%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN143-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 01:47:10 PM UTC 2026
% Result : Unsatisfiable 10.77s 1.64s
% Output : CNFRefutation 11.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 32
% Syntax : Number of clauses : 327 ( 327 unt; 0 nHn; 124 RR)
% Number of literals : 327 ( 326 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 6 con; 0-4 aty)
% Number of variables : 309 ( 79 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
m5(d,d) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c3,plain,
ifeq(true,true,m5(d,d),true) = m5(d,d),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
m5(d,d) = ifeq(true,true,m5(d,d),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
ifeq(true,true,m4(X3,X2),true) = m4(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
m4(X3,X2) = ifeq(true,true,m4(X3,X2),true),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
ifeq(true,true,s3(a,X2),true) = s3(a,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
s3(a,X2) = ifeq(true,true,s3(a,X2),true),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
ifeq(true,true,ifeq(true,true,s3(a,X2),true),true) = ifeq(true,true,s3(a,X2),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
ifeq(true,true,s3(a,X2),true) = ifeq(true,true,ifeq(true,true,s3(a,X2),true),true),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
ifeq(true,true,s2(a),true) = s2(a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
s2(a) = ifeq(true,true,s2(a),true),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
ifeq(true,true,s1(b),true) = s1(b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
s1(b) = ifeq(true,true,s1(b),true),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,axiom,
p0(b,X) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
cnf(c16,plain,
p0(b,b) = true,
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
true = p0(b,b),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
ifeq(true,true,s1(b),true) = ifeq(p0(b,b),true,s1(b),true),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,axiom,
ifeq(p0(I,I),true,s1(I),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_125) ).
cnf(c20,plain,
ifeq(p0(b,b),true,s1(b),true) = true,
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
ifeq(true,true,s1(b),true) = true,
inference(transitivity,[status(thm)],[c18,c20]) ).
cnf(c22,plain,
s1(b) = true,
inference(transitivity,[status(thm)],[c14,c21]) ).
cnf(c23,plain,
true = s1(b),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
ifeq(true,true,s2(a),true) = ifeq(s1(b),true,s2(a),true),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
ifeq(true,true,ifeq(s1(b),true,s2(a),true),true) = ifeq(s1(b),true,s2(a),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
ifeq(s1(b),true,s2(a),true) = ifeq(true,true,ifeq(s1(b),true,s2(a),true),true),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
ifeq(true,true,q2(b,a,b),true) = q2(b,a,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c28,plain,
q2(b,a,b) = ifeq(true,true,q2(b,a,b),true),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
ifeq(true,true,n1(a,X2,X2),true) = n1(a,X2,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c30,plain,
n1(a,X2,X2) = ifeq(true,true,n1(a,X2,X2),true),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
ifeq(true,true,ifeq(true,true,n1(a,X2,X2),true),true) = ifeq(true,true,n1(a,X2,X2),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c32,plain,
ifeq(true,true,n1(a,X2,X2),true) = ifeq(true,true,ifeq(true,true,n1(a,X2,X2),true),true),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,axiom,
l0(a) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c34,plain,
true = l0(a),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
ifeq(true,true,ifeq(true,true,n1(a,X2,X2),true),true) = ifeq(l0(a),true,ifeq(true,true,n1(a,X2,X2),true),true),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
ifeq(true,true,ifeq(l0(a),true,ifeq(true,true,n1(a,X2,X2),true),true),true) = ifeq(l0(a),true,ifeq(true,true,n1(a,X2,X2),true),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c37,plain,
ifeq(l0(a),true,ifeq(true,true,n1(a,X2,X2),true),true) = ifeq(true,true,ifeq(l0(a),true,ifeq(true,true,n1(a,X2,X2),true),true),true),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
ifeq(true,true,n1(a,X2,a),true) = n1(a,X2,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
n1(a,X2,a) = ifeq(true,true,n1(a,X2,a),true),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
true = l0(a),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c41,plain,
ifeq(true,true,n1(a,X2,a),true) = ifeq(l0(a),true,n1(a,X2,a),true),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
ifeq(true,true,n1(X3,X2,X3),true) = n1(X3,X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c43,plain,
n1(X3,X2,X3) = ifeq(true,true,n1(X3,X2,X3),true),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
ifeq(l0(X3),true,n1(X3,X2,X3),true) = ifeq(l0(X3),true,ifeq(true,true,n1(X3,X2,X3),true),true),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,axiom,
s0(b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c46,plain,
true = s0(b),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
ifeq(true,true,n1(X3,X2,X3),true) = ifeq(s0(b),true,n1(X3,X2,X3),true),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
ifeq(l0(X3),true,ifeq(true,true,n1(X3,X2,X3),true),true) = ifeq(l0(X3),true,ifeq(s0(b),true,n1(X3,X2,X3),true),true),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
ifeq(true,true,ifeq(s0(b),true,n1(X3,X2,X3),true),true) = ifeq(s0(b),true,n1(X3,X2,X3),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c50,plain,
ifeq(s0(b),true,n1(X3,X2,X3),true) = ifeq(true,true,ifeq(s0(b),true,n1(X3,X2,X3),true),true),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
ifeq(l0(X3),true,ifeq(s0(b),true,n1(X3,X2,X3),true),true) = ifeq(l0(X3),true,ifeq(true,true,ifeq(s0(b),true,n1(X3,X2,X3),true),true),true),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
true = p0(b,X2),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c53,plain,
ifeq(true,true,ifeq(s0(b),true,n1(X3,X2,X3),true),true) = ifeq(p0(b,X2),true,ifeq(s0(b),true,n1(X3,X2,X3),true),true),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
ifeq(l0(X3),true,ifeq(true,true,ifeq(s0(b),true,n1(X3,X2,X3),true),true),true) = ifeq(l0(X3),true,ifeq(p0(b,X2),true,ifeq(s0(b),true,n1(X3,X2,X3),true),true),true),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,axiom,
ifeq(l0(D),true,ifeq(p0(b,E),true,ifeq(s0(b),true,n1(D,E,D),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_050) ).
