%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL890-10 : TPTP v9.3.1. Released v7.3.0.
% 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 11:50:44 AM UTC 2026
% Result : Unsatisfiable 98.45s 12.84s
% Output : CNFRefutation 99.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 17
% Syntax : Number of clauses : 347 ( 347 unt; 0 nHn; 25 RR)
% Number of literals : 347 ( 346 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 : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 659 ( 48 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
'>='(sK2_goals_14_X19,sK1_goals_14_X17) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14_2) ).
cnf(c2,axiom,
'+'(A,'0') = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
cnf(c3,plain,
'+'(sK2_goals_14_X19,'0') = sK2_goals_14_X19,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
sK2_goals_14_X19 = '+'(sK2_goals_14_X19,'0'),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
'>='(sK2_goals_14_X19,sK1_goals_14_X17) = '>='('+'(sK2_goals_14_X19,'0'),sK1_goals_14_X17),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
ifeq2(A2,A2,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c7,plain,
ifeq2(true,true,'==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))) = '==>'('+'(X17,X2),X),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
'==>'('+'(X17,X2),X) = ifeq2(true,true,'==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,axiom,
ifeq(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(c10,plain,
ifeq(true,true,'>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true) = '>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
'>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))) = ifeq(true,true,'>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,axiom,
'+'(A2,B2) = '+'(B2,A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
cnf(c13,plain,
'+'(X,X2) = '+'(X2,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
'+'(X2,X) = '+'(X,X2),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
'==>'('+'(X17,X2),X) = '==>'('+'(X2,X17),X),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
'+'(X17,'==>'('+'(X17,X2),X)) = '+'(X17,'==>'('+'(X2,X17),X)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
'>='('+'(X17,'==>'('+'(X17,X2),X)),'==>'(X2,X)) = '>='('+'(X17,'==>'('+'(X2,X17),X)),'==>'(X2,X)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
ifeq(true,true,'>='('+'(X17,'==>'('+'(X2,X17),X)),'==>'(X2,X)),true) = '>='('+'(X17,'==>'('+'(X2,X17),X)),'==>'(X2,X)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c19,plain,
'>='('+'(X17,'==>'('+'(X2,X17),X)),'==>'(X2,X)) = ifeq(true,true,'>='('+'(X17,'==>'('+'(X2,X17),X)),'==>'(X2,X)),true),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,axiom,
'+'('+'(A2,B2),C2) = '+'(A2,'+'(B2,C2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_01) ).
cnf(c21,plain,
'+'('+'(X17,X2),'==>'('+'(X17,X2),X)) = '+'(X17,'+'(X2,'==>'('+'(X17,X2),X))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
'+'(X17,'+'(X2,'==>'('+'(X17,X2),X))) = '+'('+'(X17,X2),'==>'('+'(X17,X2),X)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,axiom,
'+'(A2,'==>'(A2,B2)) = '+'(B2,'==>'(B2,A2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_13) ).
cnf(c24,plain,
'+'('+'(X17,X2),'==>'('+'(X17,X2),X)) = '+'(X,'==>'(X,'+'(X17,X2))),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
'+'(X17,'+'(X2,'==>'('+'(X17,X2),X))) = '+'(X,'==>'(X,'+'(X17,X2))),
inference(transitivity,[status(thm)],[c22,c24]) ).
cnf(c26,plain,
'>='('+'(X17,'+'(X2,'==>'('+'(X17,X2),X))),X) = '>='('+'(X,'==>'(X,'+'(X17,X2))),X),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
'+'(X,'==>'(X,X2)) = '+'(X2,'==>'(X2,X)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c28,plain,
'+'(X2,'==>'(X2,X)) = '+'(X,'==>'(X,X2)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
'>='('+'(X2,'==>'(X2,X)),X2) = '>='('+'(X,'==>'(X,X2)),X2),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
ifeq(true,true,'>='('+'(X,'==>'(X,X2)),X2),true) = '>='('+'(X,'==>'(X,X2)),X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c31,plain,
'>='('+'(X,'==>'(X,X2)),X2) = ifeq(true,true,'>='('+'(X,'==>'(X,X2)),X2),true),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,axiom,
'>='(A2,A2) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_05) ).
cnf(c33,plain,
'>='('==>'(X,X2),'==>'(X,X2)) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
true = '>='('==>'(X,X2),'==>'(X,X2)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
ifeq(true,true,'>='('+'(X,'==>'(X,X2)),X2),true) = ifeq('>='('==>'(X,X2),'==>'(X,X2)),true,'>='('+'(X,'==>'(X,X2)),X2),true),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,axiom,
ifeq('>='(X6,'==>'(X5,X7)),true,'>='('+'(X5,X6),X7),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
cnf(c37,plain,
ifeq('>='('==>'(X,X2),'==>'(X,X2)),true,'>='('+'(X,'==>'(X,X2)),X2),true) = true,
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
ifeq(true,true,'>='('+'(X,'==>'(X,X2)),X2),true) = true,
inference(transitivity,[status(thm)],[c35,c37]) ).
cnf(c39,plain,
'>='('+'(X,'==>'(X,X2)),X2) = true,
inference(transitivity,[status(thm)],[c31,c38]) ).
cnf(c40,plain,
'>='('+'(X2,'==>'(X2,X)),X2) = true,
inference(transitivity,[status(thm)],[c29,c39]) ).
cnf(c41,plain,
'>='('+'(X,'==>'(X,'+'(X17,X2))),X) = true,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
'>='('+'(X17,'+'(X2,'==>'('+'(X17,X2),X))),X) = true,
inference(transitivity,[status(thm)],[c26,c41]) ).
cnf(c43,plain,
'>='('+'(X2,'+'(X17,'==>'('+'(X2,X17),X))),X) = true,
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
true = '>='('+'(X2,'+'(X17,'==>'('+'(X2,X17),X))),X),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
ifeq(true,true,'>='('+'(X17,'==>'('+'(X2,X17),X)),'==>'(X2,X)),true) = ifeq('>='('+'(X2,'+'(X17,'==>'('+'(X2,X17),X))),X),true,'>='('+'(X17,'==>'('+'(X2,X17),X)),'==>'(X2,X)),true),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,axiom,
ifeq('>='('+'(X5_2,X6_2),X7_2),true,'>='(X6_2,'==>'(X5_2,X7_2)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08_1) ).
cnf(c47,plain,
ifeq('>='('+'(X2,'+'(X17,'==>'('+'(X2,X17),X))),X),true,'>='('+'(X17,'==>'('+'(X2,X17),X)),'==>'(X2,X)),true) = true,
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
ifeq(true,true,'>='('+'(X17,'==>'('+'(X2,X17),X)),'==>'(X2,X)),true) = true,
inference(transitivity,[status(thm)],[c45,c47]) ).
cnf(c49,plain,
'>='('+'(X17,'==>'('+'(X2,X17),X)),'==>'(X2,X)) = true,
inference(transitivity,[status(thm)],[c19,c48]) ).
