%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HWC001-1 : TPTP v8.1.0. Bugfixed v1.1.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 : Sat Jul 16 13:07:23 EDT 2022
% Result : Unsatisfiable 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 29
% Syntax : Number of clauses : 87 ( 30 unt; 0 nHn; 72 RR)
% Number of literals : 167 ( 65 equ; 81 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 91 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(nand_definition,axiom,
nand(X,Y) = not(and(X,Y)) ).
cnf(and_definition1,axiom,
and(X,n0) = n0 ).
cnf(and_definition2,axiom,
and(X,n1) = X ).
cnf(not_definition1,axiom,
not(n0) = n1 ).
cnf(not_definition2,axiom,
not(n1) = n0 ).
cnf(nand_table_definition,negated_conjecture,
( ~ output(X1,X2,X3,X4)
| ~ output(Y1,Y2,Y3,Y4)
| output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4)) ) ).
cnf(input1,negated_conjecture,
output(n0,n0,n1,n1) ).
cnf(input2,negated_conjecture,
output(n0,n1,n0,n1) ).
cnf(prove_cannot_make_or,negated_conjecture,
~ output(n0,n1,n1,n1) ).
cnf(refute_0_0,plain,
( ~ output(n0,n0,n1,n1)
| output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1)) ),
inference(subst,[],[nand_table_definition:[bind(X1,$fot(n0)),bind(X2,$fot(n0)),bind(X3,$fot(n1)),bind(X4,$fot(n1)),bind(Y1,$fot(n0)),bind(Y2,$fot(n0)),bind(Y3,$fot(n1)),bind(Y4,$fot(n1))]]) ).
cnf(refute_0_1,plain,
output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1)),
inference(resolve,[$cnf( output(n0,n0,n1,n1) )],[input1,refute_0_0]) ).
cnf(refute_0_2,plain,
nand(X_2,n0) = not(and(X_2,n0)),
inference(subst,[],[nand_definition:[bind(X,$fot(X_2)),bind(Y,$fot(n0))]]) ).
cnf(refute_0_3,plain,
and(X_2,n0) = n0,
inference(subst,[],[and_definition1:[bind(X,$fot(X_2))]]) ).
cnf(refute_0_4,plain,
( and(X_2,n0) != n0
| nand(X_2,n0) != not(and(X_2,n0))
| nand(X_2,n0) = not(n0) ),
introduced(tautology,[equality,[$cnf( $equal(nand(X_2,n0),not(and(X_2,n0))) ),[1,0],$fot(n0)]]) ).
cnf(refute_0_5,plain,
( nand(X_2,n0) != not(and(X_2,n0))
| nand(X_2,n0) = not(n0) ),
inference(resolve,[$cnf( $equal(and(X_2,n0),n0) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
nand(X_2,n0) = not(n0),
inference(resolve,[$cnf( $equal(nand(X_2,n0),not(and(X_2,n0))) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
( nand(X_2,n0) != not(n0)
| not(n0) != n1
| nand(X_2,n0) = n1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(nand(X_2,n0),n1) ),[0],$fot(not(n0))]]) ).
cnf(refute_0_8,plain,
( nand(X_2,n0) != not(n0)
| nand(X_2,n0) = n1 ),
inference(resolve,[$cnf( $equal(not(n0),n1) )],[not_definition1,refute_0_7]) ).
cnf(refute_0_9,plain,
nand(X_2,n0) = n1,
inference(resolve,[$cnf( $equal(nand(X_2,n0),not(n0)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
nand(n0,n0) = n1,
inference(subst,[],[refute_0_9:[bind(X_2,$fot(n0))]]) ).
cnf(refute_0_11,plain,
( nand(n0,n0) != n1
| ~ output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1))
| output(n1,nand(n0,n0),nand(n1,n1),nand(n1,n1)) ),
introduced(tautology,[equality,[$cnf( output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1)) ),[0],$fot(n1)]]) ).
