%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SWX203-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 01:45:33 PM UTC 2026
% Result : Unsatisfiable 21.19s 3.01s
% Output : CNFRefutation 23.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 24
% Syntax : Number of clauses : 258 ( 258 unt; 0 nHn; 35 RR)
% Number of literals : 258 ( 257 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 4 con; 0-3 aty)
% Number of variables : 404 ( 40 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
eq2(psorted_rev(X),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
psorted_rev(X2) = impl(eq2(sorted(rev(X2)),btrue),impl(eq2(unique(X2),btrue),eq2(leqNat(lengthNat(X2),s(s(s(z)))),btrue))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
cnf(c3,plain,
psorted_rev(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = impl(eq2(sorted(rev(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(unique(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
elemNat(X2,cons(Z,Xs)) = orb(eq(X2,Z),elemNat(X2,Xs)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
cnf(c5,plain,
elemNat(s(X2),cons(z,X3)) = orb(eq(s(X2),z),elemNat(s(X2),X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,axiom,
eq(s(X2),z) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c7,plain,
orb(eq(s(X3),z),elemNat(s(X3),X2)) = orb(bfalse,elemNat(s(X3),X2)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
orb(bfalse,Q) = Q,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
cnf(c9,plain,
orb(bfalse,elemNat(s(X3),X2)) = elemNat(s(X3),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
orb(eq(s(X3),z),elemNat(s(X3),X2)) = elemNat(s(X3),X2),
inference(transitivity,[status(thm)],[c7,c9]) ).
cnf(c11,plain,
elemNat(s(X3),cons(z,X2)) = elemNat(s(X3),X2),
inference(transitivity,[status(thm)],[c5,c10]) ).
cnf(c12,plain,
elemNat(s(s(s(X3))),cons(z,X2)) = elemNat(s(s(s(X3))),X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
elemNat(s(s(s(X3))),X2) = elemNat(s(s(s(X3))),cons(z,X2)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
aux(s(s(s(X3))),cons(s(s(z)),cons(s(z),cons(z,X2))),elemNat(s(s(s(X3))),X2)) = aux(s(s(s(X3))),cons(s(s(z)),cons(s(z),cons(z,X2))),elemNat(s(s(s(X3))),cons(z,X2))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,axiom,
eq(s(X2),s(Y)) = eq(X2,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
cnf(c16,plain,
eq(s(X3),s(X2)) = eq(X3,X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
eq(X3,X2) = eq(s(X3),s(X2)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
orb(eq(X3,X2),elemNat(s(X3),X4)) = orb(eq(s(X3),s(X2)),elemNat(s(X3),X4)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
elemNat(s(X4),cons(s(X3),X2)) = orb(eq(s(X4),s(X3)),elemNat(s(X4),X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c20,plain,
orb(eq(s(X4),s(X3)),elemNat(s(X4),X2)) = elemNat(s(X4),cons(s(X3),X2)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
orb(eq(X4,X3),elemNat(s(X4),X2)) = elemNat(s(X4),cons(s(X3),X2)),
inference(transitivity,[status(thm)],[c18,c20]) ).
cnf(c22,plain,
orb(eq(s(X3),z),elemNat(s(s(X3)),X2)) = elemNat(s(s(X3)),cons(s(z),X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
elemNat(s(s(X3)),cons(s(z),X2)) = orb(eq(s(X3),z),elemNat(s(s(X3)),X2)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
orb(eq(s(X3),z),elemNat(s(s(X3)),X2)) = orb(bfalse,elemNat(s(s(X3)),X2)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c25,plain,
orb(bfalse,elemNat(s(s(X3)),X2)) = elemNat(s(s(X3)),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c26,plain,
orb(eq(s(X3),z),elemNat(s(s(X3)),X2)) = elemNat(s(s(X3)),X2),
inference(transitivity,[status(thm)],[c24,c25]) ).
cnf(c27,plain,
elemNat(s(s(X3)),cons(s(z),X2)) = elemNat(s(s(X3)),X2),
inference(transitivity,[status(thm)],[c23,c26]) ).
cnf(c28,plain,
elemNat(s(s(s(X3))),cons(s(z),X2)) = elemNat(s(s(s(X3))),X2),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
elemNat(s(s(s(X3))),X2) = elemNat(s(s(s(X3))),cons(s(z),X2)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
aux(s(s(s(X3))),cons(s(s(z)),cons(s(z),X2)),elemNat(s(s(s(X3))),X2)) = aux(s(s(s(X3))),cons(s(s(z)),cons(s(z),X2)),elemNat(s(s(s(X3))),cons(s(z),X2))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
eq(s(X3),s(X2)) = eq(X3,X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c32,plain,
eq(X3,X2) = eq(s(X3),s(X2)),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
orb(eq(X4,X3),elemNat(s(s(X4)),X2)) = orb(eq(s(X4),s(X3)),elemNat(s(s(X4)),X2)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
orb(eq(s(X4),s(X3)),elemNat(s(s(X4)),X2)) = elemNat(s(s(X4)),cons(s(s(X3)),X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c35,plain,
orb(eq(X4,X3),elemNat(s(s(X4)),X2)) = elemNat(s(s(X4)),cons(s(s(X3)),X2)),
inference(transitivity,[status(thm)],[c33,c34]) ).
