m(X) = m(m(m(X))),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
tptp2(m(X)) = tptp2(m(m(m(X)))),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
tptp4(m(m(X)),tptp2(m(X))) = tptp4(m(m(X)),tptp2(m(m(m(X))))),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
tptp4(X,tptp2(m(X))) = tptp1(X,tptp0(X,tptp2(m(X)))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c259,plain,
tptp4(tptp0(X,tptp2(m(X))),tptp5) = tptp0(X,tptp2(m(X))),
inference(substitution,[status(thm)],[c212]) ).
cnf(c260,plain,
tptp0(X,tptp2(m(X))) = tptp4(tptp0(X,tptp2(m(X))),tptp5),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
tptp0(tptp5,tptp0(X,tptp2(m(X)))) = tptp4(tptp0(X,tptp2(m(X))),tptp5),
inference(substitution,[status(thm)],[c165]) ).
cnf(c262,plain,
tptp4(tptp0(X,tptp2(m(X))),tptp5) = tptp0(tptp5,tptp0(X,tptp2(m(X)))),
inference(symmetry,[status(thm)],[c261]) ).
cnf(c263,plain,
n(tptp0(X,tptp2(m(X)))) = n(tptp0(m(X),tptp2(X))),
inference(substitution,[status(thm)],[c156]) ).
cnf(c264,plain,
m(X) = n(tptp2(X)),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c265,plain,
tptp0(m(X),tptp2(X)) = tptp0(n(tptp2(X)),tptp2(X)),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
n(tptp0(m(X),tptp2(X))) = n(tptp0(n(tptp2(X)),tptp2(X))),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
v(n(X2),n(tptp0(X,X2))) = tptp4(tptp0(tptp0(n(X2),n(tptp0(X,X2))),n(tptp0(X,X2))),tptp0(tptp0(n(tptp0(X,X2)),n(X2)),n(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c268,plain,
n(X) = m(tptp2(X)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c269,plain,
tptp0(n(X2),n(tptp0(X,X2))) = tptp0(m(tptp2(X2)),n(tptp0(X,X2))),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
n(tptp0(X,X2)) = n(tptp0(tptp2(X2),tptp2(X))),
inference(substitution,[status(thm)],[c153]) ).
cnf(c271,plain,
tptp0(m(tptp2(X2)),n(tptp0(X,X2))) = tptp0(m(tptp2(X2)),n(tptp0(tptp2(X2),tptp2(X)))),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
X = tptp4(X,m(m(X))),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c273,plain,
tptp0(X2,X) = tptp0(tptp4(X2,m(m(X2))),X),
inference(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
n(tptp0(X2,X)) = n(tptp0(tptp4(X2,m(m(X2))),X)),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
tptp0(m(X2),n(tptp0(X2,X))) = tptp0(m(X2),n(tptp0(tptp4(X2,m(m(X2))),X))),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
tptp4(X,m(X2)) = tptp4(m(X2),X),
inference(substitution,[status(thm)],[c54]) ).
cnf(c277,plain,
tptp0(tptp4(X2,m(X3)),X) = tptp0(tptp4(m(X3),X2),X),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
n(tptp0(tptp4(X2,m(X3)),X)) = n(tptp0(tptp4(m(X3),X2),X)),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
tptp0(X3,n(tptp0(tptp4(X2,m(X3)),X))) = tptp0(X3,n(tptp0(tptp4(m(X3),X2),X))),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
tptp0(tptp1(X3,tptp0(X3,X2)),X) = tptp0(X3,tptp0(tptp0(X3,X2),X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c281,plain,
tptp0(X3,tptp0(tptp0(X3,X2),X)) = tptp0(tptp1(X3,tptp0(X3,X2)),X),
inference(symmetry,[status(thm)],[c280]) ).
cnf(c282,plain,
tptp4(X2,X) = tptp1(X2,tptp0(X2,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c283,plain,
tptp1(X2,tptp0(X2,X)) = tptp4(X2,X),
inference(symmetry,[status(thm)],[c282]) ).
cnf(c284,plain,
tptp0(tptp1(X3,tptp0(X3,X2)),X) = tptp0(tptp4(X3,X2),X),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
tptp0(X3,tptp0(tptp0(X3,X2),X)) = tptp0(tptp4(X3,X2),X),
inference(transitivity,[status(thm)],[c281,c284]) ).
cnf(c286,plain,
tptp0(m(X3),tptp0(tptp0(m(X3),X2),X)) = tptp0(tptp4(m(X3),X2),X),
inference(substitution,[status(thm)],[c285]) ).
cnf(c287,plain,
tptp0(tptp4(m(X3),X2),X) = tptp0(m(X3),tptp0(tptp0(m(X3),X2),X)),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
n(tptp0(tptp4(m(X3),X2),X)) = n(tptp0(m(X3),tptp0(tptp0(m(X3),X2),X))),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
tptp0(X3,n(tptp0(tptp4(m(X3),X2),X))) = tptp0(X3,n(tptp0(m(X3),tptp0(tptp0(m(X3),X2),X)))),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
m(X) = tptp0(X,tptp3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c291,plain,
n(m(X)) = n(tptp0(X,tptp3)),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
tptp3 = tptp2(tptp5),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c293,plain,
tptp0(X,tptp3) = tptp0(X,tptp2(tptp5)),
inference(congruence,[status(thm)],[c292]) ).
cnf(c294,plain,
n(tptp0(X,tptp3)) = n(tptp0(X,tptp2(tptp5))),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
n(tptp0(tptp5,tptp2(X))) = n(tptp0(X,tptp2(tptp5))),
inference(substitution,[status(thm)],[c156]) ).
cnf(c296,plain,
n(tptp0(X,tptp2(tptp5))) = n(tptp0(tptp5,tptp2(X))),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
tptp0(tptp5,tptp2(X)) = tptp4(tptp2(X),tptp5),
inference(substitution,[status(thm)],[c165]) ).
cnf(c298,plain,
n(tptp0(tptp5,tptp2(X))) = n(tptp4(tptp2(X),tptp5)),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
tptp4(tptp2(X),tptp5) = tptp2(X),
inference(substitution,[status(thm)],[c212]) ).
cnf(c300,plain,
n(tptp4(tptp2(X),tptp5)) = n(tptp2(X)),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
n(tptp4(tptp2(X),tptp5)) = m(X),
inference(transitivity,[status(thm)],[c300,c218]) ).
cnf(c302,plain,
n(tptp0(tptp5,tptp2(X))) = m(X),
inference(transitivity,[status(thm)],[c298,c301]) ).
cnf(c303,plain,
n(tptp0(X,tptp2(tptp5))) = m(X),
inference(transitivity,[status(thm)],[c296,c302]) ).
cnf(c304,plain,
n(tptp0(X,tptp3)) = m(X),
inference(transitivity,[status(thm)],[c294,c303]) ).
cnf(c305,plain,
n(m(X)) = m(X),
inference(transitivity,[status(thm)],[c291,c304]) ).
cnf(c306,plain,
m(X) = n(m(X)),
inference(symmetry,[status(thm)],[c305]) ).
cnf(c307,plain,
tptp0(m(X2),X) = tptp0(n(m(X2)),X),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
n(tptp0(m(X2),X)) = n(tptp0(n(m(X2)),X)),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
tptp0(X2,n(tptp0(m(X2),X))) = tptp0(X2,n(tptp0(n(m(X2)),X))),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
n(m(X)) = m(tptp2(m(X))),
inference(substitution,[status(thm)],[c100]) ).
cnf(c311,plain,
tptp0(n(m(X2)),X) = tptp0(m(tptp2(m(X2))),X),
inference(congruence,[status(thm)],[c310]) ).
