TSTP Solution File: LCL116-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL116-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:49:43 EDT 2022
% Result : Unsatisfiable 0.40s 0.57s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 63
% Syntax : Number of clauses : 228 ( 120 unt; 0 nHn; 113 RR)
% Number of literals : 387 ( 386 equ; 161 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 314 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X ).
cnf(wajsberg_2,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ).
cnf(wajsberg_3,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth ).
cnf(prove_mv_50,negated_conjecture,
implies(not(a),implies(b,not(implies(b,a)))) != truth ).
cnf(refute_0_0,plain,
implies(implies(truth,X_16),implies(implies(X_16,X_17),implies(truth,X_17))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_16)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_1,plain,
implies(truth,X_17) = X_17,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_2,plain,
( implies(implies(truth,X_16),implies(implies(X_16,X_17),implies(truth,X_17))) != truth
| implies(truth,X_17) != X_17
| implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(X_16,X_17),implies(truth,X_17))),truth) ),[0,1,1],$fot(X_17)]]) ).
cnf(refute_0_3,plain,
( implies(implies(truth,X_16),implies(implies(X_16,X_17),implies(truth,X_17))) != truth
| implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_17),X_17) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(X_16,X_17),implies(truth,X_17))),truth) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
implies(truth,X_16) = X_16,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_16))]]) ).
cnf(refute_0_6,plain,
implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) = implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)))]]) ).
cnf(refute_0_7,plain,
( implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) != implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17))
| implies(truth,X_16) != X_16
| implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) = implies(X_16,implies(implies(X_16,X_17),X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)),implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17))) ),[1,0],$fot(X_16)]]) ).
cnf(refute_0_8,plain,
( implies(truth,X_16) != X_16
| implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) = implies(X_16,implies(implies(X_16,X_17),X_17)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)),implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) = implies(X_16,implies(implies(X_16,X_17),X_17)),
inference(resolve,[$cnf( $equal(implies(truth,X_16),X_16) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) != implies(X_16,implies(implies(X_16,X_17),X_17))
| implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) != truth
| implies(X_16,implies(implies(X_16,X_17),X_17)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)),truth) ),[0],$fot(implies(X_16,implies(implies(X_16,X_17),X_17)))]]) ).
cnf(refute_0_11,plain,
( implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) != truth
| implies(X_16,implies(implies(X_16,X_17),X_17)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)),implies(X_16,implies(implies(X_16,X_17),X_17))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
implies(X_16,implies(implies(X_16,X_17),X_17)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)),truth) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
implies(not(X_57),implies(implies(not(X_57),not(X_56)),not(X_56))) = truth,
inference(subst,[],[refute_0_12:[bind(X_16,$fot(not(X_57))),bind(X_17,$fot(not(X_56)))]]) ).
cnf(refute_0_14,plain,
implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) = implies(implies(implies(not(X_42),X_43),implies(not(X_43),X_42)),implies(not(X_43),X_42)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(not(X_43),X_42))),bind(Y,$fot(implies(not(X_42),X_43)))]]) ).
cnf(refute_0_15,plain,
implies(implies(not(X),not(not(X_37))),implies(not(X_37),X)) = truth,
inference(subst,[],[wajsberg_4:[bind(Y,$fot(not(X_37)))]]) ).
cnf(refute_0_16,plain,
implies(implies(not(not(Y)),Y),Y) = implies(implies(Y,not(not(Y))),not(not(Y))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_17,plain,
implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_18,plain,
implies(implies(X_15,implies(not(X_17),not(truth))),implies(implies(implies(not(X_17),not(truth)),X_17),implies(X_15,X_17))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_15)),bind(Y,$fot(implies(not(X_17),not(truth)))),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_19,plain,
implies(implies(not(X_1),not(truth)),implies(truth,X_1)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_1)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_20,plain,
implies(truth,X_1) = X_1,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_21,plain,
( implies(implies(not(X_1),not(truth)),implies(truth,X_1)) != truth
| implies(truth,X_1) != X_1
| implies(implies(not(X_1),not(truth)),X_1) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_1),not(truth)),implies(truth,X_1)),truth) ),[0,1],$fot(X_1)]]) ).
cnf(refute_0_22,plain,
( implies(implies(not(X_1),not(truth)),implies(truth,X_1)) != truth
| implies(implies(not(X_1),not(truth)),X_1) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_1),X_1) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
implies(implies(not(X_1),not(truth)),X_1) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_1),not(truth)),implies(truth,X_1)),truth) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
implies(implies(not(X_17),not(truth)),X_17) = truth,
inference(subst,[],[refute_0_23:[bind(X_1,$fot(X_17))]]) ).
cnf(refute_0_25,plain,
( implies(implies(X_15,implies(not(X_17),not(truth))),implies(implies(implies(not(X_17),not(truth)),X_17),implies(X_15,X_17))) != truth
| implies(implies(not(X_17),not(truth)),X_17) != truth
| implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_15,implies(not(X_17),not(truth))),implies(implies(implies(not(X_17),not(truth)),X_17),implies(X_15,X_17))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_26,plain,
( implies(implies(X_15,implies(not(X_17),not(truth))),implies(implies(implies(not(X_17),not(truth)),X_17),implies(X_15,X_17))) != truth
| implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_17),not(truth)),X_17),truth) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_15,implies(not(X_17),not(truth))),implies(implies(implies(not(X_17),not(truth)),X_17),implies(X_15,X_17))),truth) )],[refute_0_18,refute_0_26]) ).
cnf(refute_0_28,plain,
implies(truth,implies(X_15,X_17)) = implies(X_15,X_17),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_15,X_17)))]]) ).
cnf(refute_0_29,plain,
implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))) = implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))),
introduced(tautology,[refl,[$fot(implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))))]]) ).
cnf(refute_0_30,plain,
( implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))) != implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17)))
| implies(truth,implies(X_15,X_17)) != implies(X_15,X_17)
| implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))) = implies(implies(X_15,implies(not(X_17),not(truth))),implies(X_15,X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))),implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17)))) ),[1,1],$fot(implies(X_15,X_17))]]) ).
