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Twee---2.7.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL203-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 11:49:19 AM UTC 2026

% Result   : Unsatisfiable 18.14s 2.84s
% Output   : CNFRefutation 18.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   43
%            Number of leaves      :   10
% Syntax   : Number of clauses     :  209 ( 209 unt;   0 nHn;   3 RR)
%            Number of literals    :  209 ( 208 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-4 aty)
%            Number of variables   :  472 (  39 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
    theorem(implies(not(or(p,q)),or(not(p),not(q)))) != 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(implies(not(or(X4,X3)),or(X2,not(X3)))),true) = theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c4,plain,
    theorem(implies(not(or(X4,X3)),or(X2,not(X3)))) = ifeq(true,true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),true),
    inference(symmetry,[status(thm)],[c3]) ).

cnf(c5,plain,
    ifeq(true,true,ifeq(true,true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),true),true) = ifeq(true,true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c6,plain,
    ifeq(true,true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),true) = ifeq(true,true,ifeq(true,true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),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(X4,or(X2,X3)) = or(not(X4),or(X2,X3)),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c9,plain,
    or(not(or(not(X4),X3)),implies(X4,or(X2,X3))) = or(not(or(not(X4),X3)),or(not(X4),or(X2,X3))),
    inference(congruence,[status(thm)],[c8]) ).

cnf(c10,plain,
    theorem(or(not(or(not(X4),X3)),implies(X4,or(X2,X3)))) = theorem(or(not(or(not(X4),X3)),or(not(X4),or(X2,X3)))),
    inference(congruence,[status(thm)],[c9]) ).

cnf(c11,plain,
    ifeq(true,true,theorem(or(not(or(X4,X3)),or(X4,or(X2,X3)))),true) = theorem(or(not(or(X4,X3)),or(X4,or(X2,X3)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c12,plain,
    theorem(or(not(or(X4,X3)),or(X4,or(X2,X3)))) = ifeq(true,true,theorem(or(not(or(X4,X3)),or(X4,or(X2,X3)))),true),
    inference(symmetry,[status(thm)],[c11]) ).

cnf(c13,plain,
    ifeq(true,true,theorem(or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3)))),true) = theorem(or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c14,plain,
    theorem(or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3)))) = ifeq(true,true,theorem(or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3)))),true),
    inference(symmetry,[status(thm)],[c13]) ).

cnf(c15,plain,
    implies(or(X2,X4),or(X2,X3)) = or(not(or(X2,X4)),or(X2,X3)),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c16,plain,
    or(not(or(X2,X4)),or(X2,X3)) = implies(or(X2,X4),or(X2,X3)),
    inference(symmetry,[status(thm)],[c15]) ).

cnf(c17,plain,
    or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3))) = or(not(or(not(X4),X3)),implies(or(X2,X4),or(X2,X3))),
    inference(congruence,[status(thm)],[c16]) ).

cnf(c18,plain,
    axiom(or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3)))) = axiom(or(not(or(not(X4),X3)),implies(or(X2,X4),or(X2,X3)))),
    inference(congruence,[status(thm)],[c17]) ).

cnf(c19,plain,
    implies(X3,X2) = or(not(X3),X2),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c20,plain,
    or(not(X3),X2) = implies(X3,X2),
    inference(symmetry,[status(thm)],[c19]) ).

cnf(c21,plain,
    not(or(not(X3),X2)) = not(implies(X3,X2)),
    inference(congruence,[status(thm)],[c20]) ).

cnf(c22,plain,
    or(not(or(not(X4),X3)),implies(or(X2,X4),or(X2,X3))) = or(not(implies(X4,X3)),implies(or(X2,X4),or(X2,X3))),
    inference(congruence,[status(thm)],[c21]) ).

cnf(c23,plain,
    axiom(or(not(or(not(X4),X3)),implies(or(X2,X4),or(X2,X3)))) = axiom(or(not(implies(X4,X3)),implies(or(X2,X4),or(X2,X3)))),
    inference(congruence,[status(thm)],[c22]) ).

cnf(c24,plain,
    implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3))) = or(not(implies(X4,X3)),implies(or(X2,X4),or(X2,X3))),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c25,plain,
    or(not(implies(X4,X3)),implies(or(X2,X4),or(X2,X3))) = implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3))),
    inference(symmetry,[status(thm)],[c24]) ).

cnf(c26,plain,
    axiom(or(not(implies(X4,X3)),implies(or(X2,X4),or(X2,X3)))) = axiom(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))),
    inference(congruence,[status(thm)],[c25]) ).

cnf(c27,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(c28,plain,
    axiom(implies(implies(X4,X3),implies(or(X2,X4),or(X2,X3)))) = true,
    inference(substitution,[status(thm)],[c27]) ).

cnf(c29,plain,
    axiom(or(not(implies(X4,X3)),implies(or(X2,X4),or(X2,X3)))) = true,
    inference(transitivity,[status(thm)],[c26,c28]) ).

cnf(c30,plain,
    axiom(or(not(or(not(X4),X3)),implies(or(X2,X4),or(X2,X3)))) = true,
    inference(transitivity,[status(thm)],[c23,c29]) ).

