%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL265-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 11:49:31 AM UTC 2026
% Result : Unsatisfiable 37.36s 5.26s
% Output : CNFRefutation 40.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 12
% Syntax : Number of clauses : 269 ( 269 unt; 0 nHn; 3 RR)
% Number of literals : 269 ( 268 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-4 aty)
% Number of variables : 487 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
theorem(equivalent(p,not(not(p)))) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c3,plain,
ifeq(true,true,theorem(equivalent(X2,not(not(X2)))),true) = theorem(equivalent(X2,not(not(X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
theorem(equivalent(X2,not(not(X2)))) = ifeq(true,true,theorem(equivalent(X2,not(not(X2)))),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
ifeq(true,true,ifeq(true,true,theorem(equivalent(X2,not(not(X2)))),true),true) = ifeq(true,true,theorem(equivalent(X2,not(not(X2)))),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
ifeq(true,true,theorem(equivalent(X2,not(not(X2)))),true) = ifeq(true,true,ifeq(true,true,theorem(equivalent(X2,not(not(X2)))),true),true),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,axiom,
implies(X,Y) = or(not(X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
cnf(c8,plain,
implies(implies(not(not(X2)),X2),equivalent(X2,not(not(X2)))) = or(not(implies(not(not(X2)),X2)),equivalent(X2,not(not(X2)))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
theorem(implies(implies(not(not(X2)),X2),equivalent(X2,not(not(X2))))) = theorem(or(not(implies(not(not(X2)),X2)),equivalent(X2,not(not(X2))))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
ifeq(true,true,theorem(or(not(implies(not(not(X2)),X2)),equivalent(X2,not(not(X2))))),true) = theorem(or(not(implies(not(not(X2)),X2)),equivalent(X2,not(not(X2))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c11,plain,
theorem(or(not(implies(not(not(X2)),X2)),equivalent(X2,not(not(X2))))) = ifeq(true,true,theorem(or(not(implies(not(not(X2)),X2)),equivalent(X2,not(not(X2))))),true),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
implies(X2,not(X3)) = or(not(X2),not(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c13,plain,
not(implies(X3,not(X2))) = not(or(not(X3),not(X2))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
and(P,Q) = not(or(not(P),not(Q))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_defn) ).
cnf(c15,plain,
and(X3,X2) = not(or(not(X3),not(X2))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
not(or(not(X3),not(X2))) = and(X3,X2),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
not(implies(X3,not(X2))) = and(X3,X2),
inference(transitivity,[status(thm)],[c13,c16]) ).
cnf(c18,plain,
and(X3,X2) = not(implies(X3,not(X2))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
or(and(X3,X2),X4) = or(not(implies(X3,not(X2))),X4),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
implies(implies(X4,not(X3)),X2) = or(not(implies(X4,not(X3))),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c21,plain,
or(not(implies(X4,not(X3))),X2) = implies(implies(X4,not(X3)),X2),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
or(and(X4,X3),X2) = implies(implies(X4,not(X3)),X2),
inference(transitivity,[status(thm)],[c19,c21]) ).
cnf(c23,plain,
or(and(implies(X4,X3),implies(X3,X4)),X2) = implies(implies(implies(X4,X3),not(implies(X3,X4))),X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
implies(implies(implies(X4,X3),not(implies(X3,X4))),X2) = or(and(implies(X4,X3),implies(X3,X4)),X2),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,axiom,
equivalent(P2,Q2) = and(implies(P2,Q2),implies(Q2,P2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalent_defn) ).
cnf(c26,plain,
equivalent(X3,X2) = and(implies(X3,X2),implies(X2,X3)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
and(implies(X3,X2),implies(X2,X3)) = equivalent(X3,X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
or(and(implies(X4,X3),implies(X3,X4)),X2) = or(equivalent(X4,X3),X2),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
implies(implies(implies(X4,X3),not(implies(X3,X4))),X2) = or(equivalent(X4,X3),X2),
inference(transitivity,[status(thm)],[c24,c28]) ).
