TSTP Solution File: BOO075-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO075-1 : TPTP v8.1.0. Released v2.6.0.
% 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 : Thu Jul 14 23:46:08 EDT 2022
% Result : Unsatisfiable 0.41s 0.58s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 42
% Syntax : Number of clauses : 127 ( 64 unt; 0 nHn; 65 RR)
% Number of literals : 220 ( 219 equ; 95 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 246 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sh_1,axiom,
nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A))) = B ).
cnf(prove_meredith_2_basis_1,negated_conjecture,
nand(nand(a,a),nand(b,a)) != a ).
cnf(refute_0_0,plain,
nand(nand(B,nand(nand(B,B),B)),nand(B,nand(C,B))) = B,
inference(subst,[],[sh_1:[bind(A,$fot(B))]]) ).
cnf(refute_0_1,plain,
nand(nand(nand(X_1,nand(X_2,X_0)),nand(nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(X_1,nand(X_2,X_0))),nand(X_1,nand(X_2,X_0)))),nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(C,nand(X_1,nand(X_2,X_0))))) = nand(X_0,nand(nand(X_1,X_0),X_0)),
inference(subst,[],[sh_1:[bind(A,$fot(nand(X_1,nand(X_2,X_0)))),bind(B,$fot(nand(X_0,nand(nand(X_1,X_0),X_0))))]]) ).
cnf(refute_0_2,plain,
nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(X_1,nand(X_2,X_0))) = X_1,
inference(subst,[],[sh_1:[bind(A,$fot(X_0)),bind(B,$fot(X_1)),bind(C,$fot(X_2))]]) ).
cnf(refute_0_3,plain,
( nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(X_1,nand(X_2,X_0))) != X_1
| nand(nand(nand(X_1,nand(X_2,X_0)),nand(nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(X_1,nand(X_2,X_0))),nand(X_1,nand(X_2,X_0)))),nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(C,nand(X_1,nand(X_2,X_0))))) != nand(X_0,nand(nand(X_1,X_0),X_0))
| nand(nand(nand(X_1,nand(X_2,X_0)),nand(X_1,nand(X_1,nand(X_2,X_0)))),nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(C,nand(X_1,nand(X_2,X_0))))) = nand(X_0,nand(nand(X_1,X_0),X_0)) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(nand(X_1,nand(X_2,X_0)),nand(nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(X_1,nand(X_2,X_0))),nand(X_1,nand(X_2,X_0)))),nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(C,nand(X_1,nand(X_2,X_0))))),nand(X_0,nand(nand(X_1,X_0),X_0))) ),[0,0,1,0],$fot(X_1)]]) ).
cnf(refute_0_4,plain,
( nand(nand(nand(X_1,nand(X_2,X_0)),nand(nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(X_1,nand(X_2,X_0))),nand(X_1,nand(X_2,X_0)))),nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(C,nand(X_1,nand(X_2,X_0))))) != nand(X_0,nand(nand(X_1,X_0),X_0))
| nand(nand(nand(X_1,nand(X_2,X_0)),nand(X_1,nand(X_1,nand(X_2,X_0)))),nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(C,nand(X_1,nand(X_2,X_0))))) = nand(X_0,nand(nand(X_1,X_0),X_0)) ),
inference(resolve,[$cnf( $equal(nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(X_1,nand(X_2,X_0))),X_1) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
nand(nand(nand(X_1,nand(X_2,X_0)),nand(X_1,nand(X_1,nand(X_2,X_0)))),nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(C,nand(X_1,nand(X_2,X_0))))) = nand(X_0,nand(nand(X_1,X_0),X_0)),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_1,nand(X_2,X_0)),nand(nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(X_1,nand(X_2,X_0))),nand(X_1,nand(X_2,X_0)))),nand(nand(X_0,nand(nand(X_1,X_0),X_0)),nand(C,nand(X_1,nand(X_2,X_0))))),nand(X_0,nand(nand(X_1,X_0),X_0))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))) = nand(X_0,nand(nand(X_0,X_0),X_0)),
inference(subst,[],[refute_0_5:[bind(C,$fot(X_0)),bind(X_1,$fot(X_0)),bind(X_2,$fot(nand(X_0,X_0)))]]) ).
cnf(refute_0_7,plain,
nand(nand(A,nand(nand(B,A),A)),nand(B,nand(nand(nand(X_5,X_4),nand(nand(nand(X_4,nand(nand(A,X_4),X_4)),nand(X_5,X_4)),nand(X_5,X_4))),A))) = B,
inference(subst,[],[sh_1:[bind(C,$fot(nand(nand(X_5,X_4),nand(nand(nand(X_4,nand(nand(A,X_4),X_4)),nand(X_5,X_4)),nand(X_5,X_4)))))]]) ).