cnf(c312,plain,
n(tptp0(n(m(X2)),X)) = n(tptp0(m(tptp2(m(X2))),X)),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
tptp0(X2,n(tptp0(n(m(X2)),X))) = tptp0(X2,n(tptp0(m(tptp2(m(X2))),X))),
inference(congruence,[status(thm)],[c312]) ).
cnf(c314,plain,
tptp2(tptp2(X)) = X,
inference(substitution,[status(thm)],[c148]) ).
cnf(c315,plain,
X = tptp2(tptp2(X)),
inference(symmetry,[status(thm)],[c314]) ).
cnf(c316,plain,
tptp0(tptp2(X),X2) = tptp0(tptp2(X),tptp2(tptp2(X2))),
inference(congruence,[status(thm)],[c315]) ).
cnf(c317,plain,
n(tptp0(tptp2(X),X2)) = n(tptp0(tptp2(X),tptp2(tptp2(X2)))),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
n(tptp0(tptp2(X2),X)) = n(tptp0(tptp2(X),tptp2(tptp2(X2)))),
inference(substitution,[status(thm)],[c153]) ).
cnf(c319,plain,
n(tptp0(tptp2(X),tptp2(tptp2(X2)))) = n(tptp0(tptp2(X2),X)),
inference(symmetry,[status(thm)],[c318]) ).
cnf(c320,plain,
n(tptp0(tptp2(X),X2)) = n(tptp0(tptp2(X2),X)),
inference(transitivity,[status(thm)],[c317,c319]) ).
cnf(c321,plain,
n(tptp0(tptp2(m(X2)),X)) = n(tptp0(tptp2(X),m(X2))),
inference(substitution,[status(thm)],[c320]) ).
cnf(c322,plain,
tptp0(tptp2(X),m(X2)) = m(tptp1(tptp2(X),X2)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c323,plain,
n(tptp0(tptp2(X),m(X2))) = n(m(tptp1(tptp2(X),X2))),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
n(m(tptp1(tptp2(X),X2))) = m(tptp1(tptp2(X),X2)),
inference(substitution,[status(thm)],[c305]) ).
cnf(c325,plain,
tptp1(X,tptp2(X2)) = tptp1(tptp2(X2),X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c326,plain,
tptp1(tptp2(X2),X) = tptp1(X,tptp2(X2)),
inference(symmetry,[status(thm)],[c325]) ).
cnf(c327,plain,
m(tptp1(tptp2(X2),X)) = m(tptp1(X,tptp2(X2))),
inference(congruence,[status(thm)],[c326]) ).
cnf(c328,plain,
tptp0(X2,m(tptp2(X))) = m(tptp1(X2,tptp2(X))),
inference(substitution,[status(thm)],[c24]) ).
cnf(c329,plain,
m(tptp1(X2,tptp2(X))) = tptp0(X2,m(tptp2(X))),
inference(symmetry,[status(thm)],[c328]) ).
cnf(c330,plain,
n(X) = m(tptp2(X)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c331,plain,
m(tptp2(X)) = n(X),
inference(symmetry,[status(thm)],[c330]) ).
cnf(c332,plain,
tptp0(X2,m(tptp2(X))) = tptp0(X2,n(X)),
inference(congruence,[status(thm)],[c331]) ).
cnf(c333,plain,
m(tptp1(X2,tptp2(X))) = tptp0(X2,n(X)),
inference(transitivity,[status(thm)],[c329,c332]) ).
cnf(c334,plain,
m(tptp1(X,tptp2(X2))) = tptp0(X,n(X2)),
inference(substitution,[status(thm)],[c333]) ).
cnf(c335,plain,
m(tptp1(tptp2(X2),X)) = tptp0(X,n(X2)),
inference(transitivity,[status(thm)],[c327,c334]) ).
cnf(c336,plain,
m(tptp1(tptp2(X),X2)) = tptp0(X2,n(X)),
inference(substitution,[status(thm)],[c335]) ).
cnf(c337,plain,
n(m(tptp1(tptp2(X),X2))) = tptp0(X2,n(X)),
inference(transitivity,[status(thm)],[c324,c336]) ).
cnf(c338,plain,
n(tptp0(tptp2(X),m(X2))) = tptp0(X2,n(X)),
inference(transitivity,[status(thm)],[c323,c337]) ).
cnf(c339,plain,
n(tptp0(tptp2(m(X2)),X)) = tptp0(X2,n(X)),
inference(transitivity,[status(thm)],[c321,c338]) ).
cnf(c340,plain,
n(tptp0(tptp2(m(X2)),tptp0(m(tptp2(m(X2))),X))) = tptp0(X2,n(tptp0(m(tptp2(m(X2))),X))),
inference(substitution,[status(thm)],[c339]) ).
cnf(c341,plain,
tptp0(X2,n(tptp0(m(tptp2(m(X2))),X))) = n(tptp0(tptp2(m(X2)),tptp0(m(tptp2(m(X2))),X))),
inference(symmetry,[status(thm)],[c340]) ).
cnf(c342,plain,
tptp0(tptp2(m(X2)),tptp0(m(tptp2(m(X2))),X)) = tptp5,
inference(substitution,[status(thm)],[c74]) ).
cnf(c343,plain,
n(tptp0(tptp2(m(X2)),tptp0(m(tptp2(m(X2))),X))) = n(tptp5),
inference(congruence,[status(thm)],[c342]) ).
cnf(c344,plain,
n(tptp0(tptp2(m(X2)),tptp0(m(tptp2(m(X2))),X))) = tptp5,
inference(transitivity,[status(thm)],[c343,c224]) ).
cnf(c345,plain,
tptp0(X2,n(tptp0(m(tptp2(m(X2))),X))) = tptp5,
inference(transitivity,[status(thm)],[c341,c344]) ).
cnf(c346,plain,
tptp0(X2,n(tptp0(n(m(X2)),X))) = tptp5,
inference(transitivity,[status(thm)],[c313,c345]) ).
cnf(c347,plain,
tptp0(X2,n(tptp0(m(X2),X))) = tptp5,
inference(transitivity,[status(thm)],[c309,c346]) ).
cnf(c348,plain,
tptp0(X3,n(tptp0(m(X3),tptp0(tptp0(m(X3),X2),X)))) = tptp5,
inference(substitution,[status(thm)],[c347]) ).
cnf(c349,plain,
tptp0(X3,n(tptp0(tptp4(m(X3),X2),X))) = tptp5,
inference(transitivity,[status(thm)],[c289,c348]) ).
cnf(c350,plain,
tptp0(X3,n(tptp0(tptp4(X2,m(X3)),X))) = tptp5,
inference(transitivity,[status(thm)],[c279,c349]) ).
cnf(c351,plain,
tptp0(m(X2),n(tptp0(tptp4(X2,m(m(X2))),X))) = tptp5,
inference(substitution,[status(thm)],[c350]) ).
cnf(c352,plain,
tptp0(m(X2),n(tptp0(X2,X))) = tptp5,
inference(transitivity,[status(thm)],[c275,c351]) ).
cnf(c353,plain,
tptp0(m(tptp2(X2)),n(tptp0(tptp2(X2),tptp2(X)))) = tptp5,
inference(substitution,[status(thm)],[c352]) ).
cnf(c354,plain,
tptp0(m(tptp2(X2)),n(tptp0(X,X2))) = tptp5,
inference(transitivity,[status(thm)],[c271,c353]) ).
cnf(c355,plain,
tptp0(n(X2),n(tptp0(X,X2))) = tptp5,
inference(transitivity,[status(thm)],[c269,c354]) ).
