%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL241-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 : Mon Sep 7 12:42:18 PM UTC 2026
% Result : Unsatisfiable 4.26s 4.55s
% Output : CNFRefutation 4.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 43
% Syntax : Number of clauses : 221 ( 117 unt; 0 nHn; 100 RR)
% Number of literals : 361 ( 137 equ; 141 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 475 ( 23 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(implies(or(A,A),A)) ).
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(axiom_1_4,axiom,
axiom(implies(or(A,B),or(B,A))) ).
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ).
cnf(axiom_1_6,axiom,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ) ).
cnf(and_defn,axiom,
and(P,Q) = not(or(not(P),not(Q))) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(and(p,q),q)) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(or(X_7,X_8),or(X_8,X_7)))
| theorem(implies(or(X_7,X_8),or(X_8,X_7))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_7,X_8),or(X_8,X_7))))]]) ).
cnf(refute_0_1,plain,
axiom(implies(or(X_7,X_8),or(X_8,X_7))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).
cnf(refute_0_2,plain,
theorem(implies(or(X_7,X_8),or(X_8,X_7))),
inference(resolve,[$cnf( axiom(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( ~ theorem(implies(or(X_7,X_8),or(X_8,X_7)))
| ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_8,X_7))),bind(Y,$fot(or(X_7,X_8)))]]) ).
cnf(refute_0_4,plain,
( ~ theorem(or(X_7,X_8))
| theorem(or(X_8,X_7)) ),
inference(resolve,[$cnf( theorem(implies(or(X_7,X_8),or(X_8,X_7))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ theorem(or(X_2918,not(and(X_2917,X_2918))))
| theorem(or(not(and(X_2917,X_2918)),X_2918)) ),
inference(subst,[],[refute_0_4:[bind(X_7,$fot(X_2918)),bind(X_8,$fot(not(and(X_2917,X_2918))))]]) ).
cnf(refute_0_6,plain,
( ~ axiom(implies(X_3,or(X_4,X_3)))
| theorem(implies(X_3,or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_7,plain,
axiom(implies(X_3,or(X_4,X_3))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_8,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
theorem(implies(X_77,or(X_4,X_77))),
inference(subst,[],[refute_0_8:[bind(X_3,$fot(X_77))]]) ).
cnf(refute_0_10,plain,
( ~ theorem(X_77)
| ~ theorem(implies(X_77,or(X_4,X_77)))
| theorem(or(X_4,X_77)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_4,X_77))),bind(Y,$fot(X_77))]]) ).
cnf(refute_0_11,plain,
( ~ theorem(X_77)
| theorem(or(X_4,X_77)) ),
inference(resolve,[$cnf( theorem(implies(X_77,or(X_4,X_77))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ theorem(or(X_1147,not(X_1147)))
| theorem(or(X_4,or(X_1147,not(X_1147)))) ),
inference(subst,[],[refute_0_11:[bind(X_77,$fot(or(X_1147,not(X_1147))))]]) ).
cnf(refute_0_13,plain,
theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))),
inference(subst,[],[refute_0_2:[bind(X_7,$fot(not(X_11)))]]) ).
cnf(refute_0_14,plain,
implies(X_11,X_8) = or(not(X_11),X_8),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_15,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_16,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_17,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( implies(X_11,X_8) != or(not(X_11),X_8)
| or(not(X_11),X_8) = implies(X_11,X_8) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(implies(X_11,X_8))),bind(Y0,$fot(or(not(X_11),X_8)))]]) ).
cnf(refute_0_19,plain,
or(not(X_11),X_8) = implies(X_11,X_8),
inference(resolve,[$cnf( $equal(implies(X_11,X_8),or(not(X_11),X_8)) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( or(not(X_11),X_8) != implies(X_11,X_8)
| ~ theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11))))
| theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))) ),[0,0],$fot(implies(X_11,X_8))]]) ).
cnf(refute_0_21,plain,
( ~ theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11))))
| theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),X_8),implies(X_11,X_8)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))),
inference(resolve,[$cnf( theorem(implies(or(not(X_11),X_8),or(X_8,not(X_11)))) )],[refute_0_13,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ theorem(implies(X_11,X_8))
| ~ theorem(implies(implies(X_11,X_8),or(X_8,not(X_11))))
| theorem(or(X_8,not(X_11))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_8,not(X_11)))),bind(Y,$fot(implies(X_11,X_8)))]]) ).
cnf(refute_0_24,plain,
( ~ theorem(implies(X_11,X_8))
| theorem(or(X_8,not(X_11))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_11,X_8),or(X_8,not(X_11)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ theorem(implies(X_1146,X_1146))
| theorem(or(X_1146,not(X_1146))) ),
inference(subst,[],[refute_0_24:[bind(X_11,$fot(X_1146)),bind(X_8,$fot(X_1146))]]) ).
cnf(refute_0_26,plain,
( ~ theorem(X_98)
| ~ theorem(implies(X_98,and(X_98,X_98)))
| theorem(and(X_98,X_98)) ),
inference(subst,[],[rule_2:[bind(X,$fot(and(X_98,X_98))),bind(Y,$fot(X_98))]]) ).
cnf(refute_0_27,plain,
( ~ axiom(or(and(X_18,X_18),not(X_18)))
| theorem(or(and(X_18,X_18),not(X_18))) ),
inference(subst,[],[rule_1:[bind(X,$fot(or(and(X_18,X_18),not(X_18))))]]) ).
cnf(refute_0_28,plain,
axiom(implies(or(not(X_11),not(X_11)),not(X_11))),
inference(subst,[],[axiom_1_2:[bind(A,$fot(not(X_11)))]]) ).
cnf(refute_0_29,plain,
implies(X_11,not(X_11)) = or(not(X_11),not(X_11)),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(not(X_11)))]]) ).
cnf(refute_0_30,plain,
( implies(X_11,not(X_11)) != or(not(X_11),not(X_11))
| or(not(X_11),not(X_11)) = implies(X_11,not(X_11)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(implies(X_11,not(X_11)))),bind(Y0,$fot(or(not(X_11),not(X_11))))]]) ).
cnf(refute_0_31,plain,
or(not(X_11),not(X_11)) = implies(X_11,not(X_11)),
inference(resolve,[$cnf( $equal(implies(X_11,not(X_11)),or(not(X_11),not(X_11))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( or(not(X_11),not(X_11)) != implies(X_11,not(X_11))
| ~ axiom(implies(or(not(X_11),not(X_11)),not(X_11)))
| axiom(implies(implies(X_11,not(X_11)),not(X_11))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X_11),not(X_11)),not(X_11))) ),[0,0],$fot(implies(X_11,not(X_11)))]]) ).