cnf(c30,plain,
implies(implies(implies(X2,not(not(X2))),not(implies(not(not(X2)),X2))),not(implies(not(not(X2)),X2))) = or(equivalent(X2,not(not(X2))),not(implies(not(not(X2)),X2))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
or(equivalent(X2,not(not(X2))),not(implies(not(not(X2)),X2))) = implies(implies(implies(X2,not(not(X2))),not(implies(not(not(X2)),X2))),not(implies(not(not(X2)),X2))),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
theorem(or(equivalent(X2,not(not(X2))),not(implies(not(not(X2)),X2)))) = theorem(implies(implies(implies(X2,not(not(X2))),not(implies(not(not(X2)),X2))),not(implies(not(not(X2)),X2)))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
implies(X2,not(not(X2))) = or(not(X2),not(not(X2))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c34,plain,
implies(implies(X3,not(not(X3))),X2) = implies(or(not(X3),not(not(X3))),X2),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
implies(implies(implies(X3,not(not(X3))),X2),X2) = implies(implies(or(not(X3),not(not(X3))),X2),X2),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
theorem(implies(implies(implies(X3,not(not(X3))),X2),X2)) = theorem(implies(implies(or(not(X3),not(not(X3))),X2),X2)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
ifeq(true,true,theorem(implies(implies(or(X3,not(X3)),X2),X2)),true) = theorem(implies(implies(or(X3,not(X3)),X2),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c38,plain,
theorem(implies(implies(or(X3,not(X3)),X2),X2)) = ifeq(true,true,theorem(implies(implies(or(X3,not(X3)),X2),X2)),true),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
ifeq(true,true,theorem(implies(X3,implies(implies(X3,X2),X2))),true) = theorem(implies(X3,implies(implies(X3,X2),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c40,plain,
theorem(implies(X3,implies(implies(X3,X2),X2))) = ifeq(true,true,theorem(implies(X3,implies(implies(X3,X2),X2))),true),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
ifeq(true,true,theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true) = theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c42,plain,
theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))) = ifeq(true,true,theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
implies(X3,implies(X4,X2)) = or(not(X3),implies(X4,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c44,plain,
implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2))) = implies(implies(X4,implies(X3,X2)),or(not(X3),implies(X4,X2))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
axiom(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))) = axiom(implies(implies(X4,implies(X3,X2)),or(not(X3),implies(X4,X2)))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
implies(X3,X2) = or(not(X3),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c47,plain,
implies(X4,implies(X3,X2)) = implies(X4,or(not(X3),X2)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
implies(implies(X4,implies(X3,X2)),or(not(X3),implies(X4,X2))) = implies(implies(X4,or(not(X3),X2)),or(not(X3),implies(X4,X2))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
axiom(implies(implies(X4,implies(X3,X2)),or(not(X3),implies(X4,X2)))) = axiom(implies(implies(X4,or(not(X3),X2)),or(not(X3),implies(X4,X2)))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
implies(X3,X2) = or(not(X3),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c51,plain,
or(X3,implies(X4,X2)) = or(X3,or(not(X4),X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2))) = implies(implies(X4,or(X3,X2)),or(X3,or(not(X4),X2))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
axiom(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))) = axiom(implies(implies(X4,or(X3,X2)),or(X3,or(not(X4),X2)))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
implies(X4,or(X3,X2)) = or(not(X4),or(X3,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c55,plain,
implies(implies(X4,or(X3,X2)),or(X3,or(not(X4),X2))) = implies(or(not(X4),or(X3,X2)),or(X3,or(not(X4),X2))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
axiom(implies(implies(X4,or(X3,X2)),or(X3,or(not(X4),X2)))) = axiom(implies(or(not(X4),or(X3,X2)),or(X3,or(not(X4),X2)))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,axiom,
axiom(implies(or(A2,or(B2,C2)),or(B2,or(A2,C2)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
cnf(c58,plain,
axiom(implies(or(not(X4),or(X3,X2)),or(X3,or(not(X4),X2)))) = true,
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
axiom(implies(implies(X4,or(X3,X2)),or(X3,or(not(X4),X2)))) = true,
inference(transitivity,[status(thm)],[c56,c58]) ).
cnf(c60,plain,
axiom(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))) = true,
inference(transitivity,[status(thm)],[c53,c59]) ).
cnf(c61,plain,
axiom(implies(implies(X4,or(not(X3),X2)),or(not(X3),implies(X4,X2)))) = true,
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
axiom(implies(implies(X4,implies(X3,X2)),or(not(X3),implies(X4,X2)))) = true,
inference(transitivity,[status(thm)],[c49,c61]) ).
cnf(c63,plain,
axiom(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))) = true,
inference(transitivity,[status(thm)],[c45,c62]) ).
cnf(c64,plain,
true = axiom(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
ifeq(true,true,theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true) = ifeq(axiom(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true,theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,axiom,
ifeq(axiom(X2),true,theorem(X2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
cnf(c67,plain,
ifeq(axiom(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true,theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true) = true,
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
ifeq(true,true,theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true) = true,
inference(transitivity,[status(thm)],[c65,c67]) ).
cnf(c69,plain,
theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))) = true,
inference(transitivity,[status(thm)],[c42,c68]) ).
cnf(c70,plain,
theorem(implies(implies(implies(X3,X2),implies(X3,X2)),implies(X3,implies(implies(X3,X2),X2)))) = true,
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
true = theorem(implies(implies(implies(X3,X2),implies(X3,X2)),implies(X3,implies(implies(X3,X2),X2)))),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
ifeq(true,true,theorem(implies(X3,implies(implies(X3,X2),X2))),true) = ifeq(theorem(implies(implies(implies(X3,X2),implies(X3,X2)),implies(X3,implies(implies(X3,X2),X2)))),true,theorem(implies(X3,implies(implies(X3,X2),X2))),true),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
ifeq(true,true,theorem(X2),true) = theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c74,plain,
theorem(X2) = ifeq(true,true,theorem(X2),true),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
ifeq(theorem(implies(implies(X3,X3),X2)),true,theorem(X2),true) = ifeq(theorem(implies(implies(X3,X3),X2)),true,ifeq(true,true,theorem(X2),true),true),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
ifeq(true,true,theorem(implies(X2,X2)),true) = theorem(implies(X2,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c77,plain,
theorem(implies(X2,X2)) = ifeq(true,true,theorem(implies(X2,X2)),true),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
ifeq(true,true,theorem(or(X3,implies(X2,X2))),true) = theorem(or(X3,implies(X2,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c79,plain,
theorem(or(X3,implies(X2,X2))) = ifeq(true,true,theorem(or(X3,implies(X2,X2))),true),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
ifeq(true,true,theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true) = theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c81,plain,
theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))) = ifeq(true,true,theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
true = axiom(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c83,plain,
ifeq(true,true,theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true) = ifeq(axiom(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true,theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
ifeq(axiom(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true,theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true) = true,
inference(substitution,[status(thm)],[c66]) ).