cnf(c50,plain,
'>='('+'(X17,'==>'('+'(X17,X2),X)),'==>'(X2,X)) = true,
inference(transitivity,[status(thm)],[c17,c49]) ).
cnf(c51,plain,
true = '>='('+'(X17,'==>'('+'(X17,X2),X)),'==>'(X2,X)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
ifeq(true,true,'>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true) = ifeq('>='('+'(X17,'==>'('+'(X17,X2),X)),'==>'(X2,X)),true,'>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
ifeq('>='('+'(X17,'==>'('+'(X17,X2),X)),'==>'(X2,X)),true,'>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true) = true,
inference(substitution,[status(thm)],[c46]) ).
cnf(c54,plain,
ifeq(true,true,'>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true) = true,
inference(transitivity,[status(thm)],[c52,c53]) ).
cnf(c55,plain,
'>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))) = true,
inference(transitivity,[status(thm)],[c11,c54]) ).
cnf(c56,plain,
true = '>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
ifeq2(true,true,'==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))) = ifeq2('>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true,'==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
ifeq2(true,true,ifeq2('>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true,'==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),'==>'(X17,'==>'(X2,X))) = ifeq2('>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true,'==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c59,plain,
ifeq2('>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true,'==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))) = ifeq2(true,true,ifeq2('>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true,'==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),'==>'(X17,'==>'(X2,X))),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
ifeq(true,true,'>='('==>'(X17,'==>'(X2,X)),'==>'('+'(X17,X2),X)),true) = '>='('==>'(X17,'==>'(X2,X)),'==>'('+'(X17,X2),X)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c61,plain,
'>='('==>'(X17,'==>'(X2,X)),'==>'('+'(X17,X2),X)) = ifeq(true,true,'>='('==>'(X17,'==>'(X2,X)),'==>'('+'(X17,X2),X)),true),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
'+'('==>'(X17,X),'==>'('==>'(X17,X),X2)) = '+'(X2,'==>'(X2,'==>'(X17,X))),
inference(substitution,[status(thm)],[c23]) ).
cnf(c63,plain,
'+'(X2,'==>'(X2,'==>'(X17,X))) = '+'('==>'(X17,X),'==>'('==>'(X17,X),X2)),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
'+'(X17,'+'(X2,'==>'(X2,'==>'(X17,X)))) = '+'(X17,'+'('==>'(X17,X),'==>'('==>'(X17,X),X2))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
'>='('+'(X17,'+'(X2,'==>'(X2,'==>'(X17,X)))),X) = '>='('+'(X17,'+'('==>'(X17,X),'==>'('==>'(X17,X),X2))),X),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
'+'('+'(X,'==>'(X,X17)),X2) = '+'(X,'+'('==>'(X,X17),X2)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c67,plain,
'+'(X,'+'('==>'(X,X17),X2)) = '+'('+'(X,'==>'(X,X17)),X2),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
'+'(X2,'==>'(X2,X)) = '+'(X,'==>'(X,X2)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c69,plain,
'+'(X,'==>'(X,X2)) = '+'(X2,'==>'(X2,X)),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
'+'('+'(X,'==>'(X,X17)),X2) = '+'('+'(X17,'==>'(X17,X)),X2),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
'+'('+'(X17,'==>'(X17,X)),X2) = '+'(X17,'+'('==>'(X17,X),X2)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c72,plain,
'+'('==>'(X17,X),X2) = '+'(X2,'==>'(X17,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c73,plain,
'+'(X17,'+'('==>'(X17,X),X2)) = '+'(X17,'+'(X2,'==>'(X17,X))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
'+'('+'(X17,'==>'(X17,X)),X2) = '+'(X17,'+'(X2,'==>'(X17,X))),
inference(transitivity,[status(thm)],[c71,c73]) ).
cnf(c75,plain,
'+'('+'(X,'==>'(X,X17)),X2) = '+'(X17,'+'(X2,'==>'(X17,X))),
inference(transitivity,[status(thm)],[c70,c74]) ).
cnf(c76,plain,
'+'(X,'+'('==>'(X,X17),X2)) = '+'(X17,'+'(X2,'==>'(X17,X))),
inference(transitivity,[status(thm)],[c67,c75]) ).
cnf(c77,plain,
'+'(X17,'+'('==>'(X17,X2),X)) = '+'(X2,'+'(X,'==>'(X2,X17))),
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
'>='('+'(X17,'+'('==>'(X17,X2),X)),X2) = '>='('+'(X2,'+'(X,'==>'(X2,X17))),X2),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
'+'(X,X2) = '+'(X2,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c80,plain,
'+'(X2,X) = '+'(X,X2),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
'>='('+'(X2,X),X2) = '>='('+'(X,X2),X2),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
'+'(X,'0') = '+'('0',X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c83,plain,
'+'('0',X) = '+'(X,'0'),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
'+'(X,'0') = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c85,plain,
'+'('0',X) = X,
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
X = '+'('0',X),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
'>='('+'(X,X2),X2) = '>='('+'(X,X2),'+'('0',X2)),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
ifeq(true,true,'>='('+'(X,X2),'+'('0',X2)),true) = '>='('+'(X,X2),'+'('0',X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c89,plain,
'>='('+'(X,X2),'+'('0',X2)) = ifeq(true,true,'>='('+'(X,X2),'+'('0',X2)),true),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,axiom,
'>='(A2,'0') = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
cnf(c91,plain,
'>='(X,'0') = true,
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
true = '>='(X,'0'),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
ifeq(true,true,'>='('+'(X,X2),'+'('0',X2)),true) = ifeq('>='(X,'0'),true,'>='('+'(X,X2),'+'('0',X2)),true),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,axiom,
ifeq('>='(X8,X9),true,'>='('+'(X8,X10),'+'(X9,X10)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_10) ).
cnf(c95,plain,
ifeq('>='(X,'0'),true,'>='('+'(X,X2),'+'('0',X2)),true) = true,
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
ifeq(true,true,'>='('+'(X,X2),'+'('0',X2)),true) = true,
inference(transitivity,[status(thm)],[c93,c95]) ).
cnf(c97,plain,
'>='('+'(X,X2),'+'('0',X2)) = true,
inference(transitivity,[status(thm)],[c89,c96]) ).
cnf(c98,plain,
'>='('+'(X,X2),X2) = true,
inference(transitivity,[status(thm)],[c87,c97]) ).
cnf(c99,plain,
'>='('+'(X2,X),X2) = true,
inference(transitivity,[status(thm)],[c81,c98]) ).
cnf(c100,plain,
'>='('+'(X2,'+'(X,'==>'(X2,X17))),X2) = true,
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
'>='('+'(X17,'+'('==>'(X17,X2),X)),X2) = true,
inference(transitivity,[status(thm)],[c78,c100]) ).
cnf(c102,plain,
'>='('+'(X17,'+'('==>'(X17,X),'==>'('==>'(X17,X),X2))),X) = true,
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
'>='('+'(X17,'+'(X2,'==>'(X2,'==>'(X17,X)))),X) = true,
inference(transitivity,[status(thm)],[c65,c102]) ).