cnf(c36,plain,
orb(eq(s(X3),z),elemNat(s(s(s(X3))),X2)) = elemNat(s(s(s(X3))),cons(s(s(z)),X2)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
elemNat(s(s(s(X3))),cons(s(s(z)),X2)) = orb(eq(s(X3),z),elemNat(s(s(s(X3))),X2)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
orb(eq(s(X3),z),elemNat(s(s(s(X3))),X2)) = orb(bfalse,elemNat(s(s(s(X3))),X2)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c39,plain,
orb(bfalse,elemNat(s(s(s(X3))),X2)) = elemNat(s(s(s(X3))),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c40,plain,
orb(eq(s(X3),z),elemNat(s(s(s(X3))),X2)) = elemNat(s(s(s(X3))),X2),
inference(transitivity,[status(thm)],[c38,c39]) ).
cnf(c41,plain,
elemNat(s(s(s(X3))),cons(s(s(z)),X2)) = elemNat(s(s(s(X3))),X2),
inference(transitivity,[status(thm)],[c37,c40]) ).
cnf(c42,plain,
elemNat(s(s(s(X3))),X2) = elemNat(s(s(s(X3))),cons(s(s(z)),X2)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
aux(s(s(s(X3))),cons(s(s(z)),X2),elemNat(s(s(s(X3))),X2)) = aux(s(s(s(X3))),cons(s(s(z)),X2),elemNat(s(s(s(X3))),cons(s(s(z)),X2))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,axiom,
unique(cons(Y3,Xs2)) = aux(Y3,Xs2,elemNat(Y3,Xs2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
cnf(c45,plain,
unique(cons(s(s(s(X3))),cons(s(s(z)),X2))) = aux(s(s(s(X3))),cons(s(s(z)),X2),elemNat(s(s(s(X3))),cons(s(s(z)),X2))),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
aux(s(s(s(X3))),cons(s(s(z)),X2),elemNat(s(s(s(X3))),cons(s(s(z)),X2))) = unique(cons(s(s(s(X3))),cons(s(s(z)),X2))),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
aux(s(s(s(X3))),cons(s(s(z)),X2),elemNat(s(s(s(X3))),X2)) = unique(cons(s(s(s(X3))),cons(s(s(z)),X2))),
inference(transitivity,[status(thm)],[c43,c46]) ).
cnf(c48,plain,
aux(s(s(s(X3))),cons(s(s(z)),cons(s(z),X2)),elemNat(s(s(s(X3))),cons(s(z),X2))) = unique(cons(s(s(s(X3))),cons(s(s(z)),cons(s(z),X2)))),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
aux(s(s(s(X3))),cons(s(s(z)),cons(s(z),X2)),elemNat(s(s(s(X3))),X2)) = unique(cons(s(s(s(X3))),cons(s(s(z)),cons(s(z),X2)))),
inference(transitivity,[status(thm)],[c30,c48]) ).
cnf(c50,plain,
aux(s(s(s(X3))),cons(s(s(z)),cons(s(z),cons(z,X2))),elemNat(s(s(s(X3))),cons(z,X2))) = unique(cons(s(s(s(X3))),cons(s(s(z)),cons(s(z),cons(z,X2))))),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
aux(s(s(s(X3))),cons(s(s(z)),cons(s(z),cons(z,X2))),elemNat(s(s(s(X3))),X2)) = unique(cons(s(s(s(X3))),cons(s(s(z)),cons(s(z),cons(z,X2))))),
inference(transitivity,[status(thm)],[c14,c50]) ).
cnf(c52,plain,
aux(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(s(X2))),nil)) = unique(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
unique(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = aux(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(s(X2))),nil)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,axiom,
elemNat(X2,nil) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
cnf(c55,plain,
elemNat(s(s(s(X2))),nil) = bfalse,
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
aux(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(s(X2))),nil)) = aux(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,axiom,
aux(Y3,Xs2,bfalse) = unique(Xs2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
cnf(c58,plain,
aux(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse) = unique(cons(s(s(z)),cons(s(z),cons(z,nil)))),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
elemNat(s(s(X3)),cons(z,X2)) = elemNat(s(s(X3)),X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c60,plain,
elemNat(s(s(X3)),X2) = elemNat(s(s(X3)),cons(z,X2)),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
aux(s(s(X3)),cons(s(z),cons(z,X2)),elemNat(s(s(X3)),X2)) = aux(s(s(X3)),cons(s(z),cons(z,X2)),elemNat(s(s(X3)),cons(z,X2))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
elemNat(s(s(X3)),X2) = elemNat(s(s(X3)),cons(s(z),X2)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c63,plain,
aux(s(s(X3)),cons(s(z),X2),elemNat(s(s(X3)),X2)) = aux(s(s(X3)),cons(s(z),X2),elemNat(s(s(X3)),cons(s(z),X2))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
unique(cons(s(s(X3)),cons(s(z),X2))) = aux(s(s(X3)),cons(s(z),X2),elemNat(s(s(X3)),cons(s(z),X2))),
inference(substitution,[status(thm)],[c44]) ).