cnf(c85,plain,
ifeq(true,true,theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))),true) = true,
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
theorem(implies(implies(X4,or(X3,X2)),or(X3,implies(X4,X2)))) = true,
inference(transitivity,[status(thm)],[c81,c85]) ).
cnf(c87,plain,
theorem(implies(implies(X2,or(X3,X2)),or(X3,implies(X2,X2)))) = true,
inference(substitution,[status(thm)],[c86]) ).
cnf(c88,plain,
true = theorem(implies(implies(X2,or(X3,X2)),or(X3,implies(X2,X2)))),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
ifeq(true,true,theorem(or(X3,implies(X2,X2))),true) = ifeq(theorem(implies(implies(X2,or(X3,X2)),or(X3,implies(X2,X2)))),true,theorem(or(X3,implies(X2,X2))),true),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
ifeq(true,true,theorem(X2),true) = theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c91,plain,
theorem(X2) = ifeq(true,true,theorem(X2),true),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
ifeq(theorem(implies(implies(X4,or(X3,X4)),X2)),true,theorem(X2),true) = ifeq(theorem(implies(implies(X4,or(X3,X4)),X2)),true,ifeq(true,true,theorem(X2),true),true),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
ifeq(true,true,theorem(implies(X3,or(X2,X3))),true) = theorem(implies(X3,or(X2,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c94,plain,
theorem(implies(X3,or(X2,X3))) = ifeq(true,true,theorem(implies(X3,or(X2,X3))),true),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,axiom,
axiom(implies(A2,or(B2,A2))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
cnf(c96,plain,
axiom(implies(X3,or(X2,X3))) = true,
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
true = axiom(implies(X3,or(X2,X3))),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
ifeq(true,true,theorem(implies(X3,or(X2,X3))),true) = ifeq(axiom(implies(X3,or(X2,X3))),true,theorem(implies(X3,or(X2,X3))),true),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
ifeq(axiom(implies(X3,or(X2,X3))),true,theorem(implies(X3,or(X2,X3))),true) = true,
inference(substitution,[status(thm)],[c66]) ).
cnf(c100,plain,
ifeq(true,true,theorem(implies(X3,or(X2,X3))),true) = true,
inference(transitivity,[status(thm)],[c98,c99]) ).
cnf(c101,plain,
theorem(implies(X3,or(X2,X3))) = true,
inference(transitivity,[status(thm)],[c94,c100]) ).
cnf(c102,plain,
true = theorem(implies(X3,or(X2,X3))),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
ifeq(true,true,theorem(X2),true) = ifeq(theorem(implies(X4,or(X3,X4))),true,theorem(X2),true),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
ifeq(theorem(implies(implies(X4,or(X3,X4)),X2)),true,ifeq(true,true,theorem(X2),true),true) = ifeq(theorem(implies(implies(X4,or(X3,X4)),X2)),true,ifeq(theorem(implies(X4,or(X3,X4))),true,theorem(X2),true),true),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,axiom,
ifeq(theorem(implies(Y2,X2)),true,ifeq(theorem(Y2),true,theorem(X2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
cnf(c106,plain,
ifeq(theorem(implies(implies(X4,or(X3,X4)),X2)),true,ifeq(theorem(implies(X4,or(X3,X4))),true,theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
ifeq(theorem(implies(implies(X4,or(X3,X4)),X2)),true,ifeq(true,true,theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c104,c106]) ).
cnf(c108,plain,
ifeq(theorem(implies(implies(X4,or(X3,X4)),X2)),true,theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c92,c107]) ).
cnf(c109,plain,
ifeq(theorem(implies(implies(X2,or(X3,X2)),or(X3,implies(X2,X2)))),true,theorem(or(X3,implies(X2,X2))),true) = true,
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
ifeq(true,true,theorem(or(X3,implies(X2,X2))),true) = true,
inference(transitivity,[status(thm)],[c89,c109]) ).
cnf(c111,plain,
theorem(or(X3,implies(X2,X2))) = true,
inference(transitivity,[status(thm)],[c79,c110]) ).
cnf(c112,plain,
theorem(or(implies(X2,X2),implies(X2,X2))) = true,
inference(substitution,[status(thm)],[c111]) ).