cnf(c356,plain,
tptp0(tptp0(n(X2),n(tptp0(X,X2))),n(tptp0(X,X2))) = tptp0(tptp5,n(tptp0(X,X2))),
inference(congruence,[status(thm)],[c355]) ).
cnf(c357,plain,
tptp4(tptp0(tptp0(n(X2),n(tptp0(X,X2))),n(tptp0(X,X2))),tptp0(tptp0(n(tptp0(X,X2)),n(X2)),n(X2))) = tptp4(tptp0(tptp5,n(tptp0(X,X2))),tptp0(tptp0(n(tptp0(X,X2)),n(X2)),n(X2))),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
tptp0(tptp5,n(tptp0(X,X2))) = tptp4(n(tptp0(X,X2)),tptp5),
inference(substitution,[status(thm)],[c165]) ).
cnf(c359,plain,
tptp4(tptp0(tptp5,n(tptp0(X,X2))),tptp0(tptp0(n(tptp0(X,X2)),n(X2)),n(X2))) = tptp4(tptp4(n(tptp0(X,X2)),tptp5),tptp0(tptp0(n(tptp0(X,X2)),n(X2)),n(X2))),
inference(congruence,[status(thm)],[c358]) ).
cnf(c360,plain,
tptp4(n(tptp0(X,X2)),tptp5) = n(tptp0(X,X2)),
inference(substitution,[status(thm)],[c212]) ).
cnf(c361,plain,
tptp4(tptp4(n(tptp0(X,X2)),tptp5),tptp0(tptp0(n(tptp0(X,X2)),n(X2)),n(X2))) = tptp4(n(tptp0(X,X2)),tptp0(tptp0(n(tptp0(X,X2)),n(X2)),n(X2))),
inference(congruence,[status(thm)],[c360]) ).
cnf(c362,plain,
tptp1(X2,tptp0(tptp0(X2,X),tptp0(X2,X))) = tptp4(X2,tptp0(tptp0(X2,X),X)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c363,plain,
tptp4(X2,tptp0(tptp0(X2,X),X)) = tptp1(X2,tptp0(tptp0(X2,X),tptp0(X2,X))),
inference(symmetry,[status(thm)],[c362]) ).
cnf(c364,plain,
X = tptp4(X,tptp5),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c365,plain,
tptp0(X,X) = tptp0(tptp4(X,tptp5),X),
inference(congruence,[status(thm)],[c364]) ).
cnf(c366,plain,
tptp4(X,tptp5) = tptp0(tptp5,X),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c367,plain,
tptp0(tptp4(X,tptp5),X) = tptp0(tptp0(tptp5,X),X),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
tptp4(tptp5,X) = tptp4(X,tptp5),
inference(substitution,[status(thm)],[c54]) ).
cnf(c369,plain,
tptp4(tptp5,X) = X,
inference(transitivity,[status(thm)],[c368,c212]) ).
cnf(c370,plain,
tptp4(tptp5,tptp0(tptp0(tptp5,X),X)) = tptp0(tptp0(tptp5,X),X),
inference(substitution,[status(thm)],[c369]) ).
cnf(c371,plain,
tptp0(tptp0(tptp5,X),X) = tptp4(tptp5,tptp0(tptp0(tptp5,X),X)),
inference(symmetry,[status(thm)],[c370]) ).
cnf(c372,plain,
tptp0(tptp0(X,tptp5),tptp5) = tptp5,
inference(substitution,[status(thm)],[c209]) ).
cnf(c373,plain,
tptp5 = tptp0(tptp0(X,tptp5),tptp5),
inference(symmetry,[status(thm)],[c372]) ).
cnf(c374,plain,
tptp4(tptp5,tptp0(tptp0(tptp5,X),X)) = tptp4(tptp0(tptp0(X,tptp5),tptp5),tptp0(tptp0(tptp5,X),X)),
inference(congruence,[status(thm)],[c373]) ).
cnf(c375,plain,
v(X,tptp5) = tptp4(tptp0(tptp0(X,tptp5),tptp5),tptp0(tptp0(tptp5,X),X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c376,plain,
tptp4(tptp0(tptp0(X,tptp5),tptp5),tptp0(tptp0(tptp5,X),X)) = v(X,tptp5),
inference(symmetry,[status(thm)],[c375]) ).
cnf(c377,plain,
X = tptp4(X,tptp5),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c378,plain,
tptp0(X,X) = tptp0(tptp4(X,tptp5),X),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
tptp4(X,tptp5) = tptp0(tptp5,X),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c380,plain,
tptp0(tptp4(X,tptp5),X) = tptp0(tptp0(tptp5,X),X),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
tptp4(tptp5,tptp0(tptp0(tptp5,X),X)) = tptp0(tptp0(tptp5,X),X),
inference(substitution,[status(thm)],[c369]) ).
cnf(c382,plain,
tptp0(tptp0(tptp5,X),X) = tptp4(tptp5,tptp0(tptp0(tptp5,X),X)),
inference(symmetry,[status(thm)],[c381]) ).
cnf(c383,plain,
tptp0(tptp0(X,tptp5),tptp5) = tptp5,
inference(substitution,[status(thm)],[c209]) ).
cnf(c384,plain,
tptp5 = tptp0(tptp0(X,tptp5),tptp5),
inference(symmetry,[status(thm)],[c383]) ).
cnf(c385,plain,
tptp4(tptp5,tptp0(tptp0(tptp5,X),X)) = tptp4(tptp0(tptp0(X,tptp5),tptp5),tptp0(tptp0(tptp5,X),X)),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
v(X,tptp5) = tptp4(tptp0(tptp0(X,tptp5),tptp5),tptp0(tptp0(tptp5,X),X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c387,plain,
tptp4(tptp0(tptp0(X,tptp5),tptp5),tptp0(tptp0(tptp5,X),X)) = v(X,tptp5),
inference(symmetry,[status(thm)],[c386]) ).
cnf(c388,plain,
tptp4(tptp5,tptp0(tptp0(tptp5,X),X)) = v(X,tptp5),
inference(transitivity,[status(thm)],[c385,c387]) ).
cnf(c389,plain,
tptp0(tptp0(tptp5,X),X) = v(X,tptp5),
inference(transitivity,[status(thm)],[c382,c388]) ).
cnf(c390,plain,
tptp0(tptp4(X,tptp5),X) = v(X,tptp5),
inference(transitivity,[status(thm)],[c380,c389]) ).
cnf(c391,plain,
tptp0(X,X) = v(X,tptp5),
inference(transitivity,[status(thm)],[c378,c390]) ).
cnf(c392,plain,
v(X,tptp5) = tptp0(X,X),
inference(symmetry,[status(thm)],[c391]) ).
cnf(c393,plain,
X = tptp4(X,tptp5),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c394,plain,
tptp0(X,X) = tptp0(X,tptp4(X,tptp5)),
inference(congruence,[status(thm)],[c393]) ).
cnf(c395,plain,
tptp4(X,tptp5) = tptp0(tptp5,X),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c396,plain,
tptp0(X,tptp4(X,tptp5)) = tptp0(X,tptp0(tptp5,X)),
inference(congruence,[status(thm)],[c395]) ).
cnf(c397,plain,
tptp0(tptp3,X) = tptp5,
inference(substitution,[status(thm)],[c57]) ).
cnf(c398,plain,
tptp5 = tptp0(tptp3,X),
inference(symmetry,[status(thm)],[c397]) ).
cnf(c399,plain,
tptp0(tptp5,X) = tptp0(tptp0(tptp3,X),X),
inference(congruence,[status(thm)],[c398]) ).
cnf(c400,plain,
tptp0(X,tptp0(tptp5,X)) = tptp0(X,tptp0(tptp0(tptp3,X),X)),
inference(congruence,[status(thm)],[c399]) ).