cnf(c104,plain,
'>='('+'(X2,'+'(X17,'==>'(X17,'==>'(X2,X)))),X) = true,
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
true = '>='('+'(X2,'+'(X17,'==>'(X17,'==>'(X2,X)))),X),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
ifeq(true,true,'>='('==>'(X17,'==>'(X2,X)),'==>'('+'(X17,X2),X)),true) = ifeq('>='('+'(X2,'+'(X17,'==>'(X17,'==>'(X2,X)))),X),true,'>='('==>'(X17,'==>'(X2,X)),'==>'('+'(X17,X2),X)),true),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
'+'(X,X2) = '+'(X2,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c108,plain,
'+'(X2,X) = '+'(X,X2),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
'+'(X17,'+'(X2,X)) = '+'(X17,'+'(X,X2)),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
'>='('+'(X17,'+'(X2,X)),X18) = '>='('+'(X17,'+'(X,X2)),X18),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
ifeq('>='('+'(X18,'+'(X17,X2)),X),true,'>='(X2,'==>'('+'(X17,X18),X)),true) = ifeq('>='('+'(X18,'+'(X2,X17)),X),true,'>='(X2,'==>'('+'(X17,X18),X)),true),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
'+'(X,X2) = '+'(X2,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c113,plain,
'+'(X2,X) = '+'(X,X2),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
'+'(X17,'+'(X2,X)) = '+'(X17,'+'(X,X2)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
'>='('+'(X18,'+'(X17,X2)),X) = '>='('+'(X18,'+'(X2,X17)),X),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
ifeq('>='('+'(X18,'+'(X17,X2)),X),true,'>='(X17,'==>'('+'(X2,X18),X)),true) = ifeq('>='('+'(X18,'+'(X2,X17)),X),true,'>='(X17,'==>'('+'(X2,X18),X)),true),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
'+'('+'(X2,X),X17) = '+'(X17,'+'(X2,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c118,plain,
'+'(X17,'+'(X2,X)) = '+'('+'(X2,X),X17),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
'+'('+'(X2,X),X17) = '+'(X2,'+'(X,X17)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c120,plain,
'+'(X,X2) = '+'(X2,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c121,plain,
'+'(X2,'+'(X,X17)) = '+'(X2,'+'(X17,X)),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
'+'('+'(X2,X),X17) = '+'(X2,'+'(X17,X)),
inference(transitivity,[status(thm)],[c119,c121]) ).
cnf(c123,plain,
'+'(X17,'+'(X2,X)) = '+'(X2,'+'(X17,X)),
inference(transitivity,[status(thm)],[c118,c122]) ).
cnf(c124,plain,
'+'(X,'+'(X17,X2)) = '+'(X17,'+'(X,X2)),
inference(substitution,[status(thm)],[c123]) ).
cnf(c125,plain,
'+'(X17,'+'(X,X2)) = '+'(X,'+'(X17,X2)),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
'>='('+'(X18,'+'(X2,X17)),X) = '>='('+'(X2,'+'(X18,X17)),X),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
ifeq('>='('+'(X18,'+'(X2,X17)),X),true,'>='(X17,'==>'('+'(X2,X18),X)),true) = ifeq('>='('+'(X2,'+'(X18,X17)),X),true,'>='(X17,'==>'('+'(X2,X18),X)),true),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
'+'('+'(X,X17),X2) = '+'(X,'+'(X17,X2)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c129,plain,
'+'(X,'+'(X17,X2)) = '+'('+'(X,X17),X2),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
'>='('+'(X2,'+'(X18,X17)),X) = '>='('+'('+'(X2,X18),X17),X),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
ifeq('>='('+'(X2,'+'(X18,X17)),X),true,'>='(X17,'==>'('+'(X2,X18),X)),true) = ifeq('>='('+'('+'(X2,X18),X17),X),true,'>='(X17,'==>'('+'(X2,X18),X)),true),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
ifeq('>='('+'('+'(X2,X18),X17),X),true,'>='(X17,'==>'('+'(X2,X18),X)),true) = true,
inference(substitution,[status(thm)],[c46]) ).
cnf(c133,plain,
ifeq('>='('+'(X2,'+'(X18,X17)),X),true,'>='(X17,'==>'('+'(X2,X18),X)),true) = true,
inference(transitivity,[status(thm)],[c131,c132]) ).
cnf(c134,plain,
ifeq('>='('+'(X18,'+'(X2,X17)),X),true,'>='(X17,'==>'('+'(X2,X18),X)),true) = true,
inference(transitivity,[status(thm)],[c127,c133]) ).
cnf(c135,plain,
ifeq('>='('+'(X18,'+'(X17,X2)),X),true,'>='(X17,'==>'('+'(X2,X18),X)),true) = true,
inference(transitivity,[status(thm)],[c116,c134]) ).
cnf(c136,plain,
ifeq('>='('+'(X18,'+'(X2,X17)),X),true,'>='(X2,'==>'('+'(X17,X18),X)),true) = true,
inference(substitution,[status(thm)],[c135]) ).
cnf(c137,plain,
ifeq('>='('+'(X18,'+'(X17,X2)),X),true,'>='(X2,'==>'('+'(X17,X18),X)),true) = true,
inference(transitivity,[status(thm)],[c111,c136]) ).
cnf(c138,plain,
ifeq('>='('+'(X2,'+'(X17,'==>'(X17,'==>'(X2,X)))),X),true,'>='('==>'(X17,'==>'(X2,X)),'==>'('+'(X17,X2),X)),true) = true,
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
ifeq(true,true,'>='('==>'(X17,'==>'(X2,X)),'==>'('+'(X17,X2),X)),true) = true,
inference(transitivity,[status(thm)],[c106,c138]) ).
cnf(c140,plain,
'>='('==>'(X17,'==>'(X2,X)),'==>'('+'(X17,X2),X)) = true,
inference(transitivity,[status(thm)],[c61,c139]) ).
cnf(c141,plain,
true = '>='('==>'(X17,'==>'(X2,X)),'==>'('+'(X17,X2),X)),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
ifeq2(true,true,ifeq2('>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true,'==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),'==>'(X17,'==>'(X2,X))) = ifeq2('>='('==>'(X17,'==>'(X2,X)),'==>'('+'(X17,X2),X)),true,ifeq2('>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true,'==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),'==>'(X17,'==>'(X2,X))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,axiom,
ifeq2('>='(X4,X3),true,ifeq2('>='(X3,X4),true,X3,X4),X4) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
cnf(c144,plain,
ifeq2('>='('==>'(X17,'==>'(X2,X)),'==>'('+'(X17,X2),X)),true,ifeq2('>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true,'==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),'==>'(X17,'==>'(X2,X))) = '==>'(X17,'==>'(X2,X)),
inference(substitution,[status(thm)],[c143]) ).
cnf(c145,plain,
ifeq2(true,true,ifeq2('>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true,'==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),'==>'(X17,'==>'(X2,X))) = '==>'(X17,'==>'(X2,X)),
inference(transitivity,[status(thm)],[c142,c144]) ).