cnf(c113,plain,
true = theorem(or(implies(X2,X2),implies(X2,X2))),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
ifeq(true,true,theorem(implies(X2,X2)),true) = ifeq(theorem(or(implies(X2,X2),implies(X2,X2))),true,theorem(implies(X2,X2)),true),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
ifeq(true,true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true) = ifeq(theorem(or(X2,X2)),true,theorem(X2),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c116,plain,
ifeq(theorem(or(X2,X2)),true,theorem(X2),true) = ifeq(true,true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
ifeq(true,true,theorem(implies(or(X2,X2),X2)),true) = theorem(implies(or(X2,X2),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c118,plain,
theorem(implies(or(X2,X2),X2)) = ifeq(true,true,theorem(implies(or(X2,X2),X2)),true),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,axiom,
axiom(implies(or(A2,A2),A2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
cnf(c120,plain,
axiom(implies(or(X2,X2),X2)) = true,
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
true = axiom(implies(or(X2,X2),X2)),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
ifeq(true,true,theorem(implies(or(X2,X2),X2)),true) = ifeq(axiom(implies(or(X2,X2),X2)),true,theorem(implies(or(X2,X2),X2)),true),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
ifeq(axiom(implies(or(X2,X2),X2)),true,theorem(implies(or(X2,X2),X2)),true) = true,
inference(substitution,[status(thm)],[c66]) ).
cnf(c124,plain,
ifeq(true,true,theorem(implies(or(X2,X2),X2)),true) = true,
inference(transitivity,[status(thm)],[c122,c123]) ).
cnf(c125,plain,
theorem(implies(or(X2,X2),X2)) = true,
inference(transitivity,[status(thm)],[c118,c124]) ).
cnf(c126,plain,
true = theorem(implies(or(X2,X2),X2)),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
ifeq(true,true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true) = ifeq(theorem(implies(or(X2,X2),X2)),true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
ifeq(theorem(implies(or(X2,X2),X2)),true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c105]) ).
cnf(c129,plain,
ifeq(true,true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c127,c128]) ).
cnf(c130,plain,
ifeq(theorem(or(X2,X2)),true,theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c116,c129]) ).
cnf(c131,plain,
ifeq(theorem(or(implies(X2,X2),implies(X2,X2))),true,theorem(implies(X2,X2)),true) = true,
inference(substitution,[status(thm)],[c130]) ).
cnf(c132,plain,
ifeq(true,true,theorem(implies(X2,X2)),true) = true,
inference(transitivity,[status(thm)],[c114,c131]) ).
cnf(c133,plain,
theorem(implies(X2,X2)) = true,
inference(transitivity,[status(thm)],[c77,c132]) ).
cnf(c134,plain,
true = theorem(implies(X2,X2)),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c135,plain,
ifeq(true,true,theorem(X2),true) = ifeq(theorem(implies(X3,X3)),true,theorem(X2),true),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
ifeq(theorem(implies(implies(X3,X3),X2)),true,ifeq(true,true,theorem(X2),true),true) = ifeq(theorem(implies(implies(X3,X3),X2)),true,ifeq(theorem(implies(X3,X3)),true,theorem(X2),true),true),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
ifeq(theorem(implies(implies(X3,X3),X2)),true,ifeq(theorem(implies(X3,X3)),true,theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c105]) ).
cnf(c138,plain,
ifeq(theorem(implies(implies(X3,X3),X2)),true,ifeq(true,true,theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c136,c137]) ).
cnf(c139,plain,
ifeq(theorem(implies(implies(X3,X3),X2)),true,theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c75,c138]) ).
cnf(c140,plain,
ifeq(theorem(implies(implies(implies(X3,X2),implies(X3,X2)),implies(X3,implies(implies(X3,X2),X2)))),true,theorem(implies(X3,implies(implies(X3,X2),X2))),true) = true,
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
ifeq(true,true,theorem(implies(X3,implies(implies(X3,X2),X2))),true) = true,
inference(transitivity,[status(thm)],[c72,c140]) ).
cnf(c142,plain,
theorem(implies(X3,implies(implies(X3,X2),X2))) = true,
inference(transitivity,[status(thm)],[c40,c141]) ).
cnf(c143,plain,
theorem(implies(or(X3,not(X3)),implies(implies(or(X3,not(X3)),X2),X2))) = true,
inference(substitution,[status(thm)],[c142]) ).
cnf(c144,plain,
true = theorem(implies(or(X3,not(X3)),implies(implies(or(X3,not(X3)),X2),X2))),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
ifeq(true,true,theorem(implies(implies(or(X3,not(X3)),X2),X2)),true) = ifeq(theorem(implies(or(X3,not(X3)),implies(implies(or(X3,not(X3)),X2),X2))),true,theorem(implies(implies(or(X3,not(X3)),X2),X2)),true),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
ifeq(true,true,theorem(X2),true) = theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c147,plain,
theorem(X2) = ifeq(true,true,theorem(X2),true),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
ifeq(theorem(implies(or(X3,not(X3)),X2)),true,theorem(X2),true) = ifeq(theorem(implies(or(X3,not(X3)),X2)),true,ifeq(true,true,theorem(X2),true),true),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
ifeq(true,true,theorem(or(X2,not(X2))),true) = theorem(or(X2,not(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c150,plain,
theorem(or(X2,not(X2))) = ifeq(true,true,theorem(or(X2,not(X2))),true),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
true = theorem(implies(X2,X2)),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c152,plain,
ifeq(true,true,theorem(or(X2,not(X2))),true) = ifeq(theorem(implies(X2,X2)),true,theorem(or(X2,not(X2))),true),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
ifeq(true,true,ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true),true) = ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c154,plain,
ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true) = ifeq(true,true,ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true),true),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
implies(X3,X2) = or(not(X3),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c156,plain,
implies(implies(X3,X2),or(X2,not(X3))) = implies(or(not(X3),X2),or(X2,not(X3))),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
theorem(implies(implies(X3,X2),or(X2,not(X3)))) = theorem(implies(or(not(X3),X2),or(X2,not(X3)))),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
ifeq(true,true,theorem(implies(or(X3,X2),or(X2,X3))),true) = theorem(implies(or(X3,X2),or(X2,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c159,plain,
theorem(implies(or(X3,X2),or(X2,X3))) = ifeq(true,true,theorem(implies(or(X3,X2),or(X2,X3))),true),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,axiom,
axiom(implies(or(A2,B2),or(B2,A2))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
cnf(c161,plain,
axiom(implies(or(X3,X2),or(X2,X3))) = true,
inference(substitution,[status(thm)],[c160]) ).