cnf(refute_0_12,plain,
( ~ output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1))
| output(n1,nand(n0,n0),nand(n1,n1),nand(n1,n1)) ),
inference(resolve,[$cnf( $equal(nand(n0,n0),n1) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( nand(n0,n0) != n1
| ~ output(n1,nand(n0,n0),nand(n1,n1),nand(n1,n1))
| output(n1,n1,nand(n1,n1),nand(n1,n1)) ),
introduced(tautology,[equality,[$cnf( output(n1,nand(n0,n0),nand(n1,n1),nand(n1,n1)) ),[1],$fot(n1)]]) ).
cnf(refute_0_14,plain,
( ~ output(n1,nand(n0,n0),nand(n1,n1),nand(n1,n1))
| output(n1,n1,nand(n1,n1),nand(n1,n1)) ),
inference(resolve,[$cnf( $equal(nand(n0,n0),n1) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
nand(X_2,n1) = not(and(X_2,n1)),
inference(subst,[],[nand_definition:[bind(X,$fot(X_2)),bind(Y,$fot(n1))]]) ).
cnf(refute_0_16,plain,
and(X_2,n1) = X_2,
inference(subst,[],[and_definition2:[bind(X,$fot(X_2))]]) ).
cnf(refute_0_17,plain,
( and(X_2,n1) != X_2
| nand(X_2,n1) != not(and(X_2,n1))
| nand(X_2,n1) = not(X_2) ),
introduced(tautology,[equality,[$cnf( $equal(nand(X_2,n1),not(and(X_2,n1))) ),[1,0],$fot(X_2)]]) ).
cnf(refute_0_18,plain,
( nand(X_2,n1) != not(and(X_2,n1))
| nand(X_2,n1) = not(X_2) ),
inference(resolve,[$cnf( $equal(and(X_2,n1),X_2) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
nand(X_2,n1) = not(X_2),
inference(resolve,[$cnf( $equal(nand(X_2,n1),not(and(X_2,n1))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
nand(n1,n1) = not(n1),
inference(subst,[],[refute_0_19:[bind(X_2,$fot(n1))]]) ).
cnf(refute_0_21,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_22,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_23,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_25,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( nand(n1,n1) != not(n1)
| not(n1) != n0
| nand(n1,n1) = n0 ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(nand(n1,n1))),bind(Y0,$fot(not(n1))),bind(Z,$fot(n0))]]) ).
cnf(refute_0_27,plain,
( not(n1) != n0
| nand(n1,n1) = n0 ),
inference(resolve,[$cnf( $equal(nand(n1,n1),not(n1)) )],[refute_0_20,refute_0_26]) ).
cnf(refute_0_28,plain,
nand(n1,n1) = n0,
inference(resolve,[$cnf( $equal(not(n1),n0) )],[not_definition2,refute_0_27]) ).
cnf(refute_0_29,plain,
( nand(n1,n1) != n0
| ~ output(n1,n1,nand(n1,n1),nand(n1,n1))
| output(n1,n1,n0,nand(n1,n1)) ),
introduced(tautology,[equality,[$cnf( output(n1,n1,nand(n1,n1),nand(n1,n1)) ),[2],$fot(n0)]]) ).
cnf(refute_0_30,plain,
( ~ output(n1,n1,nand(n1,n1),nand(n1,n1))
| output(n1,n1,n0,nand(n1,n1)) ),
inference(resolve,[$cnf( $equal(nand(n1,n1),n0) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( nand(n1,n1) != n0
| ~ output(n1,n1,n0,nand(n1,n1))
| output(n1,n1,n0,n0) ),
introduced(tautology,[equality,[$cnf( output(n1,n1,n0,nand(n1,n1)) ),[3],$fot(n0)]]) ).