cnf(c65,plain,
aux(s(s(X3)),cons(s(z),X2),elemNat(s(s(X3)),cons(s(z),X2))) = unique(cons(s(s(X3)),cons(s(z),X2))),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
aux(s(s(X3)),cons(s(z),X2),elemNat(s(s(X3)),X2)) = unique(cons(s(s(X3)),cons(s(z),X2))),
inference(transitivity,[status(thm)],[c63,c65]) ).
cnf(c67,plain,
aux(s(s(X3)),cons(s(z),cons(z,X2)),elemNat(s(s(X3)),cons(z,X2))) = unique(cons(s(s(X3)),cons(s(z),cons(z,X2)))),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
aux(s(s(X3)),cons(s(z),cons(z,X2)),elemNat(s(s(X3)),X2)) = unique(cons(s(s(X3)),cons(s(z),cons(z,X2)))),
inference(transitivity,[status(thm)],[c61,c67]) ).
cnf(c69,plain,
aux(s(s(X2)),cons(s(z),cons(z,nil)),elemNat(s(s(X2)),nil)) = unique(cons(s(s(X2)),cons(s(z),cons(z,nil)))),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
unique(cons(s(s(X2)),cons(s(z),cons(z,nil)))) = aux(s(s(X2)),cons(s(z),cons(z,nil)),elemNat(s(s(X2)),nil)),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
elemNat(s(s(X2)),nil) = bfalse,
inference(substitution,[status(thm)],[c54]) ).
cnf(c72,plain,
aux(s(s(X2)),cons(s(z),cons(z,nil)),elemNat(s(s(X2)),nil)) = aux(s(s(X2)),cons(s(z),cons(z,nil)),bfalse),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
aux(s(s(X2)),cons(s(z),cons(z,nil)),bfalse) = unique(cons(s(z),cons(z,nil))),
inference(substitution,[status(thm)],[c57]) ).
cnf(c74,plain,
elemNat(s(X3),X2) = elemNat(s(X3),cons(z,X2)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c75,plain,
aux(s(X3),cons(z,X2),elemNat(s(X3),X2)) = aux(s(X3),cons(z,X2),elemNat(s(X3),cons(z,X2))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
unique(cons(s(X3),cons(z,X2))) = aux(s(X3),cons(z,X2),elemNat(s(X3),cons(z,X2))),
inference(substitution,[status(thm)],[c44]) ).
cnf(c77,plain,
aux(s(X3),cons(z,X2),elemNat(s(X3),cons(z,X2))) = unique(cons(s(X3),cons(z,X2))),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
aux(s(X3),cons(z,X2),elemNat(s(X3),X2)) = unique(cons(s(X3),cons(z,X2))),
inference(transitivity,[status(thm)],[c75,c77]) ).
cnf(c79,plain,
aux(s(X2),cons(z,nil),elemNat(s(X2),nil)) = unique(cons(s(X2),cons(z,nil))),
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
unique(cons(s(X2),cons(z,nil))) = aux(s(X2),cons(z,nil),elemNat(s(X2),nil)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
elemNat(s(X2),nil) = bfalse,
inference(substitution,[status(thm)],[c54]) ).
cnf(c82,plain,
aux(s(X2),cons(z,nil),elemNat(s(X2),nil)) = aux(s(X2),cons(z,nil),bfalse),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
aux(s(X2),cons(z,nil),bfalse) = unique(cons(z,nil)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c84,plain,
unique(cons(X2,nil)) = aux(X2,nil,elemNat(X2,nil)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c85,plain,
aux(X2,nil,elemNat(X2,nil)) = aux(X2,nil,bfalse),
inference(congruence,[status(thm)],[c54]) ).
cnf(c86,plain,
aux(X2,nil,bfalse) = unique(nil),
inference(substitution,[status(thm)],[c57]) ).
cnf(c87,axiom,
unique(nil) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c88,plain,
aux(X2,nil,bfalse) = btrue,
inference(transitivity,[status(thm)],[c86,c87]) ).
cnf(c89,plain,
aux(X2,nil,elemNat(X2,nil)) = btrue,
inference(transitivity,[status(thm)],[c85,c88]) ).
cnf(c90,plain,
unique(cons(X2,nil)) = btrue,
inference(transitivity,[status(thm)],[c84,c89]) ).
cnf(c91,plain,
unique(cons(z,nil)) = btrue,
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
aux(s(X2),cons(z,nil),bfalse) = btrue,
inference(transitivity,[status(thm)],[c83,c91]) ).
cnf(c93,plain,
aux(s(X2),cons(z,nil),elemNat(s(X2),nil)) = btrue,
inference(transitivity,[status(thm)],[c82,c92]) ).
cnf(c94,plain,
unique(cons(s(X2),cons(z,nil))) = btrue,
inference(transitivity,[status(thm)],[c80,c93]) ).