cnf(c162,plain,
true = axiom(implies(or(X3,X2),or(X2,X3))),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
ifeq(true,true,theorem(implies(or(X3,X2),or(X2,X3))),true) = ifeq(axiom(implies(or(X3,X2),or(X2,X3))),true,theorem(implies(or(X3,X2),or(X2,X3))),true),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
ifeq(axiom(implies(or(X3,X2),or(X2,X3))),true,theorem(implies(or(X3,X2),or(X2,X3))),true) = true,
inference(substitution,[status(thm)],[c66]) ).
cnf(c165,plain,
ifeq(true,true,theorem(implies(or(X3,X2),or(X2,X3))),true) = true,
inference(transitivity,[status(thm)],[c163,c164]) ).
cnf(c166,plain,
theorem(implies(or(X3,X2),or(X2,X3))) = true,
inference(transitivity,[status(thm)],[c159,c165]) ).
cnf(c167,plain,
theorem(implies(or(not(X3),X2),or(X2,not(X3)))) = true,
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
theorem(implies(implies(X3,X2),or(X2,not(X3)))) = true,
inference(transitivity,[status(thm)],[c157,c167]) ).
cnf(c169,plain,
true = theorem(implies(implies(X3,X2),or(X2,not(X3)))),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
ifeq(true,true,ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true),true) = ifeq(theorem(implies(implies(X3,X2),or(X2,not(X3)))),true,ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true),true),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
ifeq(theorem(implies(implies(X3,X2),or(X2,not(X3)))),true,ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true),true) = true,
inference(substitution,[status(thm)],[c105]) ).
cnf(c172,plain,
ifeq(true,true,ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true),true) = true,
inference(transitivity,[status(thm)],[c170,c171]) ).
cnf(c173,plain,
ifeq(theorem(implies(X3,X2)),true,theorem(or(X2,not(X3))),true) = true,
inference(transitivity,[status(thm)],[c154,c172]) ).
cnf(c174,plain,
ifeq(theorem(implies(X2,X2)),true,theorem(or(X2,not(X2))),true) = true,
inference(substitution,[status(thm)],[c173]) ).
cnf(c175,plain,
ifeq(true,true,theorem(or(X2,not(X2))),true) = true,
inference(transitivity,[status(thm)],[c152,c174]) ).
cnf(c176,plain,
theorem(or(X2,not(X2))) = true,
inference(transitivity,[status(thm)],[c150,c175]) ).
cnf(c177,plain,
true = theorem(or(X2,not(X2))),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
ifeq(true,true,theorem(X2),true) = ifeq(theorem(or(X3,not(X3))),true,theorem(X2),true),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
ifeq(theorem(implies(or(X3,not(X3)),X2)),true,ifeq(true,true,theorem(X2),true),true) = ifeq(theorem(implies(or(X3,not(X3)),X2)),true,ifeq(theorem(or(X3,not(X3))),true,theorem(X2),true),true),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
ifeq(theorem(implies(or(X3,not(X3)),X2)),true,ifeq(theorem(or(X3,not(X3))),true,theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c105]) ).
cnf(c181,plain,
ifeq(theorem(implies(or(X3,not(X3)),X2)),true,ifeq(true,true,theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c179,c180]) ).
cnf(c182,plain,
ifeq(theorem(implies(or(X3,not(X3)),X2)),true,theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c148,c181]) ).
cnf(c183,plain,
ifeq(theorem(implies(or(X3,not(X3)),implies(implies(or(X3,not(X3)),X2),X2))),true,theorem(implies(implies(or(X3,not(X3)),X2),X2)),true) = true,
inference(substitution,[status(thm)],[c182]) ).
cnf(c184,plain,
ifeq(true,true,theorem(implies(implies(or(X3,not(X3)),X2),X2)),true) = true,
inference(transitivity,[status(thm)],[c145,c183]) ).
cnf(c185,plain,
theorem(implies(implies(or(X3,not(X3)),X2),X2)) = true,
inference(transitivity,[status(thm)],[c38,c184]) ).
cnf(c186,plain,
theorem(implies(implies(or(not(X3),not(not(X3))),X2),X2)) = true,
inference(substitution,[status(thm)],[c185]) ).