cnf(refute_0_32,plain,
( ~ output(n1,n1,n0,nand(n1,n1))
| output(n1,n1,n0,n0) ),
inference(resolve,[$cnf( $equal(nand(n1,n1),n0) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ output(n1,n1,nand(n1,n1),nand(n1,n1))
| output(n1,n1,n0,n0) ),
inference(resolve,[$cnf( output(n1,n1,n0,nand(n1,n1)) )],[refute_0_30,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ output(n1,nand(n0,n0),nand(n1,n1),nand(n1,n1))
| output(n1,n1,n0,n0) ),
inference(resolve,[$cnf( output(n1,n1,nand(n1,n1),nand(n1,n1)) )],[refute_0_14,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1))
| output(n1,n1,n0,n0) ),
inference(resolve,[$cnf( output(n1,nand(n0,n0),nand(n1,n1),nand(n1,n1)) )],[refute_0_12,refute_0_34]) ).
cnf(refute_0_36,plain,
output(n1,n1,n0,n0),
inference(resolve,[$cnf( output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1)) )],[refute_0_1,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ output(n0,n1,n0,n1)
| output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1)) ),
inference(subst,[],[nand_table_definition:[bind(X1,$fot(n0)),bind(X2,$fot(n1)),bind(X3,$fot(n0)),bind(X4,$fot(n1)),bind(Y1,$fot(n0)),bind(Y2,$fot(n1)),bind(Y3,$fot(n0)),bind(Y4,$fot(n1))]]) ).
cnf(refute_0_38,plain,
output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1)),
inference(resolve,[$cnf( output(n0,n1,n0,n1) )],[input2,refute_0_37]) ).
cnf(refute_0_39,plain,
( nand(n0,n0) != n1
| ~ output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1))
| output(n1,nand(n1,n1),nand(n0,n0),nand(n1,n1)) ),
introduced(tautology,[equality,[$cnf( output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1)) ),[0],$fot(n1)]]) ).
cnf(refute_0_40,plain,
( ~ output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1))
| output(n1,nand(n1,n1),nand(n0,n0),nand(n1,n1)) ),
inference(resolve,[$cnf( $equal(nand(n0,n0),n1) )],[refute_0_10,refute_0_39]) ).
cnf(refute_0_41,plain,
( nand(n1,n1) != n0
| ~ output(n1,nand(n1,n1),nand(n0,n0),nand(n1,n1))
| output(n1,n0,nand(n0,n0),nand(n1,n1)) ),
introduced(tautology,[equality,[$cnf( output(n1,nand(n1,n1),nand(n0,n0),nand(n1,n1)) ),[1],$fot(n0)]]) ).
cnf(refute_0_42,plain,
( ~ output(n1,nand(n1,n1),nand(n0,n0),nand(n1,n1))
| output(n1,n0,nand(n0,n0),nand(n1,n1)) ),
inference(resolve,[$cnf( $equal(nand(n1,n1),n0) )],[refute_0_28,refute_0_41]) ).
cnf(refute_0_43,plain,
( nand(n0,n0) != n1
| ~ output(n1,n0,nand(n0,n0),nand(n1,n1))
| output(n1,n0,n1,nand(n1,n1)) ),
introduced(tautology,[equality,[$cnf( output(n1,n0,nand(n0,n0),nand(n1,n1)) ),[2],$fot(n1)]]) ).
cnf(refute_0_44,plain,
( ~ output(n1,n0,nand(n0,n0),nand(n1,n1))
| output(n1,n0,n1,nand(n1,n1)) ),
inference(resolve,[$cnf( $equal(nand(n0,n0),n1) )],[refute_0_10,refute_0_43]) ).
cnf(refute_0_45,plain,
( nand(n1,n1) != n0
| ~ output(n1,n0,n1,nand(n1,n1))
| output(n1,n0,n1,n0) ),
introduced(tautology,[equality,[$cnf( output(n1,n0,n1,nand(n1,n1)) ),[3],$fot(n0)]]) ).