cnf(refute_0_33,plain,
( ~ axiom(implies(or(not(X_11),not(X_11)),not(X_11)))
| axiom(implies(implies(X_11,not(X_11)),not(X_11))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),not(X_11)),implies(X_11,not(X_11))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
axiom(implies(implies(X_11,not(X_11)),not(X_11))),
inference(resolve,[$cnf( axiom(implies(or(not(X_11),not(X_11)),not(X_11))) )],[refute_0_28,refute_0_33]) ).
cnf(refute_0_35,plain,
implies(implies(X_16,not(X_17)),Y) = or(not(implies(X_16,not(X_17))),Y),
inference(subst,[],[implies_definition:[bind(X,$fot(implies(X_16,not(X_17))))]]) ).
cnf(refute_0_36,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_37,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[implies_definition,refute_0_36]) ).
cnf(refute_0_38,plain,
or(not(P),not(Q)) = implies(P,not(Q)),
inference(subst,[],[refute_0_37:[bind(X,$fot(P)),bind(Y,$fot(not(Q)))]]) ).
cnf(refute_0_39,plain,
not(or(not(P),not(Q))) = not(or(not(P),not(Q))),
introduced(tautology,[refl,[$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_40,plain,
( not(or(not(P),not(Q))) != not(or(not(P),not(Q)))
| or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) ),[1,0],$fot(implies(P,not(Q)))]]) ).
cnf(refute_0_41,plain,
( or(not(P),not(Q)) != implies(P,not(Q))
| not(or(not(P),not(Q))) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(or(not(P),not(Q)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
not(or(not(P),not(Q))) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(or(not(P),not(Q)),implies(P,not(Q))) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| not(or(not(P),not(Q))) != not(implies(P,not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(P,Q),not(implies(P,not(Q)))) ),[0],$fot(not(or(not(P),not(Q))))]]) ).
cnf(refute_0_44,plain,
( and(P,Q) != not(or(not(P),not(Q)))
| and(P,Q) = not(implies(P,not(Q))) ),
inference(resolve,[$cnf( $equal(not(or(not(P),not(Q))),not(implies(P,not(Q)))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
and(P,Q) = not(implies(P,not(Q))),
inference(resolve,[$cnf( $equal(and(P,Q),not(or(not(P),not(Q)))) )],[and_defn,refute_0_44]) ).
cnf(refute_0_46,plain,
and(X_16,X_17) = not(implies(X_16,not(X_17))),
inference(subst,[],[refute_0_45:[bind(P,$fot(X_16)),bind(Q,$fot(X_17))]]) ).
cnf(refute_0_47,plain,
( and(X_16,X_17) != not(implies(X_16,not(X_17)))
| not(implies(X_16,not(X_17))) = and(X_16,X_17) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(and(X_16,X_17))),bind(Y0,$fot(not(implies(X_16,not(X_17)))))]]) ).
cnf(refute_0_48,plain,
not(implies(X_16,not(X_17))) = and(X_16,X_17),
inference(resolve,[$cnf( $equal(and(X_16,X_17),not(implies(X_16,not(X_17)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( implies(implies(X_16,not(X_17)),Y) != or(not(implies(X_16,not(X_17))),Y)
| not(implies(X_16,not(X_17))) != and(X_16,X_17)
| implies(implies(X_16,not(X_17)),Y) = or(and(X_16,X_17),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,not(X_17)),Y),or(not(implies(X_16,not(X_17))),Y)) ),[1,0],$fot(and(X_16,X_17))]]) ).
cnf(refute_0_50,plain,
( implies(implies(X_16,not(X_17)),Y) != or(not(implies(X_16,not(X_17))),Y)
| implies(implies(X_16,not(X_17)),Y) = or(and(X_16,X_17),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_16,not(X_17))),and(X_16,X_17)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
implies(implies(X_16,not(X_17)),Y) = or(and(X_16,X_17),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_16,not(X_17)),Y),or(not(implies(X_16,not(X_17))),Y)) )],[refute_0_35,refute_0_50]) ).
cnf(refute_0_52,plain,
implies(implies(X_11,not(X_11)),not(X_11)) = or(and(X_11,X_11),not(X_11)),
inference(subst,[],[refute_0_51:[bind(Y,$fot(not(X_11))),bind(X_16,$fot(X_11)),bind(X_17,$fot(X_11))]]) ).
cnf(refute_0_53,plain,
( implies(implies(X_11,not(X_11)),not(X_11)) != or(and(X_11,X_11),not(X_11))
| ~ axiom(implies(implies(X_11,not(X_11)),not(X_11)))
| axiom(or(and(X_11,X_11),not(X_11))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(implies(X_11,not(X_11)),not(X_11))) ),[0],$fot(or(and(X_11,X_11),not(X_11)))]]) ).
cnf(refute_0_54,plain,
( ~ axiom(implies(implies(X_11,not(X_11)),not(X_11)))
| axiom(or(and(X_11,X_11),not(X_11))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_11,not(X_11)),not(X_11)),or(and(X_11,X_11),not(X_11))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
axiom(or(and(X_11,X_11),not(X_11))),
inference(resolve,[$cnf( axiom(implies(implies(X_11,not(X_11)),not(X_11))) )],[refute_0_34,refute_0_54]) ).
cnf(refute_0_56,plain,
axiom(or(and(X_18,X_18),not(X_18))),
inference(subst,[],[refute_0_55:[bind(X_11,$fot(X_18))]]) ).
cnf(refute_0_57,plain,
theorem(or(and(X_18,X_18),not(X_18))),
inference(resolve,[$cnf( axiom(or(and(X_18,X_18),not(X_18))) )],[refute_0_56,refute_0_27]) ).
cnf(refute_0_58,plain,
theorem(or(and(X_96,X_96),not(X_96))),
inference(subst,[],[refute_0_57:[bind(X_18,$fot(X_96))]]) ).
cnf(refute_0_59,plain,
theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7))),
inference(subst,[],[refute_0_2:[bind(X_8,$fot(not(X_11)))]]) ).
cnf(refute_0_60,plain,
implies(X_11,X_7) = or(not(X_11),X_7),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_61,plain,
( implies(X_11,X_7) != or(not(X_11),X_7)
| or(not(X_11),X_7) = implies(X_11,X_7) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(implies(X_11,X_7))),bind(Y0,$fot(or(not(X_11),X_7)))]]) ).
cnf(refute_0_62,plain,
or(not(X_11),X_7) = implies(X_11,X_7),
inference(resolve,[$cnf( $equal(implies(X_11,X_7),or(not(X_11),X_7)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( or(not(X_11),X_7) != implies(X_11,X_7)
| ~ theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7)))
| theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7))) ),[0,1],$fot(implies(X_11,X_7))]]) ).