cnf(refute_0_8,plain,
nand(nand(nand(X_2,X_0),nand(nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(C,nand(X_2,X_0)))) = nand(X_0,nand(nand(C,X_0),X_0)),
inference(subst,[],[sh_1:[bind(A,$fot(nand(X_2,X_0))),bind(B,$fot(nand(X_0,nand(nand(C,X_0),X_0))))]]) ).
cnf(refute_0_9,plain,
nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(C,nand(X_2,X_0))) = C,
inference(subst,[],[sh_1:[bind(A,$fot(X_0)),bind(B,$fot(C)),bind(C,$fot(X_2))]]) ).
cnf(refute_0_10,plain,
( nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(C,nand(X_2,X_0))) != C
| nand(nand(nand(X_2,X_0),nand(nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(C,nand(X_2,X_0)))) != nand(X_0,nand(nand(C,X_0),X_0))
| nand(nand(nand(X_2,X_0),nand(nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(X_2,X_0)),nand(X_2,X_0))),C) = nand(X_0,nand(nand(C,X_0),X_0)) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(nand(X_2,X_0),nand(nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(C,nand(X_2,X_0)))),nand(X_0,nand(nand(C,X_0),X_0))) ),[0,1],$fot(C)]]) ).
cnf(refute_0_11,plain,
( nand(nand(nand(X_2,X_0),nand(nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(C,nand(X_2,X_0)))) != nand(X_0,nand(nand(C,X_0),X_0))
| nand(nand(nand(X_2,X_0),nand(nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(X_2,X_0)),nand(X_2,X_0))),C) = nand(X_0,nand(nand(C,X_0),X_0)) ),
inference(resolve,[$cnf( $equal(nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(C,nand(X_2,X_0))),C) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
nand(nand(nand(X_2,X_0),nand(nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(X_2,X_0)),nand(X_2,X_0))),C) = nand(X_0,nand(nand(C,X_0),X_0)),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_2,X_0),nand(nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_0,nand(nand(C,X_0),X_0)),nand(C,nand(X_2,X_0)))),nand(X_0,nand(nand(C,X_0),X_0))) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
nand(nand(nand(X_5,X_4),nand(nand(nand(X_4,nand(nand(A,X_4),X_4)),nand(X_5,X_4)),nand(X_5,X_4))),A) = nand(X_4,nand(nand(A,X_4),X_4)),
inference(subst,[],[refute_0_12:[bind(C,$fot(A)),bind(X_0,$fot(X_4)),bind(X_2,$fot(X_5))]]) ).
cnf(refute_0_14,plain,
( nand(nand(A,nand(nand(B,A),A)),nand(B,nand(nand(nand(X_5,X_4),nand(nand(nand(X_4,nand(nand(A,X_4),X_4)),nand(X_5,X_4)),nand(X_5,X_4))),A))) != B
| nand(nand(nand(X_5,X_4),nand(nand(nand(X_4,nand(nand(A,X_4),X_4)),nand(X_5,X_4)),nand(X_5,X_4))),A) != nand(X_4,nand(nand(A,X_4),X_4))
| nand(nand(A,nand(nand(B,A),A)),nand(B,nand(X_4,nand(nand(A,X_4),X_4)))) = B ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(A,nand(nand(B,A),A)),nand(B,nand(nand(nand(X_5,X_4),nand(nand(nand(X_4,nand(nand(A,X_4),X_4)),nand(X_5,X_4)),nand(X_5,X_4))),A))),B) ),[0,1,1],$fot(nand(X_4,nand(nand(A,X_4),X_4)))]]) ).
cnf(refute_0_15,plain,
( nand(nand(A,nand(nand(B,A),A)),nand(B,nand(nand(nand(X_5,X_4),nand(nand(nand(X_4,nand(nand(A,X_4),X_4)),nand(X_5,X_4)),nand(X_5,X_4))),A))) != B
| nand(nand(A,nand(nand(B,A),A)),nand(B,nand(X_4,nand(nand(A,X_4),X_4)))) = B ),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_5,X_4),nand(nand(nand(X_4,nand(nand(A,X_4),X_4)),nand(X_5,X_4)),nand(X_5,X_4))),A),nand(X_4,nand(nand(A,X_4),X_4))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
nand(nand(A,nand(nand(B,A),A)),nand(B,nand(X_4,nand(nand(A,X_4),X_4)))) = B,
inference(resolve,[$cnf( $equal(nand(nand(A,nand(nand(B,A),A)),nand(B,nand(nand(nand(X_5,X_4),nand(nand(nand(X_4,nand(nand(A,X_4),X_4)),nand(X_5,X_4)),nand(X_5,X_4))),A))),B) )],[refute_0_7,refute_0_15]) ).