cnf(refute_0_31,plain,
( implies(truth,implies(X_15,X_17)) != implies(X_15,X_17)
| implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))) = implies(implies(X_15,implies(not(X_17),not(truth))),implies(X_15,X_17)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))),implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17)))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))) = implies(implies(X_15,implies(not(X_17),not(truth))),implies(X_15,X_17)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_15,X_17)),implies(X_15,X_17)) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))) != implies(implies(X_15,implies(not(X_17),not(truth))),implies(X_15,X_17))
| implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))) != truth
| implies(implies(X_15,implies(not(X_17),not(truth))),implies(X_15,X_17)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))),truth) ),[0],$fot(implies(implies(X_15,implies(not(X_17),not(truth))),implies(X_15,X_17)))]]) ).
cnf(refute_0_34,plain,
( implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))) != truth
| implies(implies(X_15,implies(not(X_17),not(truth))),implies(X_15,X_17)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))),implies(implies(X_15,implies(not(X_17),not(truth))),implies(X_15,X_17))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
implies(implies(X_15,implies(not(X_17),not(truth))),implies(X_15,X_17)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_15,implies(not(X_17),not(truth))),implies(truth,implies(X_15,X_17))),truth) )],[refute_0_27,refute_0_34]) ).
cnf(refute_0_36,plain,
implies(implies(implies(not(not(truth)),not(not(X_32))),implies(not(X_32),not(truth))),implies(implies(not(not(truth)),not(not(X_32))),X_32)) = truth,
inference(subst,[],[refute_0_35:[bind(X_15,$fot(implies(not(not(truth)),not(not(X_32))))),bind(X_17,$fot(X_32))]]) ).
cnf(refute_0_37,plain,
implies(implies(not(not(truth)),not(not(X_32))),implies(not(X_32),not(truth))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(truth))),bind(Y,$fot(not(X_32)))]]) ).
cnf(refute_0_38,plain,
( implies(implies(implies(not(not(truth)),not(not(X_32))),implies(not(X_32),not(truth))),implies(implies(not(not(truth)),not(not(X_32))),X_32)) != truth
| implies(implies(not(not(truth)),not(not(X_32))),implies(not(X_32),not(truth))) != truth
| implies(truth,implies(implies(not(not(truth)),not(not(X_32))),X_32)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_32))),implies(not(X_32),not(truth))),implies(implies(not(not(truth)),not(not(X_32))),X_32)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_39,plain,
( implies(implies(implies(not(not(truth)),not(not(X_32))),implies(not(X_32),not(truth))),implies(implies(not(not(truth)),not(not(X_32))),X_32)) != truth
| implies(truth,implies(implies(not(not(truth)),not(not(X_32))),X_32)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_32))),implies(not(X_32),not(truth))),truth) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
implies(truth,implies(implies(not(not(truth)),not(not(X_32))),X_32)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_32))),implies(not(X_32),not(truth))),implies(implies(not(not(truth)),not(not(X_32))),X_32)),truth) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
implies(truth,implies(implies(not(not(truth)),not(not(X_32))),X_32)) = implies(implies(not(not(truth)),not(not(X_32))),X_32),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(not(truth)),not(not(X_32))),X_32)))]]) ).
cnf(refute_0_42,plain,
( implies(truth,implies(implies(not(not(truth)),not(not(X_32))),X_32)) != implies(implies(not(not(truth)),not(not(X_32))),X_32)
| implies(truth,implies(implies(not(not(truth)),not(not(X_32))),X_32)) != truth
| implies(implies(not(not(truth)),not(not(X_32))),X_32) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_32))),X_32)),truth) ),[0],$fot(implies(implies(not(not(truth)),not(not(X_32))),X_32))]]) ).
cnf(refute_0_43,plain,
( implies(truth,implies(implies(not(not(truth)),not(not(X_32))),X_32)) != truth
| implies(implies(not(not(truth)),not(not(X_32))),X_32) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_32))),X_32)),implies(implies(not(not(truth)),not(not(X_32))),X_32)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
implies(implies(not(not(truth)),not(not(X_32))),X_32) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_32))),X_32)),truth) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
implies(truth,not(not(X_32))) = not(not(X_32)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(X_32))))]]) ).
cnf(refute_0_46,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
inference(subst,[],[refute_0_23:[bind(X_1,$fot(not(truth)))]]) ).
cnf(refute_0_47,plain,
implies(implies(X,not(truth)),not(truth)) = implies(implies(not(truth),X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_48,plain,
implies(implies(not(truth),implies(not(X_32),not(truth))),implies(not(truth),X_32)) = truth,
inference(subst,[],[refute_0_35:[bind(X_15,$fot(not(truth))),bind(X_17,$fot(X_32))]]) ).
cnf(refute_0_49,plain,
implies(implies(X_15,truth),implies(implies(truth,X_17),implies(X_15,X_17))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_15)),bind(Y,$fot(truth)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_50,plain,
( implies(implies(X_15,truth),implies(implies(truth,X_17),implies(X_15,X_17))) != truth
| implies(truth,X_17) != X_17
| implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_15,truth),implies(implies(truth,X_17),implies(X_15,X_17))),truth) ),[0,1,0],$fot(X_17)]]) ).
cnf(refute_0_51,plain,
( implies(implies(X_15,truth),implies(implies(truth,X_17),implies(X_15,X_17))) != truth
| implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_17),X_17) )],[refute_0_1,refute_0_50]) ).
cnf(refute_0_52,plain,
implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_15,truth),implies(implies(truth,X_17),implies(X_15,X_17))),truth) )],[refute_0_49,refute_0_51]) ).
cnf(refute_0_53,plain,
implies(truth,implies(X_17,implies(X_15,X_17))) = implies(X_17,implies(X_15,X_17)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_17,implies(X_15,X_17))))]]) ).
cnf(refute_0_54,plain,
implies(X_19,implies(implies(X_19,truth),truth)) = truth,
inference(subst,[],[refute_0_12:[bind(X_16,$fot(X_19)),bind(X_17,$fot(truth))]]) ).