cnf(c95,plain,
unique(cons(s(z),cons(z,nil))) = btrue,
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
aux(s(s(X2)),cons(s(z),cons(z,nil)),bfalse) = btrue,
inference(transitivity,[status(thm)],[c73,c95]) ).
cnf(c97,plain,
aux(s(s(X2)),cons(s(z),cons(z,nil)),elemNat(s(s(X2)),nil)) = btrue,
inference(transitivity,[status(thm)],[c72,c96]) ).
cnf(c98,plain,
unique(cons(s(s(X2)),cons(s(z),cons(z,nil)))) = btrue,
inference(transitivity,[status(thm)],[c70,c97]) ).
cnf(c99,plain,
unique(cons(s(s(z)),cons(s(z),cons(z,nil)))) = btrue,
inference(substitution,[status(thm)],[c98]) ).
cnf(c100,plain,
aux(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))),bfalse) = btrue,
inference(transitivity,[status(thm)],[c58,c99]) ).
cnf(c101,plain,
aux(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))),elemNat(s(s(s(X2))),nil)) = btrue,
inference(transitivity,[status(thm)],[c56,c100]) ).
cnf(c102,plain,
unique(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = btrue,
inference(transitivity,[status(thm)],[c53,c101]) ).
cnf(c103,plain,
eq2(unique(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),btrue) = eq2(btrue,btrue),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
impl(eq2(unique(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
impl(eq2(sorted(rev(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(unique(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(eq2(sorted(rev(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,axiom,
rev(cons(Y3,Xs2)) = append(rev(Xs2),cons(Y3,nil)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
cnf(c107,plain,
rev(cons(X4,cons(X3,cons(X2,cons(X5,nil))))) = append(rev(cons(X3,cons(X2,cons(X5,nil)))),cons(X4,nil)),
inference(substitution,[status(thm)],[c106]) ).
cnf(c108,plain,
rev(cons(X4,cons(X3,cons(X2,nil)))) = append(rev(cons(X3,cons(X2,nil))),cons(X4,nil)),
inference(substitution,[status(thm)],[c106]) ).
cnf(c109,plain,
rev(cons(X3,cons(X2,nil))) = append(rev(cons(X2,nil)),cons(X3,nil)),
inference(substitution,[status(thm)],[c106]) ).
cnf(c110,plain,
rev(cons(X2,nil)) = append(rev(nil),cons(X2,nil)),
inference(substitution,[status(thm)],[c106]) ).
cnf(c111,axiom,
rev(nil) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c112,plain,
append(rev(nil),cons(X2,nil)) = append(nil,cons(X2,nil)),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,axiom,
append(nil,Y3) = Y3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
cnf(c114,plain,
append(nil,cons(X2,nil)) = cons(X2,nil),
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
append(rev(nil),cons(X2,nil)) = cons(X2,nil),
inference(transitivity,[status(thm)],[c112,c114]) ).
cnf(c116,plain,
rev(cons(X2,nil)) = cons(X2,nil),
inference(transitivity,[status(thm)],[c110,c115]) ).
cnf(c117,plain,
append(rev(cons(X2,nil)),cons(X3,nil)) = append(cons(X2,nil),cons(X3,nil)),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,axiom,
append(cons(Z2,Xs2),Y3) = cons(Z2,append(Xs2,Y3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
cnf(c119,plain,
append(cons(X2,nil),cons(X3,nil)) = cons(X2,append(nil,cons(X3,nil))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c120,plain,
append(nil,cons(X2,nil)) = cons(X2,nil),
inference(substitution,[status(thm)],[c113]) ).
cnf(c121,plain,
cons(X2,append(nil,cons(X3,nil))) = cons(X2,cons(X3,nil)),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
append(cons(X2,nil),cons(X3,nil)) = cons(X2,cons(X3,nil)),
inference(transitivity,[status(thm)],[c119,c121]) ).
cnf(c123,plain,
append(rev(cons(X2,nil)),cons(X3,nil)) = cons(X2,cons(X3,nil)),
inference(transitivity,[status(thm)],[c117,c122]) ).
cnf(c124,plain,
rev(cons(X3,cons(X2,nil))) = cons(X2,cons(X3,nil)),
inference(transitivity,[status(thm)],[c109,c123]) ).
cnf(c125,plain,
append(rev(cons(X3,cons(X2,nil))),cons(X4,nil)) = append(cons(X2,cons(X3,nil)),cons(X4,nil)),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
append(cons(X2,cons(X3,nil)),cons(X4,nil)) = cons(X2,append(cons(X3,nil),cons(X4,nil))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c127,plain,
append(cons(X2,nil),cons(X3,nil)) = cons(X2,append(nil,cons(X3,nil))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c128,plain,
cons(X2,append(cons(X3,nil),cons(X4,nil))) = cons(X2,cons(X3,append(nil,cons(X4,nil)))),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
append(nil,cons(X2,nil)) = cons(X2,nil),
inference(substitution,[status(thm)],[c113]) ).