cnf(c31,plain,
    axiom(or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3)))) = true,
    inference(transitivity,[status(thm)],[c18,c30]) ).

cnf(c32,plain,
    true = axiom(or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3)))),
    inference(symmetry,[status(thm)],[c31]) ).

cnf(c33,plain,
    ifeq(true,true,theorem(or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3)))),true) = ifeq(axiom(or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3)))),true,theorem(or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3)))),true),
    inference(congruence,[status(thm)],[c32]) ).

cnf(c34,axiom,
    ifeq(axiom(X2),true,theorem(X2),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).

cnf(c35,plain,
    ifeq(axiom(or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3)))),true,theorem(or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3)))),true) = true,
    inference(substitution,[status(thm)],[c34]) ).

cnf(c36,plain,
    ifeq(true,true,theorem(or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3)))),true) = true,
    inference(transitivity,[status(thm)],[c33,c35]) ).

cnf(c37,plain,
    theorem(or(not(or(not(X4),X3)),or(not(or(X2,X4)),or(X2,X3)))) = true,
    inference(transitivity,[status(thm)],[c14,c36]) ).

cnf(c38,plain,
    theorem(or(not(or(not(X3),or(X2,X3))),or(not(or(X4,X3)),or(X4,or(X2,X3))))) = true,
    inference(substitution,[status(thm)],[c37]) ).

cnf(c39,plain,
    true = theorem(or(not(or(not(X3),or(X2,X3))),or(not(or(X4,X3)),or(X4,or(X2,X3))))),
    inference(symmetry,[status(thm)],[c38]) ).

cnf(c40,plain,
    ifeq(true,true,theorem(or(not(or(X4,X3)),or(X4,or(X2,X3)))),true) = ifeq(theorem(or(not(or(not(X3),or(X2,X3))),or(not(or(X4,X3)),or(X4,or(X2,X3))))),true,theorem(or(not(or(X4,X3)),or(X4,or(X2,X3)))),true),
    inference(congruence,[status(thm)],[c39]) ).

cnf(c41,plain,
    ifeq(true,true,theorem(X2),true) = theorem(X2),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c42,plain,
    theorem(X2) = ifeq(true,true,theorem(X2),true),
    inference(symmetry,[status(thm)],[c41]) ).

cnf(c43,plain,
    ifeq(theorem(or(not(or(not(X4),or(X3,X4))),X2)),true,theorem(X2),true) = ifeq(theorem(or(not(or(not(X4),or(X3,X4))),X2)),true,ifeq(true,true,theorem(X2),true),true),
    inference(congruence,[status(thm)],[c42]) ).

cnf(c44,plain,
    ifeq(true,true,theorem(or(not(X3),or(X2,X3))),true) = theorem(or(not(X3),or(X2,X3))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c45,plain,
    theorem(or(not(X3),or(X2,X3))) = ifeq(true,true,theorem(or(not(X3),or(X2,X3))),true),
    inference(symmetry,[status(thm)],[c44]) ).

cnf(c46,plain,
    implies(X3,or(X2,X3)) = or(not(X3),or(X2,X3)),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c47,plain,
    or(not(X3),or(X2,X3)) = implies(X3,or(X2,X3)),
    inference(symmetry,[status(thm)],[c46]) ).

cnf(c48,plain,
    axiom(or(not(X3),or(X2,X3))) = axiom(implies(X3,or(X2,X3))),
    inference(congruence,[status(thm)],[c47]) ).

cnf(c49,axiom,
    axiom(implies(A2,or(B2,A2))) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).

cnf(c50,plain,
    axiom(implies(X3,or(X2,X3))) = true,
    inference(substitution,[status(thm)],[c49]) ).

cnf(c51,plain,
    axiom(or(not(X3),or(X2,X3))) = true,
    inference(transitivity,[status(thm)],[c48,c50]) ).

cnf(c52,plain,
    true = axiom(or(not(X3),or(X2,X3))),
    inference(symmetry,[status(thm)],[c51]) ).

cnf(c53,plain,
    ifeq(true,true,theorem(or(not(X3),or(X2,X3))),true) = ifeq(axiom(or(not(X3),or(X2,X3))),true,theorem(or(not(X3),or(X2,X3))),true),
    inference(congruence,[status(thm)],[c52]) ).

cnf(c54,plain,
    ifeq(axiom(or(not(X3),or(X2,X3))),true,theorem(or(not(X3),or(X2,X3))),true) = true,
    inference(substitution,[status(thm)],[c34]) ).

cnf(c55,plain,
    ifeq(true,true,theorem(or(not(X3),or(X2,X3))),true) = true,
    inference(transitivity,[status(thm)],[c53,c54]) ).

cnf(c56,plain,
    theorem(or(not(X3),or(X2,X3))) = true,
    inference(transitivity,[status(thm)],[c45,c55]) ).

cnf(c57,plain,
    true = theorem(or(not(X3),or(X2,X3))),
    inference(symmetry,[status(thm)],[c56]) ).

cnf(c58,plain,
    ifeq(true,true,theorem(X2),true) = ifeq(theorem(or(not(X4),or(X3,X4))),true,theorem(X2),true),
    inference(congruence,[status(thm)],[c57]) ).