cnf(refute_0_55,plain,
implies(implies(truth,X_6),X_6) = implies(implies(X_6,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_56,plain,
implies(truth,X_6) = X_6,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_57,plain,
( implies(implies(truth,X_6),X_6) != implies(implies(X_6,truth),truth)
| implies(truth,X_6) != X_6
| implies(X_6,X_6) = implies(implies(X_6,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_6),X_6),implies(implies(X_6,truth),truth)) ),[0,0],$fot(X_6)]]) ).
cnf(refute_0_58,plain,
( implies(implies(truth,X_6),X_6) != implies(implies(X_6,truth),truth)
| implies(X_6,X_6) = implies(implies(X_6,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,X_6),X_6) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
implies(X_6,X_6) = implies(implies(X_6,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_6),X_6),implies(implies(X_6,truth),truth)) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
implies(X_19,X_19) = implies(implies(X_19,truth),truth),
inference(subst,[],[refute_0_59:[bind(X_6,$fot(X_19))]]) ).
cnf(refute_0_61,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_62,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_63,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( implies(X_19,X_19) != implies(implies(X_19,truth),truth)
| implies(implies(X_19,truth),truth) = implies(X_19,X_19) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(X_19,X_19))),bind(Y0,$fot(implies(implies(X_19,truth),truth)))]]) ).
cnf(refute_0_65,plain,
implies(implies(X_19,truth),truth) = implies(X_19,X_19),
inference(resolve,[$cnf( $equal(implies(X_19,X_19),implies(implies(X_19,truth),truth)) )],[refute_0_60,refute_0_64]) ).
cnf(refute_0_66,plain,
( implies(X_19,implies(implies(X_19,truth),truth)) != truth
| implies(implies(X_19,truth),truth) != implies(X_19,X_19)
| implies(X_19,implies(X_19,X_19)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_19,implies(implies(X_19,truth),truth)),truth) ),[0,1],$fot(implies(X_19,X_19))]]) ).
cnf(refute_0_67,plain,
( implies(X_19,implies(implies(X_19,truth),truth)) != truth
| implies(X_19,implies(X_19,X_19)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_19,truth),truth),implies(X_19,X_19)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
implies(X_19,implies(X_19,X_19)) = truth,
inference(resolve,[$cnf( $equal(implies(X_19,implies(implies(X_19,truth),truth)),truth) )],[refute_0_54,refute_0_67]) ).
cnf(refute_0_69,plain,
implies(truth,implies(implies(truth,X_20),X_20)) = implies(implies(truth,X_20),X_20),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,X_20),X_20)))]]) ).
cnf(refute_0_70,plain,
implies(truth,implies(implies(truth,X_20),X_20)) = truth,
inference(subst,[],[refute_0_12:[bind(X_16,$fot(truth)),bind(X_17,$fot(X_20))]]) ).
cnf(refute_0_71,plain,
( implies(truth,implies(implies(truth,X_20),X_20)) != implies(implies(truth,X_20),X_20)
| implies(truth,implies(implies(truth,X_20),X_20)) != truth
| truth = implies(implies(truth,X_20),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,X_20),X_20)),implies(implies(truth,X_20),X_20)) ),[0],$fot(truth)]]) ).
cnf(refute_0_72,plain,
( implies(truth,implies(implies(truth,X_20),X_20)) != implies(implies(truth,X_20),X_20)
| truth = implies(implies(truth,X_20),X_20) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_20),X_20)),truth) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
truth = implies(implies(truth,X_20),X_20),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_20),X_20)),implies(implies(truth,X_20),X_20)) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
implies(truth,X_20) = X_20,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_20))]]) ).
cnf(refute_0_75,plain,
implies(implies(truth,X_20),X_20) = implies(implies(truth,X_20),X_20),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_20),X_20))]]) ).
cnf(refute_0_76,plain,
( implies(implies(truth,X_20),X_20) != implies(implies(truth,X_20),X_20)
| implies(truth,X_20) != X_20
| implies(implies(truth,X_20),X_20) = implies(X_20,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_20),X_20),implies(implies(truth,X_20),X_20)) ),[1,0],$fot(X_20)]]) ).
cnf(refute_0_77,plain,
( implies(truth,X_20) != X_20
| implies(implies(truth,X_20),X_20) = implies(X_20,X_20) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_20),X_20),implies(implies(truth,X_20),X_20)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
implies(implies(truth,X_20),X_20) = implies(X_20,X_20),
inference(resolve,[$cnf( $equal(implies(truth,X_20),X_20) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
( implies(implies(truth,X_20),X_20) != implies(X_20,X_20)
| truth != implies(implies(truth,X_20),X_20)
| truth = implies(X_20,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(truth,implies(implies(truth,X_20),X_20)) ),[1],$fot(implies(X_20,X_20))]]) ).
cnf(refute_0_80,plain,
( truth != implies(implies(truth,X_20),X_20)
| truth = implies(X_20,X_20) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_20),X_20),implies(X_20,X_20)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
truth = implies(X_20,X_20),
inference(resolve,[$cnf( $equal(truth,implies(implies(truth,X_20),X_20)) )],[refute_0_73,refute_0_80]) ).
cnf(refute_0_82,plain,
( truth != implies(X_20,X_20)
| implies(X_20,X_20) = truth ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X_20,X_20)))]]) ).
cnf(refute_0_83,plain,
implies(X_20,X_20) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X_20,X_20)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
implies(X_19,X_19) = truth,
inference(subst,[],[refute_0_83:[bind(X_20,$fot(X_19))]]) ).
cnf(refute_0_85,plain,
implies(X_19,implies(X_19,X_19)) = implies(X_19,implies(X_19,X_19)),
introduced(tautology,[refl,[$fot(implies(X_19,implies(X_19,X_19)))]]) ).