cnf(c130,plain,
cons(X2,append(nil,cons(X3,nil))) = cons(X2,cons(X3,nil)),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
cons(X2,cons(X3,append(nil,cons(X4,nil)))) = cons(X2,cons(X3,cons(X4,nil))),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
cons(X2,append(cons(X3,nil),cons(X4,nil))) = cons(X2,cons(X3,cons(X4,nil))),
inference(transitivity,[status(thm)],[c128,c131]) ).
cnf(c133,plain,
append(cons(X2,cons(X3,nil)),cons(X4,nil)) = cons(X2,cons(X3,cons(X4,nil))),
inference(transitivity,[status(thm)],[c126,c132]) ).
cnf(c134,plain,
append(rev(cons(X3,cons(X2,nil))),cons(X4,nil)) = cons(X2,cons(X3,cons(X4,nil))),
inference(transitivity,[status(thm)],[c125,c133]) ).
cnf(c135,plain,
rev(cons(X4,cons(X3,cons(X2,nil)))) = cons(X2,cons(X3,cons(X4,nil))),
inference(transitivity,[status(thm)],[c108,c134]) ).
cnf(c136,plain,
append(rev(cons(X4,cons(X3,cons(X2,nil)))),cons(X5,nil)) = append(cons(X2,cons(X3,cons(X4,nil))),cons(X5,nil)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
append(cons(X2,cons(X3,cons(X4,nil))),cons(X5,nil)) = cons(X2,append(cons(X3,cons(X4,nil)),cons(X5,nil))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c138,plain,
append(cons(X2,cons(X3,nil)),cons(X4,nil)) = cons(X2,append(cons(X3,nil),cons(X4,nil))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c139,plain,
cons(X2,append(cons(X3,cons(X4,nil)),cons(X5,nil))) = cons(X2,cons(X3,append(cons(X4,nil),cons(X5,nil)))),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
append(cons(X2,nil),cons(X3,nil)) = cons(X2,append(nil,cons(X3,nil))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c141,plain,
cons(X2,append(cons(X3,nil),cons(X4,nil))) = cons(X2,cons(X3,append(nil,cons(X4,nil)))),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
cons(X2,cons(X3,append(cons(X4,nil),cons(X5,nil)))) = cons(X2,cons(X3,cons(X4,append(nil,cons(X5,nil))))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
append(nil,cons(X2,nil)) = cons(X2,nil),
inference(substitution,[status(thm)],[c113]) ).
cnf(c144,plain,
cons(X2,append(nil,cons(X3,nil))) = cons(X2,cons(X3,nil)),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
cons(X2,cons(X3,append(nil,cons(X4,nil)))) = cons(X2,cons(X3,cons(X4,nil))),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
cons(X2,cons(X3,cons(X4,append(nil,cons(X5,nil))))) = cons(X2,cons(X3,cons(X4,cons(X5,nil)))),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
cons(X2,cons(X3,append(cons(X4,nil),cons(X5,nil)))) = cons(X2,cons(X3,cons(X4,cons(X5,nil)))),
inference(transitivity,[status(thm)],[c142,c146]) ).
cnf(c148,plain,
cons(X2,append(cons(X3,cons(X4,nil)),cons(X5,nil))) = cons(X2,cons(X3,cons(X4,cons(X5,nil)))),
inference(transitivity,[status(thm)],[c139,c147]) ).
cnf(c149,plain,
append(cons(X2,cons(X3,cons(X4,nil))),cons(X5,nil)) = cons(X2,cons(X3,cons(X4,cons(X5,nil)))),
inference(transitivity,[status(thm)],[c137,c148]) ).
cnf(c150,plain,
append(rev(cons(X4,cons(X3,cons(X2,nil)))),cons(X5,nil)) = cons(X2,cons(X3,cons(X4,cons(X5,nil)))),
inference(transitivity,[status(thm)],[c136,c149]) ).
cnf(c151,plain,
rev(cons(X5,cons(X4,cons(X3,cons(X2,nil))))) = cons(X2,cons(X3,cons(X4,cons(X5,nil)))),
inference(transitivity,[status(thm)],[c107,c150]) ).
cnf(c152,plain,
rev(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil)))),
inference(substitution,[status(thm)],[c151]) ).
cnf(c153,plain,
sorted(rev(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil)))))) = sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil))))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
eq2(sorted(rev(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue) = eq2(sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil))))),btrue),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
impl(eq2(sorted(rev(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(eq2(sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,axiom,
sorted(cons(Y3,cons(Y2,Xs2))) = andb(leqNat(Y3,Y2),sorted(cons(Y2,Xs2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
cnf(c157,plain,
sorted(cons(z,cons(X3,X2))) = andb(leqNat(z,X3),sorted(cons(X3,X2))),
inference(substitution,[status(thm)],[c156]) ).
cnf(c158,axiom,
leqNat(z,Y3) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
cnf(c159,plain,
leqNat(z,X2) = btrue,
inference(substitution,[status(thm)],[c158]) ).