cnf(c401,plain,
X = tptp4(X,tptp5),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c402,plain,
tptp0(X2,tptp0(tptp0(X,X2),X2)) = tptp0(tptp4(X2,tptp5),tptp0(tptp0(X,X2),X2)),
inference(congruence,[status(thm)],[c401]) ).
cnf(c403,plain,
tptp4(X,tptp5) = tptp0(tptp5,X),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c404,plain,
tptp0(tptp4(X2,tptp5),tptp0(tptp0(X,X2),X2)) = tptp0(tptp0(tptp5,X2),tptp0(tptp0(X,X2),X2)),
inference(congruence,[status(thm)],[c403]) ).
cnf(c405,plain,
tptp5 = tptp0(X,tptp5),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c406,plain,
tptp0(tptp5,X2) = tptp0(tptp0(X,tptp5),X2),
inference(congruence,[status(thm)],[c405]) ).
cnf(c407,plain,
tptp0(tptp0(tptp5,X2),tptp0(tptp0(X,X2),X2)) = tptp0(tptp0(tptp0(X,tptp5),X2),tptp0(tptp0(X,X2),X2)),
inference(congruence,[status(thm)],[c406]) ).
cnf(c408,plain,
tptp1(tptp5,tptp0(tptp5,X)) = tptp0(tptp5,X),
inference(substitution,[status(thm)],[c62]) ).
cnf(c409,plain,
tptp0(tptp5,X) = tptp1(tptp5,tptp0(tptp5,X)),
inference(symmetry,[status(thm)],[c408]) ).
cnf(c410,plain,
tptp4(tptp5,X) = tptp1(tptp5,tptp0(tptp5,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c411,plain,
tptp1(tptp5,tptp0(tptp5,X)) = tptp4(tptp5,X),
inference(symmetry,[status(thm)],[c410]) ).
cnf(c412,plain,
tptp4(X,tptp5) = tptp4(tptp5,X),
inference(substitution,[status(thm)],[c54]) ).
cnf(c413,plain,
tptp4(tptp5,X) = tptp4(X,tptp5),
inference(symmetry,[status(thm)],[c412]) ).
cnf(c414,plain,
tptp4(tptp5,X) = X,
inference(transitivity,[status(thm)],[c413,c212]) ).
cnf(c415,plain,
tptp1(tptp5,tptp0(tptp5,X)) = X,
inference(transitivity,[status(thm)],[c411,c414]) ).
cnf(c416,plain,
tptp0(tptp5,X) = X,
inference(transitivity,[status(thm)],[c409,c415]) ).
cnf(c417,plain,
X = tptp0(tptp5,X),
inference(symmetry,[status(thm)],[c416]) ).
cnf(c418,plain,
tptp0(X,X2) = tptp0(tptp0(tptp5,X),X2),
inference(congruence,[status(thm)],[c417]) ).
cnf(c419,plain,
tptp0(tptp0(X,X2),X2) = tptp0(tptp0(tptp0(tptp5,X),X2),X2),
inference(congruence,[status(thm)],[c418]) ).
cnf(c420,plain,
tptp0(tptp0(tptp0(X,tptp5),X2),tptp0(tptp0(X,X2),X2)) = tptp0(tptp0(tptp0(X,tptp5),X2),tptp0(tptp0(tptp0(tptp5,X),X2),X2)),
inference(congruence,[status(thm)],[c419]) ).
cnf(c421,axiom,
tptp0(tptp0(tptp0(A2,B2),C2),tptp0(tptp0(tptp0(B2,A2),C2),C2)) = tptp5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
cnf(c422,plain,
tptp0(tptp0(tptp0(X,tptp5),X2),tptp0(tptp0(tptp0(tptp5,X),X2),X2)) = tptp5,
inference(substitution,[status(thm)],[c421]) ).
cnf(c423,plain,
tptp0(tptp0(tptp0(X,tptp5),X2),tptp0(tptp0(X,X2),X2)) = tptp5,
inference(transitivity,[status(thm)],[c420,c422]) ).
cnf(c424,plain,
tptp0(tptp0(tptp5,X2),tptp0(tptp0(X,X2),X2)) = tptp5,
inference(transitivity,[status(thm)],[c407,c423]) ).
cnf(c425,plain,
tptp0(tptp4(X2,tptp5),tptp0(tptp0(X,X2),X2)) = tptp5,
inference(transitivity,[status(thm)],[c404,c424]) ).
cnf(c426,plain,
tptp0(X2,tptp0(tptp0(X,X2),X2)) = tptp5,
inference(transitivity,[status(thm)],[c402,c425]) ).
cnf(c427,plain,
tptp0(X,tptp0(tptp0(tptp3,X),X)) = tptp5,
inference(substitution,[status(thm)],[c426]) ).
cnf(c428,plain,
tptp0(X,tptp0(tptp5,X)) = tptp5,
inference(transitivity,[status(thm)],[c400,c427]) ).
cnf(c429,plain,
tptp0(X,tptp4(X,tptp5)) = tptp5,
inference(transitivity,[status(thm)],[c396,c428]) ).
cnf(c430,plain,
tptp0(X,X) = tptp5,
inference(transitivity,[status(thm)],[c394,c429]) ).
cnf(c431,plain,
v(X,tptp5) = tptp5,
inference(transitivity,[status(thm)],[c392,c430]) ).
cnf(c432,plain,
tptp4(tptp0(tptp0(X,tptp5),tptp5),tptp0(tptp0(tptp5,X),X)) = tptp5,
inference(transitivity,[status(thm)],[c376,c431]) ).
cnf(c433,plain,
tptp4(tptp5,tptp0(tptp0(tptp5,X),X)) = tptp5,
inference(transitivity,[status(thm)],[c374,c432]) ).
cnf(c434,plain,
tptp0(tptp0(tptp5,X),X) = tptp5,
inference(transitivity,[status(thm)],[c371,c433]) ).
cnf(c435,plain,
tptp0(tptp4(X,tptp5),X) = tptp5,
inference(transitivity,[status(thm)],[c367,c434]) ).
cnf(c436,plain,
tptp0(X,X) = tptp5,
inference(transitivity,[status(thm)],[c365,c435]) ).
cnf(c437,plain,
tptp0(tptp0(X2,X),tptp0(X2,X)) = tptp5,
inference(substitution,[status(thm)],[c436]) ).
cnf(c438,plain,
tptp1(X2,tptp0(tptp0(X2,X),tptp0(X2,X))) = tptp1(X2,tptp5),
inference(congruence,[status(thm)],[c437]) ).
cnf(c439,plain,
tptp1(X2,tptp0(tptp0(X2,X),tptp0(X2,X))) = X2,
inference(transitivity,[status(thm)],[c438,c64]) ).
cnf(c440,plain,
tptp4(X2,tptp0(tptp0(X2,X),X)) = X2,
inference(transitivity,[status(thm)],[c363,c439]) ).
cnf(c441,plain,
tptp4(n(tptp0(X,X2)),tptp0(tptp0(n(tptp0(X,X2)),n(X2)),n(X2))) = n(tptp0(X,X2)),
inference(substitution,[status(thm)],[c440]) ).
cnf(c442,plain,
tptp4(tptp4(n(tptp0(X,X2)),tptp5),tptp0(tptp0(n(tptp0(X,X2)),n(X2)),n(X2))) = n(tptp0(X,X2)),
inference(transitivity,[status(thm)],[c361,c441]) ).
cnf(c443,plain,
tptp4(tptp0(tptp5,n(tptp0(X,X2))),tptp0(tptp0(n(tptp0(X,X2)),n(X2)),n(X2))) = n(tptp0(X,X2)),
inference(transitivity,[status(thm)],[c359,c442]) ).