cnf(c59,plain,
    ifeq(theorem(or(not(or(not(X4),or(X3,X4))),X2)),true,ifeq(true,true,theorem(X2),true),true) = ifeq(theorem(or(not(or(not(X4),or(X3,X4))),X2)),true,ifeq(theorem(or(not(X4),or(X3,X4))),true,theorem(X2),true),true),
    inference(congruence,[status(thm)],[c58]) ).

cnf(c60,plain,
    implies(X3,X2) = or(not(X3),X2),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c61,plain,
    or(not(X3),X2) = implies(X3,X2),
    inference(symmetry,[status(thm)],[c60]) ).

cnf(c62,plain,
    theorem(or(not(X3),X2)) = theorem(implies(X3,X2)),
    inference(congruence,[status(thm)],[c61]) ).

cnf(c63,plain,
    ifeq(theorem(or(not(X3),X2)),true,ifeq(theorem(X3),true,theorem(X2),true),true) = ifeq(theorem(implies(X3,X2)),true,ifeq(theorem(X3),true,theorem(X2),true),true),
    inference(congruence,[status(thm)],[c62]) ).

cnf(c64,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(c65,plain,
    ifeq(theorem(implies(X3,X2)),true,ifeq(theorem(X3),true,theorem(X2),true),true) = true,
    inference(substitution,[status(thm)],[c64]) ).

cnf(c66,plain,
    ifeq(theorem(or(not(X3),X2)),true,ifeq(theorem(X3),true,theorem(X2),true),true) = true,
    inference(transitivity,[status(thm)],[c63,c65]) ).

cnf(c67,plain,
    ifeq(theorem(or(not(or(not(X4),or(X3,X4))),X2)),true,ifeq(theorem(or(not(X4),or(X3,X4))),true,theorem(X2),true),true) = true,
    inference(substitution,[status(thm)],[c66]) ).

cnf(c68,plain,
    ifeq(theorem(or(not(or(not(X4),or(X3,X4))),X2)),true,ifeq(true,true,theorem(X2),true),true) = true,
    inference(transitivity,[status(thm)],[c59,c67]) ).

cnf(c69,plain,
    ifeq(theorem(or(not(or(not(X4),or(X3,X4))),X2)),true,theorem(X2),true) = true,
    inference(transitivity,[status(thm)],[c43,c68]) ).

cnf(c70,plain,
    ifeq(theorem(or(not(or(not(X3),or(X2,X3))),or(not(or(X4,X3)),or(X4,or(X2,X3))))),true,theorem(or(not(or(X4,X3)),or(X4,or(X2,X3)))),true) = true,
    inference(substitution,[status(thm)],[c69]) ).

cnf(c71,plain,
    ifeq(true,true,theorem(or(not(or(X4,X3)),or(X4,or(X2,X3)))),true) = true,
    inference(transitivity,[status(thm)],[c40,c70]) ).

cnf(c72,plain,
    theorem(or(not(or(X4,X3)),or(X4,or(X2,X3)))) = true,
    inference(transitivity,[status(thm)],[c12,c71]) ).

cnf(c73,plain,
    theorem(or(not(or(not(X4),X3)),or(not(X4),or(X2,X3)))) = true,
    inference(substitution,[status(thm)],[c72]) ).

cnf(c74,plain,
    theorem(or(not(or(not(X4),X3)),implies(X4,or(X2,X3)))) = true,
    inference(transitivity,[status(thm)],[c10,c73]) ).

cnf(c75,plain,
    theorem(or(not(or(not(not(or(X4,X3))),not(X3))),implies(not(or(X4,X3)),or(X2,not(X3))))) = true,
    inference(substitution,[status(thm)],[c74]) ).

cnf(c76,plain,
    true = theorem(or(not(or(not(not(or(X4,X3))),not(X3))),implies(not(or(X4,X3)),or(X2,not(X3))))),
    inference(symmetry,[status(thm)],[c75]) ).

cnf(c77,plain,
    ifeq(true,true,ifeq(true,true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),true),true) = ifeq(theorem(or(not(or(not(not(or(X4,X3))),not(X3))),implies(not(or(X4,X3)),or(X2,not(X3))))),true,ifeq(true,true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),true),true),
    inference(congruence,[status(thm)],[c76]) ).

cnf(c78,plain,
    ifeq(true,true,theorem(or(not(not(or(X3,X2))),not(X2))),true) = theorem(or(not(not(or(X3,X2))),not(X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c79,plain,
    theorem(or(not(not(or(X3,X2))),not(X2))) = ifeq(true,true,theorem(or(not(not(or(X3,X2))),not(X2))),true),
    inference(symmetry,[status(thm)],[c78]) ).

cnf(c80,plain,
    ifeq(true,true,theorem(or(not(X3),not(not(or(X2,X3))))),true) = theorem(or(not(X3),not(not(or(X2,X3))))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c81,plain,
    theorem(or(not(X3),not(not(or(X2,X3))))) = ifeq(true,true,theorem(or(not(X3),not(not(or(X2,X3))))),true),
    inference(symmetry,[status(thm)],[c80]) ).

cnf(c82,plain,
    ifeq(true,true,theorem(or(X2,not(X2))),true) = theorem(or(X2,not(X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c83,plain,
    theorem(or(X2,not(X2))) = ifeq(true,true,theorem(or(X2,not(X2))),true),
    inference(symmetry,[status(thm)],[c82]) ).