cnf(refute_0_64,plain,
( ~ theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7)))
| theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),X_7),implies(X_11,X_7)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))),
inference(resolve,[$cnf( theorem(implies(or(X_7,not(X_11)),or(not(X_11),X_7))) )],[refute_0_59,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7)))
| ~ theorem(or(X_7,not(X_11)))
| theorem(implies(X_11,X_7)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_11,X_7))),bind(Y,$fot(or(X_7,not(X_11))))]]) ).
cnf(refute_0_67,plain,
( ~ theorem(or(X_7,not(X_11)))
| theorem(implies(X_11,X_7)) ),
inference(resolve,[$cnf( theorem(implies(or(X_7,not(X_11)),implies(X_11,X_7))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ theorem(or(and(X_96,X_96),not(X_96)))
| theorem(implies(X_96,and(X_96,X_96))) ),
inference(subst,[],[refute_0_67:[bind(X_11,$fot(X_96)),bind(X_7,$fot(and(X_96,X_96)))]]) ).
cnf(refute_0_69,plain,
theorem(implies(X_96,and(X_96,X_96))),
inference(resolve,[$cnf( theorem(or(and(X_96,X_96),not(X_96))) )],[refute_0_58,refute_0_68]) ).
cnf(refute_0_70,plain,
theorem(implies(X_98,and(X_98,X_98))),
inference(subst,[],[refute_0_69:[bind(X_96,$fot(X_98))]]) ).
cnf(refute_0_71,plain,
( ~ theorem(X_98)
| theorem(and(X_98,X_98)) ),
inference(resolve,[$cnf( theorem(implies(X_98,and(X_98,X_98))) )],[refute_0_70,refute_0_26]) ).
cnf(refute_0_72,plain,
( ~ theorem(implies(implies(X_106,or(X_107,X_108)),or(X_107,implies(X_106,X_108))))
| theorem(and(implies(implies(X_106,or(X_107,X_108)),or(X_107,implies(X_106,X_108))),implies(implies(X_106,or(X_107,X_108)),or(X_107,implies(X_106,X_108))))) ),
inference(subst,[],[refute_0_71:[bind(X_98,$fot(implies(implies(X_106,or(X_107,X_108)),or(X_107,implies(X_106,X_108)))))]]) ).
cnf(refute_0_73,plain,
( ~ axiom(implies(implies(X_46,or(X_47,X_48)),or(X_47,implies(X_46,X_48))))
| theorem(implies(implies(X_46,or(X_47,X_48)),or(X_47,implies(X_46,X_48)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_46,or(X_47,X_48)),or(X_47,implies(X_46,X_48)))))]]) ).
cnf(refute_0_74,plain,
axiom(implies(or(not(X),or(X_37,X_38)),or(X_37,or(not(X),X_38)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(X))),bind(B,$fot(X_37)),bind(C,$fot(X_38))]]) ).
cnf(refute_0_75,plain,
implies(X,X_38) = or(not(X),X_38),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_38))]]) ).
cnf(refute_0_76,plain,
( implies(X,X_38) != or(not(X),X_38)
| or(not(X),X_38) = implies(X,X_38) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(implies(X,X_38))),bind(Y0,$fot(or(not(X),X_38)))]]) ).
cnf(refute_0_77,plain,
or(not(X),X_38) = implies(X,X_38),
inference(resolve,[$cnf( $equal(implies(X,X_38),or(not(X),X_38)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
( or(not(X),X_38) != implies(X,X_38)
| ~ axiom(implies(or(not(X),or(X_37,X_38)),or(X_37,or(not(X),X_38))))
| axiom(implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_37,X_38)),or(X_37,or(not(X),X_38)))) ),[0,1,1],$fot(implies(X,X_38))]]) ).
cnf(refute_0_79,plain,
( ~ axiom(implies(or(not(X),or(X_37,X_38)),or(X_37,or(not(X),X_38))))
| axiom(implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_38),implies(X,X_38)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
axiom(implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_37,X_38)),or(X_37,or(not(X),X_38)))) )],[refute_0_74,refute_0_79]) ).
cnf(refute_0_81,plain,
or(not(X),or(X_37,X_38)) = implies(X,or(X_37,X_38)),
inference(subst,[],[refute_0_37:[bind(Y,$fot(or(X_37,X_38)))]]) ).
cnf(refute_0_82,plain,
implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38))) = implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38))))]]) ).
cnf(refute_0_83,plain,
( implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38))) != implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38)))
| or(not(X),or(X_37,X_38)) != implies(X,or(X_37,X_38))
| implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38))) = implies(implies(X,or(X_37,X_38)),or(X_37,implies(X,X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38))),implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38)))) ),[1,0],$fot(implies(X,or(X_37,X_38)))]]) ).
cnf(refute_0_84,plain,
( or(not(X),or(X_37,X_38)) != implies(X,or(X_37,X_38))
| implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38))) = implies(implies(X,or(X_37,X_38)),or(X_37,implies(X,X_38))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38))),implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38)))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38))) = implies(implies(X,or(X_37,X_38)),or(X_37,implies(X,X_38))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_37,X_38)),implies(X,or(X_37,X_38))) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
( implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38))) != implies(implies(X,or(X_37,X_38)),or(X_37,implies(X,X_38)))
| ~ axiom(implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38))))
| axiom(implies(implies(X,or(X_37,X_38)),or(X_37,implies(X,X_38)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38)))) ),[0],$fot(implies(implies(X,or(X_37,X_38)),or(X_37,implies(X,X_38))))]]) ).
cnf(refute_0_87,plain,
( ~ axiom(implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38))))
| axiom(implies(implies(X,or(X_37,X_38)),or(X_37,implies(X,X_38)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38))),implies(implies(X,or(X_37,X_38)),or(X_37,implies(X,X_38)))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
axiom(implies(implies(X,or(X_37,X_38)),or(X_37,implies(X,X_38)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),or(X_37,X_38)),or(X_37,implies(X,X_38)))) )],[refute_0_80,refute_0_87]) ).
cnf(refute_0_89,plain,
axiom(implies(implies(X_46,or(X_47,X_48)),or(X_47,implies(X_46,X_48)))),
inference(subst,[],[refute_0_88:[bind(X,$fot(X_46)),bind(X_37,$fot(X_47)),bind(X_38,$fot(X_48))]]) ).
cnf(refute_0_90,plain,
theorem(implies(implies(X_46,or(X_47,X_48)),or(X_47,implies(X_46,X_48)))),
inference(resolve,[$cnf( axiom(implies(implies(X_46,or(X_47,X_48)),or(X_47,implies(X_46,X_48)))) )],[refute_0_89,refute_0_73]) ).