cnf(c56,plain,
ifeq(l0(X3),true,ifeq(p0(b,X2),true,ifeq(s0(b),true,n1(X3,X2,X3),true),true),true) = true,
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
ifeq(l0(X3),true,ifeq(true,true,ifeq(s0(b),true,n1(X3,X2,X3),true),true),true) = true,
inference(transitivity,[status(thm)],[c54,c56]) ).
cnf(c58,plain,
ifeq(l0(X3),true,ifeq(s0(b),true,n1(X3,X2,X3),true),true) = true,
inference(transitivity,[status(thm)],[c51,c57]) ).
cnf(c59,plain,
ifeq(l0(X3),true,ifeq(true,true,n1(X3,X2,X3),true),true) = true,
inference(transitivity,[status(thm)],[c48,c58]) ).
cnf(c60,plain,
ifeq(l0(X3),true,n1(X3,X2,X3),true) = true,
inference(transitivity,[status(thm)],[c44,c59]) ).
cnf(c61,plain,
ifeq(l0(a),true,n1(a,X2,a),true) = true,
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
ifeq(true,true,n1(a,X2,a),true) = true,
inference(transitivity,[status(thm)],[c41,c61]) ).
cnf(c63,plain,
n1(a,X2,a) = true,
inference(transitivity,[status(thm)],[c39,c62]) ).
cnf(c64,plain,
true = n1(a,X2,a),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
ifeq(true,true,ifeq(l0(a),true,ifeq(true,true,n1(a,X2,X2),true),true),true) = ifeq(n1(a,X2,a),true,ifeq(l0(a),true,ifeq(true,true,n1(a,X2,X2),true),true),true),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
ifeq(true,true,l1(a,a),true) = l1(a,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c67,plain,
l1(a,a) = ifeq(true,true,l1(a,a),true),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,axiom,
n0(b,a) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c69,plain,
true = n0(b,a),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
ifeq(true,true,l1(a,a),true) = ifeq(n0(b,a),true,l1(a,a),true),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,axiom,
ifeq(n0(H,G),true,l1(G,G),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_002) ).
cnf(c72,plain,
ifeq(n0(b,a),true,l1(a,a),true) = true,
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
ifeq(true,true,l1(a,a),true) = true,
inference(transitivity,[status(thm)],[c70,c72]) ).
cnf(c74,plain,
l1(a,a) = true,
inference(transitivity,[status(thm)],[c67,c73]) ).
cnf(c75,plain,
true = l1(a,a),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
ifeq(true,true,n1(a,X2,X2),true) = ifeq(l1(a,a),true,n1(a,X2,X2),true),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
ifeq(l0(a),true,ifeq(true,true,n1(a,X2,X2),true),true) = ifeq(l0(a),true,ifeq(l1(a,a),true,n1(a,X2,X2),true),true),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
ifeq(n1(a,X2,a),true,ifeq(l0(a),true,ifeq(true,true,n1(a,X2,X2),true),true),true) = ifeq(n1(a,X2,a),true,ifeq(l0(a),true,ifeq(l1(a,a),true,n1(a,X2,X2),true),true),true),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,axiom,
ifeq(n1(E2,F,E2),true,ifeq(l0(G2),true,ifeq(l1(G2,E2),true,n1(E2,F,F),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_054) ).
cnf(c80,plain,
ifeq(n1(a,X2,a),true,ifeq(l0(a),true,ifeq(l1(a,a),true,n1(a,X2,X2),true),true),true) = true,
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
ifeq(n1(a,X2,a),true,ifeq(l0(a),true,ifeq(true,true,n1(a,X2,X2),true),true),true) = true,
inference(transitivity,[status(thm)],[c78,c80]) ).
cnf(c82,plain,
ifeq(true,true,ifeq(l0(a),true,ifeq(true,true,n1(a,X2,X2),true),true),true) = true,
inference(transitivity,[status(thm)],[c65,c81]) ).
cnf(c83,plain,
ifeq(l0(a),true,ifeq(true,true,n1(a,X2,X2),true),true) = true,
inference(transitivity,[status(thm)],[c37,c82]) ).
cnf(c84,plain,
ifeq(true,true,ifeq(true,true,n1(a,X2,X2),true),true) = true,
inference(transitivity,[status(thm)],[c35,c83]) ).
cnf(c85,plain,
ifeq(true,true,n1(a,X2,X2),true) = true,
inference(transitivity,[status(thm)],[c32,c84]) ).
cnf(c86,plain,
n1(a,X2,X2) = true,
inference(transitivity,[status(thm)],[c30,c85]) ).
cnf(c87,plain,
n1(a,b,b) = true,
inference(substitution,[status(thm)],[c86]) ).