cnf(c444,plain,
tptp4(tptp0(tptp0(n(X2),n(tptp0(X,X2))),n(tptp0(X,X2))),tptp0(tptp0(n(tptp0(X,X2)),n(X2)),n(X2))) = n(tptp0(X,X2)),
inference(transitivity,[status(thm)],[c357,c443]) ).
cnf(c445,plain,
v(n(X2),n(tptp0(X,X2))) = n(tptp0(X,X2)),
inference(transitivity,[status(thm)],[c267,c444]) ).
cnf(c446,plain,
v(n(X),n(tptp0(n(X),X))) = n(tptp0(n(X),X)),
inference(substitution,[status(thm)],[c445]) ).
cnf(c447,plain,
n(tptp0(n(X),X)) = v(n(X),n(tptp0(n(X),X))),
inference(symmetry,[status(thm)],[c446]) ).
cnf(c448,plain,
tptp0(X2,m(tptp2(X))) = m(tptp1(X2,tptp2(X))),
inference(substitution,[status(thm)],[c24]) ).
cnf(c449,plain,
m(tptp1(X2,tptp2(X))) = tptp0(X2,m(tptp2(X))),
inference(symmetry,[status(thm)],[c448]) ).
cnf(c450,plain,
v(m(X2),m(tptp2(X))) = tptp0(X2,m(tptp2(X))),
inference(substitution,[status(thm)],[c188]) ).
cnf(c451,plain,
tptp0(X2,m(tptp2(X))) = v(m(X2),m(tptp2(X))),
inference(symmetry,[status(thm)],[c450]) ).
cnf(c452,plain,
n(X) = m(tptp2(X)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c453,plain,
m(tptp2(X)) = n(X),
inference(symmetry,[status(thm)],[c452]) ).
cnf(c454,plain,
v(m(X2),m(tptp2(X))) = v(m(X2),n(X)),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
v(X,X2) = tptp4(tptp0(tptp0(X,X2),X2),tptp0(tptp0(X2,X),X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c456,plain,
tptp4(tptp0(tptp0(X,X2),X2),tptp0(tptp0(X2,X),X)) = tptp4(tptp0(tptp0(X2,X),X),tptp0(tptp0(X,X2),X2)),
inference(substitution,[status(thm)],[c54]) ).
cnf(c457,plain,
v(X2,X) = tptp4(tptp0(tptp0(X2,X),X),tptp0(tptp0(X,X2),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c458,plain,
tptp4(tptp0(tptp0(X2,X),X),tptp0(tptp0(X,X2),X2)) = v(X2,X),
inference(symmetry,[status(thm)],[c457]) ).
cnf(c459,plain,
tptp4(tptp0(tptp0(X,X2),X2),tptp0(tptp0(X2,X),X)) = v(X2,X),
inference(transitivity,[status(thm)],[c456,c458]) ).
cnf(c460,plain,
v(X,X2) = v(X2,X),
inference(transitivity,[status(thm)],[c455,c459]) ).
cnf(c461,plain,
v(n(X),m(X2)) = v(m(X2),n(X)),
inference(substitution,[status(thm)],[c460]) ).
cnf(c462,plain,
v(m(X2),n(X)) = v(n(X),m(X2)),
inference(symmetry,[status(thm)],[c461]) ).
cnf(c463,plain,
v(m(X2),m(tptp2(X))) = v(n(X),m(X2)),
inference(transitivity,[status(thm)],[c454,c462]) ).
cnf(c464,plain,
tptp0(X2,m(tptp2(X))) = v(n(X),m(X2)),
inference(transitivity,[status(thm)],[c451,c463]) ).
cnf(c465,plain,
m(tptp1(X2,tptp2(X))) = v(n(X),m(X2)),
inference(transitivity,[status(thm)],[c449,c464]) ).
cnf(c466,plain,
m(tptp1(X,tptp2(X2))) = v(n(X2),m(X)),
inference(substitution,[status(thm)],[c465]) ).
cnf(c467,plain,
v(n(X2),m(X)) = m(tptp1(X,tptp2(X2))),
inference(symmetry,[status(thm)],[c466]) ).
cnf(c468,plain,
m(tptp1(X,tptp2(X2))) = tptp0(X,n(X2)),
inference(substitution,[status(thm)],[c333]) ).
cnf(c469,plain,
v(n(X2),m(X)) = tptp0(X,n(X2)),
inference(transitivity,[status(thm)],[c467,c468]) ).
cnf(c470,plain,
v(n(X),m(tptp2(X2))) = tptp0(tptp2(X2),n(X)),
inference(substitution,[status(thm)],[c469]) ).
cnf(c471,plain,
tptp0(tptp2(X2),n(X)) = v(n(X),m(tptp2(X2))),
inference(symmetry,[status(thm)],[c470]) ).
cnf(c472,plain,
n(X) = m(tptp2(X)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c473,plain,
m(tptp2(X)) = n(X),
inference(symmetry,[status(thm)],[c472]) ).
cnf(c474,plain,
v(n(X),m(tptp2(X2))) = v(n(X),n(X2)),
inference(congruence,[status(thm)],[c473]) ).
cnf(c475,plain,
v(n(X2),n(X)) = v(n(X),n(X2)),
inference(substitution,[status(thm)],[c460]) ).
cnf(c476,plain,
v(n(X),n(X2)) = v(n(X2),n(X)),
inference(symmetry,[status(thm)],[c475]) ).
cnf(c477,plain,
v(n(X),m(tptp2(X2))) = v(n(X2),n(X)),
inference(transitivity,[status(thm)],[c474,c476]) ).
cnf(c478,plain,
tptp0(tptp2(X2),n(X)) = v(n(X2),n(X)),
inference(transitivity,[status(thm)],[c471,c477]) ).
cnf(c479,plain,
tptp0(tptp2(X2),n(tptp0(n(X2),X))) = v(n(X2),n(tptp0(n(X2),X))),
inference(substitution,[status(thm)],[c478]) ).
cnf(c480,plain,
v(n(X2),n(tptp0(n(X2),X))) = tptp0(tptp2(X2),n(tptp0(n(X2),X))),
inference(symmetry,[status(thm)],[c479]) ).
cnf(c481,plain,
n(X) = m(tptp2(X)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c482,plain,
tptp0(n(X2),X) = tptp0(m(tptp2(X2)),X),
inference(congruence,[status(thm)],[c481]) ).
cnf(c483,plain,
n(tptp0(n(X2),X)) = n(tptp0(m(tptp2(X2)),X)),
inference(congruence,[status(thm)],[c482]) ).
cnf(c484,plain,
tptp0(tptp2(X2),n(tptp0(n(X2),X))) = tptp0(tptp2(X2),n(tptp0(m(tptp2(X2)),X))),
inference(congruence,[status(thm)],[c483]) ).
cnf(c485,plain,
tptp0(tptp2(X2),n(tptp0(m(tptp2(X2)),X))) = tptp5,
inference(substitution,[status(thm)],[c347]) ).
cnf(c486,plain,
tptp0(tptp2(X2),n(tptp0(n(X2),X))) = tptp5,
inference(transitivity,[status(thm)],[c484,c485]) ).
cnf(c487,plain,
v(n(X2),n(tptp0(n(X2),X))) = tptp5,
inference(transitivity,[status(thm)],[c480,c486]) ).
cnf(c488,plain,
v(n(X),n(tptp0(n(X),X))) = tptp5,
inference(substitution,[status(thm)],[c487]) ).
cnf(c489,plain,
n(tptp0(n(X),X)) = tptp5,
inference(transitivity,[status(thm)],[c447,c488]) ).