cnf(c146,plain,
ifeq2('>='('==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))),true,'==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))) = '==>'(X17,'==>'(X2,X)),
inference(transitivity,[status(thm)],[c59,c145]) ).
cnf(c147,plain,
ifeq2(true,true,'==>'('+'(X17,X2),X),'==>'(X17,'==>'(X2,X))) = '==>'(X17,'==>'(X2,X)),
inference(transitivity,[status(thm)],[c57,c146]) ).
cnf(c148,plain,
'==>'('+'(X17,X2),X) = '==>'(X17,'==>'(X2,X)),
inference(transitivity,[status(thm)],[c8,c147]) ).
cnf(c149,plain,
'==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),sK1_goals_14_X17) = '==>'(sK2_goals_14_X19,'==>'('==>'(sK1_goals_14_X17,sK2_goals_14_X19),sK1_goals_14_X17)),
inference(substitution,[status(thm)],[c148]) ).
cnf(c150,plain,
'==>'(sK2_goals_14_X19,'==>'('==>'(sK1_goals_14_X17,sK2_goals_14_X19),sK1_goals_14_X17)) = '==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),sK1_goals_14_X17),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
'+'('0','==>'('0',X)) = '==>'('0',X),
inference(substitution,[status(thm)],[c85]) ).
cnf(c152,plain,
'==>'('0',X) = '+'('0','==>'('0',X)),
inference(symmetry,[status(thm)],[c151]) ).
cnf(c153,plain,
'+'(X,'==>'(X,'0')) = '+'('0','==>'('0',X)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c154,plain,
'+'('0','==>'('0',X)) = '+'(X,'==>'(X,'0')),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
ifeq2(true,true,ifeq2('>='('0',X),true,'0',X),X) = ifeq2('>='('0',X),true,'0',X),
inference(substitution,[status(thm)],[c6]) ).
cnf(c156,plain,
ifeq2('>='('0',X),true,'0',X) = ifeq2(true,true,ifeq2('>='('0',X),true,'0',X),X),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
'>='(X,'0') = true,
inference(substitution,[status(thm)],[c90]) ).
cnf(c158,plain,
true = '>='(X,'0'),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
ifeq2(true,true,ifeq2('>='('0',X),true,'0',X),X) = ifeq2('>='(X,'0'),true,ifeq2('>='('0',X),true,'0',X),X),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
ifeq2('>='(X,'0'),true,ifeq2('>='('0',X),true,'0',X),X) = X,
inference(substitution,[status(thm)],[c143]) ).
cnf(c161,plain,
ifeq2(true,true,ifeq2('>='('0',X),true,'0',X),X) = X,
inference(transitivity,[status(thm)],[c159,c160]) ).
cnf(c162,plain,
ifeq2('>='('0',X),true,'0',X) = X,
inference(transitivity,[status(thm)],[c156,c161]) ).
cnf(c163,plain,
ifeq2('>='('0','==>'(X,'0')),true,'0','==>'(X,'0')) = '==>'(X,'0'),
inference(substitution,[status(thm)],[c162]) ).
cnf(c164,plain,
'==>'(X,'0') = ifeq2('>='('0','==>'(X,'0')),true,'0','==>'(X,'0')),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
ifeq(true,true,'>='(X2,'==>'(X,'0')),true) = '>='(X2,'==>'(X,'0')),
inference(substitution,[status(thm)],[c9]) ).
cnf(c166,plain,
'>='(X2,'==>'(X,'0')) = ifeq(true,true,'>='(X2,'==>'(X,'0')),true),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
'>='('+'(X,X2),'0') = true,
inference(substitution,[status(thm)],[c90]) ).
cnf(c168,plain,
true = '>='('+'(X,X2),'0'),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
ifeq(true,true,'>='(X2,'==>'(X,'0')),true) = ifeq('>='('+'(X,X2),'0'),true,'>='(X2,'==>'(X,'0')),true),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
ifeq('>='('+'(X,X2),'0'),true,'>='(X2,'==>'(X,'0')),true) = true,
inference(substitution,[status(thm)],[c46]) ).
cnf(c171,plain,
ifeq(true,true,'>='(X2,'==>'(X,'0')),true) = true,
inference(transitivity,[status(thm)],[c169,c170]) ).
cnf(c172,plain,
'>='(X2,'==>'(X,'0')) = true,
inference(transitivity,[status(thm)],[c166,c171]) ).
cnf(c173,plain,
'>='('0','==>'(X,'0')) = true,
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
ifeq2('>='('0','==>'(X,'0')),true,'0','==>'(X,'0')) = ifeq2(true,true,'0','==>'(X,'0')),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
ifeq2(true,true,'0','==>'(X,'0')) = '0',
inference(substitution,[status(thm)],[c6]) ).
cnf(c176,plain,
ifeq2('>='('0','==>'(X,'0')),true,'0','==>'(X,'0')) = '0',
inference(transitivity,[status(thm)],[c174,c175]) ).
cnf(c177,plain,
'==>'(X,'0') = '0',
inference(transitivity,[status(thm)],[c164,c176]) ).
cnf(c178,plain,
'+'(X,'==>'(X,'0')) = '+'(X,'0'),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
'+'(X,'0') = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c180,plain,
'+'(X,'==>'(X,'0')) = X,
inference(transitivity,[status(thm)],[c178,c179]) ).
cnf(c181,plain,
'+'('0','==>'('0',X)) = X,
inference(transitivity,[status(thm)],[c154,c180]) ).
cnf(c182,plain,
'==>'('0',X) = X,
inference(transitivity,[status(thm)],[c152,c181]) ).
cnf(c183,plain,
'==>'('0','==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),sK1_goals_14_X17)) = '==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),sK1_goals_14_X17),
inference(substitution,[status(thm)],[c182]) ).
cnf(c184,plain,
'==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),sK1_goals_14_X17) = '==>'('0','==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),sK1_goals_14_X17)),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
ifeq2(true,true,'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0') = '==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c186,plain,
'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)) = ifeq2(true,true,'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
'>='('==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0') = true,
inference(substitution,[status(thm)],[c90]) ).
cnf(c188,plain,
true = '>='('==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
ifeq2(true,true,'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0') = ifeq2('>='('==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),true,'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
ifeq2(true,true,ifeq2('>='('==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),true,'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),'0') = ifeq2('>='('==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),true,'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),
inference(substitution,[status(thm)],[c6]) ).
cnf(c191,plain,
ifeq2('>='('==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),true,'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0') = ifeq2(true,true,ifeq2('>='('==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),true,'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),'0'),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
ifeq(true,true,'>='('0','==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18))),true) = '>='('0','==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c193,plain,
'>='('0','==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18))) = ifeq(true,true,'>='('0','==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18))),true),
inference(symmetry,[status(thm)],[c192]) ).