cnf(c187,plain,
theorem(implies(implies(implies(X3,not(not(X3))),X2),X2)) = true,
inference(transitivity,[status(thm)],[c36,c186]) ).
cnf(c188,plain,
theorem(implies(implies(implies(X2,not(not(X2))),not(implies(not(not(X2)),X2))),not(implies(not(not(X2)),X2)))) = true,
inference(substitution,[status(thm)],[c187]) ).
cnf(c189,plain,
theorem(or(equivalent(X2,not(not(X2))),not(implies(not(not(X2)),X2)))) = true,
inference(transitivity,[status(thm)],[c32,c188]) ).
cnf(c190,plain,
true = theorem(or(equivalent(X2,not(not(X2))),not(implies(not(not(X2)),X2)))),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
ifeq(true,true,theorem(or(not(implies(not(not(X2)),X2)),equivalent(X2,not(not(X2))))),true) = ifeq(theorem(or(equivalent(X2,not(not(X2))),not(implies(not(not(X2)),X2)))),true,theorem(or(not(implies(not(not(X2)),X2)),equivalent(X2,not(not(X2))))),true),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
ifeq(true,true,ifeq(theorem(or(X3,X2)),true,theorem(or(X2,X3)),true),true) = ifeq(theorem(or(X3,X2)),true,theorem(or(X2,X3)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c193,plain,
ifeq(theorem(or(X3,X2)),true,theorem(or(X2,X3)),true) = ifeq(true,true,ifeq(theorem(or(X3,X2)),true,theorem(or(X2,X3)),true),true),
inference(symmetry,[status(thm)],[c192]) ).
cnf(c194,plain,
true = theorem(implies(or(X3,X2),or(X2,X3))),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c195,plain,
ifeq(true,true,ifeq(theorem(or(X3,X2)),true,theorem(or(X2,X3)),true),true) = ifeq(theorem(implies(or(X3,X2),or(X2,X3))),true,ifeq(theorem(or(X3,X2)),true,theorem(or(X2,X3)),true),true),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
ifeq(theorem(implies(or(X3,X2),or(X2,X3))),true,ifeq(theorem(or(X3,X2)),true,theorem(or(X2,X3)),true),true) = true,
inference(substitution,[status(thm)],[c105]) ).
cnf(c197,plain,
ifeq(true,true,ifeq(theorem(or(X3,X2)),true,theorem(or(X2,X3)),true),true) = true,
inference(transitivity,[status(thm)],[c195,c196]) ).
cnf(c198,plain,
ifeq(theorem(or(X3,X2)),true,theorem(or(X2,X3)),true) = true,
inference(transitivity,[status(thm)],[c193,c197]) ).
cnf(c199,plain,
ifeq(theorem(or(equivalent(X2,not(not(X2))),not(implies(not(not(X2)),X2)))),true,theorem(or(not(implies(not(not(X2)),X2)),equivalent(X2,not(not(X2))))),true) = true,
inference(substitution,[status(thm)],[c198]) ).
cnf(c200,plain,
ifeq(true,true,theorem(or(not(implies(not(not(X2)),X2)),equivalent(X2,not(not(X2))))),true) = true,
inference(transitivity,[status(thm)],[c191,c199]) ).
cnf(c201,plain,
theorem(or(not(implies(not(not(X2)),X2)),equivalent(X2,not(not(X2))))) = true,
inference(transitivity,[status(thm)],[c11,c200]) ).
cnf(c202,plain,
theorem(implies(implies(not(not(X2)),X2),equivalent(X2,not(not(X2))))) = true,
inference(transitivity,[status(thm)],[c9,c201]) ).
cnf(c203,plain,
true = theorem(implies(implies(not(not(X2)),X2),equivalent(X2,not(not(X2))))),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
ifeq(true,true,ifeq(true,true,theorem(equivalent(X2,not(not(X2)))),true),true) = ifeq(theorem(implies(implies(not(not(X2)),X2),equivalent(X2,not(not(X2))))),true,ifeq(true,true,theorem(equivalent(X2,not(not(X2)))),true),true),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
implies(not(not(X2)),X2) = or(not(not(not(X2))),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c206,plain,
theorem(implies(not(not(X2)),X2)) = theorem(or(not(not(not(X2))),X2)),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
ifeq(true,true,theorem(or(not(not(not(X2))),X2)),true) = theorem(or(not(not(not(X2))),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c208,plain,
theorem(or(not(not(not(X2))),X2)) = ifeq(true,true,theorem(or(not(not(not(X2))),X2)),true),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
ifeq(true,true,theorem(or(X2,not(not(not(X2))))),true) = theorem(or(X2,not(not(not(X2))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c210,plain,
theorem(or(X2,not(not(not(X2))))) = ifeq(true,true,theorem(or(X2,not(not(not(X2))))),true),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
ifeq(true,true,theorem(implies(or(X3,X2),or(X3,not(not(X2))))),true) = theorem(implies(or(X3,X2),or(X3,not(not(X2))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c212,plain,
theorem(implies(or(X3,X2),or(X3,not(not(X2))))) = ifeq(true,true,theorem(implies(or(X3,X2),or(X3,not(not(X2))))),true),
inference(symmetry,[status(thm)],[c211]) ).