cnf(refute_0_86,plain,
( implies(X_19,X_19) != truth
| implies(X_19,implies(X_19,X_19)) != implies(X_19,implies(X_19,X_19))
| implies(X_19,implies(X_19,X_19)) = implies(X_19,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_19,implies(X_19,X_19)),implies(X_19,implies(X_19,X_19))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_87,plain,
( implies(X_19,X_19) != truth
| implies(X_19,implies(X_19,X_19)) = implies(X_19,truth) ),
inference(resolve,[$cnf( $equal(implies(X_19,implies(X_19,X_19)),implies(X_19,implies(X_19,X_19))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
implies(X_19,implies(X_19,X_19)) = implies(X_19,truth),
inference(resolve,[$cnf( $equal(implies(X_19,X_19),truth) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
( implies(X_19,implies(X_19,X_19)) != implies(X_19,truth)
| implies(X_19,implies(X_19,X_19)) != truth
| implies(X_19,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_19,implies(X_19,X_19)),truth) ),[0],$fot(implies(X_19,truth))]]) ).
cnf(refute_0_90,plain,
( implies(X_19,implies(X_19,X_19)) != truth
| implies(X_19,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(X_19,implies(X_19,X_19)),implies(X_19,truth)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
implies(X_19,truth) = truth,
inference(resolve,[$cnf( $equal(implies(X_19,implies(X_19,X_19)),truth) )],[refute_0_68,refute_0_90]) ).
cnf(refute_0_92,plain,
implies(X_15,truth) = truth,
inference(subst,[],[refute_0_91:[bind(X_19,$fot(X_15))]]) ).
cnf(refute_0_93,plain,
implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) = implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))),
introduced(tautology,[refl,[$fot(implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))))]]) ).
cnf(refute_0_94,plain,
( implies(X_15,truth) != truth
| implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) != implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17)))
| implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) = implies(truth,implies(X_17,implies(X_15,X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))),implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_95,plain,
( implies(X_15,truth) != truth
| implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) = implies(truth,implies(X_17,implies(X_15,X_17))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))),implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17)))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) = implies(truth,implies(X_17,implies(X_15,X_17))),
inference(resolve,[$cnf( $equal(implies(X_15,truth),truth) )],[refute_0_92,refute_0_95]) ).
cnf(refute_0_97,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_98,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_63,refute_0_97]) ).
cnf(refute_0_99,plain,
( implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) != implies(truth,implies(X_17,implies(X_15,X_17)))
| implies(truth,implies(X_17,implies(X_15,X_17))) != implies(X_17,implies(X_15,X_17))
| implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) = implies(X_17,implies(X_15,X_17)) ),
inference(subst,[],[refute_0_98:[bind(X0,$fot(implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))))),bind(Y0,$fot(implies(truth,implies(X_17,implies(X_15,X_17))))),bind(Z0,$fot(implies(X_17,implies(X_15,X_17))))]]) ).
cnf(refute_0_100,plain,
( implies(truth,implies(X_17,implies(X_15,X_17))) != implies(X_17,implies(X_15,X_17))
| implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) = implies(X_17,implies(X_15,X_17)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))),implies(truth,implies(X_17,implies(X_15,X_17)))) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) = implies(X_17,implies(X_15,X_17)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_17,implies(X_15,X_17))),implies(X_17,implies(X_15,X_17))) )],[refute_0_53,refute_0_100]) ).
cnf(refute_0_102,plain,
( implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) != implies(X_17,implies(X_15,X_17))
| implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) != truth
| implies(X_17,implies(X_15,X_17)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))),truth) ),[0],$fot(implies(X_17,implies(X_15,X_17)))]]) ).
cnf(refute_0_103,plain,
( implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))) != truth
| implies(X_17,implies(X_15,X_17)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))),implies(X_17,implies(X_15,X_17))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
implies(X_17,implies(X_15,X_17)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_15,truth),implies(X_17,implies(X_15,X_17))),truth) )],[refute_0_52,refute_0_103]) ).
cnf(refute_0_105,plain,
implies(not(truth),implies(not(X_32),not(truth))) = truth,
inference(subst,[],[refute_0_104:[bind(X_15,$fot(not(X_32))),bind(X_17,$fot(not(truth)))]]) ).
cnf(refute_0_106,plain,
( implies(implies(not(truth),implies(not(X_32),not(truth))),implies(not(truth),X_32)) != truth
| implies(not(truth),implies(not(X_32),not(truth))) != truth
| implies(truth,implies(not(truth),X_32)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),implies(not(X_32),not(truth))),implies(not(truth),X_32)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_107,plain,
( implies(implies(not(truth),implies(not(X_32),not(truth))),implies(not(truth),X_32)) != truth
| implies(truth,implies(not(truth),X_32)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),implies(not(X_32),not(truth))),truth) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
implies(truth,implies(not(truth),X_32)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(X_32),not(truth))),implies(not(truth),X_32)),truth) )],[refute_0_48,refute_0_107]) ).
cnf(refute_0_109,plain,
implies(truth,implies(not(truth),X_32)) = implies(not(truth),X_32),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(truth),X_32)))]]) ).
cnf(refute_0_110,plain,
( implies(truth,implies(not(truth),X_32)) != implies(not(truth),X_32)
| implies(truth,implies(not(truth),X_32)) != truth
| implies(not(truth),X_32) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(not(truth),X_32)),truth) ),[0],$fot(implies(not(truth),X_32))]]) ).
cnf(refute_0_111,plain,
( implies(truth,implies(not(truth),X_32)) != truth
| implies(not(truth),X_32) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),X_32)),implies(not(truth),X_32)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
implies(not(truth),X_32) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),X_32)),truth) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
implies(not(truth),X) = truth,
inference(subst,[],[refute_0_112:[bind(X_32,$fot(X))]]) ).
cnf(refute_0_114,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(implies(not(truth),X),X)
| implies(not(truth),X) != truth
| implies(implies(X,not(truth)),not(truth)) = implies(truth,X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(implies(not(truth),X),X)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_115,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(implies(not(truth),X),X)
| implies(implies(X,not(truth)),not(truth)) = implies(truth,X) ),
inference(resolve,[$cnf( $equal(implies(not(truth),X),truth) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
implies(implies(X,not(truth)),not(truth)) = implies(truth,X),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(implies(not(truth),X),X)) )],[refute_0_47,refute_0_115]) ).
cnf(refute_0_117,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(truth,X)
| implies(truth,X) != X
| implies(implies(X,not(truth)),not(truth)) = X ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X,not(truth)),not(truth)),X) ),[0],$fot(implies(truth,X))]]) ).