cnf(c490,plain,
n(tptp0(n(tptp2(X)),tptp2(X))) = tptp5,
inference(substitution,[status(thm)],[c489]) ).
cnf(c491,plain,
n(tptp0(m(X),tptp2(X))) = tptp5,
inference(transitivity,[status(thm)],[c266,c490]) ).
cnf(c492,plain,
n(tptp0(X,tptp2(m(X)))) = tptp5,
inference(transitivity,[status(thm)],[c263,c491]) ).
cnf(c493,plain,
tptp5 = n(tptp0(X,tptp2(m(X)))),
inference(symmetry,[status(thm)],[c492]) ).
cnf(c494,plain,
tptp0(tptp5,tptp0(X,tptp2(m(X)))) = tptp0(n(tptp0(X,tptp2(m(X)))),tptp0(X,tptp2(m(X)))),
inference(congruence,[status(thm)],[c493]) ).
cnf(c495,plain,
tptp2(tptp2(tptp0(n(X),X))) = tptp0(n(X),X),
inference(substitution,[status(thm)],[c148]) ).
cnf(c496,plain,
tptp0(n(X),X) = tptp2(tptp2(tptp0(n(X),X))),
inference(symmetry,[status(thm)],[c495]) ).
cnf(c497,plain,
tptp1(tptp5,tptp2(tptp0(n(X),X))) = tptp2(tptp0(n(X),X)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c498,plain,
tptp2(tptp0(n(X),X)) = tptp1(tptp5,tptp2(tptp0(n(X),X))),
inference(symmetry,[status(thm)],[c497]) ).
cnf(c499,plain,
tptp5 = n(tptp0(n(X),X)),
inference(symmetry,[status(thm)],[c489]) ).
cnf(c500,plain,
tptp1(tptp5,tptp2(tptp0(n(X),X))) = tptp1(n(tptp0(n(X),X)),tptp2(tptp0(n(X),X))),
inference(congruence,[status(thm)],[c499]) ).
cnf(c501,plain,
tptp1(n(tptp0(n(X),X)),tptp2(tptp0(n(X),X))) = tptp3,
inference(substitution,[status(thm)],[c105]) ).
cnf(c502,plain,
tptp1(tptp5,tptp2(tptp0(n(X),X))) = tptp3,
inference(transitivity,[status(thm)],[c500,c501]) ).
cnf(c503,plain,
tptp2(tptp0(n(X),X)) = tptp3,
inference(transitivity,[status(thm)],[c498,c502]) ).
cnf(c504,plain,
tptp2(tptp2(tptp0(n(X),X))) = tptp2(tptp3),
inference(congruence,[status(thm)],[c503]) ).
cnf(c505,plain,
tptp3 = tptp2(tptp5),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c506,plain,
tptp2(tptp3) = tptp2(tptp2(tptp5)),
inference(congruence,[status(thm)],[c505]) ).
cnf(c507,plain,
tptp2(tptp2(tptp5)) = tptp5,
inference(substitution,[status(thm)],[c148]) ).
cnf(c508,plain,
tptp2(tptp3) = tptp5,
inference(transitivity,[status(thm)],[c506,c507]) ).
cnf(c509,plain,
tptp2(tptp2(tptp0(n(X),X))) = tptp5,
inference(transitivity,[status(thm)],[c504,c508]) ).
cnf(c510,plain,
tptp0(n(X),X) = tptp5,
inference(transitivity,[status(thm)],[c496,c509]) ).
cnf(c511,plain,
tptp0(n(tptp0(X,tptp2(m(X)))),tptp0(X,tptp2(m(X)))) = tptp5,
inference(substitution,[status(thm)],[c510]) ).
cnf(c512,plain,
tptp0(tptp5,tptp0(X,tptp2(m(X)))) = tptp5,
inference(transitivity,[status(thm)],[c494,c511]) ).
cnf(c513,plain,
tptp4(tptp0(X,tptp2(m(X))),tptp5) = tptp5,
inference(transitivity,[status(thm)],[c262,c512]) ).
cnf(c514,plain,
tptp0(X,tptp2(m(X))) = tptp5,
inference(transitivity,[status(thm)],[c260,c513]) ).
cnf(c515,plain,
tptp1(X,tptp0(X,tptp2(m(X)))) = tptp1(X,tptp5),
inference(congruence,[status(thm)],[c514]) ).
cnf(c516,plain,
tptp1(X,tptp0(X,tptp2(m(X)))) = X,
inference(transitivity,[status(thm)],[c515,c64]) ).
cnf(c517,plain,
tptp4(X,tptp2(m(X))) = X,
inference(transitivity,[status(thm)],[c258,c516]) ).
cnf(c518,plain,
tptp4(m(m(X)),tptp2(m(m(m(X))))) = m(m(X)),
inference(substitution,[status(thm)],[c517]) ).
cnf(c519,plain,
tptp4(m(m(X)),tptp2(m(X))) = m(m(X)),
inference(transitivity,[status(thm)],[c257,c518]) ).
cnf(c520,plain,
tptp2(m(X)) = m(m(X)),
inference(transitivity,[status(thm)],[c248,c519]) ).
cnf(c521,plain,
m(m(X)) = tptp2(m(X)),
inference(symmetry,[status(thm)],[c520]) ).
cnf(c522,plain,
tptp0(m(m(X2)),X) = tptp0(tptp2(m(X2)),X),
inference(congruence,[status(thm)],[c521]) ).
cnf(c523,plain,
n(tptp0(m(m(X2)),X)) = n(tptp0(tptp2(m(X2)),X)),
inference(congruence,[status(thm)],[c522]) ).
cnf(c524,plain,
n(tptp0(tptp2(m(X2)),X)) = n(tptp0(tptp2(X),m(X2))),
inference(substitution,[status(thm)],[c320]) ).
cnf(c525,plain,
tptp0(tptp2(X),m(X2)) = m(tptp1(tptp2(X),X2)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c526,plain,
n(tptp0(tptp2(X),m(X2))) = n(m(tptp1(tptp2(X),X2))),
inference(congruence,[status(thm)],[c525]) ).
cnf(c527,plain,
n(m(tptp1(tptp2(X),X2))) = m(tptp1(tptp2(X),X2)),
inference(substitution,[status(thm)],[c305]) ).
cnf(c528,plain,
m(tptp1(tptp2(X),X2)) = tptp0(X2,n(X)),
inference(substitution,[status(thm)],[c335]) ).
cnf(c529,plain,
n(m(tptp1(tptp2(X),X2))) = tptp0(X2,n(X)),
inference(transitivity,[status(thm)],[c527,c528]) ).
cnf(c530,plain,
n(tptp0(tptp2(X),m(X2))) = tptp0(X2,n(X)),
inference(transitivity,[status(thm)],[c526,c529]) ).
cnf(c531,plain,
n(tptp0(tptp2(m(X2)),X)) = tptp0(X2,n(X)),
inference(transitivity,[status(thm)],[c524,c530]) ).
cnf(c532,plain,
n(tptp0(m(m(X2)),X)) = tptp0(X2,n(X)),
inference(transitivity,[status(thm)],[c523,c531]) ).
cnf(c533,plain,
n(tptp0(m(m(n(X2))),X)) = tptp0(n(X2),n(X)),
inference(substitution,[status(thm)],[c532]) ).
cnf(c534,plain,
n(tptp0(n(X2),X)) = tptp0(n(X2),n(X)),
inference(transitivity,[status(thm)],[c139,c533]) ).
cnf(c535,plain,
n(tptp0(n(X2),tptp0(n(X3),X))) = tptp0(n(X2),n(tptp0(n(X3),X))),
inference(substitution,[status(thm)],[c534]) ).