cnf(c88,plain,
true = n1(a,b,b),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
ifeq(true,true,q2(b,a,b),true) = ifeq(n1(a,b,b),true,q2(b,a,b),true),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
ifeq(true,true,ifeq(n1(X2,b,b),true,q2(b,X2,b),true),true) = ifeq(n1(X2,b,b),true,q2(b,X2,b),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c91,plain,
ifeq(n1(X2,b,b),true,q2(b,X2,b),true) = ifeq(true,true,ifeq(n1(X2,b,b),true,q2(b,X2,b),true),true),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
ifeq(true,true,p1(b,X2,b),true) = p1(b,X2,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c93,plain,
p1(b,X2,b) = ifeq(true,true,p1(b,X2,b),true),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,axiom,
m0(b,b,e) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c95,plain,
true = m0(b,b,e),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
ifeq(true,true,p1(b,X2,b),true) = ifeq(m0(b,b,e),true,p1(b,X2,b),true),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
ifeq(true,true,ifeq(m0(b,b,e),true,p1(b,X2,b),true),true) = ifeq(m0(b,b,e),true,p1(b,X2,b),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c98,plain,
ifeq(m0(b,b,e),true,p1(b,X2,b),true) = ifeq(true,true,ifeq(m0(b,b,e),true,p1(b,X2,b),true),true),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
ifeq(true,true,p1(b,b,e),true) = p1(b,b,e),
inference(substitution,[status(thm)],[c2]) ).
cnf(c100,plain,
p1(b,b,e) = ifeq(true,true,p1(b,b,e),true),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,axiom,
k0(e) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c102,plain,
true = k0(e),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
ifeq(true,true,p1(b,b,e),true) = ifeq(k0(e),true,p1(b,b,e),true),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
ifeq(true,true,p1(b,b,X2),true) = p1(b,b,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c105,plain,
p1(b,b,X2) = ifeq(true,true,p1(b,b,X2),true),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
ifeq(k0(X2),true,p1(b,b,X2),true) = ifeq(k0(X2),true,ifeq(true,true,p1(b,b,X2),true),true),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,axiom,
n0(d,b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c108,plain,
true = n0(d,b),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
ifeq(true,true,p1(b,b,X2),true) = ifeq(n0(d,b),true,p1(b,b,X2),true),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
ifeq(k0(X2),true,ifeq(true,true,p1(b,b,X2),true),true) = ifeq(k0(X2),true,ifeq(n0(d,b),true,p1(b,b,X2),true),true),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,axiom,
ifeq(k0(E2),true,ifeq(n0(d,D2),true,p1(D2,D2,E2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_063) ).
cnf(c112,plain,
ifeq(k0(X2),true,ifeq(n0(d,b),true,p1(b,b,X2),true),true) = true,
inference(substitution,[status(thm)],[c111]) ).
cnf(c113,plain,
ifeq(k0(X2),true,ifeq(true,true,p1(b,b,X2),true),true) = true,
inference(transitivity,[status(thm)],[c110,c112]) ).
cnf(c114,plain,
ifeq(k0(X2),true,p1(b,b,X2),true) = true,
inference(transitivity,[status(thm)],[c106,c113]) ).
cnf(c115,plain,
ifeq(k0(e),true,p1(b,b,e),true) = true,
inference(substitution,[status(thm)],[c114]) ).
cnf(c116,plain,
ifeq(true,true,p1(b,b,e),true) = true,
inference(transitivity,[status(thm)],[c103,c115]) ).
cnf(c117,plain,
p1(b,b,e) = true,
inference(transitivity,[status(thm)],[c100,c116]) ).
cnf(c118,plain,
true = p1(b,b,e),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
ifeq(true,true,ifeq(m0(b,b,e),true,p1(b,X2,b),true),true) = ifeq(p1(b,b,e),true,ifeq(m0(b,b,e),true,p1(b,X2,b),true),true),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,axiom,
ifeq(p1(J,H2,A2),true,ifeq(m0(J,H2,A2),true,p1(H2,I2,J),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_082) ).
cnf(c121,plain,
ifeq(p1(b,b,e),true,ifeq(m0(b,b,e),true,p1(b,X2,b),true),true) = true,
inference(substitution,[status(thm)],[c120]) ).
cnf(c122,plain,
ifeq(true,true,ifeq(m0(b,b,e),true,p1(b,X2,b),true),true) = true,
inference(transitivity,[status(thm)],[c119,c121]) ).
cnf(c123,plain,
ifeq(m0(b,b,e),true,p1(b,X2,b),true) = true,
inference(transitivity,[status(thm)],[c98,c122]) ).
cnf(c124,plain,
ifeq(true,true,p1(b,X2,b),true) = true,
inference(transitivity,[status(thm)],[c96,c123]) ).
cnf(c125,plain,
p1(b,X2,b) = true,
inference(transitivity,[status(thm)],[c93,c124]) ).
cnf(c126,plain,
p1(b,b,b) = true,
inference(substitution,[status(thm)],[c125]) ).
cnf(c127,plain,
true = p1(b,b,b),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
ifeq(true,true,ifeq(n1(X2,b,b),true,q2(b,X2,b),true),true) = ifeq(p1(b,b,b),true,ifeq(n1(X2,b,b),true,q2(b,X2,b),true),true),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
ifeq(true,true,ifeq(p1(b,b,b),true,ifeq(n1(X2,b,b),true,q2(b,X2,b),true),true),true) = ifeq(p1(b,b,b),true,ifeq(n1(X2,b,b),true,q2(b,X2,b),true),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c130,plain,
ifeq(p1(b,b,b),true,ifeq(n1(X2,b,b),true,q2(b,X2,b),true),true) = ifeq(true,true,ifeq(p1(b,b,b),true,ifeq(n1(X2,b,b),true,q2(b,X2,b),true),true),true),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
ifeq(true,true,q2(X2,b,b),true) = q2(X2,b,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c132,plain,
q2(X2,b,b) = ifeq(true,true,q2(X2,b,b),true),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
ifeq(true,true,ifeq(true,true,q2(X2,b,b),true),true) = ifeq(true,true,q2(X2,b,b),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c134,plain,
ifeq(true,true,q2(X2,b,b),true) = ifeq(true,true,ifeq(true,true,q2(X2,b,b),true),true),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c135,plain,
ifeq(true,true,p1(X2,X2,X2),true) = p1(X2,X2,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c136,plain,
p1(X2,X2,X2) = ifeq(true,true,p1(X2,X2,X2),true),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
true = p0(b,X2),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c138,plain,
ifeq(true,true,p1(X2,X2,X2),true) = ifeq(p0(b,X2),true,p1(X2,X2,X2),true),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,axiom,
ifeq(p0(C2,B2),true,p1(B2,B2,B2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_085) ).