cnf(refute_0_91,plain,
theorem(implies(implies(X_106,or(X_107,X_108)),or(X_107,implies(X_106,X_108)))),
inference(subst,[],[refute_0_90:[bind(X_46,$fot(X_106)),bind(X_47,$fot(X_107)),bind(X_48,$fot(X_108))]]) ).
cnf(refute_0_92,plain,
theorem(and(implies(implies(X_106,or(X_107,X_108)),or(X_107,implies(X_106,X_108))),implies(implies(X_106,or(X_107,X_108)),or(X_107,implies(X_106,X_108))))),
inference(resolve,[$cnf( theorem(implies(implies(X_106,or(X_107,X_108)),or(X_107,implies(X_106,X_108)))) )],[refute_0_91,refute_0_72]) ).
cnf(refute_0_93,plain,
( ~ theorem(X_945)
| ~ theorem(implies(X_945,implies(X_946,X_946)))
| theorem(implies(X_946,X_946)) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_946,X_946))),bind(Y,$fot(X_945))]]) ).
cnf(refute_0_94,plain,
theorem(implies(X_3,or(not(X_11),X_3))),
inference(subst,[],[refute_0_8:[bind(X_4,$fot(not(X_11)))]]) ).
cnf(refute_0_95,plain,
implies(X_11,X_3) = or(not(X_11),X_3),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_96,plain,
( implies(X_11,X_3) != or(not(X_11),X_3)
| or(not(X_11),X_3) = implies(X_11,X_3) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(implies(X_11,X_3))),bind(Y0,$fot(or(not(X_11),X_3)))]]) ).
cnf(refute_0_97,plain,
or(not(X_11),X_3) = implies(X_11,X_3),
inference(resolve,[$cnf( $equal(implies(X_11,X_3),or(not(X_11),X_3)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
( or(not(X_11),X_3) != implies(X_11,X_3)
| ~ theorem(implies(X_3,or(not(X_11),X_3)))
| theorem(implies(X_3,implies(X_11,X_3))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(X_3,or(not(X_11),X_3))) ),[0,1],$fot(implies(X_11,X_3))]]) ).
cnf(refute_0_99,plain,
( ~ theorem(implies(X_3,or(not(X_11),X_3)))
| theorem(implies(X_3,implies(X_11,X_3))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),X_3),implies(X_11,X_3)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
theorem(implies(X_3,implies(X_11,X_3))),
inference(resolve,[$cnf( theorem(implies(X_3,or(not(X_11),X_3))) )],[refute_0_94,refute_0_99]) ).
cnf(refute_0_101,plain,
theorem(implies(X_944,implies(X_943,X_944))),
inference(subst,[],[refute_0_100:[bind(X_11,$fot(X_943)),bind(X_3,$fot(X_944))]]) ).
cnf(refute_0_102,plain,
( ~ axiom(implies(implies(X_70,implies(X_71,X_72)),implies(X_71,implies(X_70,X_72))))
| theorem(implies(implies(X_70,implies(X_71,X_72)),implies(X_71,implies(X_70,X_72)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_70,implies(X_71,X_72)),implies(X_71,implies(X_70,X_72)))))]]) ).
cnf(refute_0_103,plain,
axiom(implies(or(X_36,or(not(X),X_38)),or(not(X),or(X_36,X_38)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_36)),bind(B,$fot(not(X))),bind(C,$fot(X_38))]]) ).
cnf(refute_0_104,plain,
implies(X,or(X_36,X_38)) = or(not(X),or(X_36,X_38)),
inference(subst,[],[implies_definition:[bind(Y,$fot(or(X_36,X_38)))]]) ).
cnf(refute_0_105,plain,
( implies(X,or(X_36,X_38)) != or(not(X),or(X_36,X_38))
| or(not(X),or(X_36,X_38)) = implies(X,or(X_36,X_38)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(implies(X,or(X_36,X_38)))),bind(Y0,$fot(or(not(X),or(X_36,X_38))))]]) ).
cnf(refute_0_106,plain,
or(not(X),or(X_36,X_38)) = implies(X,or(X_36,X_38)),
inference(resolve,[$cnf( $equal(implies(X,or(X_36,X_38)),or(not(X),or(X_36,X_38))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
( or(not(X),or(X_36,X_38)) != implies(X,or(X_36,X_38))
| ~ axiom(implies(or(X_36,or(not(X),X_38)),or(not(X),or(X_36,X_38))))
| axiom(implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_36,or(not(X),X_38)),or(not(X),or(X_36,X_38)))) ),[0,1],$fot(implies(X,or(X_36,X_38)))]]) ).
cnf(refute_0_108,plain,
( ~ axiom(implies(or(X_36,or(not(X),X_38)),or(not(X),or(X_36,X_38))))
| axiom(implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38)))) ),
inference(resolve,[$cnf( $equal(or(not(X),or(X_36,X_38)),implies(X,or(X_36,X_38))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
axiom(implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38)))),
inference(resolve,[$cnf( axiom(implies(or(X_36,or(not(X),X_38)),or(not(X),or(X_36,X_38)))) )],[refute_0_103,refute_0_108]) ).
cnf(refute_0_110,plain,
or(X_36,or(not(X),X_38)) = or(X_36,or(not(X),X_38)),
introduced(tautology,[refl,[$fot(or(X_36,or(not(X),X_38)))]]) ).
cnf(refute_0_111,plain,
( or(X_36,or(not(X),X_38)) != or(X_36,or(not(X),X_38))
| or(not(X),X_38) != implies(X,X_38)
| or(X_36,or(not(X),X_38)) = or(X_36,implies(X,X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_36,or(not(X),X_38)),or(X_36,or(not(X),X_38))) ),[1,1],$fot(implies(X,X_38))]]) ).
cnf(refute_0_112,plain,
( or(not(X),X_38) != implies(X,X_38)
| or(X_36,or(not(X),X_38)) = or(X_36,implies(X,X_38)) ),
inference(resolve,[$cnf( $equal(or(X_36,or(not(X),X_38)),or(X_36,or(not(X),X_38))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
or(X_36,or(not(X),X_38)) = or(X_36,implies(X,X_38)),
inference(resolve,[$cnf( $equal(or(not(X),X_38),implies(X,X_38)) )],[refute_0_77,refute_0_112]) ).
cnf(refute_0_114,plain,
implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38))) = implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38))),
introduced(tautology,[refl,[$fot(implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38))))]]) ).