cnf(c84,plain,
    ifeq(true,true,theorem(or(not(X2),X2)),true) = theorem(or(not(X2),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c85,plain,
    theorem(or(not(X2),X2)) = ifeq(true,true,theorem(or(not(X2),X2)),true),
    inference(symmetry,[status(thm)],[c84]) ).

cnf(c86,plain,
    ifeq(true,true,theorem(or(X3,or(not(X2),X2))),true) = theorem(or(X3,or(not(X2),X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c87,plain,
    theorem(or(X3,or(not(X2),X2))) = ifeq(true,true,theorem(or(X3,or(not(X2),X2))),true),
    inference(symmetry,[status(thm)],[c86]) ).

cnf(c88,plain,
    theorem(or(not(X2),or(X3,X2))) = true,
    inference(substitution,[status(thm)],[c56]) ).

cnf(c89,plain,
    true = theorem(or(not(X2),or(X3,X2))),
    inference(symmetry,[status(thm)],[c88]) ).

cnf(c90,plain,
    ifeq(true,true,theorem(or(X3,or(not(X2),X2))),true) = ifeq(theorem(or(not(X2),or(X3,X2))),true,theorem(or(X3,or(not(X2),X2))),true),
    inference(congruence,[status(thm)],[c89]) ).

cnf(c91,plain,
    ifeq(true,true,ifeq(theorem(or(X4,or(X3,X2))),true,theorem(or(X3,or(X4,X2))),true),true) = ifeq(theorem(or(X4,or(X3,X2))),true,theorem(or(X3,or(X4,X2))),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c92,plain,
    ifeq(theorem(or(X4,or(X3,X2))),true,theorem(or(X3,or(X4,X2))),true) = ifeq(true,true,ifeq(theorem(or(X4,or(X3,X2))),true,theorem(or(X3,or(X4,X2))),true),true),
    inference(symmetry,[status(thm)],[c91]) ).

cnf(c93,plain,
    ifeq(true,true,theorem(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),true) = theorem(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c94,plain,
    theorem(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))) = ifeq(true,true,theorem(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),true),
    inference(symmetry,[status(thm)],[c93]) ).

cnf(c95,plain,
    implies(or(X4,or(X3,X2)),or(X3,or(X4,X2))) = or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2))),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c96,plain,
    or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2))) = implies(or(X4,or(X3,X2)),or(X3,or(X4,X2))),
    inference(symmetry,[status(thm)],[c95]) ).

cnf(c97,plain,
    axiom(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))) = axiom(implies(or(X4,or(X3,X2)),or(X3,or(X4,X2)))),
    inference(congruence,[status(thm)],[c96]) ).

cnf(c98,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(c99,plain,
    axiom(implies(or(X4,or(X3,X2)),or(X3,or(X4,X2)))) = true,
    inference(substitution,[status(thm)],[c98]) ).

cnf(c100,plain,
    axiom(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))) = true,
    inference(transitivity,[status(thm)],[c97,c99]) ).

cnf(c101,plain,
    true = axiom(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),
    inference(symmetry,[status(thm)],[c100]) ).

cnf(c102,plain,
    ifeq(true,true,theorem(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),true) = ifeq(axiom(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),true,theorem(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),true),
    inference(congruence,[status(thm)],[c101]) ).

cnf(c103,plain,
    ifeq(axiom(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),true,theorem(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),true) = true,
    inference(substitution,[status(thm)],[c34]) ).

cnf(c104,plain,
    ifeq(true,true,theorem(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),true) = true,
    inference(transitivity,[status(thm)],[c102,c103]) ).

cnf(c105,plain,
    theorem(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))) = true,
    inference(transitivity,[status(thm)],[c94,c104]) ).

cnf(c106,plain,
    true = theorem(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),
    inference(symmetry,[status(thm)],[c105]) ).

cnf(c107,plain,
    ifeq(true,true,ifeq(theorem(or(X4,or(X3,X2))),true,theorem(or(X3,or(X4,X2))),true),true) = ifeq(theorem(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),true,ifeq(theorem(or(X4,or(X3,X2))),true,theorem(or(X3,or(X4,X2))),true),true),
    inference(congruence,[status(thm)],[c106]) ).

cnf(c108,plain,
    ifeq(theorem(or(not(or(X4,or(X3,X2))),or(X3,or(X4,X2)))),true,ifeq(theorem(or(X4,or(X3,X2))),true,theorem(or(X3,or(X4,X2))),true),true) = true,
    inference(substitution,[status(thm)],[c66]) ).

cnf(c109,plain,
    ifeq(true,true,ifeq(theorem(or(X4,or(X3,X2))),true,theorem(or(X3,or(X4,X2))),true),true) = true,
    inference(transitivity,[status(thm)],[c107,c108]) ).

cnf(c110,plain,
    ifeq(theorem(or(X4,or(X3,X2))),true,theorem(or(X3,or(X4,X2))),true) = true,
    inference(transitivity,[status(thm)],[c92,c109]) ).