cnf(c194,plain,
ifeq(true,true,'>='('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),true) = '>='('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c195,plain,
'>='('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)) = ifeq(true,true,'>='('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),true),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
'+'(sK2_goals_14_X19,'+'(X,'==>'(X,sK2_goals_14_X19))) = '+'(X,'+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19))),
inference(substitution,[status(thm)],[c123]) ).
cnf(c197,plain,
'+'(X,'+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19))) = '+'(sK2_goals_14_X19,'+'(X,'==>'(X,sK2_goals_14_X19))),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c198,plain,
'>='('+'(X,'+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19))),sK3_goals_14_X18) = '>='('+'(sK2_goals_14_X19,'+'(X,'==>'(X,sK2_goals_14_X19))),sK3_goals_14_X18),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
'+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)) = '+'(X,'==>'(X,sK2_goals_14_X19)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c200,plain,
'+'(X,'==>'(X,sK2_goals_14_X19)) = '+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),
inference(symmetry,[status(thm)],[c199]) ).
cnf(c201,plain,
'+'(sK2_goals_14_X19,'+'(X,'==>'(X,sK2_goals_14_X19))) = '+'(sK2_goals_14_X19,'+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X))),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
'>='('+'(sK2_goals_14_X19,'+'(X,'==>'(X,sK2_goals_14_X19))),sK3_goals_14_X18) = '>='('+'(sK2_goals_14_X19,'+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X))),sK3_goals_14_X18),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
'+'('==>'(sK2_goals_14_X19,X),sK2_goals_14_X19) = '+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c204,plain,
'+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)) = '+'('==>'(sK2_goals_14_X19,X),sK2_goals_14_X19),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
'+'(sK2_goals_14_X19,'+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X))) = '+'(sK2_goals_14_X19,'+'('==>'(sK2_goals_14_X19,X),sK2_goals_14_X19)),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
'>='('+'(sK2_goals_14_X19,'+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X))),sK3_goals_14_X18) = '>='('+'(sK2_goals_14_X19,'+'('==>'(sK2_goals_14_X19,X),sK2_goals_14_X19)),sK3_goals_14_X18),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
'+'('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19) = '+'(sK2_goals_14_X19,'+'('==>'(sK2_goals_14_X19,X),sK2_goals_14_X19)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c208,plain,
'+'(sK2_goals_14_X19,'+'('==>'(sK2_goals_14_X19,X),sK2_goals_14_X19)) = '+'('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
'>='('+'(sK2_goals_14_X19,'+'('==>'(sK2_goals_14_X19,X),sK2_goals_14_X19)),sK3_goals_14_X18) = '>='('+'('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19),sK3_goals_14_X18),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
ifeq(true,true,'>='('+'('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19),sK3_goals_14_X18),true) = '>='('+'('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19),sK3_goals_14_X18),
inference(substitution,[status(thm)],[c9]) ).
cnf(c211,plain,
'>='('+'('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19),sK3_goals_14_X18) = ifeq(true,true,'>='('+'('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19),sK3_goals_14_X18),true),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
'>='('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19) = true,
inference(substitution,[status(thm)],[c40]) ).
cnf(c213,plain,
true = '>='('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
ifeq(true,true,'>='('+'('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19),sK3_goals_14_X18),true) = ifeq('>='('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19),true,'>='('+'('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19),sK3_goals_14_X18),true),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
'+'(sK2_goals_14_X19,X) = '+'(X,sK2_goals_14_X19),
inference(substitution,[status(thm)],[c12]) ).
cnf(c216,plain,
'+'(X,sK2_goals_14_X19) = '+'(sK2_goals_14_X19,X),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
'>='('+'(X,sK2_goals_14_X19),sK3_goals_14_X18) = '>='('+'(sK2_goals_14_X19,X),sK3_goals_14_X18),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
ifeq('>='(X,sK2_goals_14_X19),true,'>='('+'(X,sK2_goals_14_X19),sK3_goals_14_X18),true) = ifeq('>='(X,sK2_goals_14_X19),true,'>='('+'(sK2_goals_14_X19,X),sK3_goals_14_X18),true),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,axiom,
sK2_goals_14_X19 = '==>'(sK2_goals_14_X19,sK3_goals_14_X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c220,plain,
'>='(X,sK2_goals_14_X19) = '>='(X,'==>'(sK2_goals_14_X19,sK3_goals_14_X18)),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
ifeq('>='(X,sK2_goals_14_X19),true,'>='('+'(sK2_goals_14_X19,X),sK3_goals_14_X18),true) = ifeq('>='(X,'==>'(sK2_goals_14_X19,sK3_goals_14_X18)),true,'>='('+'(sK2_goals_14_X19,X),sK3_goals_14_X18),true),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
ifeq('>='(X,'==>'(sK2_goals_14_X19,sK3_goals_14_X18)),true,'>='('+'(sK2_goals_14_X19,X),sK3_goals_14_X18),true) = true,
inference(substitution,[status(thm)],[c36]) ).
cnf(c223,plain,
ifeq('>='(X,sK2_goals_14_X19),true,'>='('+'(sK2_goals_14_X19,X),sK3_goals_14_X18),true) = true,
inference(transitivity,[status(thm)],[c221,c222]) ).
cnf(c224,plain,
ifeq('>='(X,sK2_goals_14_X19),true,'>='('+'(X,sK2_goals_14_X19),sK3_goals_14_X18),true) = true,
inference(transitivity,[status(thm)],[c218,c223]) ).
cnf(c225,plain,
ifeq('>='('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19),true,'>='('+'('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19),sK3_goals_14_X18),true) = true,
inference(substitution,[status(thm)],[c224]) ).
cnf(c226,plain,
ifeq(true,true,'>='('+'('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19),sK3_goals_14_X18),true) = true,
inference(transitivity,[status(thm)],[c214,c225]) ).
cnf(c227,plain,
'>='('+'('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X)),sK2_goals_14_X19),sK3_goals_14_X18) = true,
inference(transitivity,[status(thm)],[c211,c226]) ).
cnf(c228,plain,
'>='('+'(sK2_goals_14_X19,'+'('==>'(sK2_goals_14_X19,X),sK2_goals_14_X19)),sK3_goals_14_X18) = true,
inference(transitivity,[status(thm)],[c209,c227]) ).
cnf(c229,plain,
'>='('+'(sK2_goals_14_X19,'+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,X))),sK3_goals_14_X18) = true,
inference(transitivity,[status(thm)],[c206,c228]) ).
cnf(c230,plain,
'>='('+'(sK2_goals_14_X19,'+'(X,'==>'(X,sK2_goals_14_X19))),sK3_goals_14_X18) = true,
inference(transitivity,[status(thm)],[c202,c229]) ).
cnf(c231,plain,
'>='('+'(X,'+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19))),sK3_goals_14_X18) = true,
inference(transitivity,[status(thm)],[c198,c230]) ).