cnf(refute_0_115,plain,
( implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38))) != implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38)))
| or(X_36,or(not(X),X_38)) != or(X_36,implies(X,X_38))
| implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38))) = implies(or(X_36,implies(X,X_38)),implies(X,or(X_36,X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38))),implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38)))) ),[1,0],$fot(or(X_36,implies(X,X_38)))]]) ).
cnf(refute_0_116,plain,
( or(X_36,or(not(X),X_38)) != or(X_36,implies(X,X_38))
| implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38))) = implies(or(X_36,implies(X,X_38)),implies(X,or(X_36,X_38))) ),
inference(resolve,[$cnf( $equal(implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38))),implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38)))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38))) = implies(or(X_36,implies(X,X_38)),implies(X,or(X_36,X_38))),
inference(resolve,[$cnf( $equal(or(X_36,or(not(X),X_38)),or(X_36,implies(X,X_38))) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
( implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38))) != implies(or(X_36,implies(X,X_38)),implies(X,or(X_36,X_38)))
| ~ axiom(implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38))))
| axiom(implies(or(X_36,implies(X,X_38)),implies(X,or(X_36,X_38)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38)))) ),[0],$fot(implies(or(X_36,implies(X,X_38)),implies(X,or(X_36,X_38))))]]) ).
cnf(refute_0_119,plain,
( ~ axiom(implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38))))
| axiom(implies(or(X_36,implies(X,X_38)),implies(X,or(X_36,X_38)))) ),
inference(resolve,[$cnf( $equal(implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38))),implies(or(X_36,implies(X,X_38)),implies(X,or(X_36,X_38)))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
axiom(implies(or(X_36,implies(X,X_38)),implies(X,or(X_36,X_38)))),
inference(resolve,[$cnf( axiom(implies(or(X_36,or(not(X),X_38)),implies(X,or(X_36,X_38)))) )],[refute_0_109,refute_0_119]) ).
cnf(refute_0_121,plain,
axiom(implies(or(not(X),implies(X_67,X_69)),implies(X_67,or(not(X),X_69)))),
inference(subst,[],[refute_0_120:[bind(X,$fot(X_67)),bind(X_36,$fot(not(X))),bind(X_38,$fot(X_69))]]) ).
cnf(refute_0_122,plain,
implies(X,X_69) = or(not(X),X_69),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_69))]]) ).
cnf(refute_0_123,plain,
( implies(X,X_69) != or(not(X),X_69)
| or(not(X),X_69) = implies(X,X_69) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(implies(X,X_69))),bind(Y0,$fot(or(not(X),X_69)))]]) ).
cnf(refute_0_124,plain,
or(not(X),X_69) = implies(X,X_69),
inference(resolve,[$cnf( $equal(implies(X,X_69),or(not(X),X_69)) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
( or(not(X),X_69) != implies(X,X_69)
| ~ axiom(implies(or(not(X),implies(X_67,X_69)),implies(X_67,or(not(X),X_69))))
| axiom(implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),implies(X_67,X_69)),implies(X_67,or(not(X),X_69)))) ),[0,1,1],$fot(implies(X,X_69))]]) ).
cnf(refute_0_126,plain,
( ~ axiom(implies(or(not(X),implies(X_67,X_69)),implies(X_67,or(not(X),X_69))))
| axiom(implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_69),implies(X,X_69)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
axiom(implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),implies(X_67,X_69)),implies(X_67,or(not(X),X_69)))) )],[refute_0_121,refute_0_126]) ).
cnf(refute_0_128,plain,
or(not(X),implies(X_67,X_69)) = implies(X,implies(X_67,X_69)),
inference(subst,[],[refute_0_37:[bind(Y,$fot(implies(X_67,X_69)))]]) ).
cnf(refute_0_129,plain,
implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69))) = implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69))),
introduced(tautology,[refl,[$fot(implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69))))]]) ).
cnf(refute_0_130,plain,
( implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69))) != implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69)))
| or(not(X),implies(X_67,X_69)) != implies(X,implies(X_67,X_69))
| implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69))) = implies(implies(X,implies(X_67,X_69)),implies(X_67,implies(X,X_69))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69))),implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69)))) ),[1,0],$fot(implies(X,implies(X_67,X_69)))]]) ).
cnf(refute_0_131,plain,
( or(not(X),implies(X_67,X_69)) != implies(X,implies(X_67,X_69))
| implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69))) = implies(implies(X,implies(X_67,X_69)),implies(X_67,implies(X,X_69))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69))),implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69)))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69))) = implies(implies(X,implies(X_67,X_69)),implies(X_67,implies(X,X_69))),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_67,X_69)),implies(X,implies(X_67,X_69))) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
( implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69))) != implies(implies(X,implies(X_67,X_69)),implies(X_67,implies(X,X_69)))
| ~ axiom(implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69))))
| axiom(implies(implies(X,implies(X_67,X_69)),implies(X_67,implies(X,X_69)))) ),
introduced(tautology,[equality,[$cnf( axiom(implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69)))) ),[0],$fot(implies(implies(X,implies(X_67,X_69)),implies(X_67,implies(X,X_69))))]]) ).
cnf(refute_0_134,plain,
( ~ axiom(implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69))))
| axiom(implies(implies(X,implies(X_67,X_69)),implies(X_67,implies(X,X_69)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69))),implies(implies(X,implies(X_67,X_69)),implies(X_67,implies(X,X_69)))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
axiom(implies(implies(X,implies(X_67,X_69)),implies(X_67,implies(X,X_69)))),
inference(resolve,[$cnf( axiom(implies(or(not(X),implies(X_67,X_69)),implies(X_67,implies(X,X_69)))) )],[refute_0_127,refute_0_134]) ).
cnf(refute_0_136,plain,
axiom(implies(implies(X_70,implies(X_71,X_72)),implies(X_71,implies(X_70,X_72)))),
inference(subst,[],[refute_0_135:[bind(X,$fot(X_70)),bind(X_67,$fot(X_71)),bind(X_69,$fot(X_72))]]) ).
cnf(refute_0_137,plain,
theorem(implies(implies(X_70,implies(X_71,X_72)),implies(X_71,implies(X_70,X_72)))),
inference(resolve,[$cnf( axiom(implies(implies(X_70,implies(X_71,X_72)),implies(X_71,implies(X_70,X_72)))) )],[refute_0_136,refute_0_102]) ).
cnf(refute_0_138,plain,
( ~ theorem(implies(X_70,implies(X_71,X_72)))
| ~ theorem(implies(implies(X_70,implies(X_71,X_72)),implies(X_71,implies(X_70,X_72))))
| theorem(implies(X_71,implies(X_70,X_72))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(X_71,implies(X_70,X_72)))),bind(Y,$fot(implies(X_70,implies(X_71,X_72))))]]) ).