cnf(c160,plain,
andb(leqNat(z,X3),sorted(cons(X3,X2))) = andb(btrue,sorted(cons(X3,X2))),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,axiom,
andb(btrue,Q2) = Q2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
cnf(c162,plain,
andb(btrue,sorted(cons(X3,X2))) = sorted(cons(X3,X2)),
inference(substitution,[status(thm)],[c161]) ).
cnf(c163,plain,
andb(leqNat(z,X3),sorted(cons(X3,X2))) = sorted(cons(X3,X2)),
inference(transitivity,[status(thm)],[c160,c162]) ).
cnf(c164,plain,
sorted(cons(z,cons(X3,X2))) = sorted(cons(X3,X2)),
inference(transitivity,[status(thm)],[c157,c163]) ).
cnf(c165,plain,
sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil))))) = sorted(cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil)))),
inference(substitution,[status(thm)],[c164]) ).
cnf(c166,plain,
eq2(sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil))))),btrue) = eq2(sorted(cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil)))),btrue),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
impl(eq2(sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(eq2(sorted(cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil)))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,axiom,
leqNat(s(Z2),s(M)) = leqNat(Z2,M),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
cnf(c169,plain,
leqNat(s(X3),s(X2)) = leqNat(X3,X2),
inference(substitution,[status(thm)],[c168]) ).
cnf(c170,plain,
leqNat(X3,X2) = leqNat(s(X3),s(X2)),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
andb(leqNat(X4,X3),sorted(cons(s(X3),X2))) = andb(leqNat(s(X4),s(X3)),sorted(cons(s(X3),X2))),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
sorted(cons(s(X4),cons(s(X3),X2))) = andb(leqNat(s(X4),s(X3)),sorted(cons(s(X3),X2))),
inference(substitution,[status(thm)],[c156]) ).
cnf(c173,plain,
andb(leqNat(s(X4),s(X3)),sorted(cons(s(X3),X2))) = sorted(cons(s(X4),cons(s(X3),X2))),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
andb(leqNat(X4,X3),sorted(cons(s(X3),X2))) = sorted(cons(s(X4),cons(s(X3),X2))),
inference(transitivity,[status(thm)],[c171,c173]) ).
cnf(c175,plain,
andb(leqNat(z,X3),sorted(cons(s(X3),X2))) = sorted(cons(s(z),cons(s(X3),X2))),
inference(substitution,[status(thm)],[c174]) ).
cnf(c176,plain,
sorted(cons(s(z),cons(s(X3),X2))) = andb(leqNat(z,X3),sorted(cons(s(X3),X2))),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
leqNat(z,X2) = btrue,
inference(substitution,[status(thm)],[c158]) ).
cnf(c178,plain,
andb(leqNat(z,X3),sorted(cons(s(X3),X2))) = andb(btrue,sorted(cons(s(X3),X2))),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
andb(btrue,sorted(cons(s(X3),X2))) = sorted(cons(s(X3),X2)),
inference(substitution,[status(thm)],[c161]) ).
cnf(c180,plain,
andb(leqNat(z,X3),sorted(cons(s(X3),X2))) = sorted(cons(s(X3),X2)),
inference(transitivity,[status(thm)],[c178,c179]) ).
cnf(c181,plain,
sorted(cons(s(z),cons(s(X3),X2))) = sorted(cons(s(X3),X2)),
inference(transitivity,[status(thm)],[c176,c180]) ).
cnf(c182,plain,
sorted(cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil)))) = sorted(cons(s(s(z)),cons(s(s(s(X2))),nil))),
inference(substitution,[status(thm)],[c181]) ).
cnf(c183,plain,
eq2(sorted(cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil)))),btrue) = eq2(sorted(cons(s(s(z)),cons(s(s(s(X2))),nil))),btrue),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
impl(eq2(sorted(cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil)))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(eq2(sorted(cons(s(s(z)),cons(s(s(s(X2))),nil))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
leqNat(s(X3),s(X2)) = leqNat(X3,X2),
inference(substitution,[status(thm)],[c168]) ).
cnf(c186,plain,
leqNat(X3,X2) = leqNat(s(X3),s(X2)),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
andb(leqNat(X4,X3),sorted(cons(s(s(X3)),X2))) = andb(leqNat(s(X4),s(X3)),sorted(cons(s(s(X3)),X2))),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
andb(leqNat(s(X4),s(X3)),sorted(cons(s(s(X3)),X2))) = sorted(cons(s(s(X4)),cons(s(s(X3)),X2))),
inference(substitution,[status(thm)],[c174]) ).
cnf(c189,plain,
andb(leqNat(X4,X3),sorted(cons(s(s(X3)),X2))) = sorted(cons(s(s(X4)),cons(s(s(X3)),X2))),
inference(transitivity,[status(thm)],[c187,c188]) ).
cnf(c190,plain,
andb(leqNat(z,X3),sorted(cons(s(s(X3)),X2))) = sorted(cons(s(s(z)),cons(s(s(X3)),X2))),
inference(substitution,[status(thm)],[c189]) ).
cnf(c191,plain,
sorted(cons(s(s(z)),cons(s(s(X3)),X2))) = andb(leqNat(z,X3),sorted(cons(s(s(X3)),X2))),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
leqNat(z,X2) = btrue,
inference(substitution,[status(thm)],[c158]) ).