cnf(c232,plain,
true = '>='('+'(X,'+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19))),sK3_goals_14_X18),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c233,plain,
ifeq(true,true,'>='('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),true) = ifeq('>='('+'(X,'+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19))),sK3_goals_14_X18),true,'>='('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),true),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
ifeq('>='('+'(X,'+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19))),sK3_goals_14_X18),true,'>='('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),true) = true,
inference(substitution,[status(thm)],[c46]) ).
cnf(c235,plain,
ifeq(true,true,'>='('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),true) = true,
inference(transitivity,[status(thm)],[c233,c234]) ).
cnf(c236,plain,
'>='('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)) = true,
inference(transitivity,[status(thm)],[c195,c235]) ).
cnf(c237,plain,
true = '>='('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),
inference(symmetry,[status(thm)],[c236]) ).
cnf(c238,plain,
ifeq(true,true,'>='('0','==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18))),true) = ifeq('>='('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),true,'>='('0','==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18))),true),
inference(congruence,[status(thm)],[c237]) ).
cnf(c239,plain,
'+'(X,'0') = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c240,plain,
X = '+'(X,'0'),
inference(symmetry,[status(thm)],[c239]) ).
cnf(c241,plain,
'>='(X2,X) = '>='('+'(X2,'0'),X),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
ifeq('>='(X2,X),true,'>='('0','==>'(X2,X)),true) = ifeq('>='('+'(X2,'0'),X),true,'>='('0','==>'(X2,X)),true),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
ifeq('>='('+'(X2,'0'),X),true,'>='('0','==>'(X2,X)),true) = true,
inference(substitution,[status(thm)],[c46]) ).
cnf(c244,plain,
ifeq('>='(X2,X),true,'>='('0','==>'(X2,X)),true) = true,
inference(transitivity,[status(thm)],[c242,c243]) ).
cnf(c245,plain,
ifeq('>='('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),true,'>='('0','==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18))),true) = true,
inference(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
ifeq(true,true,'>='('0','==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18))),true) = true,
inference(transitivity,[status(thm)],[c238,c245]) ).
cnf(c247,plain,
'>='('0','==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18))) = true,
inference(transitivity,[status(thm)],[c193,c246]) ).
cnf(c248,plain,
true = '>='('0','==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18))),
inference(symmetry,[status(thm)],[c247]) ).
cnf(c249,plain,
ifeq2(true,true,ifeq2('>='('==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),true,'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),'0') = ifeq2('>='('0','==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18))),true,ifeq2('>='('==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),true,'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),'0'),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
ifeq2('>='('0','==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18))),true,ifeq2('>='('==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),true,'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),'0') = '0',
inference(substitution,[status(thm)],[c143]) ).
cnf(c251,plain,
ifeq2(true,true,ifeq2('>='('==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),true,'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),'0') = '0',
inference(transitivity,[status(thm)],[c249,c250]) ).
cnf(c252,plain,
ifeq2('>='('==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0'),true,'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0') = '0',
inference(transitivity,[status(thm)],[c191,c251]) ).
cnf(c253,plain,
ifeq2(true,true,'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)),'0') = '0',
inference(transitivity,[status(thm)],[c189,c252]) ).
cnf(c254,plain,
'==>'('+'(sK2_goals_14_X19,'==>'(X,sK2_goals_14_X19)),'==>'(X,sK3_goals_14_X18)) = '0',
inference(transitivity,[status(thm)],[c186,c253]) ).
cnf(c255,plain,
'==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),'==>'(sK1_goals_14_X17,sK3_goals_14_X18)) = '0',
inference(substitution,[status(thm)],[c254]) ).
cnf(c256,plain,
'0' = '==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c257,plain,
'==>'('0','==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),sK1_goals_14_X17)) = '==>'('==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),sK1_goals_14_X17)),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
ifeq2(true,true,'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0') = '==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c259,plain,
'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)) = ifeq2(true,true,'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),
inference(symmetry,[status(thm)],[c258]) ).
cnf(c260,plain,
'>='('==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0') = true,
inference(substitution,[status(thm)],[c90]) ).
cnf(c261,plain,
true = '>='('==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),
inference(symmetry,[status(thm)],[c260]) ).
cnf(c262,plain,
ifeq2(true,true,'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0') = ifeq2('>='('==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),true,'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
ifeq2(true,true,ifeq2('>='('==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),true,'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),'0') = ifeq2('>='('==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),true,'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),
inference(substitution,[status(thm)],[c6]) ).
cnf(c264,plain,
ifeq2('>='('==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),true,'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0') = ifeq2(true,true,ifeq2('>='('==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),true,'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),'0'),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
ifeq(true,true,'>='('0','==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17))),true) = '>='('0','==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c266,plain,
'>='('0','==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17))) = ifeq(true,true,'>='('0','==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17))),true),
inference(symmetry,[status(thm)],[c265]) ).
cnf(c267,plain,
ifeq(true,true,'>='('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),true) = '>='('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c268,plain,
'>='('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)) = ifeq(true,true,'>='('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),true),
inference(symmetry,[status(thm)],[c267]) ).
cnf(c269,axiom,
'>='('==>'(sK1_goals_14_X17,sK3_goals_14_X18),sK1_goals_14_X17) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c270,plain,
true = '>='('==>'(sK1_goals_14_X17,sK3_goals_14_X18),sK1_goals_14_X17),
inference(symmetry,[status(thm)],[c269]) ).
cnf(c271,plain,
ifeq(true,true,'>='('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),true) = ifeq('>='('==>'(sK1_goals_14_X17,sK3_goals_14_X18),sK1_goals_14_X17),true,'>='('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),true),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,axiom,
ifeq('>='(X14,X15),true,'>='('==>'(X16,X14),'==>'(X16,X15)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
cnf(c273,plain,
ifeq('>='('==>'(sK1_goals_14_X17,sK3_goals_14_X18),sK1_goals_14_X17),true,'>='('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),true) = true,
inference(substitution,[status(thm)],[c272]) ).
cnf(c274,plain,
ifeq(true,true,'>='('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),true) = true,
inference(transitivity,[status(thm)],[c271,c273]) ).
cnf(c275,plain,
'>='('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)) = true,
inference(transitivity,[status(thm)],[c268,c274]) ).
cnf(c276,plain,
true = '>='('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),
inference(symmetry,[status(thm)],[c275]) ).
cnf(c277,plain,
ifeq(true,true,'>='('0','==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17))),true) = ifeq('>='('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),true,'>='('0','==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17))),true),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
ifeq('>='('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),true,'>='('0','==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17))),true) = true,
inference(substitution,[status(thm)],[c244]) ).
cnf(c279,plain,
ifeq(true,true,'>='('0','==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17))),true) = true,
inference(transitivity,[status(thm)],[c277,c278]) ).
cnf(c280,plain,
'>='('0','==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17))) = true,
inference(transitivity,[status(thm)],[c266,c279]) ).
cnf(c281,plain,
true = '>='('0','==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17))),
inference(symmetry,[status(thm)],[c280]) ).