cnf(refute_0_139,plain,
( ~ theorem(implies(X_70,implies(X_71,X_72)))
| theorem(implies(X_71,implies(X_70,X_72))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_70,implies(X_71,X_72)),implies(X_71,implies(X_70,X_72)))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
( ~ theorem(implies(X_944,implies(X_943,X_944)))
| theorem(implies(X_943,implies(X_944,X_944))) ),
inference(subst,[],[refute_0_139:[bind(X_70,$fot(X_944)),bind(X_71,$fot(X_943)),bind(X_72,$fot(X_944))]]) ).
cnf(refute_0_141,plain,
theorem(implies(X_943,implies(X_944,X_944))),
inference(resolve,[$cnf( theorem(implies(X_944,implies(X_943,X_944))) )],[refute_0_101,refute_0_140]) ).
cnf(refute_0_142,plain,
theorem(implies(X_945,implies(X_946,X_946))),
inference(subst,[],[refute_0_141:[bind(X_943,$fot(X_945)),bind(X_944,$fot(X_946))]]) ).
cnf(refute_0_143,plain,
( ~ theorem(X_945)
| theorem(implies(X_946,X_946)) ),
inference(resolve,[$cnf( theorem(implies(X_945,implies(X_946,X_946))) )],[refute_0_142,refute_0_93]) ).
cnf(refute_0_144,plain,
( ~ theorem(and(implies(implies(X_106,or(X_107,X_108)),or(X_107,implies(X_106,X_108))),implies(implies(X_106,or(X_107,X_108)),or(X_107,implies(X_106,X_108)))))
| theorem(implies(X_1145,X_1145)) ),
inference(subst,[],[refute_0_143:[bind(X_945,$fot(and(implies(implies(X_106,or(X_107,X_108)),or(X_107,implies(X_106,X_108))),implies(implies(X_106,or(X_107,X_108)),or(X_107,implies(X_106,X_108)))))),bind(X_946,$fot(X_1145))]]) ).
cnf(refute_0_145,plain,
theorem(implies(X_1145,X_1145)),
inference(resolve,[$cnf( theorem(and(implies(implies(X_106,or(X_107,X_108)),or(X_107,implies(X_106,X_108))),implies(implies(X_106,or(X_107,X_108)),or(X_107,implies(X_106,X_108))))) )],[refute_0_92,refute_0_144]) ).
cnf(refute_0_146,plain,
theorem(implies(X_1146,X_1146)),
inference(subst,[],[refute_0_145:[bind(X_1145,$fot(X_1146))]]) ).
cnf(refute_0_147,plain,
theorem(or(X_1146,not(X_1146))),
inference(resolve,[$cnf( theorem(implies(X_1146,X_1146)) )],[refute_0_146,refute_0_25]) ).
cnf(refute_0_148,plain,
theorem(or(X_1147,not(X_1147))),
inference(subst,[],[refute_0_147:[bind(X_1146,$fot(X_1147))]]) ).
cnf(refute_0_149,plain,
theorem(or(X_4,or(X_1147,not(X_1147)))),
inference(resolve,[$cnf( theorem(or(X_1147,not(X_1147))) )],[refute_0_148,refute_0_12]) ).
cnf(refute_0_150,plain,
theorem(or(X_1855,or(X_1856,not(X_1856)))),
inference(subst,[],[refute_0_149:[bind(X_1147,$fot(X_1856)),bind(X_4,$fot(X_1855))]]) ).
cnf(refute_0_151,plain,
( ~ axiom(implies(or(X_36,or(X_37,X_38)),or(X_37,or(X_36,X_38))))
| theorem(implies(or(X_36,or(X_37,X_38)),or(X_37,or(X_36,X_38)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_36,or(X_37,X_38)),or(X_37,or(X_36,X_38)))))]]) ).
cnf(refute_0_152,plain,
axiom(implies(or(X_36,or(X_37,X_38)),or(X_37,or(X_36,X_38)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_36)),bind(B,$fot(X_37)),bind(C,$fot(X_38))]]) ).
cnf(refute_0_153,plain,
theorem(implies(or(X_36,or(X_37,X_38)),or(X_37,or(X_36,X_38)))),
inference(resolve,[$cnf( axiom(implies(or(X_36,or(X_37,X_38)),or(X_37,or(X_36,X_38)))) )],[refute_0_152,refute_0_151]) ).
cnf(refute_0_154,plain,
( ~ theorem(implies(or(X_36,or(X_37,X_38)),or(X_37,or(X_36,X_38))))
| ~ theorem(or(X_36,or(X_37,X_38)))
| theorem(or(X_37,or(X_36,X_38))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_37,or(X_36,X_38)))),bind(Y,$fot(or(X_36,or(X_37,X_38))))]]) ).
cnf(refute_0_155,plain,
( ~ theorem(or(X_36,or(X_37,X_38)))
| theorem(or(X_37,or(X_36,X_38))) ),
inference(resolve,[$cnf( theorem(implies(or(X_36,or(X_37,X_38)),or(X_37,or(X_36,X_38)))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
( ~ theorem(or(X_1855,or(X_1856,not(X_1856))))
| theorem(or(X_1856,or(X_1855,not(X_1856)))) ),
inference(subst,[],[refute_0_155:[bind(X_36,$fot(X_1855)),bind(X_37,$fot(X_1856)),bind(X_38,$fot(not(X_1856)))]]) ).
cnf(refute_0_157,plain,
theorem(or(X_1856,or(X_1855,not(X_1856)))),
inference(resolve,[$cnf( theorem(or(X_1855,or(X_1856,not(X_1856)))) )],[refute_0_150,refute_0_156]) ).
cnf(refute_0_158,plain,
theorem(or(X_1861,or(not(X),not(X_1861)))),
inference(subst,[],[refute_0_157:[bind(X_1855,$fot(not(X))),bind(X_1856,$fot(X_1861))]]) ).
cnf(refute_0_159,plain,
implies(X,not(X_1861)) = or(not(X),not(X_1861)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_1861)))]]) ).
cnf(refute_0_160,plain,
( implies(X,not(X_1861)) != or(not(X),not(X_1861))
| or(not(X),not(X_1861)) = implies(X,not(X_1861)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(implies(X,not(X_1861)))),bind(Y0,$fot(or(not(X),not(X_1861))))]]) ).
cnf(refute_0_161,plain,
or(not(X),not(X_1861)) = implies(X,not(X_1861)),
inference(resolve,[$cnf( $equal(implies(X,not(X_1861)),or(not(X),not(X_1861))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
( or(not(X),not(X_1861)) != implies(X,not(X_1861))
| ~ theorem(or(X_1861,or(not(X),not(X_1861))))
| theorem(or(X_1861,implies(X,not(X_1861)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(X_1861,or(not(X),not(X_1861)))) ),[0,1],$fot(implies(X,not(X_1861)))]]) ).