cnf(c213,plain,
ifeq(true,true,theorem(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))),true) = theorem(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c214,plain,
theorem(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))) = ifeq(true,true,theorem(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))),true),
inference(symmetry,[status(thm)],[c213]) ).
cnf(c215,axiom,
axiom(implies(implies(A2,B2),implies(or(C2,A2),or(C2,B2)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
cnf(c216,plain,
axiom(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))) = true,
inference(substitution,[status(thm)],[c215]) ).
cnf(c217,plain,
true = axiom(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
ifeq(true,true,theorem(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))),true) = ifeq(axiom(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))),true,theorem(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))),true),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
ifeq(axiom(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))),true,theorem(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))),true) = true,
inference(substitution,[status(thm)],[c66]) ).
cnf(c220,plain,
ifeq(true,true,theorem(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))),true) = true,
inference(transitivity,[status(thm)],[c218,c219]) ).
cnf(c221,plain,
theorem(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))) = true,
inference(transitivity,[status(thm)],[c214,c220]) ).
cnf(c222,plain,
theorem(implies(implies(X2,not(not(X2))),implies(or(X3,X2),or(X3,not(not(X2)))))) = true,
inference(substitution,[status(thm)],[c221]) ).
cnf(c223,plain,
true = theorem(implies(implies(X2,not(not(X2))),implies(or(X3,X2),or(X3,not(not(X2)))))),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
ifeq(true,true,theorem(implies(or(X3,X2),or(X3,not(not(X2))))),true) = ifeq(theorem(implies(implies(X2,not(not(X2))),implies(or(X3,X2),or(X3,not(not(X2)))))),true,theorem(implies(or(X3,X2),or(X3,not(not(X2))))),true),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
ifeq(true,true,theorem(X2),true) = theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c226,plain,
theorem(X2) = ifeq(true,true,theorem(X2),true),
inference(symmetry,[status(thm)],[c225]) ).
cnf(c227,plain,
ifeq(theorem(implies(implies(X3,not(not(X3))),X2)),true,theorem(X2),true) = ifeq(theorem(implies(implies(X3,not(not(X3))),X2)),true,ifeq(true,true,theorem(X2),true),true),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
implies(X2,not(not(X2))) = or(not(X2),not(not(X2))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c229,plain,
theorem(implies(X2,not(not(X2)))) = theorem(or(not(X2),not(not(X2)))),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
ifeq(true,true,theorem(or(not(X2),not(not(X2)))),true) = theorem(or(not(X2),not(not(X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c231,plain,
theorem(or(not(X2),not(not(X2)))) = ifeq(true,true,theorem(or(not(X2),not(not(X2)))),true),
inference(symmetry,[status(thm)],[c230]) ).
cnf(c232,plain,
theorem(implies(not(X2),not(X2))) = true,
inference(substitution,[status(thm)],[c133]) ).
cnf(c233,plain,
true = theorem(implies(not(X2),not(X2))),
inference(symmetry,[status(thm)],[c232]) ).
cnf(c234,plain,
ifeq(true,true,theorem(or(not(X2),not(not(X2)))),true) = ifeq(theorem(implies(not(X2),not(X2))),true,theorem(or(not(X2),not(not(X2)))),true),
inference(congruence,[status(thm)],[c233]) ).
cnf(c235,plain,
ifeq(theorem(implies(not(X2),not(X2))),true,theorem(or(not(X2),not(not(X2)))),true) = true,
inference(substitution,[status(thm)],[c173]) ).
cnf(c236,plain,
ifeq(true,true,theorem(or(not(X2),not(not(X2)))),true) = true,
inference(transitivity,[status(thm)],[c234,c235]) ).
cnf(c237,plain,
theorem(or(not(X2),not(not(X2)))) = true,
inference(transitivity,[status(thm)],[c231,c236]) ).
cnf(c238,plain,
theorem(implies(X2,not(not(X2)))) = true,
inference(transitivity,[status(thm)],[c229,c237]) ).
cnf(c239,plain,
true = theorem(implies(X2,not(not(X2)))),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
ifeq(true,true,theorem(X2),true) = ifeq(theorem(implies(X3,not(not(X3)))),true,theorem(X2),true),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
ifeq(theorem(implies(implies(X3,not(not(X3))),X2)),true,ifeq(true,true,theorem(X2),true),true) = ifeq(theorem(implies(implies(X3,not(not(X3))),X2)),true,ifeq(theorem(implies(X3,not(not(X3)))),true,theorem(X2),true),true),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
ifeq(theorem(implies(implies(X3,not(not(X3))),X2)),true,ifeq(theorem(implies(X3,not(not(X3)))),true,theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c105]) ).
cnf(c243,plain,
ifeq(theorem(implies(implies(X3,not(not(X3))),X2)),true,ifeq(true,true,theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c241,c242]) ).
cnf(c244,plain,
ifeq(theorem(implies(implies(X3,not(not(X3))),X2)),true,theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c227,c243]) ).