cnf(c111,plain,
    ifeq(theorem(or(not(X2),or(X3,X2))),true,theorem(or(X3,or(not(X2),X2))),true) = true,
    inference(substitution,[status(thm)],[c110]) ).

cnf(c112,plain,
    ifeq(true,true,theorem(or(X3,or(not(X2),X2))),true) = true,
    inference(transitivity,[status(thm)],[c90,c111]) ).

cnf(c113,plain,
    theorem(or(X3,or(not(X2),X2))) = true,
    inference(transitivity,[status(thm)],[c87,c112]) ).

cnf(c114,plain,
    theorem(or(or(not(X2),X2),or(not(X2),X2))) = true,
    inference(substitution,[status(thm)],[c113]) ).

cnf(c115,plain,
    true = theorem(or(or(not(X2),X2),or(not(X2),X2))),
    inference(symmetry,[status(thm)],[c114]) ).

cnf(c116,plain,
    ifeq(true,true,theorem(or(not(X2),X2)),true) = ifeq(theorem(or(or(not(X2),X2),or(not(X2),X2))),true,theorem(or(not(X2),X2)),true),
    inference(congruence,[status(thm)],[c115]) ).

cnf(c117,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(c118,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)],[c117]) ).

cnf(c119,plain,
    ifeq(true,true,theorem(or(not(or(X2,X2)),X2)),true) = theorem(or(not(or(X2,X2)),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c120,plain,
    theorem(or(not(or(X2,X2)),X2)) = ifeq(true,true,theorem(or(not(or(X2,X2)),X2)),true),
    inference(symmetry,[status(thm)],[c119]) ).

cnf(c121,plain,
    implies(or(X2,X2),X2) = or(not(or(X2,X2)),X2),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c122,plain,
    or(not(or(X2,X2)),X2) = implies(or(X2,X2),X2),
    inference(symmetry,[status(thm)],[c121]) ).

cnf(c123,plain,
    axiom(or(not(or(X2,X2)),X2)) = axiom(implies(or(X2,X2),X2)),
    inference(congruence,[status(thm)],[c122]) ).

cnf(c124,axiom,
    axiom(implies(or(A2,A2),A2)) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).

cnf(c125,plain,
    axiom(implies(or(X2,X2),X2)) = true,
    inference(substitution,[status(thm)],[c124]) ).

cnf(c126,plain,
    axiom(or(not(or(X2,X2)),X2)) = true,
    inference(transitivity,[status(thm)],[c123,c125]) ).

cnf(c127,plain,
    true = axiom(or(not(or(X2,X2)),X2)),
    inference(symmetry,[status(thm)],[c126]) ).

cnf(c128,plain,
    ifeq(true,true,theorem(or(not(or(X2,X2)),X2)),true) = ifeq(axiom(or(not(or(X2,X2)),X2)),true,theorem(or(not(or(X2,X2)),X2)),true),
    inference(congruence,[status(thm)],[c127]) ).

cnf(c129,plain,
    ifeq(axiom(or(not(or(X2,X2)),X2)),true,theorem(or(not(or(X2,X2)),X2)),true) = true,
    inference(substitution,[status(thm)],[c34]) ).

cnf(c130,plain,
    ifeq(true,true,theorem(or(not(or(X2,X2)),X2)),true) = true,
    inference(transitivity,[status(thm)],[c128,c129]) ).

cnf(c131,plain,
    theorem(or(not(or(X2,X2)),X2)) = true,
    inference(transitivity,[status(thm)],[c120,c130]) ).

cnf(c132,plain,
    true = theorem(or(not(or(X2,X2)),X2)),
    inference(symmetry,[status(thm)],[c131]) ).

cnf(c133,plain,
    ifeq(true,true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true) = ifeq(theorem(or(not(or(X2,X2)),X2)),true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true),
    inference(congruence,[status(thm)],[c132]) ).

cnf(c134,plain,
    ifeq(theorem(or(not(or(X2,X2)),X2)),true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true) = true,
    inference(substitution,[status(thm)],[c66]) ).

cnf(c135,plain,
    ifeq(true,true,ifeq(theorem(or(X2,X2)),true,theorem(X2),true),true) = true,
    inference(transitivity,[status(thm)],[c133,c134]) ).

cnf(c136,plain,
    ifeq(theorem(or(X2,X2)),true,theorem(X2),true) = true,
    inference(transitivity,[status(thm)],[c118,c135]) ).

cnf(c137,plain,
    ifeq(theorem(or(or(not(X2),X2),or(not(X2),X2))),true,theorem(or(not(X2),X2)),true) = true,
    inference(substitution,[status(thm)],[c136]) ).

cnf(c138,plain,
    ifeq(true,true,theorem(or(not(X2),X2)),true) = true,
    inference(transitivity,[status(thm)],[c116,c137]) ).

cnf(c139,plain,
    theorem(or(not(X2),X2)) = true,
    inference(transitivity,[status(thm)],[c85,c138]) ).

cnf(c140,plain,
    true = theorem(or(not(X2),X2)),
    inference(symmetry,[status(thm)],[c139]) ).

cnf(c141,plain,
    ifeq(true,true,theorem(or(X2,not(X2))),true) = ifeq(theorem(or(not(X2),X2)),true,theorem(or(X2,not(X2))),true),
    inference(congruence,[status(thm)],[c140]) ).