cnf(refute_0_163,plain,
( ~ theorem(or(X_1861,or(not(X),not(X_1861))))
| theorem(or(X_1861,implies(X,not(X_1861)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_1861)),implies(X,not(X_1861))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
theorem(or(X_1861,implies(X,not(X_1861)))),
inference(resolve,[$cnf( theorem(or(X_1861,or(not(X),not(X_1861)))) )],[refute_0_158,refute_0_163]) ).
cnf(refute_0_165,plain,
theorem(or(X_2879,implies(X,not(X_2879)))),
inference(subst,[],[refute_0_164:[bind(X_1861,$fot(X_2879))]]) ).
cnf(refute_0_166,plain,
( ~ theorem(implies(or(X_1389,X_1388),or(X_1389,not(not(X_1388)))))
| ~ theorem(or(X_1389,X_1388))
| theorem(or(X_1389,not(not(X_1388)))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_1389,not(not(X_1388))))),bind(Y,$fot(or(X_1389,X_1388)))]]) ).
cnf(refute_0_167,plain,
( ~ axiom(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40))))
| theorem(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40)))))]]) ).
cnf(refute_0_168,plain,
axiom(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40)))),
inference(subst,[],[axiom_1_6:[bind(A,$fot(X_39)),bind(B,$fot(X_40)),bind(C,$fot(X_41))]]) ).
cnf(refute_0_169,plain,
theorem(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40)))),
inference(resolve,[$cnf( axiom(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40)))) )],[refute_0_168,refute_0_167]) ).
cnf(refute_0_170,plain,
( ~ theorem(implies(X_39,X_40))
| ~ theorem(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40))))
| theorem(implies(or(X_41,X_39),or(X_41,X_40))) ),
inference(subst,[],[rule_2:[bind(X,$fot(implies(or(X_41,X_39),or(X_41,X_40)))),bind(Y,$fot(implies(X_39,X_40)))]]) ).
cnf(refute_0_171,plain,
( ~ theorem(implies(X_39,X_40))
| theorem(implies(or(X_41,X_39),or(X_41,X_40))) ),
inference(resolve,[$cnf( theorem(implies(implies(X_39,X_40),implies(or(X_41,X_39),or(X_41,X_40)))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
( ~ theorem(implies(X_1148,not(not(X_1148))))
| theorem(implies(or(X_41,X_1148),or(X_41,not(not(X_1148))))) ),
inference(subst,[],[refute_0_171:[bind(X_39,$fot(X_1148)),bind(X_40,$fot(not(not(X_1148))))]]) ).
cnf(refute_0_173,plain,
( ~ theorem(or(not(X),not(X_96)))
| theorem(implies(X_96,not(X))) ),
inference(subst,[],[refute_0_67:[bind(X_11,$fot(X_96)),bind(X_7,$fot(not(X)))]]) ).
cnf(refute_0_174,plain,
implies(X,not(X_96)) = or(not(X),not(X_96)),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(X_96)))]]) ).
cnf(refute_0_175,plain,
( implies(X,not(X_96)) != or(not(X),not(X_96))
| or(not(X),not(X_96)) = implies(X,not(X_96)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(implies(X,not(X_96)))),bind(Y0,$fot(or(not(X),not(X_96))))]]) ).
cnf(refute_0_176,plain,
or(not(X),not(X_96)) = implies(X,not(X_96)),
inference(resolve,[$cnf( $equal(implies(X,not(X_96)),or(not(X),not(X_96))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
( or(not(X),not(X_96)) != implies(X,not(X_96))
| ~ theorem(implies(X,not(X_96)))
| theorem(or(not(X),not(X_96))) ),
introduced(tautology,[equality,[$cnf( ~ theorem(or(not(X),not(X_96))) ),[0],$fot(implies(X,not(X_96)))]]) ).
cnf(refute_0_178,plain,
( ~ theorem(implies(X,not(X_96)))
| theorem(or(not(X),not(X_96))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(X_96)),implies(X,not(X_96))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
( ~ theorem(implies(X,not(X_96)))
| theorem(implies(X_96,not(X))) ),
inference(resolve,[$cnf( theorem(or(not(X),not(X_96))) )],[refute_0_178,refute_0_173]) ).
cnf(refute_0_180,plain,
( ~ theorem(implies(not(X_96),not(X_96)))
| theorem(implies(X_96,not(not(X_96)))) ),
inference(subst,[],[refute_0_179:[bind(X,$fot(not(X_96)))]]) ).
cnf(refute_0_181,plain,
theorem(implies(not(X_96),not(X_96))),
inference(subst,[],[refute_0_145:[bind(X_1145,$fot(not(X_96)))]]) ).
cnf(refute_0_182,plain,
theorem(implies(X_96,not(not(X_96)))),
inference(resolve,[$cnf( theorem(implies(not(X_96),not(X_96))) )],[refute_0_181,refute_0_180]) ).
cnf(refute_0_183,plain,
theorem(implies(X_1148,not(not(X_1148)))),
inference(subst,[],[refute_0_182:[bind(X_96,$fot(X_1148))]]) ).
cnf(refute_0_184,plain,
theorem(implies(or(X_41,X_1148),or(X_41,not(not(X_1148))))),
inference(resolve,[$cnf( theorem(implies(X_1148,not(not(X_1148)))) )],[refute_0_183,refute_0_172]) ).
cnf(refute_0_185,plain,
theorem(implies(or(X_1389,X_1388),or(X_1389,not(not(X_1388))))),
inference(subst,[],[refute_0_184:[bind(X_1148,$fot(X_1388)),bind(X_41,$fot(X_1389))]]) ).
cnf(refute_0_186,plain,
( ~ theorem(or(X_1389,X_1388))
| theorem(or(X_1389,not(not(X_1388)))) ),
inference(resolve,[$cnf( theorem(implies(or(X_1389,X_1388),or(X_1389,not(not(X_1388))))) )],[refute_0_185,refute_0_166]) ).
cnf(refute_0_187,plain,
( ~ theorem(or(X_2879,implies(X,not(X_2879))))
| theorem(or(X_2879,not(not(implies(X,not(X_2879)))))) ),
inference(subst,[],[refute_0_186:[bind(X_1388,$fot(implies(X,not(X_2879)))),bind(X_1389,$fot(X_2879))]]) ).
cnf(refute_0_188,plain,
theorem(or(X_2879,not(not(implies(X,not(X_2879)))))),
inference(resolve,[$cnf( theorem(or(X_2879,implies(X,not(X_2879)))) )],[refute_0_165,refute_0_187]) ).