cnf(refute_0_17,plain,
nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))) = X_0,
inference(subst,[],[refute_0_16:[bind(A,$fot(X_0)),bind(B,$fot(X_0)),bind(X_4,$fot(X_0))]]) ).
cnf(refute_0_18,plain,
( nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))) != X_0
| nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))) != nand(X_0,nand(nand(X_0,X_0),X_0))
| nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) = nand(X_0,nand(nand(X_0,X_0),X_0)) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))),nand(X_0,nand(nand(X_0,X_0),X_0))) ),[0,1],$fot(X_0)]]) ).
cnf(refute_0_19,plain,
( nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))) != nand(X_0,nand(nand(X_0,X_0),X_0))
| nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) = nand(X_0,nand(nand(X_0,X_0),X_0)) ),
inference(resolve,[$cnf( $equal(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) = nand(X_0,nand(nand(X_0,X_0),X_0)),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))),nand(X_0,nand(nand(X_0,X_0),X_0))) )],[refute_0_6,refute_0_19]) ).
cnf(refute_0_21,plain,
nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) = nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0),
introduced(tautology,[refl,[$fot(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0))]]) ).
cnf(refute_0_22,plain,
( nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))) != X_0
| nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) != nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0)
| nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) = nand(X_0,X_0) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0),nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0)) ),[1,0],$fot(X_0)]]) ).
cnf(refute_0_23,plain,
( nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))) != X_0
| nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) = nand(X_0,X_0) ),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0),nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) = nand(X_0,X_0),
inference(resolve,[$cnf( $equal(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) )],[refute_0_17,refute_0_23]) ).
cnf(refute_0_25,plain,
( nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) != nand(X_0,X_0)
| nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) != nand(X_0,nand(nand(X_0,X_0),X_0))
| nand(X_0,X_0) = nand(X_0,nand(nand(X_0,X_0),X_0)) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0),nand(X_0,nand(nand(X_0,X_0),X_0))) ),[0],$fot(nand(X_0,X_0))]]) ).
cnf(refute_0_26,plain,
( nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) != nand(X_0,nand(nand(X_0,X_0),X_0))
| nand(X_0,X_0) = nand(X_0,nand(nand(X_0,X_0),X_0)) ),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0),nand(X_0,X_0)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
nand(X_0,X_0) = nand(X_0,nand(nand(X_0,X_0),X_0)),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0),nand(X_0,nand(nand(X_0,X_0),X_0))) )],[refute_0_20,refute_0_26]) ).
cnf(refute_0_28,plain,
nand(B,B) = nand(B,nand(nand(B,B),B)),
inference(subst,[],[refute_0_27:[bind(X_0,$fot(B))]]) ).
cnf(refute_0_29,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_30,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_31,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( nand(B,B) != nand(B,nand(nand(B,B),B))
| nand(B,nand(nand(B,B),B)) = nand(B,B) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(nand(B,B))),bind(Y,$fot(nand(B,nand(nand(B,B),B))))]]) ).
cnf(refute_0_33,plain,
nand(B,nand(nand(B,B),B)) = nand(B,B),
inference(resolve,[$cnf( $equal(nand(B,B),nand(B,nand(nand(B,B),B))) )],[refute_0_28,refute_0_32]) ).
cnf(refute_0_34,plain,
( nand(B,nand(nand(B,B),B)) != nand(B,B)
| nand(nand(B,nand(nand(B,B),B)),nand(B,nand(C,B))) != B
| nand(nand(B,B),nand(B,nand(C,B))) = B ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(B,nand(nand(B,B),B)),nand(B,nand(C,B))),B) ),[0,0],$fot(nand(B,B))]]) ).
cnf(refute_0_35,plain,
( nand(nand(B,nand(nand(B,B),B)),nand(B,nand(C,B))) != B
| nand(nand(B,B),nand(B,nand(C,B))) = B ),
inference(resolve,[$cnf( $equal(nand(B,nand(nand(B,B),B)),nand(B,B)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
nand(nand(B,B),nand(B,nand(C,B))) = B,
inference(resolve,[$cnf( $equal(nand(nand(B,nand(nand(B,B),B)),nand(B,nand(C,B))),B) )],[refute_0_0,refute_0_35]) ).