cnf(c193,plain,
andb(leqNat(z,X3),sorted(cons(s(s(X3)),X2))) = andb(btrue,sorted(cons(s(s(X3)),X2))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
andb(btrue,sorted(cons(s(s(X3)),X2))) = sorted(cons(s(s(X3)),X2)),
inference(substitution,[status(thm)],[c161]) ).
cnf(c195,plain,
andb(leqNat(z,X3),sorted(cons(s(s(X3)),X2))) = sorted(cons(s(s(X3)),X2)),
inference(transitivity,[status(thm)],[c193,c194]) ).
cnf(c196,plain,
sorted(cons(s(s(z)),cons(s(s(X3)),X2))) = sorted(cons(s(s(X3)),X2)),
inference(transitivity,[status(thm)],[c191,c195]) ).
cnf(c197,plain,
sorted(cons(s(s(z)),cons(s(s(s(X2))),nil))) = sorted(cons(s(s(s(X2))),nil)),
inference(substitution,[status(thm)],[c196]) ).
cnf(c198,plain,
eq2(sorted(cons(s(s(z)),cons(s(s(s(X2))),nil))),btrue) = eq2(sorted(cons(s(s(s(X2))),nil)),btrue),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
impl(eq2(sorted(cons(s(s(z)),cons(s(s(s(X2))),nil))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(eq2(sorted(cons(s(s(s(X2))),nil)),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,axiom,
sorted(cons(Y3,nil)) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
cnf(c201,plain,
sorted(cons(s(s(s(X2))),nil)) = btrue,
inference(substitution,[status(thm)],[c200]) ).
cnf(c202,plain,
eq2(sorted(cons(s(s(s(X2))),nil)),btrue) = eq2(btrue,btrue),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
impl(eq2(sorted(cons(s(s(s(X2))),nil)),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(eq2(btrue,btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,axiom,
eq2(X2,X2) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_031) ).
cnf(c205,plain,
eq2(btrue,btrue) = btrue,
inference(substitution,[status(thm)],[c204]) ).
cnf(c206,plain,
impl(eq2(btrue,btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
eq2(btrue,btrue) = btrue,
inference(substitution,[status(thm)],[c204]) ).
cnf(c208,plain,
impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(btrue,impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,axiom,
impl(btrue,Q2) = Q2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
cnf(c211,plain,
impl(btrue,impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)),
inference(substitution,[status(thm)],[c210]) ).
cnf(c212,plain,
impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue),
inference(substitution,[status(thm)],[c210]) ).
cnf(c213,axiom,
lengthNat(cons(Y3,Xs2)) = s(lengthNat(Xs2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
cnf(c214,plain,
lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))),
inference(substitution,[status(thm)],[c213]) ).
cnf(c215,plain,
leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))) = leqNat(s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) = eq2(leqNat(s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
leqNat(s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))) = leqNat(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))),s(s(z))),
inference(substitution,[status(thm)],[c168]) ).
cnf(c218,plain,
eq2(leqNat(s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) = eq2(leqNat(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))),s(s(z))),btrue),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))) = s(lengthNat(cons(s(z),cons(z,nil)))),
inference(substitution,[status(thm)],[c213]) ).
cnf(c220,plain,
leqNat(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))),s(s(z))) = leqNat(s(lengthNat(cons(s(z),cons(z,nil)))),s(s(z))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
eq2(leqNat(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))),s(s(z))),btrue) = eq2(leqNat(s(lengthNat(cons(s(z),cons(z,nil)))),s(s(z))),btrue),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
leqNat(s(lengthNat(cons(s(z),cons(z,nil)))),s(s(z))) = leqNat(lengthNat(cons(s(z),cons(z,nil))),s(z)),
inference(substitution,[status(thm)],[c168]) ).
cnf(c223,plain,
eq2(leqNat(s(lengthNat(cons(s(z),cons(z,nil)))),s(s(z))),btrue) = eq2(leqNat(lengthNat(cons(s(z),cons(z,nil))),s(z)),btrue),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
lengthNat(cons(s(z),cons(z,nil))) = s(lengthNat(cons(z,nil))),
inference(substitution,[status(thm)],[c213]) ).
cnf(c225,plain,
leqNat(lengthNat(cons(s(z),cons(z,nil))),s(z)) = leqNat(s(lengthNat(cons(z,nil))),s(z)),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
eq2(leqNat(lengthNat(cons(s(z),cons(z,nil))),s(z)),btrue) = eq2(leqNat(s(lengthNat(cons(z,nil))),s(z)),btrue),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
leqNat(s(lengthNat(cons(z,nil))),s(z)) = leqNat(lengthNat(cons(z,nil)),z),
inference(substitution,[status(thm)],[c168]) ).
cnf(c228,plain,
eq2(leqNat(s(lengthNat(cons(z,nil))),s(z)),btrue) = eq2(leqNat(lengthNat(cons(z,nil)),z),btrue),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
lengthNat(cons(z,nil)) = s(lengthNat(nil)),
inference(substitution,[status(thm)],[c213]) ).