cnf(c140,plain,
ifeq(p0(b,X2),true,p1(X2,X2,X2),true) = true,
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
ifeq(true,true,p1(X2,X2,X2),true) = true,
inference(transitivity,[status(thm)],[c138,c140]) ).
cnf(c142,plain,
p1(X2,X2,X2) = true,
inference(transitivity,[status(thm)],[c136,c141]) ).
cnf(c143,plain,
true = p1(X2,X2,X2),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
ifeq(true,true,ifeq(true,true,q2(X2,b,b),true),true) = ifeq(p1(X2,X2,X2),true,ifeq(true,true,q2(X2,b,b),true),true),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,axiom,
k0(b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c146,plain,
true = k0(b),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
ifeq(true,true,q2(X2,b,b),true) = ifeq(k0(b),true,q2(X2,b,b),true),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
ifeq(p1(X2,X2,X2),true,ifeq(true,true,q2(X2,b,b),true),true) = ifeq(p1(X2,X2,X2),true,ifeq(k0(b),true,q2(X2,b,b),true),true),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,axiom,
ifeq(p1(E2,E2,E2),true,ifeq(k0(F2),true,q2(E2,F2,F2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_177) ).
cnf(c150,plain,
ifeq(p1(X2,X2,X2),true,ifeq(k0(b),true,q2(X2,b,b),true),true) = true,
inference(substitution,[status(thm)],[c149]) ).
cnf(c151,plain,
ifeq(p1(X2,X2,X2),true,ifeq(true,true,q2(X2,b,b),true),true) = true,
inference(transitivity,[status(thm)],[c148,c150]) ).
cnf(c152,plain,
ifeq(true,true,ifeq(true,true,q2(X2,b,b),true),true) = true,
inference(transitivity,[status(thm)],[c144,c151]) ).
cnf(c153,plain,
ifeq(true,true,q2(X2,b,b),true) = true,
inference(transitivity,[status(thm)],[c134,c152]) ).
cnf(c154,plain,
q2(X2,b,b) = true,
inference(transitivity,[status(thm)],[c132,c153]) ).
cnf(c155,plain,
true = q2(X2,b,b),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
ifeq(true,true,ifeq(p1(b,b,b),true,ifeq(n1(X2,b,b),true,q2(b,X2,b),true),true),true) = ifeq(q2(X2,b,b),true,ifeq(p1(b,b,b),true,ifeq(n1(X2,b,b),true,q2(b,X2,b),true),true),true),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,axiom,
ifeq(q2(G2,H2,F2),true,ifeq(p1(F2,F2,H2),true,ifeq(n1(G2,F2,H2),true,q2(F2,G2,F2),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_182) ).
cnf(c158,plain,
ifeq(q2(X2,b,b),true,ifeq(p1(b,b,b),true,ifeq(n1(X2,b,b),true,q2(b,X2,b),true),true),true) = true,
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
ifeq(true,true,ifeq(p1(b,b,b),true,ifeq(n1(X2,b,b),true,q2(b,X2,b),true),true),true) = true,
inference(transitivity,[status(thm)],[c156,c158]) ).
cnf(c160,plain,
ifeq(p1(b,b,b),true,ifeq(n1(X2,b,b),true,q2(b,X2,b),true),true) = true,
inference(transitivity,[status(thm)],[c130,c159]) ).
cnf(c161,plain,
ifeq(true,true,ifeq(n1(X2,b,b),true,q2(b,X2,b),true),true) = true,
inference(transitivity,[status(thm)],[c128,c160]) ).
cnf(c162,plain,
ifeq(n1(X2,b,b),true,q2(b,X2,b),true) = true,
inference(transitivity,[status(thm)],[c91,c161]) ).
cnf(c163,plain,
ifeq(n1(a,b,b),true,q2(b,a,b),true) = true,
inference(substitution,[status(thm)],[c162]) ).
cnf(c164,plain,
ifeq(true,true,q2(b,a,b),true) = true,
inference(transitivity,[status(thm)],[c89,c163]) ).
cnf(c165,plain,
q2(b,a,b) = true,
inference(transitivity,[status(thm)],[c28,c164]) ).
cnf(c166,plain,
true = q2(b,a,b),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
ifeq(true,true,ifeq(s1(b),true,s2(a),true),true) = ifeq(q2(b,a,b),true,ifeq(s1(b),true,s2(a),true),true),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,axiom,
ifeq(q2(b,H2,b),true,ifeq(s1(b),true,s2(H2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_189) ).
cnf(c169,plain,
ifeq(q2(b,a,b),true,ifeq(s1(b),true,s2(a),true),true) = true,
inference(substitution,[status(thm)],[c168]) ).
cnf(c170,plain,
ifeq(true,true,ifeq(s1(b),true,s2(a),true),true) = true,
inference(transitivity,[status(thm)],[c167,c169]) ).
cnf(c171,plain,
ifeq(s1(b),true,s2(a),true) = true,
inference(transitivity,[status(thm)],[c26,c170]) ).
