TSTP Solution File: LCL096-10 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL096-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 12:49:27 EDT 2022
% Result : Unsatisfiable 4.29s 4.52s
% Output : CNFRefutation 4.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 28
% Syntax : Number of clauses : 91 ( 53 unt; 0 nHn; 41 RR)
% Number of literals : 148 ( 147 equ; 59 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 414 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(A,A,B,C) = B ).
cnf(condensed_detachment,axiom,
ifeq(is_a_theorem(equivalent(X,Y)),true,ifeq(is_a_theorem(X),true,is_a_theorem(Y),true),true) = true ).
cnf(lg_2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),U),U)) = true ).
cnf(lg_3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),V),V)) = true ).
cnf(lg_4,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),U),equivalent(equivalent(equivalent(X,V),Z),equivalent(equivalent(Y,V),U)))) = true ).
cnf(prove_lg_1,negated_conjecture,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) != true ).
cnf(refute_0_0,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162),equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true) = true,
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162))),bind(Y,$fot(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)))]]) ).
cnf(refute_0_1,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10)),true,is_a_theorem(Y),true),true) = true,
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10)))]]) ).
cnf(refute_0_2,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10)) = true,
inference(subst,[],[lg_2:[bind(U,$fot(X_10)),bind(X,$fot(X_11)),bind(Y,$fot(X_12)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_3,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10)),true,is_a_theorem(Y),true),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10)) != true
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10)),true,is_a_theorem(Y),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_4,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10)),true,is_a_theorem(Y),true),true) != true
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) = true ),
inference(resolve,[$cnf( $equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10)),true) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10)),true,is_a_theorem(Y),true),true),true) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
ifeq(true,true,is_a_theorem(Y),true) = is_a_theorem(Y),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(is_a_theorem(Y))),bind(C,$fot(true))]]) ).
cnf(refute_0_7,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true),
introduced(tautology,[refl,[$fot(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true))]]) ).
cnf(refute_0_8,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) != ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true)
| ifeq(true,true,is_a_theorem(Y),true) != is_a_theorem(Y)
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,is_a_theorem(Y),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true),ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true)) ),[1,2],$fot(is_a_theorem(Y))]]) ).
cnf(refute_0_9,plain,
( ifeq(true,true,is_a_theorem(Y),true) != is_a_theorem(Y)
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,is_a_theorem(Y),true) ),
inference(resolve,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true),ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,is_a_theorem(Y),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,is_a_theorem(Y),true),is_a_theorem(Y)) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) != ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,is_a_theorem(Y),true)
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) != true
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,is_a_theorem(Y),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true),true) ),[0],$fot(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,is_a_theorem(Y),true))]]) ).
cnf(refute_0_12,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) != true
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,is_a_theorem(Y),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true),ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,is_a_theorem(Y),true)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,is_a_theorem(Y),true) = true,
inference(resolve,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_11,X_12),equivalent(X_11,X_13)),equivalent(X_12,X_13)),X_10),X_10),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true),true) )],[refute_0_5,refute_0_12]) ).
cnf(refute_0_14,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),equivalent(X_38,X_39)),X_36),X_36),equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true) = true,
inference(subst,[],[refute_0_13:[bind(Y,$fot(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36)))),bind(X_10,$fot(X_36)),bind(X_11,$fot(X_37)),bind(X_12,$fot(X_38)),bind(X_13,$fot(X_39))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),equivalent(X_38,X_39)),X_36),X_36),equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36)))) = true,
inference(subst,[],[lg_4:[bind(U,$fot(X_36)),bind(X,$fot(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)))),bind(Y,$fot(equivalent(X_38,X_39))),bind(Z,$fot(X_36))]]) ).
cnf(refute_0_16,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),equivalent(X_38,X_39)),X_36),X_36),equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),equivalent(X_38,X_39)),X_36),X_36),equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36)))) != true
| ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),equivalent(X_38,X_39)),X_36),X_36),equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_17,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),equivalent(X_38,X_39)),X_36),X_36),equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true) != true
| ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true) = true ),
inference(resolve,[$cnf( $equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),equivalent(X_38,X_39)),X_36),X_36),equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36)))),true) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),equivalent(X_38,X_39)),X_36),X_36),equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true),true) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))))),bind(C,$fot(true))]]) ).
cnf(refute_0_20,plain,
( ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true) != is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36)))
| ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true),true) ),[0],$fot(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))))]]) ).
cnf(refute_0_21,plain,
( ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true),is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_37,X_38),equivalent(X_37,X_39)),V),X_36),equivalent(equivalent(equivalent(X_38,X_39),V),X_36))),true),true) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162),equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162))) = true,
inference(subst,[],[refute_0_22:[bind(V,$fot(X_161)),bind(X_36,$fot(X_162)),bind(X_37,$fot(X_163)),bind(X_38,$fot(X_164)),bind(X_39,$fot(X_165))]]) ).