cnf(c536,plain,
tptp0(n(X2),n(tptp0(n(X3),X))) = tptp0(n(X2),tptp0(n(X3),n(X))),
inference(congruence,[status(thm)],[c534]) ).
cnf(c537,plain,
tptp0(tptp1(n(X3),n(X2)),n(X)) = tptp0(n(X2),tptp0(n(X3),n(X))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c538,plain,
tptp0(n(X2),tptp0(n(X3),n(X))) = tptp0(tptp1(n(X3),n(X2)),n(X)),
inference(symmetry,[status(thm)],[c537]) ).
cnf(c539,plain,
tptp0(n(X2),n(tptp0(n(X3),X))) = tptp0(tptp1(n(X3),n(X2)),n(X)),
inference(transitivity,[status(thm)],[c536,c538]) ).
cnf(c540,plain,
n(tptp0(n(X2),tptp0(n(X3),X))) = tptp0(tptp1(n(X3),n(X2)),n(X)),
inference(transitivity,[status(thm)],[c535,c539]) ).
cnf(c541,plain,
n(tptp0(tptp1(n(X3),n(X2)),X)) = tptp0(tptp1(n(X3),n(X2)),n(X)),
inference(transitivity,[status(thm)],[c11,c540]) ).
cnf(c542,plain,
n(tptp0(tptp1(n(X2),n(tptp0(X2,X))),X)) = tptp0(tptp1(n(X2),n(tptp0(X2,X))),n(X)),
inference(substitution,[status(thm)],[c541]) ).
cnf(c543,plain,
tptp0(tptp1(n(X2),n(tptp0(X2,X))),n(X)) = n(tptp0(tptp1(n(X2),n(tptp0(X2,X))),X)),
inference(symmetry,[status(thm)],[c542]) ).
cnf(c544,plain,
X = tptp4(X,tptp5),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c545,plain,
tptp0(tptp1(n(X2),n(tptp0(X2,X))),X) = tptp0(tptp1(n(X2),n(tptp0(X2,X))),tptp4(X,tptp5)),
inference(congruence,[status(thm)],[c544]) ).
cnf(c546,plain,
tptp4(X,tptp5) = tptp0(tptp5,X),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c547,plain,
tptp0(tptp1(n(X2),n(tptp0(X2,X))),tptp4(X,tptp5)) = tptp0(tptp1(n(X2),n(tptp0(X2,X))),tptp0(tptp5,X)),
inference(congruence,[status(thm)],[c546]) ).
cnf(c548,plain,
tptp5 = tptp0(n(X),X),
inference(symmetry,[status(thm)],[c510]) ).
cnf(c549,plain,
tptp0(tptp5,X) = tptp0(tptp0(n(X2),X2),X),
inference(congruence,[status(thm)],[c548]) ).
cnf(c550,plain,
tptp0(tptp1(n(X2),n(tptp0(X2,X))),tptp0(tptp5,X)) = tptp0(tptp1(n(X2),n(tptp0(X2,X))),tptp0(tptp0(n(X2),X2),X)),
inference(congruence,[status(thm)],[c549]) ).
cnf(c551,plain,
tptp0(tptp1(X,X3),tptp0(tptp0(X,X2),X4)) = tptp0(X3,tptp0(X,tptp0(tptp0(X,X2),X4))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c552,plain,
tptp0(X2,tptp0(tptp0(X2,X3),X)) = tptp0(tptp4(X2,X3),X),
inference(substitution,[status(thm)],[c285]) ).
cnf(c553,plain,
tptp0(X4,tptp0(X2,tptp0(tptp0(X2,X3),X))) = tptp0(X4,tptp0(tptp4(X2,X3),X)),
inference(congruence,[status(thm)],[c552]) ).
cnf(c554,plain,
tptp4(X2,X) = tptp4(X,X2),
inference(substitution,[status(thm)],[c54]) ).
cnf(c555,plain,
tptp4(X,X2) = tptp4(X2,X),
inference(symmetry,[status(thm)],[c554]) ).
cnf(c556,plain,
tptp0(tptp4(X2,X3),X) = tptp0(tptp4(X3,X2),X),
inference(congruence,[status(thm)],[c555]) ).
cnf(c557,plain,
tptp0(X4,tptp0(tptp4(X2,X3),X)) = tptp0(X4,tptp0(tptp4(X3,X2),X)),
inference(congruence,[status(thm)],[c556]) ).
cnf(c558,plain,
tptp0(X4,tptp0(X2,tptp0(tptp0(X2,X3),X))) = tptp0(X4,tptp0(tptp4(X3,X2),X)),
inference(transitivity,[status(thm)],[c553,c557]) ).
cnf(c559,plain,
tptp0(tptp1(X2,X4),tptp0(tptp0(X2,X3),X)) = tptp0(X4,tptp0(tptp4(X3,X2),X)),
inference(transitivity,[status(thm)],[c551,c558]) ).
cnf(c560,plain,
tptp0(tptp1(n(X2),n(tptp0(X2,X))),tptp0(tptp0(n(X2),X2),X)) = tptp0(n(tptp0(X2,X)),tptp0(tptp4(X2,n(X2)),X)),
inference(substitution,[status(thm)],[c559]) ).
cnf(c561,plain,
tptp0(tptp0(X4,X3),tptp0(X2,tptp0(X4,X))) = tptp0(X2,tptp0(tptp0(X4,X3),tptp0(X4,X))),
inference(substitution,[status(thm)],[c34]) ).
cnf(c562,plain,
tptp0(X3,tptp0(tptp0(X3,X2),X)) = tptp0(tptp0(X3,X2),tptp0(X3,X)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c563,plain,
tptp0(tptp0(X3,X2),tptp0(X3,X)) = tptp0(X3,tptp0(tptp0(X3,X2),X)),
inference(symmetry,[status(thm)],[c562]) ).
cnf(c564,plain,
tptp4(X2,X) = tptp4(X,X2),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c565,plain,
tptp0(tptp4(X3,X2),X) = tptp0(tptp4(X2,X3),X),
inference(congruence,[status(thm)],[c564]) ).
cnf(c566,plain,
tptp0(X3,tptp0(tptp0(X3,X2),X)) = tptp0(tptp4(X2,X3),X),
inference(transitivity,[status(thm)],[c285,c565]) ).
cnf(c567,plain,
tptp0(tptp0(X3,X2),tptp0(X3,X)) = tptp0(tptp4(X2,X3),X),
inference(transitivity,[status(thm)],[c563,c566]) ).
cnf(c568,plain,
tptp0(X2,tptp0(tptp0(X4,X3),tptp0(X4,X))) = tptp0(X2,tptp0(tptp4(X3,X4),X)),
inference(congruence,[status(thm)],[c567]) ).
cnf(c569,plain,
tptp0(tptp0(X4,X3),tptp0(X2,tptp0(X4,X))) = tptp0(X2,tptp0(tptp4(X3,X4),X)),
inference(transitivity,[status(thm)],[c561,c568]) ).
cnf(c570,plain,
tptp4(X2,X) = tptp4(X,X2),
inference(substitution,[status(thm)],[c54]) ).
cnf(c571,plain,
tptp4(X,X2) = tptp4(X2,X),
inference(symmetry,[status(thm)],[c570]) ).
cnf(c572,plain,
tptp0(tptp4(X2,X3),X) = tptp0(tptp4(X3,X2),X),
inference(congruence,[status(thm)],[c571]) ).
cnf(c573,plain,
tptp0(X2,tptp0(tptp4(X3,X4),X)) = tptp0(X2,tptp0(tptp4(X4,X3),X)),
inference(congruence,[status(thm)],[c572]) ).