cnf(c172,plain,
ifeq(true,true,s2(a),true) = true,
inference(transitivity,[status(thm)],[c24,c171]) ).
cnf(c173,plain,
s2(a) = true,
inference(transitivity,[status(thm)],[c12,c172]) ).
cnf(c174,plain,
true = s2(a),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
ifeq(true,true,ifeq(true,true,s3(a,X2),true),true) = ifeq(s2(a),true,ifeq(true,true,s3(a,X2),true),true),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
ifeq(true,true,q2(X2,X2,X2),true) = q2(X2,X2,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c177,plain,
q2(X2,X2,X2) = ifeq(true,true,q2(X2,X2,X2),true),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
true = p1(X2,X2,X2),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c179,plain,
ifeq(true,true,q2(X2,X2,X2),true) = ifeq(p1(X2,X2,X2),true,q2(X2,X2,X2),true),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,axiom,
ifeq(p1(I2,I2,I2),true,q2(I2,I2,I2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_181) ).
cnf(c181,plain,
ifeq(p1(X2,X2,X2),true,q2(X2,X2,X2),true) = true,
inference(substitution,[status(thm)],[c180]) ).
cnf(c182,plain,
ifeq(true,true,q2(X2,X2,X2),true) = true,
inference(transitivity,[status(thm)],[c179,c181]) ).
cnf(c183,plain,
q2(X2,X2,X2) = true,
inference(transitivity,[status(thm)],[c177,c182]) ).
cnf(c184,plain,
q2(a,a,a) = true,
inference(substitution,[status(thm)],[c183]) ).
cnf(c185,plain,
true = q2(a,a,a),
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,plain,
ifeq(true,true,s3(a,X2),true) = ifeq(q2(a,a,a),true,s3(a,X2),true),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
ifeq(s2(a),true,ifeq(true,true,s3(a,X2),true),true) = ifeq(s2(a),true,ifeq(q2(a,a,a),true,s3(a,X2),true),true),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
ifeq(true,true,s3(X2,X3),true) = s3(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c189,plain,
s3(X3,X2) = ifeq(true,true,s3(X3,X2),true),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c190,plain,
ifeq(q2(X3,X4,X3),true,s3(X4,X2),true) = ifeq(q2(X3,X4,X3),true,ifeq(true,true,s3(X4,X2),true),true),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
ifeq(s2(X4),true,ifeq(q2(X3,X4,X3),true,s3(X4,X2),true),true) = ifeq(s2(X4),true,ifeq(q2(X3,X4,X3),true,ifeq(true,true,s3(X4,X2),true),true),true),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,axiom,
m0(X2,d,Y) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
cnf(c193,plain,
m0(X3,d,X2) = true,
inference(substitution,[status(thm)],[c192]) ).
cnf(c194,plain,
true = m0(X3,d,X2),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c195,plain,
ifeq(true,true,s3(X4,X2),true) = ifeq(m0(X3,d,X2),true,s3(X4,X2),true),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
ifeq(q2(X3,X4,X3),true,ifeq(true,true,s3(X4,X2),true),true) = ifeq(q2(X3,X4,X3),true,ifeq(m0(X3,d,X2),true,s3(X4,X2),true),true),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
ifeq(s2(X4),true,ifeq(q2(X3,X4,X3),true,ifeq(true,true,s3(X4,X2),true),true),true) = ifeq(s2(X4),true,ifeq(q2(X3,X4,X3),true,ifeq(m0(X3,d,X2),true,s3(X4,X2),true),true),true),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,axiom,
ifeq(s2(I2),true,ifeq(q2(A2,I2,A2),true,ifeq(m0(A2,B2,J2),true,s3(I2,J2),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_273) ).
cnf(c199,plain,
ifeq(s2(X4),true,ifeq(q2(X3,X4,X3),true,ifeq(m0(X3,d,X2),true,s3(X4,X2),true),true),true) = true,
inference(substitution,[status(thm)],[c198]) ).
cnf(c200,plain,
ifeq(s2(X4),true,ifeq(q2(X3,X4,X3),true,ifeq(true,true,s3(X4,X2),true),true),true) = true,
inference(transitivity,[status(thm)],[c197,c199]) ).
cnf(c201,plain,
ifeq(s2(X4),true,ifeq(q2(X3,X4,X3),true,s3(X4,X2),true),true) = true,
inference(transitivity,[status(thm)],[c191,c200]) ).
cnf(c202,plain,
ifeq(s2(a),true,ifeq(q2(a,a,a),true,s3(a,X2),true),true) = true,
inference(substitution,[status(thm)],[c201]) ).
cnf(c203,plain,
ifeq(s2(a),true,ifeq(true,true,s3(a,X2),true),true) = true,
inference(transitivity,[status(thm)],[c187,c202]) ).
cnf(c204,plain,
ifeq(true,true,ifeq(true,true,s3(a,X2),true),true) = true,
inference(transitivity,[status(thm)],[c175,c203]) ).
cnf(c205,plain,
ifeq(true,true,s3(a,X2),true) = true,
inference(transitivity,[status(thm)],[c10,c204]) ).
cnf(c206,plain,
s3(a,X2) = true,
inference(transitivity,[status(thm)],[c8,c205]) ).