cnf(c230,plain,
leqNat(lengthNat(cons(z,nil)),z) = leqNat(s(lengthNat(nil)),z),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
eq2(leqNat(lengthNat(cons(z,nil)),z),btrue) = eq2(leqNat(s(lengthNat(nil)),z),btrue),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,axiom,
leqNat(s(Z2),z) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
cnf(c233,plain,
leqNat(s(lengthNat(nil)),z) = bfalse,
inference(substitution,[status(thm)],[c232]) ).
cnf(c234,plain,
eq2(leqNat(s(lengthNat(nil)),z),btrue) = eq2(bfalse,btrue),
inference(congruence,[status(thm)],[c233]) ).
cnf(c235,axiom,
eq2(bfalse,btrue) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c236,plain,
eq2(leqNat(s(lengthNat(nil)),z),btrue) = bfalse,
inference(transitivity,[status(thm)],[c234,c235]) ).
cnf(c237,plain,
eq2(leqNat(lengthNat(cons(z,nil)),z),btrue) = bfalse,
inference(transitivity,[status(thm)],[c231,c236]) ).
cnf(c238,plain,
eq2(leqNat(s(lengthNat(cons(z,nil))),s(z)),btrue) = bfalse,
inference(transitivity,[status(thm)],[c228,c237]) ).
cnf(c239,plain,
eq2(leqNat(lengthNat(cons(s(z),cons(z,nil))),s(z)),btrue) = bfalse,
inference(transitivity,[status(thm)],[c226,c238]) ).
cnf(c240,plain,
eq2(leqNat(s(lengthNat(cons(s(z),cons(z,nil)))),s(s(z))),btrue) = bfalse,
inference(transitivity,[status(thm)],[c223,c239]) ).
cnf(c241,plain,
eq2(leqNat(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil)))),s(s(z))),btrue) = bfalse,
inference(transitivity,[status(thm)],[c221,c240]) ).
cnf(c242,plain,
eq2(leqNat(s(lengthNat(cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) = bfalse,
inference(transitivity,[status(thm)],[c218,c241]) ).
cnf(c243,plain,
eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue) = bfalse,
inference(transitivity,[status(thm)],[c216,c242]) ).
cnf(c244,plain,
impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue)) = bfalse,
inference(transitivity,[status(thm)],[c212,c243]) ).
cnf(c245,plain,
impl(btrue,impl(btrue,eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = bfalse,
inference(transitivity,[status(thm)],[c211,c244]) ).
cnf(c246,plain,
impl(btrue,impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = bfalse,
inference(transitivity,[status(thm)],[c209,c245]) ).
cnf(c247,plain,
impl(eq2(btrue,btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = bfalse,
inference(transitivity,[status(thm)],[c206,c246]) ).
cnf(c248,plain,
impl(eq2(sorted(cons(s(s(s(X2))),nil)),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = bfalse,
inference(transitivity,[status(thm)],[c203,c247]) ).
cnf(c249,plain,
impl(eq2(sorted(cons(s(s(z)),cons(s(s(s(X2))),nil))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = bfalse,
inference(transitivity,[status(thm)],[c199,c248]) ).
cnf(c250,plain,
impl(eq2(sorted(cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil)))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = bfalse,
inference(transitivity,[status(thm)],[c184,c249]) ).
cnf(c251,plain,
impl(eq2(sorted(cons(z,cons(s(z),cons(s(s(z)),cons(s(s(s(X2))),nil))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = bfalse,
inference(transitivity,[status(thm)],[c167,c250]) ).
cnf(c252,plain,
impl(eq2(sorted(rev(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(btrue,btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = bfalse,
inference(transitivity,[status(thm)],[c155,c251]) ).
cnf(c253,plain,
impl(eq2(sorted(rev(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil)))))),btrue),impl(eq2(unique(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),btrue),eq2(leqNat(lengthNat(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),s(s(s(z)))),btrue))) = bfalse,
inference(transitivity,[status(thm)],[c105,c252]) ).
cnf(c254,plain,
psorted_rev(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))) = bfalse,
inference(transitivity,[status(thm)],[c3,c253]) ).
cnf(c255,plain,
eq2(psorted_rev(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),bfalse) = eq2(bfalse,bfalse),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
eq2(bfalse,bfalse) = btrue,
inference(substitution,[status(thm)],[c204]) ).
cnf(c257,plain,
eq2(psorted_rev(cons(s(s(s(X2))),cons(s(s(z)),cons(s(z),cons(z,nil))))),bfalse) = btrue,
inference(transitivity,[status(thm)],[c255,c256]) ).
cnf(c258,plain,
$false,
inference(resolution,[status(thm)],[c1,c257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX203-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 15:10:49 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.19/3.01 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 21.19/3.01
% 21.19/3.01 % SZS status Unsatisfiable
% 21.19/3.01
% 21.19/3.03 % SZS output start CNFRefutation
% See solution above
% 23.22/3.18
% 23.22/3.18 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------