cnf(refute_0_118,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(truth,X)
| implies(implies(X,not(truth)),not(truth)) = X ),
inference(resolve,[$cnf( $equal(implies(truth,X),X) )],[wajsberg_1,refute_0_117]) ).
cnf(refute_0_119,plain,
implies(implies(X,not(truth)),not(truth)) = X,
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(truth,X)) )],[refute_0_116,refute_0_118]) ).
cnf(refute_0_120,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = not(not(truth)),
inference(subst,[],[refute_0_119:[bind(X,$fot(not(not(truth))))]]) ).
cnf(refute_0_121,plain,
( implies(implies(not(not(truth)),not(truth)),not(truth)) != not(not(truth))
| implies(implies(not(not(truth)),not(truth)),not(truth)) != truth
| not(not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) ),[0],$fot(not(not(truth)))]]) ).
cnf(refute_0_122,plain,
( implies(implies(not(not(truth)),not(truth)),not(truth)) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) )],[refute_0_46,refute_0_122]) ).
cnf(refute_0_124,plain,
implies(not(not(truth)),not(not(X_32))) = implies(not(not(truth)),not(not(X_32))),
introduced(tautology,[refl,[$fot(implies(not(not(truth)),not(not(X_32))))]]) ).
cnf(refute_0_125,plain,
( implies(not(not(truth)),not(not(X_32))) != implies(not(not(truth)),not(not(X_32)))
| not(not(truth)) != truth
| implies(not(not(truth)),not(not(X_32))) = implies(truth,not(not(X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(not(X_32))),implies(not(not(truth)),not(not(X_32)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_126,plain,
( not(not(truth)) != truth
| implies(not(not(truth)),not(not(X_32))) = implies(truth,not(not(X_32))) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_32))),implies(not(not(truth)),not(not(X_32)))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
implies(not(not(truth)),not(not(X_32))) = implies(truth,not(not(X_32))),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
( implies(not(not(truth)),not(not(X_32))) != implies(truth,not(not(X_32)))
| implies(truth,not(not(X_32))) != not(not(X_32))
| implies(not(not(truth)),not(not(X_32))) = not(not(X_32)) ),
inference(subst,[],[refute_0_98:[bind(X0,$fot(implies(not(not(truth)),not(not(X_32))))),bind(Y0,$fot(implies(truth,not(not(X_32))))),bind(Z0,$fot(not(not(X_32))))]]) ).
cnf(refute_0_129,plain,
( implies(truth,not(not(X_32))) != not(not(X_32))
| implies(not(not(truth)),not(not(X_32))) = not(not(X_32)) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_32))),implies(truth,not(not(X_32)))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
implies(not(not(truth)),not(not(X_32))) = not(not(X_32)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(X_32))),not(not(X_32))) )],[refute_0_45,refute_0_129]) ).
cnf(refute_0_131,plain,
implies(implies(not(not(truth)),not(not(X_32))),X_32) = implies(implies(not(not(truth)),not(not(X_32))),X_32),
introduced(tautology,[refl,[$fot(implies(implies(not(not(truth)),not(not(X_32))),X_32))]]) ).
cnf(refute_0_132,plain,
( implies(implies(not(not(truth)),not(not(X_32))),X_32) != implies(implies(not(not(truth)),not(not(X_32))),X_32)
| implies(not(not(truth)),not(not(X_32))) != not(not(X_32))
| implies(implies(not(not(truth)),not(not(X_32))),X_32) = implies(not(not(X_32)),X_32) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_32))),X_32),implies(implies(not(not(truth)),not(not(X_32))),X_32)) ),[1,0],$fot(not(not(X_32)))]]) ).
cnf(refute_0_133,plain,
( implies(not(not(truth)),not(not(X_32))) != not(not(X_32))
| implies(implies(not(not(truth)),not(not(X_32))),X_32) = implies(not(not(X_32)),X_32) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_32))),X_32),implies(implies(not(not(truth)),not(not(X_32))),X_32)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
implies(implies(not(not(truth)),not(not(X_32))),X_32) = implies(not(not(X_32)),X_32),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_32))),not(not(X_32))) )],[refute_0_130,refute_0_133]) ).
cnf(refute_0_135,plain,
( implies(implies(not(not(truth)),not(not(X_32))),X_32) != implies(not(not(X_32)),X_32)
| implies(implies(not(not(truth)),not(not(X_32))),X_32) != truth
| implies(not(not(X_32)),X_32) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_32))),X_32),truth) ),[0],$fot(implies(not(not(X_32)),X_32))]]) ).
cnf(refute_0_136,plain,
( implies(implies(not(not(truth)),not(not(X_32))),X_32) != truth
| implies(not(not(X_32)),X_32) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_32))),X_32),implies(not(not(X_32)),X_32)) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
implies(not(not(X_32)),X_32) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_32))),X_32),truth) )],[refute_0_44,refute_0_136]) ).
cnf(refute_0_138,plain,
implies(not(not(not(Y))),not(Y)) = truth,
inference(subst,[],[refute_0_137:[bind(X_32,$fot(not(Y)))]]) ).
cnf(refute_0_139,plain,
( implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))) != truth
| implies(not(not(not(Y))),not(Y)) != truth
| implies(truth,implies(Y,not(not(Y)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_140,plain,
( implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))) != truth
| implies(truth,implies(Y,not(not(Y)))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(not(Y))),not(Y)),truth) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
implies(truth,implies(Y,not(not(Y)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))),truth) )],[refute_0_17,refute_0_140]) ).
cnf(refute_0_142,plain,
implies(truth,implies(Y,not(not(Y)))) = implies(Y,not(not(Y))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(Y,not(not(Y)))))]]) ).
cnf(refute_0_143,plain,
( implies(truth,implies(Y,not(not(Y)))) != implies(Y,not(not(Y)))
| implies(truth,implies(Y,not(not(Y)))) != truth
| implies(Y,not(not(Y))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(Y,not(not(Y)))),truth) ),[0],$fot(implies(Y,not(not(Y))))]]) ).