cnf(refute_0_24,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162),equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162),equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162))) != true
| ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162),equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_25,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162),equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true) != true
| ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true) = true ),
inference(resolve,[$cnf( $equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162),equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162))),true) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162),equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true),true) )],[refute_0_0,refute_0_25]) ).
cnf(refute_0_27,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_28,plain,
( ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true) != ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true)
| ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true) != true
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true),true) ),[0],$fot(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true))]]) ).
cnf(refute_0_29,plain,
( ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true) != true
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true),ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_163,X_164),equivalent(X_163,X_165)),X_161),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,X_165),X_161),X_162)),true),true),true) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_602,X_604),X_164),equivalent(equivalent(X_602,X_604),equivalent(equivalent(X_602,X_602),X_164))),X_162),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true) = true,
inference(subst,[],[refute_0_30:[bind(X_161,$fot(X_162)),bind(X_163,$fot(equivalent(X_602,X_604))),bind(X_165,$fot(equivalent(equivalent(X_602,X_602),X_164)))]]) ).
cnf(refute_0_32,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6)),true,is_a_theorem(Y),true),true) = true,
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6)))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6)) = true,
inference(subst,[],[lg_3:[bind(U,$fot(X_5)),bind(V,$fot(X_6)),bind(X,$fot(X_7)),bind(Y,$fot(X_8)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_34,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6)),true,is_a_theorem(Y),true),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6)) != true
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6)),true,is_a_theorem(Y),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_35,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6)),true,is_a_theorem(Y),true),true) != true
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) = true ),
inference(resolve,[$cnf( $equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6)),true) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6)),true,is_a_theorem(Y),true),true),true) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true),
introduced(tautology,[refl,[$fot(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true))]]) ).
cnf(refute_0_38,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) != ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true)
| ifeq(true,true,is_a_theorem(Y),true) != is_a_theorem(Y)
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,is_a_theorem(Y),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true),ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true)) ),[1,2],$fot(is_a_theorem(Y))]]) ).
cnf(refute_0_39,plain,
( ifeq(true,true,is_a_theorem(Y),true) != is_a_theorem(Y)
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,is_a_theorem(Y),true) ),
inference(resolve,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true),ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,is_a_theorem(Y),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,is_a_theorem(Y),true),is_a_theorem(Y)) )],[refute_0_6,refute_0_39]) ).
cnf(refute_0_41,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) != ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,is_a_theorem(Y),true)
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) != true
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,is_a_theorem(Y),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true),true) ),[0],$fot(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,is_a_theorem(Y),true))]]) ).
cnf(refute_0_42,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true) != true
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,is_a_theorem(Y),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true),ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,is_a_theorem(Y),true)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,is_a_theorem(Y),true) = true,
inference(resolve,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),X_5),equivalent(equivalent(X_8,X_9),X_5)),X_6),X_6),Y)),true,ifeq(true,true,is_a_theorem(Y),true),true),true) )],[refute_0_36,refute_0_42]) ).
cnf(refute_0_44,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),equivalent(equivalent(X_7,X_8),X_373)),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6),equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true) = true,
inference(subst,[],[refute_0_43:[bind(Y,$fot(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6))),bind(X_5,$fot(equivalent(equivalent(X_7,X_8),X_373)))]]) ).
cnf(refute_0_45,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18),equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18)))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true) = true,
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18))),bind(Y,$fot(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))))]]) ).
cnf(refute_0_46,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18),equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18)))) = true,
inference(subst,[],[lg_4:[bind(U,$fot(X_18)),bind(V,$fot(X_19)),bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_47,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18),equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18)))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18),equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18)))) != true
| ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18),equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18)))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_48,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18),equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18)))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true) != true
| ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true) = true ),
inference(resolve,[$cnf( $equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18),equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18)))),true) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18),equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18)))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true),true) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_51,plain,
( ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true) != ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true)
| ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true) != true
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true),true) ),[0],$fot(ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true))]]) ).
cnf(refute_0_52,plain,
( ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true) != true
| ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true),ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X_20,X_21),X_22),X_18)),true,is_a_theorem(equivalent(equivalent(equivalent(X_20,X_19),X_22),equivalent(equivalent(X_21,X_19),X_18))),true),true),true) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),X_59),X_59)),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true) = true,
inference(subst,[],[refute_0_53:[bind(X_18,$fot(X_59)),bind(X_19,$fot(X_60)),bind(X_20,$fot(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U))),bind(X_21,$fot(equivalent(equivalent(Y,Z),U))),bind(X_22,$fot(X_59))]]) ).
cnf(refute_0_55,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),X_59),X_59)) = true,
inference(subst,[],[lg_3:[bind(V,$fot(X_59))]]) ).
cnf(refute_0_56,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),X_59),X_59)),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),X_59),X_59)) != true
| ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),X_59),X_59)),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_57,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),X_59),X_59)),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true) != true
| ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true) = true ),
inference(resolve,[$cnf( $equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),X_59),X_59)),true) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),X_59),X_59)),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true),true) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))))),bind(C,$fot(true))]]) ).