cnf(c142,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(c143,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)],[c142]) ).

cnf(c144,plain,
    ifeq(true,true,theorem(or(not(or(X3,X2)),or(X2,X3))),true) = theorem(or(not(or(X3,X2)),or(X2,X3))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c145,plain,
    theorem(or(not(or(X3,X2)),or(X2,X3))) = ifeq(true,true,theorem(or(not(or(X3,X2)),or(X2,X3))),true),
    inference(symmetry,[status(thm)],[c144]) ).

cnf(c146,plain,
    implies(or(X3,X2),or(X2,X3)) = or(not(or(X3,X2)),or(X2,X3)),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c147,plain,
    or(not(or(X3,X2)),or(X2,X3)) = implies(or(X3,X2),or(X2,X3)),
    inference(symmetry,[status(thm)],[c146]) ).

cnf(c148,plain,
    axiom(or(not(or(X3,X2)),or(X2,X3))) = axiom(implies(or(X3,X2),or(X2,X3))),
    inference(congruence,[status(thm)],[c147]) ).

cnf(c149,axiom,
    axiom(implies(or(A2,B2),or(B2,A2))) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).

cnf(c150,plain,
    axiom(implies(or(X3,X2),or(X2,X3))) = true,
    inference(substitution,[status(thm)],[c149]) ).

cnf(c151,plain,
    axiom(or(not(or(X3,X2)),or(X2,X3))) = true,
    inference(transitivity,[status(thm)],[c148,c150]) ).

cnf(c152,plain,
    true = axiom(or(not(or(X3,X2)),or(X2,X3))),
    inference(symmetry,[status(thm)],[c151]) ).

cnf(c153,plain,
    ifeq(true,true,theorem(or(not(or(X3,X2)),or(X2,X3))),true) = ifeq(axiom(or(not(or(X3,X2)),or(X2,X3))),true,theorem(or(not(or(X3,X2)),or(X2,X3))),true),
    inference(congruence,[status(thm)],[c152]) ).

cnf(c154,plain,
    ifeq(axiom(or(not(or(X3,X2)),or(X2,X3))),true,theorem(or(not(or(X3,X2)),or(X2,X3))),true) = true,
    inference(substitution,[status(thm)],[c34]) ).

cnf(c155,plain,
    ifeq(true,true,theorem(or(not(or(X3,X2)),or(X2,X3))),true) = true,
    inference(transitivity,[status(thm)],[c153,c154]) ).

cnf(c156,plain,
    theorem(or(not(or(X3,X2)),or(X2,X3))) = true,
    inference(transitivity,[status(thm)],[c145,c155]) ).

cnf(c157,plain,
    true = theorem(or(not(or(X3,X2)),or(X2,X3))),
    inference(symmetry,[status(thm)],[c156]) ).

cnf(c158,plain,
    ifeq(true,true,ifeq(theorem(or(X3,X2)),true,theorem(or(X2,X3)),true),true) = ifeq(theorem(or(not(or(X3,X2)),or(X2,X3))),true,ifeq(theorem(or(X3,X2)),true,theorem(or(X2,X3)),true),true),
    inference(congruence,[status(thm)],[c157]) ).

cnf(c159,plain,
    ifeq(theorem(or(not(or(X3,X2)),or(X2,X3))),true,ifeq(theorem(or(X3,X2)),true,theorem(or(X2,X3)),true),true) = true,
    inference(substitution,[status(thm)],[c66]) ).

cnf(c160,plain,
    ifeq(true,true,ifeq(theorem(or(X3,X2)),true,theorem(or(X2,X3)),true),true) = true,
    inference(transitivity,[status(thm)],[c158,c159]) ).

cnf(c161,plain,
    ifeq(theorem(or(X3,X2)),true,theorem(or(X2,X3)),true) = true,
    inference(transitivity,[status(thm)],[c143,c160]) ).

cnf(c162,plain,
    ifeq(theorem(or(not(X2),X2)),true,theorem(or(X2,not(X2))),true) = true,
    inference(substitution,[status(thm)],[c161]) ).

cnf(c163,plain,
    ifeq(true,true,theorem(or(X2,not(X2))),true) = true,
    inference(transitivity,[status(thm)],[c141,c162]) ).

cnf(c164,plain,
    theorem(or(X2,not(X2))) = true,
    inference(transitivity,[status(thm)],[c83,c163]) ).

cnf(c165,plain,
    theorem(or(not(or(X2,X3)),not(not(or(X2,X3))))) = true,
    inference(substitution,[status(thm)],[c164]) ).

cnf(c166,plain,
    true = theorem(or(not(or(X2,X3)),not(not(or(X2,X3))))),
    inference(symmetry,[status(thm)],[c165]) ).

cnf(c167,plain,
    ifeq(true,true,theorem(or(not(X3),not(not(or(X2,X3))))),true) = ifeq(theorem(or(not(or(X2,X3)),not(not(or(X2,X3))))),true,theorem(or(not(X3),not(not(or(X2,X3))))),true),
    inference(congruence,[status(thm)],[c166]) ).