cnf(refute_0_144,plain,
( implies(truth,implies(Y,not(not(Y)))) != truth
| implies(Y,not(not(Y))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(Y,not(not(Y)))),implies(Y,not(not(Y)))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
implies(Y,not(not(Y))) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(Y,not(not(Y)))),truth) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
( implies(Y,not(not(Y))) != truth
| implies(implies(not(not(Y)),Y),Y) != implies(implies(Y,not(not(Y))),not(not(Y)))
| implies(implies(not(not(Y)),Y),Y) = implies(truth,not(not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(Y,not(not(Y))),not(not(Y)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_147,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(implies(Y,not(not(Y))),not(not(Y)))
| implies(implies(not(not(Y)),Y),Y) = implies(truth,not(not(Y))) ),
inference(resolve,[$cnf( $equal(implies(Y,not(not(Y))),truth) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
implies(implies(not(not(Y)),Y),Y) = implies(truth,not(not(Y))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(Y,not(not(Y))),not(not(Y)))) )],[refute_0_16,refute_0_147]) ).
cnf(refute_0_149,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_150,plain,
implies(not(not(Y)),Y) = truth,
inference(subst,[],[refute_0_137:[bind(X_32,$fot(Y))]]) ).
cnf(refute_0_151,plain,
implies(implies(not(not(Y)),Y),Y) = implies(implies(not(not(Y)),Y),Y),
introduced(tautology,[refl,[$fot(implies(implies(not(not(Y)),Y),Y))]]) ).
cnf(refute_0_152,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(implies(not(not(Y)),Y),Y)
| implies(not(not(Y)),Y) != truth
| implies(implies(not(not(Y)),Y),Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(not(not(Y)),Y),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_153,plain,
( implies(not(not(Y)),Y) != truth
| implies(implies(not(not(Y)),Y),Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(not(not(Y)),Y),Y)) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
implies(implies(not(not(Y)),Y),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),truth) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,Y)
| implies(truth,Y) != Y
| implies(implies(not(not(Y)),Y),Y) = Y ),
inference(subst,[],[refute_0_98:[bind(X0,$fot(implies(implies(not(not(Y)),Y),Y))),bind(Y0,$fot(implies(truth,Y))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_156,plain,
( implies(truth,Y) != Y
| implies(implies(not(not(Y)),Y),Y) = Y ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,Y)) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
implies(implies(not(not(Y)),Y),Y) = Y,
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_149,refute_0_156]) ).
cnf(refute_0_158,plain,
( implies(implies(not(not(Y)),Y),Y) != Y
| implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = implies(truth,not(not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,not(not(Y)))) ),[0],$fot(Y)]]) ).
cnf(refute_0_159,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = implies(truth,not(not(Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),Y) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
implies(truth,not(not(Y))) = not(not(Y)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_161,plain,
( Y != implies(truth,not(not(Y)))
| implies(truth,not(not(Y))) != not(not(Y))
| Y = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(Y,not(not(Y))) ),[0],$fot(implies(truth,not(not(Y))))]]) ).
cnf(refute_0_162,plain,
( Y != implies(truth,not(not(Y)))
| Y = not(not(Y)) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(Y))),not(not(Y))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = not(not(Y)) ),
inference(resolve,[$cnf( $equal(Y,implies(truth,not(not(Y)))) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
Y = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,not(not(Y)))) )],[refute_0_148,refute_0_163]) ).
cnf(refute_0_165,plain,
X_37 = not(not(X_37)),
inference(subst,[],[refute_0_164:[bind(Y,$fot(X_37))]]) ).
cnf(refute_0_166,plain,
( X_37 != not(not(X_37))
| not(not(X_37)) = X_37 ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(X_37)),bind(Y0,$fot(not(not(X_37))))]]) ).
cnf(refute_0_167,plain,
not(not(X_37)) = X_37,
inference(resolve,[$cnf( $equal(X_37,not(not(X_37))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
( implies(implies(not(X),not(not(X_37))),implies(not(X_37),X)) != truth
| not(not(X_37)) != X_37
| implies(implies(not(X),X_37),implies(not(X_37),X)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(not(X_37))),implies(not(X_37),X)),truth) ),[0,0,1],$fot(X_37)]]) ).
cnf(refute_0_169,plain,
( implies(implies(not(X),not(not(X_37))),implies(not(X_37),X)) != truth
| implies(implies(not(X),X_37),implies(not(X_37),X)) = truth ),
inference(resolve,[$cnf( $equal(not(not(X_37)),X_37) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
implies(implies(not(X),X_37),implies(not(X_37),X)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(not(X_37))),implies(not(X_37),X)),truth) )],[refute_0_15,refute_0_169]) ).
cnf(refute_0_171,plain,
implies(implies(not(X_42),X_43),implies(not(X_43),X_42)) = truth,
inference(subst,[],[refute_0_170:[bind(X,$fot(X_42)),bind(X_37,$fot(X_43))]]) ).
cnf(refute_0_172,plain,
( implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) != implies(implies(implies(not(X_42),X_43),implies(not(X_43),X_42)),implies(not(X_43),X_42))
| implies(implies(not(X_42),X_43),implies(not(X_43),X_42)) != truth
| implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) = implies(truth,implies(not(X_43),X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)),implies(implies(implies(not(X_42),X_43),implies(not(X_43),X_42)),implies(not(X_43),X_42))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_173,plain,
( implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) != implies(implies(implies(not(X_42),X_43),implies(not(X_43),X_42)),implies(not(X_43),X_42))
| implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) = implies(truth,implies(not(X_43),X_42)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_42),X_43),implies(not(X_43),X_42)),truth) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) = implies(truth,implies(not(X_43),X_42)),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)),implies(implies(implies(not(X_42),X_43),implies(not(X_43),X_42)),implies(not(X_43),X_42))) )],[refute_0_14,refute_0_173]) ).
cnf(refute_0_175,plain,
implies(truth,implies(not(X_42),X_43)) = implies(not(X_42),X_43),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(X_42),X_43)))]]) ).
cnf(refute_0_176,plain,
implies(implies(not(X_43),X_42),implies(not(X_42),X_43)) = truth,
inference(subst,[],[refute_0_170:[bind(X,$fot(X_43)),bind(X_37,$fot(X_42))]]) ).