cnf(refute_0_46,plain,
( ~ output(n1,n0,n1,nand(n1,n1))
| output(n1,n0,n1,n0) ),
inference(resolve,[$cnf( $equal(nand(n1,n1),n0) )],[refute_0_28,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ output(n1,n0,nand(n0,n0),nand(n1,n1))
| output(n1,n0,n1,n0) ),
inference(resolve,[$cnf( output(n1,n0,n1,nand(n1,n1)) )],[refute_0_44,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ output(n1,nand(n1,n1),nand(n0,n0),nand(n1,n1))
| output(n1,n0,n1,n0) ),
inference(resolve,[$cnf( output(n1,n0,nand(n0,n0),nand(n1,n1)) )],[refute_0_42,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1))
| output(n1,n0,n1,n0) ),
inference(resolve,[$cnf( output(n1,nand(n1,n1),nand(n0,n0),nand(n1,n1)) )],[refute_0_40,refute_0_48]) ).
cnf(refute_0_50,plain,
output(n1,n0,n1,n0),
inference(resolve,[$cnf( output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1)) )],[refute_0_38,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ output(X_10,X_11,X_12,X_13)
| ~ output(n1,n0,n1,n0)
| output(nand(X_10,n1),nand(X_11,n0),nand(X_12,n1),nand(X_13,n0)) ),
inference(subst,[],[nand_table_definition:[bind(X1,$fot(X_10)),bind(X2,$fot(X_11)),bind(X3,$fot(X_12)),bind(X4,$fot(X_13)),bind(Y1,$fot(n1)),bind(Y2,$fot(n0)),bind(Y3,$fot(n1)),bind(Y4,$fot(n0))]]) ).
cnf(refute_0_52,plain,
( ~ output(X_10,X_11,X_12,X_13)
| output(nand(X_10,n1),nand(X_11,n0),nand(X_12,n1),nand(X_13,n0)) ),
inference(resolve,[$cnf( output(n1,n0,n1,n0) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
nand(X_10,n1) = not(X_10),
inference(subst,[],[refute_0_19:[bind(X_2,$fot(X_10))]]) ).
cnf(refute_0_54,plain,
( nand(X_10,n1) != not(X_10)
| ~ output(nand(X_10,n1),nand(X_11,n0),nand(X_12,n1),nand(X_13,n0))
| output(not(X_10),nand(X_11,n0),nand(X_12,n1),nand(X_13,n0)) ),
introduced(tautology,[equality,[$cnf( output(nand(X_10,n1),nand(X_11,n0),nand(X_12,n1),nand(X_13,n0)) ),[0],$fot(not(X_10))]]) ).
cnf(refute_0_55,plain,
( ~ output(nand(X_10,n1),nand(X_11,n0),nand(X_12,n1),nand(X_13,n0))
| output(not(X_10),nand(X_11,n0),nand(X_12,n1),nand(X_13,n0)) ),
inference(resolve,[$cnf( $equal(nand(X_10,n1),not(X_10)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
nand(X_11,n0) = n1,
inference(subst,[],[refute_0_9:[bind(X_2,$fot(X_11))]]) ).
cnf(refute_0_57,plain,
( nand(X_11,n0) != n1
| ~ output(not(X_10),nand(X_11,n0),nand(X_12,n1),nand(X_13,n0))
| output(not(X_10),n1,nand(X_12,n1),nand(X_13,n0)) ),
introduced(tautology,[equality,[$cnf( output(not(X_10),nand(X_11,n0),nand(X_12,n1),nand(X_13,n0)) ),[1],$fot(n1)]]) ).
cnf(refute_0_58,plain,
( ~ output(not(X_10),nand(X_11,n0),nand(X_12,n1),nand(X_13,n0))
| output(not(X_10),n1,nand(X_12,n1),nand(X_13,n0)) ),
inference(resolve,[$cnf( $equal(nand(X_11,n0),n1) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
nand(X_12,n1) = not(X_12),
inference(subst,[],[refute_0_19:[bind(X_2,$fot(X_12))]]) ).