cnf(refute_0_60,plain,
( ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true) != is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59)))
| ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true),true) ),[0],$fot(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))))]]) ).
cnf(refute_0_61,plain,
( ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true),is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59)))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),X_60),X_59),equivalent(equivalent(equivalent(equivalent(Y,Z),U),X_60),X_59))),true),true) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),equivalent(equivalent(X_7,X_8),X_373)),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6),equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6))) = true,
inference(subst,[],[refute_0_62:[bind(U,$fot(equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373)))),bind(X,$fot(equivalent(X_7,X_8))),bind(Y,$fot(equivalent(X_7,X_9))),bind(Z,$fot(X_373)),bind(X_59,$fot(X_6)),bind(X_60,$fot(X_6))]]) ).
cnf(refute_0_64,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),equivalent(equivalent(X_7,X_8),X_373)),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6),equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),equivalent(equivalent(X_7,X_8),X_373)),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6),equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6))) != true
| ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),equivalent(equivalent(X_7,X_8),X_373)),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6),equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_65,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),equivalent(equivalent(X_7,X_8),X_373)),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6),equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true) != true
| ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true) = true ),
inference(resolve,[$cnf( $equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),equivalent(equivalent(X_7,X_8),X_373)),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6),equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6))),true) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_8),equivalent(X_7,X_9)),equivalent(equivalent(X_7,X_8),X_373)),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6),equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true),true) )],[refute_0_44,refute_0_65]) ).
cnf(refute_0_67,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)))),bind(C,$fot(true))]]) ).
cnf(refute_0_68,plain,
( ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true) != is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6))
| ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true),true) ),[0],$fot(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)))]]) ).
cnf(refute_0_69,plain,
( ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true),is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_7,X_9),X_373),equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_7,X_8),X_373))),X_6),X_6)),true),true) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_602,X_604),X_164),equivalent(equivalent(X_602,X_604),equivalent(equivalent(X_602,X_602),X_164))),X_162),X_162)) = true,
inference(subst,[],[refute_0_70:[bind(X_373,$fot(X_164)),bind(X_6,$fot(X_162)),bind(X_7,$fot(X_602)),bind(X_8,$fot(X_602)),bind(X_9,$fot(X_604))]]) ).
cnf(refute_0_72,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_602,X_604),X_164),equivalent(equivalent(X_602,X_604),equivalent(equivalent(X_602,X_602),X_164))),X_162),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_602,X_604),X_164),equivalent(equivalent(X_602,X_604),equivalent(equivalent(X_602,X_602),X_164))),X_162),X_162)) != true
| ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_602,X_604),X_164),equivalent(equivalent(X_602,X_604),equivalent(equivalent(X_602,X_602),X_164))),X_162),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_73,plain,
( ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_602,X_604),X_164),equivalent(equivalent(X_602,X_604),equivalent(equivalent(X_602,X_602),X_164))),X_162),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true) != true
| ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true) = true ),
inference(resolve,[$cnf( $equal(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_602,X_604),X_164),equivalent(equivalent(X_602,X_604),equivalent(equivalent(X_602,X_602),X_164))),X_162),X_162)),true) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_602,X_604),X_164),equivalent(equivalent(X_602,X_604),equivalent(equivalent(X_602,X_602),X_164))),X_162),X_162)),true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true),true) )],[refute_0_31,refute_0_73]) ).
cnf(refute_0_75,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true) = is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)))),bind(C,$fot(true))]]) ).
cnf(refute_0_76,plain,
( ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true) != is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162))
| ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true),true) ),[0],$fot(is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)))]]) ).
cnf(refute_0_77,plain,
( ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true) != true
| is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true),is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X_164,equivalent(equivalent(X_602,X_602),X_164)),X_162),X_162)),true),true) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) = true,
inference(subst,[],[refute_0_78:[bind(X_162,$fot(c)),bind(X_164,$fot(a)),bind(X_602,$fot(b))]]) ).
cnf(refute_0_80,plain,
( is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) != true
| true != true
| is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) = true ),
introduced(tautology,[equality,[$cnf( ~ $equal(is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),true) ),[0],$fot(true)]]) ).
cnf(refute_0_81,plain,
( true != true
| is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) = true ),
inference(resolve,[$cnf( $equal(is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),true) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
true != true,
inference(resolve,[$cnf( $equal(is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),true) )],[refute_0_81,prove_lg_1]) ).
cnf(refute_0_83,plain,
true = true,
introduced(tautology,[refl,[$fot(true)]]) ).
cnf(refute_0_84,plain,
$false,
inference(resolve,[$cnf( $equal(true,true) )],[refute_0_83,refute_0_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL096-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 05:30:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.29/4.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.29/4.52
% 4.29/4.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.38/4.55
%------------------------------------------------------------------------------