cnf(c207,plain,
true = s3(a,X2),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c208,plain,
ifeq(true,true,m4(X3,X2),true) = ifeq(s3(a,X3),true,m4(X3,X2),true),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
ifeq(true,true,m4(X3,X2),true) = m4(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c210,plain,
m4(X3,X2) = ifeq(true,true,m4(X3,X2),true),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
ifeq(s3(a,X3),true,m4(X3,X2),true) = ifeq(s3(a,X3),true,ifeq(true,true,m4(X3,X2),true),true),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
ifeq(true,true,l2(X2,X2),true) = l2(X2,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c213,plain,
l2(X2,X2) = ifeq(true,true,l2(X2,X2),true),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
p0(b,b) = true,
inference(substitution,[status(thm)],[c15]) ).
cnf(c215,plain,
true = p0(b,b),
inference(symmetry,[status(thm)],[c214]) ).
cnf(c216,plain,
ifeq(true,true,l2(X2,X2),true) = ifeq(p0(b,b),true,l2(X2,X2),true),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
ifeq(true,true,l2(X2,X2),true) = l2(X2,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c218,plain,
l2(X2,X2) = ifeq(true,true,l2(X2,X2),true),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
ifeq(p0(X3,X3),true,l2(X2,X2),true) = ifeq(p0(X3,X3),true,ifeq(true,true,l2(X2,X2),true),true),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
ifeq(true,true,ifeq(p0(X3,X3),true,ifeq(true,true,l2(X2,X2),true),true),true) = ifeq(p0(X3,X3),true,ifeq(true,true,l2(X2,X2),true),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c221,plain,
ifeq(p0(X3,X3),true,ifeq(true,true,l2(X2,X2),true),true) = ifeq(true,true,ifeq(p0(X3,X3),true,ifeq(true,true,l2(X2,X2),true),true),true),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
ifeq(true,true,s1(X2),true) = s1(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c223,plain,
s1(X2) = ifeq(true,true,s1(X2),true),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
true = s1(b),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c225,plain,
ifeq(true,true,s1(X2),true) = ifeq(s1(b),true,s1(X2),true),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
ifeq(true,true,s1(X2),true) = s1(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c227,plain,
s1(X2) = ifeq(true,true,s1(X2),true),
inference(symmetry,[status(thm)],[c226]) ).
cnf(c228,plain,
ifeq(s1(X3),true,s1(X2),true) = ifeq(s1(X3),true,ifeq(true,true,s1(X2),true),true),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,axiom,
q0(X2,d) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c230,plain,
true = q0(X2,d),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c231,plain,
ifeq(true,true,s1(X2),true) = ifeq(q0(X2,d),true,s1(X2),true),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
ifeq(s1(X3),true,ifeq(true,true,s1(X2),true),true) = ifeq(s1(X3),true,ifeq(q0(X2,d),true,s1(X2),true),true),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,axiom,
ifeq(s1(H2),true,ifeq(q0(F2,G2),true,s1(F2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_126) ).
cnf(c234,plain,
ifeq(s1(X3),true,ifeq(q0(X2,d),true,s1(X2),true),true) = true,
inference(substitution,[status(thm)],[c233]) ).
cnf(c235,plain,
ifeq(s1(X3),true,ifeq(true,true,s1(X2),true),true) = true,
inference(transitivity,[status(thm)],[c232,c234]) ).
cnf(c236,plain,
ifeq(s1(X3),true,s1(X2),true) = true,
inference(transitivity,[status(thm)],[c228,c235]) ).
cnf(c237,plain,
ifeq(s1(b),true,s1(X2),true) = true,
inference(substitution,[status(thm)],[c236]) ).
cnf(c238,plain,
ifeq(true,true,s1(X2),true) = true,
inference(transitivity,[status(thm)],[c225,c237]) ).
cnf(c239,plain,
s1(X2) = true,
inference(transitivity,[status(thm)],[c223,c238]) ).
cnf(c240,plain,
s1(d) = true,
inference(substitution,[status(thm)],[c239]) ).
cnf(c241,plain,
true = s1(d),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
ifeq(true,true,ifeq(p0(X3,X3),true,ifeq(true,true,l2(X2,X2),true),true),true) = ifeq(s1(d),true,ifeq(p0(X3,X3),true,ifeq(true,true,l2(X2,X2),true),true),true),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
m0(X2,d,X3) = true,
inference(substitution,[status(thm)],[c192]) ).
cnf(c244,plain,
true = m0(X2,d,X3),
inference(symmetry,[status(thm)],[c243]) ).
cnf(c245,plain,
ifeq(true,true,l2(X3,X3),true) = ifeq(m0(X2,d,X3),true,l2(X3,X3),true),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
ifeq(p0(X4,X4),true,ifeq(true,true,l2(X3,X3),true),true) = ifeq(p0(X4,X4),true,ifeq(m0(X2,d,X3),true,l2(X3,X3),true),true),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
ifeq(s1(d),true,ifeq(p0(X4,X4),true,ifeq(true,true,l2(X3,X3),true),true),true) = ifeq(s1(d),true,ifeq(p0(X4,X4),true,ifeq(m0(X2,d,X3),true,l2(X3,X3),true),true),true),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,axiom,
ifeq(s1(B2),true,ifeq(p0(A2,A2),true,ifeq(m0(C2,B2,J2),true,l2(J2,J2),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_133) ).
cnf(c249,plain,
ifeq(s1(d),true,ifeq(p0(X4,X4),true,ifeq(m0(X2,d,X3),true,l2(X3,X3),true),true),true) = true,
inference(substitution,[status(thm)],[c248]) ).
cnf(c250,plain,
ifeq(s1(d),true,ifeq(p0(X3,X3),true,ifeq(true,true,l2(X2,X2),true),true),true) = true,
inference(transitivity,[status(thm)],[c247,c249]) ).
cnf(c251,plain,
ifeq(true,true,ifeq(p0(X3,X3),true,ifeq(true,true,l2(X2,X2),true),true),true) = true,
inference(transitivity,[status(thm)],[c242,c250]) ).