cnf(c574,plain,
tptp0(tptp0(X4,X3),tptp0(X2,tptp0(X4,X))) = tptp0(X2,tptp0(tptp4(X4,X3),X)),
inference(transitivity,[status(thm)],[c569,c573]) ).
cnf(c575,plain,
tptp0(tptp0(X2,n(X2)),tptp0(n(tptp0(X2,X)),tptp0(X2,X))) = tptp0(n(tptp0(X2,X)),tptp0(tptp4(X2,n(X2)),X)),
inference(substitution,[status(thm)],[c574]) ).
cnf(c576,plain,
tptp0(n(tptp0(X2,X)),tptp0(tptp4(X2,n(X2)),X)) = tptp0(tptp0(X2,n(X2)),tptp0(n(tptp0(X2,X)),tptp0(X2,X))),
inference(symmetry,[status(thm)],[c575]) ).
cnf(c577,plain,
tptp0(n(tptp0(X2,X)),tptp0(X2,X)) = tptp5,
inference(substitution,[status(thm)],[c510]) ).
cnf(c578,plain,
tptp0(tptp0(X2,n(X2)),tptp0(n(tptp0(X2,X)),tptp0(X2,X))) = tptp0(tptp0(X2,n(X2)),tptp5),
inference(congruence,[status(thm)],[c577]) ).
cnf(c579,plain,
tptp0(tptp0(X,n(X)),tptp5) = tptp5,
inference(substitution,[status(thm)],[c209]) ).
cnf(c580,plain,
tptp0(tptp0(X2,n(X2)),tptp0(n(tptp0(X2,X)),tptp0(X2,X))) = tptp5,
inference(transitivity,[status(thm)],[c578,c579]) ).
cnf(c581,plain,
tptp0(n(tptp0(X2,X)),tptp0(tptp4(X2,n(X2)),X)) = tptp5,
inference(transitivity,[status(thm)],[c576,c580]) ).
cnf(c582,plain,
tptp0(tptp1(n(X2),n(tptp0(X2,X))),tptp0(tptp0(n(X2),X2),X)) = tptp5,
inference(transitivity,[status(thm)],[c560,c581]) ).
cnf(c583,plain,
tptp0(tptp1(n(X2),n(tptp0(X2,X))),tptp0(tptp5,X)) = tptp5,
inference(transitivity,[status(thm)],[c550,c582]) ).
cnf(c584,plain,
tptp0(tptp1(n(X2),n(tptp0(X2,X))),tptp4(X,tptp5)) = tptp5,
inference(transitivity,[status(thm)],[c547,c583]) ).
cnf(c585,plain,
tptp0(tptp1(n(X2),n(tptp0(X2,X))),X) = tptp5,
inference(transitivity,[status(thm)],[c545,c584]) ).
cnf(c586,plain,
n(tptp0(tptp1(n(X2),n(tptp0(X2,X))),X)) = n(tptp5),
inference(congruence,[status(thm)],[c585]) ).
cnf(c587,plain,
n(tptp0(tptp1(n(X2),n(tptp0(X2,X))),X)) = tptp5,
inference(transitivity,[status(thm)],[c586,c224]) ).
cnf(c588,plain,
tptp0(tptp1(n(X2),n(tptp0(X2,X))),n(X)) = tptp5,
inference(transitivity,[status(thm)],[c543,c587]) ).
cnf(c589,plain,
tptp0(tptp1(n(X),n(tptp0(X,X2))),n(X2)) = tptp5,
inference(substitution,[status(thm)],[c588]) ).
cnf(c590,plain,
tptp0(tptp0(tptp1(n(X),n(tptp0(X,X2))),n(X2)),n(X2)) = tptp0(tptp5,n(X2)),
inference(congruence,[status(thm)],[c589]) ).
cnf(c591,plain,
tptp4(tptp0(tptp0(tptp1(n(X),n(tptp0(X,X2))),n(X2)),n(X2)),tptp0(tptp0(n(X2),tptp1(n(X),n(tptp0(X,X2)))),tptp1(n(X),n(tptp0(X,X2))))) = tptp4(tptp0(tptp5,n(X2)),tptp0(tptp0(n(X2),tptp1(n(X),n(tptp0(X,X2)))),tptp1(n(X),n(tptp0(X,X2))))),
inference(congruence,[status(thm)],[c590]) ).
cnf(c592,plain,
tptp0(tptp5,n(X)) = tptp4(n(X),tptp5),
inference(substitution,[status(thm)],[c165]) ).
cnf(c593,plain,
tptp4(tptp0(tptp5,n(X2)),tptp0(tptp0(n(X2),tptp1(n(X),n(tptp0(X,X2)))),tptp1(n(X),n(tptp0(X,X2))))) = tptp4(tptp4(n(X2),tptp5),tptp0(tptp0(n(X2),tptp1(n(X),n(tptp0(X,X2)))),tptp1(n(X),n(tptp0(X,X2))))),
inference(congruence,[status(thm)],[c592]) ).
cnf(c594,plain,
tptp4(n(X),tptp5) = n(X),
inference(substitution,[status(thm)],[c212]) ).
cnf(c595,plain,
tptp4(tptp4(n(X2),tptp5),tptp0(tptp0(n(X2),tptp1(n(X),n(tptp0(X,X2)))),tptp1(n(X),n(tptp0(X,X2))))) = tptp4(n(X2),tptp0(tptp0(n(X2),tptp1(n(X),n(tptp0(X,X2)))),tptp1(n(X),n(tptp0(X,X2))))),
inference(congruence,[status(thm)],[c594]) ).
cnf(c596,plain,
tptp4(n(X2),tptp0(tptp0(n(X2),tptp1(n(X),n(tptp0(X,X2)))),tptp1(n(X),n(tptp0(X,X2))))) = n(X2),
inference(substitution,[status(thm)],[c440]) ).
cnf(c597,plain,
tptp4(tptp4(n(X2),tptp5),tptp0(tptp0(n(X2),tptp1(n(X),n(tptp0(X,X2)))),tptp1(n(X),n(tptp0(X,X2))))) = n(X2),
inference(transitivity,[status(thm)],[c595,c596]) ).
cnf(c598,plain,
tptp4(tptp0(tptp5,n(X2)),tptp0(tptp0(n(X2),tptp1(n(X),n(tptp0(X,X2)))),tptp1(n(X),n(tptp0(X,X2))))) = n(X2),
inference(transitivity,[status(thm)],[c593,c597]) ).
cnf(c599,plain,
tptp4(tptp0(tptp0(tptp1(n(X),n(tptp0(X,X2))),n(X2)),n(X2)),tptp0(tptp0(n(X2),tptp1(n(X),n(tptp0(X,X2)))),tptp1(n(X),n(tptp0(X,X2))))) = n(X2),
inference(transitivity,[status(thm)],[c591,c598]) ).
cnf(c600,plain,
v(tptp1(n(X),n(tptp0(X,X2))),n(X2)) = n(X2),
inference(transitivity,[status(thm)],[c3,c599]) ).
cnf(c601,plain,
v(tptp1(n(a),n(tptp0(a,b))),n(b)) = n(b),
inference(substitution,[status(thm)],[c600]) ).
cnf(c602,plain,
$false,
inference(resolution,[status(thm)],[c1,c601]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG246-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.22 % Computer : n018.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Mon Sep 28 20:00:55 UTC 2026
% 0.12/0.22 % CPUTime :
% 0.12/0.22 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 71.32/9.36 Command-line arguments: --flatten --complete-subsets
% 71.32/9.36
% 71.32/9.36 % SZS status Unsatisfiable
% 71.32/9.36
% 71.32/9.40 % SZS output start CNFRefutation
% See solution above
% 73.71/9.65
% 73.71/9.65 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------