cnf(refute_0_37,plain,
nand(nand(B,B),nand(B,nand(nand(nand(nand(X_32,B),nand(X_32,B)),B),B))) = B,
inference(subst,[],[refute_0_36:[bind(C,$fot(nand(nand(nand(X_32,B),nand(X_32,B)),B)))]]) ).
cnf(refute_0_38,plain,
nand(nand(nand(X_2,X_0),nand(nand(nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))) = nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)),
inference(subst,[],[refute_0_12:[bind(C,$fot(nand(nand(X_2,X_0),nand(X_2,X_0))))]]) ).
cnf(refute_0_39,plain,
nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),nand(nand(X_19,nand(nand(X_19,X_19),X_19)),nand(X_19,nand(nand(X_17,X_19),X_19)))) = nand(X_19,nand(nand(X_19,X_19),X_19)),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_17)),bind(B,$fot(nand(X_19,nand(nand(X_19,X_19),X_19)))),bind(X_4,$fot(X_19))]]) ).
cnf(refute_0_40,plain,
nand(nand(X_19,nand(nand(X_19,X_19),X_19)),nand(X_19,nand(nand(X_17,X_19),X_19))) = X_19,
inference(subst,[],[sh_1:[bind(A,$fot(X_19)),bind(B,$fot(X_19)),bind(C,$fot(nand(X_17,X_19)))]]) ).
cnf(refute_0_41,plain,
( nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),nand(nand(X_19,nand(nand(X_19,X_19),X_19)),nand(X_19,nand(nand(X_17,X_19),X_19)))) != nand(X_19,nand(nand(X_19,X_19),X_19))
| nand(nand(X_19,nand(nand(X_19,X_19),X_19)),nand(X_19,nand(nand(X_17,X_19),X_19))) != X_19
| nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19) = nand(X_19,nand(nand(X_19,X_19),X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),nand(nand(X_19,nand(nand(X_19,X_19),X_19)),nand(X_19,nand(nand(X_17,X_19),X_19)))),nand(X_19,nand(nand(X_19,X_19),X_19))) ),[0,1],$fot(X_19)]]) ).
cnf(refute_0_42,plain,
( nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),nand(nand(X_19,nand(nand(X_19,X_19),X_19)),nand(X_19,nand(nand(X_17,X_19),X_19)))) != nand(X_19,nand(nand(X_19,X_19),X_19))
| nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19) = nand(X_19,nand(nand(X_19,X_19),X_19)) ),
inference(resolve,[$cnf( $equal(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),nand(X_19,nand(nand(X_17,X_19),X_19))),X_19) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19) = nand(X_19,nand(nand(X_19,X_19),X_19)),
inference(resolve,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),nand(nand(X_19,nand(nand(X_19,X_19),X_19)),nand(X_19,nand(nand(X_17,X_19),X_19)))),nand(X_19,nand(nand(X_19,X_19),X_19))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
( nand(X_0,X_0) != nand(X_0,nand(nand(X_0,X_0),X_0))
| nand(X_0,nand(nand(X_0,X_0),X_0)) = nand(X_0,X_0) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(nand(X_0,X_0))),bind(Y,$fot(nand(X_0,nand(nand(X_0,X_0),X_0))))]]) ).
cnf(refute_0_45,plain,
nand(X_0,nand(nand(X_0,X_0),X_0)) = nand(X_0,X_0),
inference(resolve,[$cnf( $equal(nand(X_0,X_0),nand(X_0,nand(nand(X_0,X_0),X_0))) )],[refute_0_27,refute_0_44]) ).
cnf(refute_0_46,plain,
nand(X_19,nand(nand(X_19,X_19),X_19)) = nand(X_19,X_19),
inference(subst,[],[refute_0_45:[bind(X_0,$fot(X_19))]]) ).
cnf(refute_0_47,plain,
nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17) = nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),
introduced(tautology,[refl,[$fot(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17))]]) ).
cnf(refute_0_48,plain,
( nand(X_19,nand(nand(X_19,X_19),X_19)) != nand(X_19,X_19)
| nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17) != nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17)
| nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17) = nand(nand(X_19,X_19),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17)) ),[1,0],$fot(nand(X_19,X_19))]]) ).
cnf(refute_0_49,plain,
( nand(X_19,nand(nand(X_19,X_19),X_19)) != nand(X_19,X_19)
| nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17) = nand(nand(X_19,X_19),X_17) ),
inference(resolve,[$cnf( $equal(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17) = nand(nand(X_19,X_19),X_17),
inference(resolve,[$cnf( $equal(nand(X_19,nand(nand(X_19,X_19),X_19)),nand(X_19,X_19)) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17) = nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17),
introduced(tautology,[refl,[$fot(nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17))]]) ).