cnf(c252,plain,
ifeq(p0(X3,X3),true,ifeq(true,true,l2(X2,X2),true),true) = true,
inference(transitivity,[status(thm)],[c221,c251]) ).
cnf(c253,plain,
ifeq(p0(X3,X3),true,l2(X2,X2),true) = true,
inference(transitivity,[status(thm)],[c219,c252]) ).
cnf(c254,plain,
ifeq(p0(b,b),true,l2(X2,X2),true) = true,
inference(substitution,[status(thm)],[c253]) ).
cnf(c255,plain,
ifeq(true,true,l2(X2,X2),true) = true,
inference(transitivity,[status(thm)],[c216,c254]) ).
cnf(c256,plain,
l2(X2,X2) = true,
inference(transitivity,[status(thm)],[c213,c255]) ).
cnf(c257,plain,
true = l2(X2,X2),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
ifeq(true,true,m4(X3,X2),true) = ifeq(l2(X2,X2),true,m4(X3,X2),true),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
ifeq(s3(a,X3),true,ifeq(true,true,m4(X3,X2),true),true) = ifeq(s3(a,X3),true,ifeq(l2(X2,X2),true,m4(X3,X2),true),true),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,axiom,
ifeq(s3(a,E2),true,ifeq(l2(G2,F2),true,m4(E2,F2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_279) ).
cnf(c261,plain,
ifeq(s3(a,X3),true,ifeq(l2(X2,X2),true,m4(X3,X2),true),true) = true,
inference(substitution,[status(thm)],[c260]) ).
cnf(c262,plain,
ifeq(s3(a,X3),true,ifeq(true,true,m4(X3,X2),true),true) = true,
inference(transitivity,[status(thm)],[c259,c261]) ).
cnf(c263,plain,
ifeq(s3(a,X3),true,m4(X3,X2),true) = true,
inference(transitivity,[status(thm)],[c211,c262]) ).
cnf(c264,plain,
ifeq(true,true,m4(X3,X2),true) = true,
inference(transitivity,[status(thm)],[c208,c263]) ).
cnf(c265,plain,
m4(X3,X2) = true,
inference(transitivity,[status(thm)],[c6,c264]) ).
cnf(c266,plain,
m4(e,e) = true,
inference(substitution,[status(thm)],[c265]) ).
cnf(c267,plain,
true = m4(e,e),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c268,plain,
ifeq(true,true,m5(d,d),true) = ifeq(m4(e,e),true,m5(d,d),true),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
ifeq(true,true,ifeq(m4(e,e),true,m5(d,d),true),true) = ifeq(m4(e,e),true,m5(d,d),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c270,plain,
ifeq(m4(e,e),true,m5(d,d),true) = ifeq(true,true,ifeq(m4(e,e),true,m5(d,d),true),true),
inference(symmetry,[status(thm)],[c269]) ).
cnf(c271,plain,
ifeq(true,true,s4(d),true) = s4(d),
inference(substitution,[status(thm)],[c2]) ).
cnf(c272,plain,
s4(d) = ifeq(true,true,s4(d),true),
inference(symmetry,[status(thm)],[c271]) ).
cnf(c273,plain,
ifeq(true,true,p3(d,d,d),true) = p3(d,d,d),
inference(substitution,[status(thm)],[c2]) ).
cnf(c274,plain,
p3(d,d,d) = ifeq(true,true,p3(d,d,d),true),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
ifeq(true,true,k1(d),true) = k1(d),
inference(substitution,[status(thm)],[c2]) ).
cnf(c276,plain,
k1(d) = ifeq(true,true,k1(d),true),
inference(symmetry,[status(thm)],[c275]) ).
cnf(c277,axiom,
n0(c,d) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c278,plain,
true = n0(c,d),
inference(symmetry,[status(thm)],[c277]) ).
cnf(c279,plain,
ifeq(true,true,k1(d),true) = ifeq(n0(c,d),true,k1(d),true),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,axiom,
ifeq(n0(J2,I2),true,k1(I2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_001) ).
cnf(c281,plain,
ifeq(n0(c,d),true,k1(d),true) = true,
inference(substitution,[status(thm)],[c280]) ).
cnf(c282,plain,
ifeq(true,true,k1(d),true) = true,
inference(transitivity,[status(thm)],[c279,c281]) ).
cnf(c283,plain,
k1(d) = true,
inference(transitivity,[status(thm)],[c276,c282]) ).
cnf(c284,plain,
true = k1(d),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
ifeq(true,true,p3(d,d,d),true) = ifeq(k1(d),true,p3(d,d,d),true),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
ifeq(true,true,ifeq(k1(d),true,p3(d,d,d),true),true) = ifeq(k1(d),true,p3(d,d,d),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c287,plain,
ifeq(k1(d),true,p3(d,d,d),true) = ifeq(true,true,ifeq(k1(d),true,p3(d,d,d),true),true),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
q2(d,d,d) = true,
inference(substitution,[status(thm)],[c183]) ).
cnf(c289,plain,
true = q2(d,d,d),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c290,plain,
ifeq(true,true,ifeq(k1(d),true,p3(d,d,d),true),true) = ifeq(q2(d,d,d),true,ifeq(k1(d),true,p3(d,d,d),true),true),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,axiom,
ifeq(q2(F2,G2,E2),true,ifeq(k1(E2),true,p3(E2,E2,E2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_250) ).
cnf(c292,plain,
ifeq(q2(d,d,d),true,ifeq(k1(d),true,p3(d,d,d),true),true) = true,
inference(substitution,[status(thm)],[c291]) ).