cnf(c168,plain,
    ifeq(true,true,ifeq(theorem(or(not(or(X4,X3)),X2)),true,theorem(or(not(X3),X2)),true),true) = ifeq(theorem(or(not(or(X4,X3)),X2)),true,theorem(or(not(X3),X2)),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c169,plain,
    ifeq(theorem(or(not(or(X4,X3)),X2)),true,theorem(or(not(X3),X2)),true) = ifeq(true,true,ifeq(theorem(or(not(or(X4,X3)),X2)),true,theorem(or(not(X3),X2)),true),true),
    inference(symmetry,[status(thm)],[c168]) ).

cnf(c170,plain,
    ifeq(true,true,theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2))),true) = theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c171,plain,
    theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2))) = ifeq(true,true,theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2))),true),
    inference(symmetry,[status(thm)],[c170]) ).

cnf(c172,plain,
    ifeq(true,true,theorem(or(not(or(X4,X3)),or(not(or(not(X3),X2)),or(X4,X2)))),true) = theorem(or(not(or(X4,X3)),or(not(or(not(X3),X2)),or(X4,X2)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c173,plain,
    theorem(or(not(or(X4,X3)),or(not(or(not(X3),X2)),or(X4,X2)))) = ifeq(true,true,theorem(or(not(or(X4,X3)),or(not(or(not(X3),X2)),or(X4,X2)))),true),
    inference(symmetry,[status(thm)],[c172]) ).

cnf(c174,plain,
    theorem(or(not(or(not(X3),X2)),or(not(or(X4,X3)),or(X4,X2)))) = true,
    inference(substitution,[status(thm)],[c37]) ).

cnf(c175,plain,
    true = theorem(or(not(or(not(X3),X2)),or(not(or(X4,X3)),or(X4,X2)))),
    inference(symmetry,[status(thm)],[c174]) ).

cnf(c176,plain,
    ifeq(true,true,theorem(or(not(or(X4,X3)),or(not(or(not(X3),X2)),or(X4,X2)))),true) = ifeq(theorem(or(not(or(not(X3),X2)),or(not(or(X4,X3)),or(X4,X2)))),true,theorem(or(not(or(X4,X3)),or(not(or(not(X3),X2)),or(X4,X2)))),true),
    inference(congruence,[status(thm)],[c175]) ).

cnf(c177,plain,
    ifeq(theorem(or(not(or(not(X3),X2)),or(not(or(X4,X3)),or(X4,X2)))),true,theorem(or(not(or(X4,X3)),or(not(or(not(X3),X2)),or(X4,X2)))),true) = true,
    inference(substitution,[status(thm)],[c110]) ).

cnf(c178,plain,
    ifeq(true,true,theorem(or(not(or(X4,X3)),or(not(or(not(X3),X2)),or(X4,X2)))),true) = true,
    inference(transitivity,[status(thm)],[c176,c177]) ).

cnf(c179,plain,
    theorem(or(not(or(X4,X3)),or(not(or(not(X3),X2)),or(X4,X2)))) = true,
    inference(transitivity,[status(thm)],[c173,c178]) ).

cnf(c180,plain,
    theorem(or(not(or(not(X3),or(X4,X3))),or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2)))) = true,
    inference(substitution,[status(thm)],[c179]) ).

cnf(c181,plain,
    true = theorem(or(not(or(not(X3),or(X4,X3))),or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2)))),
    inference(symmetry,[status(thm)],[c180]) ).

cnf(c182,plain,
    ifeq(true,true,theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2))),true) = ifeq(theorem(or(not(or(not(X3),or(X4,X3))),or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2)))),true,theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2))),true),
    inference(congruence,[status(thm)],[c181]) ).

cnf(c183,plain,
    ifeq(theorem(or(not(or(not(X3),or(X4,X3))),or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2)))),true,theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2))),true) = true,
    inference(substitution,[status(thm)],[c69]) ).

cnf(c184,plain,
    ifeq(true,true,theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2))),true) = true,
    inference(transitivity,[status(thm)],[c182,c183]) ).

cnf(c185,plain,
    theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2))) = true,
    inference(transitivity,[status(thm)],[c171,c184]) ).

cnf(c186,plain,
    true = theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2))),
    inference(symmetry,[status(thm)],[c185]) ).

cnf(c187,plain,
    ifeq(true,true,ifeq(theorem(or(not(or(X4,X3)),X2)),true,theorem(or(not(X3),X2)),true),true) = ifeq(theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2))),true,ifeq(theorem(or(not(or(X4,X3)),X2)),true,theorem(or(not(X3),X2)),true),true),
    inference(congruence,[status(thm)],[c186]) ).

cnf(c188,plain,
    ifeq(theorem(or(not(or(not(or(X4,X3)),X2)),or(not(X3),X2))),true,ifeq(theorem(or(not(or(X4,X3)),X2)),true,theorem(or(not(X3),X2)),true),true) = true,
    inference(substitution,[status(thm)],[c66]) ).

cnf(c189,plain,
    ifeq(true,true,ifeq(theorem(or(not(or(X4,X3)),X2)),true,theorem(or(not(X3),X2)),true),true) = true,
    inference(transitivity,[status(thm)],[c187,c188]) ).