cnf(refute_0_52,plain,
( nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17) != nand(nand(X_19,X_19),X_17)
| nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17) != nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)
| nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17) = nand(nand(nand(X_19,X_19),X_17),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17),nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)) ),[1,0],$fot(nand(nand(X_19,X_19),X_17))]]) ).
cnf(refute_0_53,plain,
( nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17) != nand(nand(X_19,X_19),X_17)
| nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17) = nand(nand(nand(X_19,X_19),X_17),X_17) ),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17),nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17) = nand(nand(nand(X_19,X_19),X_17),X_17),
inference(resolve,[$cnf( $equal(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),nand(nand(X_19,X_19),X_17)) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)) = nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),
introduced(tautology,[refl,[$fot(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)))]]) ).
cnf(refute_0_56,plain,
( nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)) != nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17))
| nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17) != nand(nand(nand(X_19,X_19),X_17),X_17)
| nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)) = nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17))) ),[1,1],$fot(nand(nand(nand(X_19,X_19),X_17),X_17))]]) ).
cnf(refute_0_57,plain,
( nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17) != nand(nand(nand(X_19,X_19),X_17),X_17)
| nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)) = nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)) ),
inference(resolve,[$cnf( $equal(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)) = nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17),nand(nand(nand(X_19,X_19),X_17),X_17)) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19) = nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19),
introduced(tautology,[refl,[$fot(nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19))]]) ).
cnf(refute_0_60,plain,
( nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)) != nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17))
| nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19) != nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19)
| nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19) = nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19),nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19)) ),[1,0],$fot(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)))]]) ).
cnf(refute_0_61,plain,
( nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)) != nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17))
| nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19) = nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19) ),
inference(resolve,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19),nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19) = nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19),
inference(resolve,[$cnf( $equal(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17))) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
( nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19) != nand(X_19,nand(nand(X_19,X_19),X_19))
| nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19) != nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19)
| nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19) = nand(X_19,nand(nand(X_19,X_19),X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19),nand(X_19,nand(nand(X_19,X_19),X_19))) ),[0],$fot(nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19))]]) ).
cnf(refute_0_64,plain,
( nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19) != nand(X_19,nand(nand(X_19,X_19),X_19))
| nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19) = nand(X_19,nand(nand(X_19,X_19),X_19)) ),
inference(resolve,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19),nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( nand(X_19,nand(nand(X_19,X_19),X_19)) != nand(X_19,X_19)
| nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19) != nand(X_19,nand(nand(X_19,X_19),X_19))
| nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19) = nand(X_19,X_19) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19),nand(X_19,nand(nand(X_19,X_19),X_19))) ),[1],$fot(nand(X_19,X_19))]]) ).
cnf(refute_0_66,plain,
( nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19) != nand(X_19,nand(nand(X_19,X_19),X_19))
| nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19) = nand(X_19,X_19) ),
inference(resolve,[$cnf( $equal(nand(X_19,nand(nand(X_19,X_19),X_19)),nand(X_19,X_19)) )],[refute_0_46,refute_0_65]) ).
cnf(refute_0_67,plain,
( nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19) != nand(X_19,nand(nand(X_19,X_19),X_19))
| nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19) = nand(X_19,X_19) ),
inference(resolve,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19),nand(X_19,nand(nand(X_19,X_19),X_19))) )],[refute_0_64,refute_0_66]) ).
cnf(refute_0_68,plain,
nand(nand(X_17,nand(nand(nand(X_19,X_19),X_17),X_17)),X_19) = nand(X_19,X_19),
inference(resolve,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(X_19,nand(nand(X_19,X_19),X_19)),X_17),X_17)),X_19),nand(X_19,nand(nand(X_19,X_19),X_19))) )],[refute_0_43,refute_0_67]) ).
cnf(refute_0_69,plain,
nand(nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)),nand(X_2,X_0)) = nand(nand(X_2,X_0),nand(X_2,X_0)),
inference(subst,[],[refute_0_68:[bind(X_17,$fot(X_0)),bind(X_19,$fot(nand(X_2,X_0)))]]) ).