cnf(refute_0_177,plain,
implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) = implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)))]]) ).
cnf(refute_0_178,plain,
( implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) != implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43))
| implies(implies(not(X_43),X_42),implies(not(X_42),X_43)) != truth
| implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) = implies(truth,implies(not(X_42),X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)),implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_179,plain,
( implies(implies(not(X_43),X_42),implies(not(X_42),X_43)) != truth
| implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) = implies(truth,implies(not(X_42),X_43)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)),implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) = implies(truth,implies(not(X_42),X_43)),
inference(resolve,[$cnf( $equal(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),truth) )],[refute_0_176,refute_0_179]) ).
cnf(refute_0_181,plain,
( implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) != implies(truth,implies(not(X_42),X_43))
| implies(truth,implies(not(X_42),X_43)) != implies(not(X_42),X_43)
| implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) = implies(not(X_42),X_43) ),
inference(subst,[],[refute_0_98:[bind(X0,$fot(implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)))),bind(Y0,$fot(implies(truth,implies(not(X_42),X_43)))),bind(Z0,$fot(implies(not(X_42),X_43)))]]) ).
cnf(refute_0_182,plain,
( implies(truth,implies(not(X_42),X_43)) != implies(not(X_42),X_43)
| implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) = implies(not(X_42),X_43) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)),implies(truth,implies(not(X_42),X_43))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) = implies(not(X_42),X_43),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(X_42),X_43)),implies(not(X_42),X_43)) )],[refute_0_175,refute_0_182]) ).
cnf(refute_0_184,plain,
( implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) != implies(not(X_42),X_43)
| implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) != implies(truth,implies(not(X_43),X_42))
| implies(not(X_42),X_43) = implies(truth,implies(not(X_43),X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)),implies(truth,implies(not(X_43),X_42))) ),[0],$fot(implies(not(X_42),X_43))]]) ).
cnf(refute_0_185,plain,
( implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) != implies(truth,implies(not(X_43),X_42))
| implies(not(X_42),X_43) = implies(truth,implies(not(X_43),X_42)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)),implies(not(X_42),X_43)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
implies(truth,implies(not(X_43),X_42)) = implies(not(X_43),X_42),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(X_43),X_42)))]]) ).
cnf(refute_0_187,plain,
( implies(not(X_42),X_43) != implies(truth,implies(not(X_43),X_42))
| implies(truth,implies(not(X_43),X_42)) != implies(not(X_43),X_42)
| implies(not(X_42),X_43) = implies(not(X_43),X_42) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(X_42),X_43),implies(not(X_43),X_42)) ),[0],$fot(implies(truth,implies(not(X_43),X_42)))]]) ).
cnf(refute_0_188,plain,
( implies(not(X_42),X_43) != implies(truth,implies(not(X_43),X_42))
| implies(not(X_42),X_43) = implies(not(X_43),X_42) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(X_43),X_42)),implies(not(X_43),X_42)) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
( implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)) != implies(truth,implies(not(X_43),X_42))
| implies(not(X_42),X_43) = implies(not(X_43),X_42) ),
inference(resolve,[$cnf( $equal(implies(not(X_42),X_43),implies(truth,implies(not(X_43),X_42))) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
implies(not(X_42),X_43) = implies(not(X_43),X_42),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_43),X_42),implies(not(X_42),X_43)),implies(not(X_42),X_43)),implies(truth,implies(not(X_43),X_42))) )],[refute_0_174,refute_0_189]) ).
cnf(refute_0_191,plain,
implies(not(not(Y)),X_45) = implies(not(X_45),not(Y)),
inference(subst,[],[refute_0_190:[bind(X_42,$fot(not(Y))),bind(X_43,$fot(X_45))]]) ).
cnf(refute_0_192,plain,
( Y != not(not(Y))
| not(not(Y)) = Y ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(Y)),bind(Y0,$fot(not(not(Y))))]]) ).
cnf(refute_0_193,plain,
not(not(Y)) = Y,
inference(resolve,[$cnf( $equal(Y,not(not(Y))) )],[refute_0_164,refute_0_192]) ).
cnf(refute_0_194,plain,
( implies(not(not(Y)),X_45) != implies(not(X_45),not(Y))
| not(not(Y)) != Y
| implies(Y,X_45) = implies(not(X_45),not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(Y)),X_45),implies(not(X_45),not(Y))) ),[0,0],$fot(Y)]]) ).
cnf(refute_0_195,plain,
( implies(not(not(Y)),X_45) != implies(not(X_45),not(Y))
| implies(Y,X_45) = implies(not(X_45),not(Y)) ),
inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
implies(Y,X_45) = implies(not(X_45),not(Y)),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),X_45),implies(not(X_45),not(Y))) )],[refute_0_191,refute_0_195]) ).
cnf(refute_0_197,plain,
implies(X_56,X_57) = implies(not(X_57),not(X_56)),
inference(subst,[],[refute_0_196:[bind(Y,$fot(X_56)),bind(X_45,$fot(X_57))]]) ).
cnf(refute_0_198,plain,
( implies(X_56,X_57) != implies(not(X_57),not(X_56))
| implies(not(X_57),not(X_56)) = implies(X_56,X_57) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(X_56,X_57))),bind(Y0,$fot(implies(not(X_57),not(X_56))))]]) ).
cnf(refute_0_199,plain,
implies(not(X_57),not(X_56)) = implies(X_56,X_57),
inference(resolve,[$cnf( $equal(implies(X_56,X_57),implies(not(X_57),not(X_56))) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
( implies(not(X_57),implies(implies(not(X_57),not(X_56)),not(X_56))) != truth
| implies(not(X_57),not(X_56)) != implies(X_56,X_57)
| implies(not(X_57),implies(implies(X_56,X_57),not(X_56))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_57),implies(implies(not(X_57),not(X_56)),not(X_56))),truth) ),[0,1,0],$fot(implies(X_56,X_57))]]) ).