cnf(c282,plain,
ifeq2(true,true,ifeq2('>='('==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),true,'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),'0') = ifeq2('>='('0','==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17))),true,ifeq2('>='('==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),true,'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),'0'),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
ifeq2('>='('0','==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17))),true,ifeq2('>='('==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),true,'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),'0') = '0',
inference(substitution,[status(thm)],[c143]) ).
cnf(c284,plain,
ifeq2(true,true,ifeq2('>='('==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),true,'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),'0') = '0',
inference(transitivity,[status(thm)],[c282,c283]) ).
cnf(c285,plain,
ifeq2('>='('==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0'),true,'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0') = '0',
inference(transitivity,[status(thm)],[c264,c284]) ).
cnf(c286,plain,
ifeq2(true,true,'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)),'0') = '0',
inference(transitivity,[status(thm)],[c262,c285]) ).
cnf(c287,plain,
'==>'('==>'(X,'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'(X,sK1_goals_14_X17)) = '0',
inference(transitivity,[status(thm)],[c259,c286]) ).
cnf(c288,plain,
'==>'('==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),'==>'(sK1_goals_14_X17,sK3_goals_14_X18)),'==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),sK1_goals_14_X17)) = '0',
inference(substitution,[status(thm)],[c287]) ).
cnf(c289,plain,
'==>'('0','==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),sK1_goals_14_X17)) = '0',
inference(transitivity,[status(thm)],[c257,c288]) ).
cnf(c290,plain,
'==>'('+'(sK2_goals_14_X19,'==>'(sK1_goals_14_X17,sK2_goals_14_X19)),sK1_goals_14_X17) = '0',
inference(transitivity,[status(thm)],[c184,c289]) ).
cnf(c291,plain,
'==>'(sK2_goals_14_X19,'==>'('==>'(sK1_goals_14_X17,sK2_goals_14_X19),sK1_goals_14_X17)) = '0',
inference(transitivity,[status(thm)],[c150,c290]) ).
cnf(c292,plain,
'0' = '==>'(sK2_goals_14_X19,'==>'('==>'(sK1_goals_14_X17,sK2_goals_14_X19),sK1_goals_14_X17)),
inference(symmetry,[status(thm)],[c291]) ).
cnf(c293,plain,
'+'(sK2_goals_14_X19,'0') = '+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,'==>'('==>'(sK1_goals_14_X17,sK2_goals_14_X19),sK1_goals_14_X17))),
inference(congruence,[status(thm)],[c292]) ).
cnf(c294,plain,
'>='('+'(sK2_goals_14_X19,'0'),sK1_goals_14_X17) = '>='('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,'==>'('==>'(sK1_goals_14_X17,sK2_goals_14_X19),sK1_goals_14_X17))),sK1_goals_14_X17),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
ifeq(true,true,'>='('+'(X2,'==>'(X2,'==>'('==>'(X,X2),X))),X),true) = '>='('+'(X2,'==>'(X2,'==>'('==>'(X,X2),X))),X),
inference(substitution,[status(thm)],[c9]) ).
cnf(c296,plain,
'>='('+'(X2,'==>'(X2,'==>'('==>'(X,X2),X))),X) = ifeq(true,true,'>='('+'(X2,'==>'(X2,'==>'('==>'(X,X2),X))),X),true),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
ifeq(true,true,'>='('==>'('==>'(X18,X17),X2),'==>'('==>'('==>'(X,X18),X17),X2)),true) = '>='('==>'('==>'(X18,X17),X2),'==>'('==>'('==>'(X,X18),X17),X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c298,plain,
'>='('==>'('==>'(X18,X17),X2),'==>'('==>'('==>'(X,X18),X17),X2)) = ifeq(true,true,'>='('==>'('==>'(X18,X17),X2),'==>'('==>'('==>'(X,X18),X17),X2)),true),
inference(symmetry,[status(thm)],[c297]) ).
cnf(c299,plain,
X = '==>'('0',X),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c300,plain,
'==>'(X2,X) = '==>'('==>'('0',X2),X),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
'>='('==>'('==>'(X17,X2),X),'==>'(X2,X)) = '>='('==>'('==>'(X17,X2),X),'==>'('==>'('0',X2),X)),
inference(congruence,[status(thm)],[c300]) ).
cnf(c302,plain,
ifeq(true,true,'>='('==>'('==>'(X17,X2),X),'==>'('==>'('0',X2),X)),true) = '>='('==>'('==>'(X17,X2),X),'==>'('==>'('0',X2),X)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c303,plain,
'>='('==>'('==>'(X17,X2),X),'==>'('==>'('0',X2),X)) = ifeq(true,true,'>='('==>'('==>'(X17,X2),X),'==>'('==>'('0',X2),X)),true),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c304,plain,
ifeq(true,true,'>='('==>'('0',X2),'==>'(X,X2)),true) = '>='('==>'('0',X2),'==>'(X,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c305,plain,
'>='('==>'('0',X2),'==>'(X,X2)) = ifeq(true,true,'>='('==>'('0',X2),'==>'(X,X2)),true),
inference(symmetry,[status(thm)],[c304]) ).
cnf(c306,plain,
'>='(X,'0') = true,
inference(substitution,[status(thm)],[c90]) ).
cnf(c307,plain,
true = '>='(X,'0'),
inference(symmetry,[status(thm)],[c306]) ).
cnf(c308,plain,
ifeq(true,true,'>='('==>'('0',X2),'==>'(X,X2)),true) = ifeq('>='(X,'0'),true,'>='('==>'('0',X2),'==>'(X,X2)),true),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,axiom,
ifeq('>='(X11,X12),true,'>='('==>'(X12,X13),'==>'(X11,X13)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_11) ).
cnf(c310,plain,
ifeq('>='(X,'0'),true,'>='('==>'('0',X2),'==>'(X,X2)),true) = true,
inference(substitution,[status(thm)],[c309]) ).
cnf(c311,plain,
ifeq(true,true,'>='('==>'('0',X2),'==>'(X,X2)),true) = true,
inference(transitivity,[status(thm)],[c308,c310]) ).
cnf(c312,plain,
'>='('==>'('0',X2),'==>'(X,X2)) = true,
inference(transitivity,[status(thm)],[c305,c311]) ).
cnf(c313,plain,
'>='('==>'('0',X),'==>'(X2,X)) = true,
inference(substitution,[status(thm)],[c312]) ).
cnf(c314,plain,
true = '>='('==>'('0',X),'==>'(X2,X)),
inference(symmetry,[status(thm)],[c313]) ).
cnf(c315,plain,
ifeq(true,true,'>='('==>'('==>'(X17,X2),X),'==>'('==>'('0',X2),X)),true) = ifeq('>='('==>'('0',X2),'==>'(X17,X2)),true,'>='('==>'('==>'(X17,X2),X),'==>'('==>'('0',X2),X)),true),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
ifeq('>='('==>'('0',X2),'==>'(X17,X2)),true,'>='('==>'('==>'(X17,X2),X),'==>'('==>'('0',X2),X)),true) = true,
inference(substitution,[status(thm)],[c309]) ).