cnf(refute_0_70,plain,
( nand(nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)),nand(X_2,X_0)) != nand(nand(X_2,X_0),nand(X_2,X_0))
| nand(nand(nand(X_2,X_0),nand(nand(nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))) != nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0))
| nand(nand(nand(X_2,X_0),nand(nand(nand(X_2,X_0),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))) = nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(nand(X_2,X_0),nand(nand(nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))),nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0))) ),[0,0,1,0],$fot(nand(nand(X_2,X_0),nand(X_2,X_0)))]]) ).
cnf(refute_0_71,plain,
( nand(nand(nand(X_2,X_0),nand(nand(nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))) != nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0))
| nand(nand(nand(X_2,X_0),nand(nand(nand(X_2,X_0),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))) = nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)) ),
inference(resolve,[$cnf( $equal(nand(nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)),nand(X_2,X_0)),nand(nand(X_2,X_0),nand(X_2,X_0))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
nand(nand(nand(X_2,X_0),nand(nand(nand(X_2,X_0),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))) = nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_2,X_0),nand(nand(nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))),nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0))) )],[refute_0_38,refute_0_71]) ).
cnf(refute_0_73,plain,
nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(nand(X_17,nand(X_0,nand(nand(X_0,X_0),X_0))),nand(X_0,nand(nand(X_0,X_0),X_0)))))) = nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_17)),bind(B,$fot(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))))),bind(X_4,$fot(nand(X_0,nand(nand(X_0,X_0),X_0))))]]) ).
cnf(refute_0_74,plain,
nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(nand(X_17,nand(X_0,nand(nand(X_0,X_0),X_0))),nand(X_0,nand(nand(X_0,X_0),X_0))))) = nand(X_0,nand(nand(X_0,X_0),X_0)),
inference(subst,[],[refute_0_5:[bind(C,$fot(nand(X_17,nand(X_0,nand(nand(X_0,X_0),X_0))))),bind(X_1,$fot(X_0)),bind(X_2,$fot(nand(X_0,X_0)))]]) ).
cnf(refute_0_75,plain,
( nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(nand(X_17,nand(X_0,nand(nand(X_0,X_0),X_0))),nand(X_0,nand(nand(X_0,X_0),X_0)))))) != nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))
| nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(nand(X_17,nand(X_0,nand(nand(X_0,X_0),X_0))),nand(X_0,nand(nand(X_0,X_0),X_0))))) != nand(X_0,nand(nand(X_0,X_0),X_0))
| nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) = nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(nand(X_17,nand(X_0,nand(nand(X_0,X_0),X_0))),nand(X_0,nand(nand(X_0,X_0),X_0)))))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))) ),[0,1],$fot(nand(X_0,nand(nand(X_0,X_0),X_0)))]]) ).
cnf(refute_0_76,plain,
( nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(nand(X_17,nand(X_0,nand(nand(X_0,X_0),X_0))),nand(X_0,nand(nand(X_0,X_0),X_0)))))) != nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))
| nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) = nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))) ),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(nand(X_17,nand(X_0,nand(nand(X_0,X_0),X_0))),nand(X_0,nand(nand(X_0,X_0),X_0))))),nand(X_0,nand(nand(X_0,X_0),X_0))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) = nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),
inference(resolve,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(nand(X_17,nand(X_0,nand(nand(X_0,X_0),X_0))),nand(X_0,nand(nand(X_0,X_0),X_0)))))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) = nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))),
introduced(tautology,[refl,[$fot(nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))))]]) ).
cnf(refute_0_79,plain,
( nand(X_0,nand(nand(X_0,X_0),X_0)) != nand(X_0,X_0)
| nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) != nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0)))
| nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) = nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))),nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0)))) ),[1,1],$fot(nand(X_0,X_0))]]) ).
cnf(refute_0_80,plain,
( nand(X_0,nand(nand(X_0,X_0),X_0)) != nand(X_0,X_0)
| nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) = nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)) ),
inference(resolve,[$cnf( $equal(nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))),nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0)))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) = nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)),
inference(resolve,[$cnf( $equal(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,X_0)) )],[refute_0_45,refute_0_80]) ).
cnf(refute_0_82,plain,
nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17) = nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),
introduced(tautology,[refl,[$fot(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17))]]) ).
cnf(refute_0_83,plain,
( nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))) != X_0
| nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17) != nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17)
| nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17) = nand(X_0,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17)) ),[1,0],$fot(X_0)]]) ).
cnf(refute_0_84,plain,
( nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))) != X_0
| nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17) = nand(X_0,X_17) ),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17) = nand(X_0,X_17),
inference(resolve,[$cnf( $equal(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) )],[refute_0_17,refute_0_84]) ).
cnf(refute_0_86,plain,
nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17) = nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17),
introduced(tautology,[refl,[$fot(nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17))]]) ).