cnf(refute_0_189,plain,
( and(P,Q) != not(implies(P,not(Q)))
| not(implies(P,not(Q))) = and(P,Q) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(and(P,Q))),bind(Y0,$fot(not(implies(P,not(Q)))))]]) ).
cnf(refute_0_190,plain,
not(implies(P,not(Q))) = and(P,Q),
inference(resolve,[$cnf( $equal(and(P,Q),not(implies(P,not(Q)))) )],[refute_0_45,refute_0_189]) ).
cnf(refute_0_191,plain,
not(implies(X,not(X_2879))) = and(X,X_2879),
inference(subst,[],[refute_0_190:[bind(P,$fot(X)),bind(Q,$fot(X_2879))]]) ).
cnf(refute_0_192,plain,
not(not(implies(X,not(X_2879)))) = not(not(implies(X,not(X_2879)))),
introduced(tautology,[refl,[$fot(not(not(implies(X,not(X_2879)))))]]) ).
cnf(refute_0_193,plain,
( not(implies(X,not(X_2879))) != and(X,X_2879)
| not(not(implies(X,not(X_2879)))) != not(not(implies(X,not(X_2879))))
| not(not(implies(X,not(X_2879)))) = not(and(X,X_2879)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(X,not(X_2879)))),not(not(implies(X,not(X_2879))))) ),[1,0],$fot(and(X,X_2879))]]) ).
cnf(refute_0_194,plain,
( not(implies(X,not(X_2879))) != and(X,X_2879)
| not(not(implies(X,not(X_2879)))) = not(and(X,X_2879)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(X_2879)))),not(not(implies(X,not(X_2879))))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
not(not(implies(X,not(X_2879)))) = not(and(X,X_2879)),
inference(resolve,[$cnf( $equal(not(implies(X,not(X_2879))),and(X,X_2879)) )],[refute_0_191,refute_0_194]) ).
cnf(refute_0_196,plain,
or(X_2879,not(not(implies(X,not(X_2879))))) = or(X_2879,not(not(implies(X,not(X_2879))))),
introduced(tautology,[refl,[$fot(or(X_2879,not(not(implies(X,not(X_2879))))))]]) ).
cnf(refute_0_197,plain,
( not(not(implies(X,not(X_2879)))) != not(and(X,X_2879))
| or(X_2879,not(not(implies(X,not(X_2879))))) != or(X_2879,not(not(implies(X,not(X_2879)))))
| or(X_2879,not(not(implies(X,not(X_2879))))) = or(X_2879,not(and(X,X_2879))) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_2879,not(not(implies(X,not(X_2879))))),or(X_2879,not(not(implies(X,not(X_2879)))))) ),[1,1],$fot(not(and(X,X_2879)))]]) ).
cnf(refute_0_198,plain,
( not(not(implies(X,not(X_2879)))) != not(and(X,X_2879))
| or(X_2879,not(not(implies(X,not(X_2879))))) = or(X_2879,not(and(X,X_2879))) ),
inference(resolve,[$cnf( $equal(or(X_2879,not(not(implies(X,not(X_2879))))),or(X_2879,not(not(implies(X,not(X_2879)))))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
or(X_2879,not(not(implies(X,not(X_2879))))) = or(X_2879,not(and(X,X_2879))),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(X_2879)))),not(and(X,X_2879))) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
( or(X_2879,not(not(implies(X,not(X_2879))))) != or(X_2879,not(and(X,X_2879)))
| ~ theorem(or(X_2879,not(not(implies(X,not(X_2879))))))
| theorem(or(X_2879,not(and(X,X_2879)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(X_2879,not(not(implies(X,not(X_2879)))))) ),[0],$fot(or(X_2879,not(and(X,X_2879))))]]) ).
cnf(refute_0_201,plain,
( ~ theorem(or(X_2879,not(not(implies(X,not(X_2879))))))
| theorem(or(X_2879,not(and(X,X_2879)))) ),
inference(resolve,[$cnf( $equal(or(X_2879,not(not(implies(X,not(X_2879))))),or(X_2879,not(and(X,X_2879)))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
theorem(or(X_2879,not(and(X,X_2879)))),
inference(resolve,[$cnf( theorem(or(X_2879,not(not(implies(X,not(X_2879)))))) )],[refute_0_188,refute_0_201]) ).
cnf(refute_0_203,plain,
theorem(or(X_2918,not(and(X_2917,X_2918)))),
inference(subst,[],[refute_0_202:[bind(X,$fot(X_2917)),bind(X_2879,$fot(X_2918))]]) ).
cnf(refute_0_204,plain,
theorem(or(not(and(X_2917,X_2918)),X_2918)),
inference(resolve,[$cnf( theorem(or(X_2918,not(and(X_2917,X_2918)))) )],[refute_0_203,refute_0_5]) ).
cnf(refute_0_205,plain,
or(not(and(X_2917,X_2918)),X_2918) = implies(and(X_2917,X_2918),X_2918),
inference(subst,[],[refute_0_37:[bind(X,$fot(and(X_2917,X_2918))),bind(Y,$fot(X_2918))]]) ).
cnf(refute_0_206,plain,
( or(not(and(X_2917,X_2918)),X_2918) != implies(and(X_2917,X_2918),X_2918)
| ~ theorem(or(not(and(X_2917,X_2918)),X_2918))
| theorem(implies(and(X_2917,X_2918),X_2918)) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(and(X_2917,X_2918)),X_2918)) ),[0],$fot(implies(and(X_2917,X_2918),X_2918))]]) ).
cnf(refute_0_207,plain,
( ~ theorem(or(not(and(X_2917,X_2918)),X_2918))
| theorem(implies(and(X_2917,X_2918),X_2918)) ),
inference(resolve,[$cnf( $equal(or(not(and(X_2917,X_2918)),X_2918),implies(and(X_2917,X_2918),X_2918)) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
theorem(implies(and(X_2917,X_2918),X_2918)),
inference(resolve,[$cnf( theorem(or(not(and(X_2917,X_2918)),X_2918)) )],[refute_0_204,refute_0_207]) ).
cnf(refute_0_209,plain,
theorem(implies(and(p,q),q)),
inference(subst,[],[refute_0_208:[bind(X_2917,$fot(p)),bind(X_2918,$fot(q))]]) ).
cnf(refute_0_210,plain,
$false,
inference(resolve,[$cnf( theorem(implies(and(p,q),q)) )],[refute_0_209,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL241-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 20:05:23 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.26/4.55 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.26/4.55
% 4.26/4.55 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.26/4.57
%------------------------------------------------------------------------------