cnf(c293,plain,
ifeq(true,true,ifeq(k1(d),true,p3(d,d,d),true),true) = true,
inference(transitivity,[status(thm)],[c290,c292]) ).
cnf(c294,plain,
ifeq(k1(d),true,p3(d,d,d),true) = true,
inference(transitivity,[status(thm)],[c287,c293]) ).
cnf(c295,plain,
ifeq(true,true,p3(d,d,d),true) = true,
inference(transitivity,[status(thm)],[c285,c294]) ).
cnf(c296,plain,
p3(d,d,d) = true,
inference(transitivity,[status(thm)],[c274,c295]) ).
cnf(c297,plain,
true = p3(d,d,d),
inference(symmetry,[status(thm)],[c296]) ).
cnf(c298,plain,
ifeq(true,true,s4(d),true) = ifeq(p3(d,d,d),true,s4(d),true),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
ifeq(true,true,s4(d),true) = s4(d),
inference(substitution,[status(thm)],[c2]) ).
cnf(c300,plain,
s4(d) = ifeq(true,true,s4(d),true),
inference(symmetry,[status(thm)],[c299]) ).
cnf(c301,plain,
ifeq(p3(X3,d,X2),true,s4(d),true) = ifeq(p3(X3,d,X2),true,ifeq(true,true,s4(d),true),true),
inference(congruence,[status(thm)],[c300]) ).
cnf(c302,plain,
ifeq(true,true,l1(d,d),true) = l1(d,d),
inference(substitution,[status(thm)],[c2]) ).
cnf(c303,plain,
l1(d,d) = ifeq(true,true,l1(d,d),true),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c304,plain,
true = n0(c,d),
inference(symmetry,[status(thm)],[c277]) ).
cnf(c305,plain,
ifeq(true,true,l1(d,d),true) = ifeq(n0(c,d),true,l1(d,d),true),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
ifeq(n0(c,d),true,l1(d,d),true) = true,
inference(substitution,[status(thm)],[c71]) ).
cnf(c307,plain,
ifeq(true,true,l1(d,d),true) = true,
inference(transitivity,[status(thm)],[c305,c306]) ).
cnf(c308,plain,
l1(d,d) = true,
inference(transitivity,[status(thm)],[c303,c307]) ).
cnf(c309,plain,
true = l1(d,d),
inference(symmetry,[status(thm)],[c308]) ).
cnf(c310,plain,
ifeq(true,true,s4(d),true) = ifeq(l1(d,d),true,s4(d),true),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
ifeq(p3(X3,d,X2),true,ifeq(true,true,s4(d),true),true) = ifeq(p3(X3,d,X2),true,ifeq(l1(d,d),true,s4(d),true),true),
inference(congruence,[status(thm)],[c310]) ).
cnf(c312,axiom,
ifeq(p3(B2,C2,D2),true,ifeq(l1(A2,C2),true,s4(A2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_299) ).
cnf(c313,plain,
ifeq(p3(X3,d,X2),true,ifeq(l1(d,d),true,s4(d),true),true) = true,
inference(substitution,[status(thm)],[c312]) ).
cnf(c314,plain,
ifeq(p3(X3,d,X2),true,ifeq(true,true,s4(d),true),true) = true,
inference(transitivity,[status(thm)],[c311,c313]) ).
cnf(c315,plain,
ifeq(p3(X3,d,X2),true,s4(d),true) = true,
inference(transitivity,[status(thm)],[c301,c314]) ).
cnf(c316,plain,
ifeq(p3(d,d,d),true,s4(d),true) = true,
inference(substitution,[status(thm)],[c315]) ).
cnf(c317,plain,
ifeq(true,true,s4(d),true) = true,
inference(transitivity,[status(thm)],[c298,c316]) ).
cnf(c318,plain,
s4(d) = true,
inference(transitivity,[status(thm)],[c272,c317]) ).
cnf(c319,plain,
true = s4(d),
inference(symmetry,[status(thm)],[c318]) ).
cnf(c320,plain,
ifeq(true,true,ifeq(m4(e,e),true,m5(d,d),true),true) = ifeq(s4(d),true,ifeq(m4(e,e),true,m5(d,d),true),true),
inference(congruence,[status(thm)],[c319]) ).
cnf(c321,axiom,
ifeq(s4(B2),true,ifeq(m4(e,e),true,m5(B2,B2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_305) ).
cnf(c322,plain,
ifeq(s4(d),true,ifeq(m4(e,e),true,m5(d,d),true),true) = true,
inference(substitution,[status(thm)],[c321]) ).
cnf(c323,plain,
ifeq(true,true,ifeq(m4(e,e),true,m5(d,d),true),true) = true,
inference(transitivity,[status(thm)],[c320,c322]) ).
cnf(c324,plain,
ifeq(m4(e,e),true,m5(d,d),true) = true,
inference(transitivity,[status(thm)],[c270,c323]) ).
cnf(c325,plain,
ifeq(true,true,m5(d,d),true) = true,
inference(transitivity,[status(thm)],[c268,c324]) ).
cnf(c326,plain,
m5(d,d) = true,
inference(transitivity,[status(thm)],[c4,c325]) ).
cnf(c327,plain,
$false,
inference(resolution,[status(thm)],[c1,c326]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN143-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.16 % Computer : n026.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Mon Sep 28 15:39:26 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.77/1.64 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 10.77/1.64
% 10.77/1.64 % SZS status Unsatisfiable
% 10.77/1.64
% 10.77/1.65 % SZS output start CNFRefutation
% See solution above
% 11.56/1.76
% 11.56/1.76 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------