cnf(c317,plain,
ifeq(true,true,'>='('==>'('==>'(X17,X2),X),'==>'('==>'('0',X2),X)),true) = true,
inference(transitivity,[status(thm)],[c315,c316]) ).
cnf(c318,plain,
'>='('==>'('==>'(X17,X2),X),'==>'('==>'('0',X2),X)) = true,
inference(transitivity,[status(thm)],[c303,c317]) ).
cnf(c319,plain,
'>='('==>'('==>'(X17,X2),X),'==>'(X2,X)) = true,
inference(transitivity,[status(thm)],[c301,c318]) ).
cnf(c320,plain,
'>='('==>'('==>'(X,X17),X2),'==>'(X17,X2)) = true,
inference(substitution,[status(thm)],[c319]) ).
cnf(c321,plain,
true = '>='('==>'('==>'(X,X17),X2),'==>'(X17,X2)),
inference(symmetry,[status(thm)],[c320]) ).
cnf(c322,plain,
ifeq(true,true,'>='('==>'('==>'(X18,X17),X2),'==>'('==>'('==>'(X,X18),X17),X2)),true) = ifeq('>='('==>'('==>'(X,X18),X17),'==>'(X18,X17)),true,'>='('==>'('==>'(X18,X17),X2),'==>'('==>'('==>'(X,X18),X17),X2)),true),
inference(congruence,[status(thm)],[c321]) ).
cnf(c323,plain,
ifeq('>='('==>'('==>'(X,X18),X17),'==>'(X18,X17)),true,'>='('==>'('==>'(X18,X17),X2),'==>'('==>'('==>'(X,X18),X17),X2)),true) = true,
inference(substitution,[status(thm)],[c309]) ).
cnf(c324,plain,
ifeq(true,true,'>='('==>'('==>'(X18,X17),X2),'==>'('==>'('==>'(X,X18),X17),X2)),true) = true,
inference(transitivity,[status(thm)],[c322,c323]) ).
cnf(c325,plain,
'>='('==>'('==>'(X18,X17),X2),'==>'('==>'('==>'(X,X18),X17),X2)) = true,
inference(transitivity,[status(thm)],[c298,c324]) ).
cnf(c326,plain,
'>='('==>'('==>'(X,X2),X),'==>'('==>'('==>'('==>'(X,X2),X),X2),X)) = true,
inference(substitution,[status(thm)],[c325]) ).
cnf(c327,plain,
true = '>='('==>'('==>'(X,X2),X),'==>'('==>'('==>'('==>'(X,X2),X),X2),X)),
inference(symmetry,[status(thm)],[c326]) ).
cnf(c328,plain,
ifeq(true,true,'>='('+'(X2,'==>'(X2,'==>'('==>'(X,X2),X))),X),true) = ifeq('>='('==>'('==>'(X,X2),X),'==>'('==>'('==>'('==>'(X,X2),X),X2),X)),true,'>='('+'(X2,'==>'(X2,'==>'('==>'(X,X2),X))),X),true),
inference(congruence,[status(thm)],[c327]) ).
cnf(c329,plain,
'+'(X2,'==>'(X2,X)) = '+'(X,'==>'(X,X2)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c330,plain,
'+'(X,'==>'(X,X2)) = '+'(X2,'==>'(X2,X)),
inference(symmetry,[status(thm)],[c329]) ).
cnf(c331,plain,
'>='('+'(X2,'==>'(X2,X17)),X) = '>='('+'(X17,'==>'(X17,X2)),X),
inference(congruence,[status(thm)],[c330]) ).
cnf(c332,plain,
ifeq('>='(X17,'==>'('==>'(X17,X2),X)),true,'>='('+'(X2,'==>'(X2,X17)),X),true) = ifeq('>='(X17,'==>'('==>'(X17,X2),X)),true,'>='('+'(X17,'==>'(X17,X2)),X),true),
inference(congruence,[status(thm)],[c331]) ).
cnf(c333,plain,
'+'(X,X2) = '+'(X2,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c334,plain,
'+'(X2,X) = '+'(X,X2),
inference(symmetry,[status(thm)],[c333]) ).
cnf(c335,plain,
'>='('+'(X17,X2),X) = '>='('+'(X2,X17),X),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
ifeq('>='(X17,'==>'(X2,X)),true,'>='('+'(X17,X2),X),true) = ifeq('>='(X17,'==>'(X2,X)),true,'>='('+'(X2,X17),X),true),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
ifeq('>='(X17,'==>'(X2,X)),true,'>='('+'(X2,X17),X),true) = true,
inference(substitution,[status(thm)],[c36]) ).
cnf(c338,plain,
ifeq('>='(X17,'==>'(X2,X)),true,'>='('+'(X17,X2),X),true) = true,
inference(transitivity,[status(thm)],[c336,c337]) ).
cnf(c339,plain,
ifeq('>='(X17,'==>'('==>'(X17,X2),X)),true,'>='('+'(X17,'==>'(X17,X2)),X),true) = true,
inference(substitution,[status(thm)],[c338]) ).
cnf(c340,plain,
ifeq('>='(X17,'==>'('==>'(X17,X2),X)),true,'>='('+'(X2,'==>'(X2,X17)),X),true) = true,
inference(transitivity,[status(thm)],[c332,c339]) ).
cnf(c341,plain,
ifeq('>='('==>'('==>'(X,X2),X),'==>'('==>'('==>'('==>'(X,X2),X),X2),X)),true,'>='('+'(X2,'==>'(X2,'==>'('==>'(X,X2),X))),X),true) = true,
inference(substitution,[status(thm)],[c340]) ).
cnf(c342,plain,
ifeq(true,true,'>='('+'(X2,'==>'(X2,'==>'('==>'(X,X2),X))),X),true) = true,
inference(transitivity,[status(thm)],[c328,c341]) ).
cnf(c343,plain,
'>='('+'(X2,'==>'(X2,'==>'('==>'(X,X2),X))),X) = true,
inference(transitivity,[status(thm)],[c296,c342]) ).
cnf(c344,plain,
'>='('+'(sK2_goals_14_X19,'==>'(sK2_goals_14_X19,'==>'('==>'(sK1_goals_14_X17,sK2_goals_14_X19),sK1_goals_14_X17))),sK1_goals_14_X17) = true,
inference(substitution,[status(thm)],[c343]) ).
cnf(c345,plain,
'>='('+'(sK2_goals_14_X19,'0'),sK1_goals_14_X17) = true,
inference(transitivity,[status(thm)],[c294,c344]) ).
cnf(c346,plain,
'>='(sK2_goals_14_X19,sK1_goals_14_X17) = true,
inference(transitivity,[status(thm)],[c5,c345]) ).
cnf(c347,plain,
$false,
inference(resolution,[status(thm)],[c1,c346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL890-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 17:06:53 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 98.45/12.84 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
% 98.45/12.84
% 98.45/12.84 % SZS status Unsatisfiable
% 98.45/12.84
% 98.45/12.85 % SZS output start CNFRefutation
% See solution above
% 99.27/13.04
% 99.27/13.04 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------