cnf(c245,plain,
ifeq(theorem(implies(implies(X2,not(not(X2))),implies(or(X3,X2),or(X3,not(not(X2)))))),true,theorem(implies(or(X3,X2),or(X3,not(not(X2))))),true) = true,
inference(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
ifeq(true,true,theorem(implies(or(X3,X2),or(X3,not(not(X2))))),true) = true,
inference(transitivity,[status(thm)],[c224,c245]) ).
cnf(c247,plain,
theorem(implies(or(X3,X2),or(X3,not(not(X2))))) = true,
inference(transitivity,[status(thm)],[c212,c246]) ).
cnf(c248,plain,
theorem(implies(or(X2,not(X2)),or(X2,not(not(not(X2)))))) = true,
inference(substitution,[status(thm)],[c247]) ).
cnf(c249,plain,
true = theorem(implies(or(X2,not(X2)),or(X2,not(not(not(X2)))))),
inference(symmetry,[status(thm)],[c248]) ).
cnf(c250,plain,
ifeq(true,true,theorem(or(X2,not(not(not(X2))))),true) = ifeq(theorem(implies(or(X2,not(X2)),or(X2,not(not(not(X2)))))),true,theorem(or(X2,not(not(not(X2))))),true),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
ifeq(theorem(implies(or(X2,not(X2)),or(X2,not(not(not(X2)))))),true,theorem(or(X2,not(not(not(X2))))),true) = true,
inference(substitution,[status(thm)],[c182]) ).
cnf(c252,plain,
ifeq(true,true,theorem(or(X2,not(not(not(X2))))),true) = true,
inference(transitivity,[status(thm)],[c250,c251]) ).
cnf(c253,plain,
theorem(or(X2,not(not(not(X2))))) = true,
inference(transitivity,[status(thm)],[c210,c252]) ).
cnf(c254,plain,
true = theorem(or(X2,not(not(not(X2))))),
inference(symmetry,[status(thm)],[c253]) ).
cnf(c255,plain,
ifeq(true,true,theorem(or(not(not(not(X2))),X2)),true) = ifeq(theorem(or(X2,not(not(not(X2))))),true,theorem(or(not(not(not(X2))),X2)),true),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
ifeq(theorem(or(X2,not(not(not(X2))))),true,theorem(or(not(not(not(X2))),X2)),true) = true,
inference(substitution,[status(thm)],[c198]) ).
cnf(c257,plain,
ifeq(true,true,theorem(or(not(not(not(X2))),X2)),true) = true,
inference(transitivity,[status(thm)],[c255,c256]) ).
cnf(c258,plain,
theorem(or(not(not(not(X2))),X2)) = true,
inference(transitivity,[status(thm)],[c208,c257]) ).
cnf(c259,plain,
theorem(implies(not(not(X2)),X2)) = true,
inference(transitivity,[status(thm)],[c206,c258]) ).
cnf(c260,plain,
true = theorem(implies(not(not(X2)),X2)),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
ifeq(true,true,theorem(equivalent(X2,not(not(X2)))),true) = ifeq(theorem(implies(not(not(X2)),X2)),true,theorem(equivalent(X2,not(not(X2)))),true),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
ifeq(theorem(implies(implies(not(not(X2)),X2),equivalent(X2,not(not(X2))))),true,ifeq(true,true,theorem(equivalent(X2,not(not(X2)))),true),true) = ifeq(theorem(implies(implies(not(not(X2)),X2),equivalent(X2,not(not(X2))))),true,ifeq(theorem(implies(not(not(X2)),X2)),true,theorem(equivalent(X2,not(not(X2)))),true),true),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
ifeq(theorem(implies(implies(not(not(X2)),X2),equivalent(X2,not(not(X2))))),true,ifeq(theorem(implies(not(not(X2)),X2)),true,theorem(equivalent(X2,not(not(X2)))),true),true) = true,
inference(substitution,[status(thm)],[c105]) ).
cnf(c264,plain,
ifeq(theorem(implies(implies(not(not(X2)),X2),equivalent(X2,not(not(X2))))),true,ifeq(true,true,theorem(equivalent(X2,not(not(X2)))),true),true) = true,
inference(transitivity,[status(thm)],[c262,c263]) ).
cnf(c265,plain,
ifeq(true,true,ifeq(true,true,theorem(equivalent(X2,not(not(X2)))),true),true) = true,
inference(transitivity,[status(thm)],[c204,c264]) ).
cnf(c266,plain,
ifeq(true,true,theorem(equivalent(X2,not(not(X2)))),true) = true,
inference(transitivity,[status(thm)],[c6,c265]) ).
cnf(c267,plain,
theorem(equivalent(X2,not(not(X2)))) = true,
inference(transitivity,[status(thm)],[c4,c266]) ).
cnf(c268,plain,
theorem(equivalent(p,not(not(p)))) = true,
inference(substitution,[status(thm)],[c267]) ).
cnf(c269,plain,
$false,
inference(resolution,[status(thm)],[c1,c268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL265-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 15:31:21 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.36/5.26 Command-line arguments: --flatten-regeneralise
% 37.36/5.26
% 37.36/5.26 % SZS status Unsatisfiable
% 37.36/5.26
% 38.22/5.29 % SZS output start CNFRefutation
% See solution above
% 40.02/5.54
% 40.02/5.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------