cnf(refute_0_87,plain,
( nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17) != nand(X_0,X_17)
| nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17) != nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)
| nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17) = nand(nand(X_0,X_17),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17),nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)) ),[1,0],$fot(nand(X_0,X_17))]]) ).
cnf(refute_0_88,plain,
( nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17) != nand(X_0,X_17)
| nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17) = nand(nand(X_0,X_17),X_17) ),
inference(resolve,[$cnf( $equal(nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17),nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17) = nand(nand(X_0,X_17),X_17),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),nand(X_0,X_17)) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)) = nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),
introduced(tautology,[refl,[$fot(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)))]]) ).
cnf(refute_0_91,plain,
( nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)) != nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17))
| nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17) != nand(nand(X_0,X_17),X_17)
| nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)) = nand(X_17,nand(nand(X_0,X_17),X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17))) ),[1,1],$fot(nand(nand(X_0,X_17),X_17))]]) ).
cnf(refute_0_92,plain,
( nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17) != nand(nand(X_0,X_17),X_17)
| nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)) = nand(X_17,nand(nand(X_0,X_17),X_17)) ),
inference(resolve,[$cnf( $equal(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)) = nand(X_17,nand(nand(X_0,X_17),X_17)),
inference(resolve,[$cnf( $equal(nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17),nand(nand(X_0,X_17),X_17)) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) = nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))),
introduced(tautology,[refl,[$fot(nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))))]]) ).
cnf(refute_0_95,plain,
( nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)) != nand(X_17,nand(nand(X_0,X_17),X_17))
| nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) != nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0)))
| nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) = nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))),nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0)))) ),[1,0],$fot(nand(X_17,nand(nand(X_0,X_17),X_17)))]]) ).
cnf(refute_0_96,plain,
( nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)) != nand(X_17,nand(nand(X_0,X_17),X_17))
| nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) = nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) ),
inference(resolve,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))),nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0)))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) = nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))),
inference(resolve,[$cnf( $equal(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_17,nand(nand(X_0,X_17),X_17))) )],[refute_0_93,refute_0_96]) ).
cnf(refute_0_98,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_99,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_31,refute_0_98]) ).
cnf(refute_0_100,plain,
( nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) != nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0))
| nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) != nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0)))
| nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) = nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)) ),
inference(subst,[],[refute_0_99:[bind(X,$fot(nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))))),bind(Y,$fot(nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))))),bind(Z,$fot(nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0))))]]) ).
cnf(refute_0_101,plain,
( nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) != nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0))
| nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) = nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)) ),
inference(resolve,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))),nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0)))) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) = nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)),
inference(resolve,[$cnf( $equal(nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))),nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0))) )],[refute_0_81,refute_0_101]) ).
cnf(refute_0_103,plain,
( nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) != nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))
| nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) != nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0))
| nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)) = nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))) ),[0],$fot(nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)))]]) ).
cnf(refute_0_104,plain,
( nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) != nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))
| nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)) = nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))) ),
inference(resolve,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))),nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))) != X_0
| nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)) != nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))
| nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)) = X_0 ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))) ),[1],$fot(X_0)]]) ).
cnf(refute_0_106,plain,
( nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)) != nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))
| nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)) = X_0 ),
inference(resolve,[$cnf( $equal(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_0) )],[refute_0_17,refute_0_105]) ).
cnf(refute_0_107,plain,
( nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))) != nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))
| nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)) = X_0 ),
inference(resolve,[$cnf( $equal(nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))) )],[refute_0_104,refute_0_106]) ).
cnf(refute_0_108,plain,
nand(nand(X_17,nand(nand(X_0,X_17),X_17)),nand(X_0,X_0)) = X_0,
inference(resolve,[$cnf( $equal(nand(nand(X_17,nand(nand(nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0)))),X_17),X_17)),nand(X_0,nand(nand(X_0,X_0),X_0))),nand(nand(X_0,nand(nand(X_0,X_0),X_0)),nand(X_0,nand(X_0,nand(nand(X_0,X_0),X_0))))) )],[refute_0_77,refute_0_107]) ).
cnf(refute_0_109,plain,
nand(nand(nand(X_2,X_0),nand(nand(nand(X_2,X_0),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))) = nand(X_2,X_0),
inference(subst,[],[refute_0_108:[bind(X_0,$fot(nand(X_2,X_0))),bind(X_17,$fot(nand(X_2,X_0)))]]) ).