cnf(c190,plain,
    ifeq(theorem(or(not(or(X4,X3)),X2)),true,theorem(or(not(X3),X2)),true) = true,
    inference(transitivity,[status(thm)],[c169,c189]) ).

cnf(c191,plain,
    ifeq(theorem(or(not(or(X2,X3)),not(not(or(X2,X3))))),true,theorem(or(not(X3),not(not(or(X2,X3))))),true) = true,
    inference(substitution,[status(thm)],[c190]) ).

cnf(c192,plain,
    ifeq(true,true,theorem(or(not(X3),not(not(or(X2,X3))))),true) = true,
    inference(transitivity,[status(thm)],[c167,c191]) ).

cnf(c193,plain,
    theorem(or(not(X3),not(not(or(X2,X3))))) = true,
    inference(transitivity,[status(thm)],[c81,c192]) ).

cnf(c194,plain,
    theorem(or(not(X2),not(not(or(X3,X2))))) = true,
    inference(substitution,[status(thm)],[c193]) ).

cnf(c195,plain,
    true = theorem(or(not(X2),not(not(or(X3,X2))))),
    inference(symmetry,[status(thm)],[c194]) ).

cnf(c196,plain,
    ifeq(true,true,theorem(or(not(not(or(X3,X2))),not(X2))),true) = ifeq(theorem(or(not(X2),not(not(or(X3,X2))))),true,theorem(or(not(not(or(X3,X2))),not(X2))),true),
    inference(congruence,[status(thm)],[c195]) ).

cnf(c197,plain,
    ifeq(theorem(or(not(X2),not(not(or(X3,X2))))),true,theorem(or(not(not(or(X3,X2))),not(X2))),true) = true,
    inference(substitution,[status(thm)],[c161]) ).

cnf(c198,plain,
    ifeq(true,true,theorem(or(not(not(or(X3,X2))),not(X2))),true) = true,
    inference(transitivity,[status(thm)],[c196,c197]) ).

cnf(c199,plain,
    theorem(or(not(not(or(X3,X2))),not(X2))) = true,
    inference(transitivity,[status(thm)],[c79,c198]) ).

cnf(c200,plain,
    true = theorem(or(not(not(or(X3,X2))),not(X2))),
    inference(symmetry,[status(thm)],[c199]) ).

cnf(c201,plain,
    ifeq(true,true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),true) = ifeq(theorem(or(not(not(or(X4,X3))),not(X3))),true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),true),
    inference(congruence,[status(thm)],[c200]) ).

cnf(c202,plain,
    ifeq(theorem(or(not(or(not(not(or(X4,X3))),not(X3))),implies(not(or(X4,X3)),or(X2,not(X3))))),true,ifeq(true,true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),true),true) = ifeq(theorem(or(not(or(not(not(or(X4,X3))),not(X3))),implies(not(or(X4,X3)),or(X2,not(X3))))),true,ifeq(theorem(or(not(not(or(X4,X3))),not(X3))),true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),true),true),
    inference(congruence,[status(thm)],[c201]) ).

cnf(c203,plain,
    ifeq(theorem(or(not(or(not(not(or(X4,X3))),not(X3))),implies(not(or(X4,X3)),or(X2,not(X3))))),true,ifeq(theorem(or(not(not(or(X4,X3))),not(X3))),true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),true),true) = true,
    inference(substitution,[status(thm)],[c66]) ).

cnf(c204,plain,
    ifeq(theorem(or(not(or(not(not(or(X4,X3))),not(X3))),implies(not(or(X4,X3)),or(X2,not(X3))))),true,ifeq(true,true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),true),true) = true,
    inference(transitivity,[status(thm)],[c202,c203]) ).

cnf(c205,plain,
    ifeq(true,true,ifeq(true,true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),true),true) = true,
    inference(transitivity,[status(thm)],[c77,c204]) ).

cnf(c206,plain,
    ifeq(true,true,theorem(implies(not(or(X4,X3)),or(X2,not(X3)))),true) = true,
    inference(transitivity,[status(thm)],[c6,c205]) ).

cnf(c207,plain,
    theorem(implies(not(or(X4,X3)),or(X2,not(X3)))) = true,
    inference(transitivity,[status(thm)],[c4,c206]) ).

cnf(c208,plain,
    theorem(implies(not(or(p,q)),or(not(p),not(q)))) = true,
    inference(substitution,[status(thm)],[c207]) ).

cnf(c209,plain,
    $false,
    inference(resolution,[status(thm)],[c1,c208]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : LCL203-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43  % Computer : n026.cluster.edu
% 0.16/0.43  % Model    : x86_64 x86_64
% 0.16/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43  % Memory   : 8046.5625MB
% 0.16/0.43  % OS       : Linux 6.8.0-71-generic
% 0.16/0.43  % CPULimit : 300
% 0.16/0.43  % WCLimit  : 300
% 0.16/0.43  % DateTime : Sun Sep 27 15:29:26 UTC 2026
% 0.16/0.43  % CPUTime  : 
% 0.16/0.43  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.14/2.84  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
% 18.14/2.84  
% 18.14/2.84  % SZS status Unsatisfiable
% 18.14/2.84  
% 18.14/2.85  % SZS output start CNFRefutation
% See solution above
% 18.97/2.96  
% 18.97/2.96  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------