cnf(refute_0_201,plain,
( implies(not(X_57),implies(implies(not(X_57),not(X_56)),not(X_56))) != truth
| implies(not(X_57),implies(implies(X_56,X_57),not(X_56))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_57),not(X_56)),implies(X_56,X_57)) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
implies(not(X_57),implies(implies(X_56,X_57),not(X_56))) = truth,
inference(resolve,[$cnf( $equal(implies(not(X_57),implies(implies(not(X_57),not(X_56)),not(X_56))),truth) )],[refute_0_13,refute_0_201]) ).
cnf(refute_0_203,plain,
implies(X_56,not(Y)) = implies(not(not(Y)),not(X_56)),
inference(subst,[],[refute_0_196:[bind(Y,$fot(X_56)),bind(X_45,$fot(not(Y)))]]) ).
cnf(refute_0_204,plain,
( implies(X_56,not(Y)) != implies(not(not(Y)),not(X_56))
| not(not(Y)) != Y
| implies(X_56,not(Y)) = implies(Y,not(X_56)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_56,not(Y)),implies(not(not(Y)),not(X_56))) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_205,plain,
( implies(X_56,not(Y)) != implies(not(not(Y)),not(X_56))
| implies(X_56,not(Y)) = implies(Y,not(X_56)) ),
inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_193,refute_0_204]) ).
cnf(refute_0_206,plain,
implies(X_56,not(Y)) = implies(Y,not(X_56)),
inference(resolve,[$cnf( $equal(implies(X_56,not(Y)),implies(not(not(Y)),not(X_56))) )],[refute_0_203,refute_0_205]) ).
cnf(refute_0_207,plain,
( implies(X_56,not(Y)) != implies(Y,not(X_56))
| implies(Y,not(X_56)) = implies(X_56,not(Y)) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(X_56,not(Y)))),bind(Y0,$fot(implies(Y,not(X_56))))]]) ).
cnf(refute_0_208,plain,
implies(Y,not(X_56)) = implies(X_56,not(Y)),
inference(resolve,[$cnf( $equal(implies(X_56,not(Y)),implies(Y,not(X_56))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
implies(implies(X_56,X_57),not(X_56)) = implies(X_56,not(implies(X_56,X_57))),
inference(subst,[],[refute_0_208:[bind(Y,$fot(implies(X_56,X_57)))]]) ).
cnf(refute_0_210,plain,
implies(not(X_57),implies(implies(X_56,X_57),not(X_56))) = implies(not(X_57),implies(implies(X_56,X_57),not(X_56))),
introduced(tautology,[refl,[$fot(implies(not(X_57),implies(implies(X_56,X_57),not(X_56))))]]) ).
cnf(refute_0_211,plain,
( implies(implies(X_56,X_57),not(X_56)) != implies(X_56,not(implies(X_56,X_57)))
| implies(not(X_57),implies(implies(X_56,X_57),not(X_56))) != implies(not(X_57),implies(implies(X_56,X_57),not(X_56)))
| implies(not(X_57),implies(implies(X_56,X_57),not(X_56))) = implies(not(X_57),implies(X_56,not(implies(X_56,X_57)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_57),implies(implies(X_56,X_57),not(X_56))),implies(not(X_57),implies(implies(X_56,X_57),not(X_56)))) ),[1,1],$fot(implies(X_56,not(implies(X_56,X_57))))]]) ).
cnf(refute_0_212,plain,
( implies(implies(X_56,X_57),not(X_56)) != implies(X_56,not(implies(X_56,X_57)))
| implies(not(X_57),implies(implies(X_56,X_57),not(X_56))) = implies(not(X_57),implies(X_56,not(implies(X_56,X_57)))) ),
inference(resolve,[$cnf( $equal(implies(not(X_57),implies(implies(X_56,X_57),not(X_56))),implies(not(X_57),implies(implies(X_56,X_57),not(X_56)))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
implies(not(X_57),implies(implies(X_56,X_57),not(X_56))) = implies(not(X_57),implies(X_56,not(implies(X_56,X_57)))),
inference(resolve,[$cnf( $equal(implies(implies(X_56,X_57),not(X_56)),implies(X_56,not(implies(X_56,X_57)))) )],[refute_0_209,refute_0_212]) ).
cnf(refute_0_214,plain,
( implies(not(X_57),implies(implies(X_56,X_57),not(X_56))) != implies(not(X_57),implies(X_56,not(implies(X_56,X_57))))
| implies(not(X_57),implies(implies(X_56,X_57),not(X_56))) != truth
| implies(not(X_57),implies(X_56,not(implies(X_56,X_57)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_57),implies(implies(X_56,X_57),not(X_56))),truth) ),[0],$fot(implies(not(X_57),implies(X_56,not(implies(X_56,X_57)))))]]) ).
cnf(refute_0_215,plain,
( implies(not(X_57),implies(implies(X_56,X_57),not(X_56))) != truth
| implies(not(X_57),implies(X_56,not(implies(X_56,X_57)))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_57),implies(implies(X_56,X_57),not(X_56))),implies(not(X_57),implies(X_56,not(implies(X_56,X_57))))) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
implies(not(X_57),implies(X_56,not(implies(X_56,X_57)))) = truth,
inference(resolve,[$cnf( $equal(implies(not(X_57),implies(implies(X_56,X_57),not(X_56))),truth) )],[refute_0_202,refute_0_215]) ).
cnf(refute_0_217,plain,
implies(not(a),implies(b,not(implies(b,a)))) = truth,
inference(subst,[],[refute_0_216:[bind(X_56,$fot(b)),bind(X_57,$fot(a))]]) ).
cnf(refute_0_218,plain,
( implies(not(a),implies(b,not(implies(b,a)))) != truth
| truth != truth
| implies(not(a),implies(b,not(implies(b,a)))) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(a),implies(b,not(implies(b,a)))),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_219,plain,
( truth != truth
| implies(not(a),implies(b,not(implies(b,a)))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(a),implies(b,not(implies(b,a)))),truth) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
truth != truth,
inference(resolve,[$cnf( $equal(implies(not(a),implies(b,not(implies(b,a)))),truth) )],[refute_0_219,prove_mv_50]) ).
cnf(refute_0_221,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_222,plain,
$false,
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_221,refute_0_220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL116-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 04:22:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.40/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.57
% 0.40/0.57 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.41/0.59
%------------------------------------------------------------------------------