cnf(refute_0_110,plain,
( nand(nand(nand(X_2,X_0),nand(nand(nand(X_2,X_0),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))) != nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0))
| nand(nand(nand(X_2,X_0),nand(nand(nand(X_2,X_0),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))) != nand(X_2,X_0)
| nand(X_2,X_0) = nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)) ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(nand(X_2,X_0),nand(nand(nand(X_2,X_0),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))),nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0))) ),[0],$fot(nand(X_2,X_0))]]) ).
cnf(refute_0_111,plain,
( nand(nand(nand(X_2,X_0),nand(nand(nand(X_2,X_0),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))) != nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0))
| nand(X_2,X_0) = nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)) ),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_2,X_0),nand(nand(nand(X_2,X_0),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))),nand(X_2,X_0)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
nand(X_2,X_0) = nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0)),
inference(resolve,[$cnf( $equal(nand(nand(nand(X_2,X_0),nand(nand(nand(X_2,X_0),nand(X_2,X_0)),nand(X_2,X_0))),nand(nand(X_2,X_0),nand(X_2,X_0))),nand(X_0,nand(nand(nand(nand(X_2,X_0),nand(X_2,X_0)),X_0),X_0))) )],[refute_0_72,refute_0_111]) ).
cnf(refute_0_113,plain,
nand(X_32,B) = nand(B,nand(nand(nand(nand(X_32,B),nand(X_32,B)),B),B)),
inference(subst,[],[refute_0_112:[bind(X_0,$fot(B)),bind(X_2,$fot(X_32))]]) ).
cnf(refute_0_114,plain,
( nand(X_32,B) != nand(B,nand(nand(nand(nand(X_32,B),nand(X_32,B)),B),B))
| nand(B,nand(nand(nand(nand(X_32,B),nand(X_32,B)),B),B)) = nand(X_32,B) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(nand(X_32,B))),bind(Y,$fot(nand(B,nand(nand(nand(nand(X_32,B),nand(X_32,B)),B),B))))]]) ).
cnf(refute_0_115,plain,
nand(B,nand(nand(nand(nand(X_32,B),nand(X_32,B)),B),B)) = nand(X_32,B),
inference(resolve,[$cnf( $equal(nand(X_32,B),nand(B,nand(nand(nand(nand(X_32,B),nand(X_32,B)),B),B))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( nand(B,nand(nand(nand(nand(X_32,B),nand(X_32,B)),B),B)) != nand(X_32,B)
| nand(nand(B,B),nand(B,nand(nand(nand(nand(X_32,B),nand(X_32,B)),B),B))) != B
| nand(nand(B,B),nand(X_32,B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(B,B),nand(B,nand(nand(nand(nand(X_32,B),nand(X_32,B)),B),B))),B) ),[0,1],$fot(nand(X_32,B))]]) ).
cnf(refute_0_117,plain,
( nand(nand(B,B),nand(B,nand(nand(nand(nand(X_32,B),nand(X_32,B)),B),B))) != B
| nand(nand(B,B),nand(X_32,B)) = B ),
inference(resolve,[$cnf( $equal(nand(B,nand(nand(nand(nand(X_32,B),nand(X_32,B)),B),B)),nand(X_32,B)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
nand(nand(B,B),nand(X_32,B)) = B,
inference(resolve,[$cnf( $equal(nand(nand(B,B),nand(B,nand(nand(nand(nand(X_32,B),nand(X_32,B)),B),B))),B) )],[refute_0_37,refute_0_117]) ).
cnf(refute_0_119,plain,
nand(nand(a,a),nand(b,a)) = a,
inference(subst,[],[refute_0_118:[bind(B,$fot(a)),bind(X_32,$fot(b))]]) ).
cnf(refute_0_120,plain,
( a != a
| nand(nand(a,a),nand(b,a)) != a
| nand(nand(a,a),nand(b,a)) = a ),
introduced(tautology,[equality,[$cnf( $equal(nand(nand(a,a),nand(b,a)),a) ),[0,0,0],$fot(a)]]) ).
cnf(refute_0_121,plain,
( a != a
| nand(nand(a,a),nand(b,a)) = a ),
inference(resolve,[$cnf( $equal(nand(nand(a,a),nand(b,a)),a) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
a != a,
inference(resolve,[$cnf( $equal(nand(nand(a,a),nand(b,a)),a) )],[refute_0_121,prove_meredith_2_basis_1]) ).
cnf(refute_0_123,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_124,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_123,refute_0_122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO075-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n023.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 : Wed Jun 1 20:43:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.41/0.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.58
% 0.41/0.58 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.41/0.61
%------------------------------------------------------------------------------