cnf(refute_0_60,plain,
( nand(X_12,n1) != not(X_12)
| ~ output(not(X_10),n1,nand(X_12,n1),nand(X_13,n0))
| output(not(X_10),n1,not(X_12),nand(X_13,n0)) ),
introduced(tautology,[equality,[$cnf( output(not(X_10),n1,nand(X_12,n1),nand(X_13,n0)) ),[2],$fot(not(X_12))]]) ).
cnf(refute_0_61,plain,
( ~ output(not(X_10),n1,nand(X_12,n1),nand(X_13,n0))
| output(not(X_10),n1,not(X_12),nand(X_13,n0)) ),
inference(resolve,[$cnf( $equal(nand(X_12,n1),not(X_12)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
nand(X_13,n0) = n1,
inference(subst,[],[refute_0_9:[bind(X_2,$fot(X_13))]]) ).
cnf(refute_0_63,plain,
( nand(X_13,n0) != n1
| ~ output(not(X_10),n1,not(X_12),nand(X_13,n0))
| output(not(X_10),n1,not(X_12),n1) ),
introduced(tautology,[equality,[$cnf( output(not(X_10),n1,not(X_12),nand(X_13,n0)) ),[3],$fot(n1)]]) ).
cnf(refute_0_64,plain,
( ~ output(not(X_10),n1,not(X_12),nand(X_13,n0))
| output(not(X_10),n1,not(X_12),n1) ),
inference(resolve,[$cnf( $equal(nand(X_13,n0),n1) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ output(not(X_10),n1,nand(X_12,n1),nand(X_13,n0))
| output(not(X_10),n1,not(X_12),n1) ),
inference(resolve,[$cnf( output(not(X_10),n1,not(X_12),nand(X_13,n0)) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ output(not(X_10),nand(X_11,n0),nand(X_12,n1),nand(X_13,n0))
| output(not(X_10),n1,not(X_12),n1) ),
inference(resolve,[$cnf( output(not(X_10),n1,nand(X_12,n1),nand(X_13,n0)) )],[refute_0_58,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ output(nand(X_10,n1),nand(X_11,n0),nand(X_12,n1),nand(X_13,n0))
| output(not(X_10),n1,not(X_12),n1) ),
inference(resolve,[$cnf( output(not(X_10),nand(X_11,n0),nand(X_12,n1),nand(X_13,n0)) )],[refute_0_55,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ output(X_10,X_11,X_12,X_13)
| output(not(X_10),n1,not(X_12),n1) ),
inference(resolve,[$cnf( output(nand(X_10,n1),nand(X_11,n0),nand(X_12,n1),nand(X_13,n0)) )],[refute_0_52,refute_0_67]) ).
cnf(refute_0_69,plain,
( ~ output(n1,n1,n0,n0)
| output(not(n1),n1,not(n0),n1) ),
inference(subst,[],[refute_0_68:[bind(X_10,$fot(n1)),bind(X_11,$fot(n1)),bind(X_12,$fot(n0)),bind(X_13,$fot(n0))]]) ).
cnf(refute_0_70,plain,
output(not(n1),n1,not(n0),n1),
inference(resolve,[$cnf( output(n1,n1,n0,n0) )],[refute_0_36,refute_0_69]) ).
cnf(refute_0_71,plain,
( not(n1) != n0
| ~ output(not(n1),n1,not(n0),n1)
| output(n0,n1,not(n0),n1) ),
introduced(tautology,[equality,[$cnf( output(not(n1),n1,not(n0),n1) ),[0],$fot(n0)]]) ).
cnf(refute_0_72,plain,
( ~ output(not(n1),n1,not(n0),n1)
| output(n0,n1,not(n0),n1) ),
inference(resolve,[$cnf( $equal(not(n1),n0) )],[not_definition2,refute_0_71]) ).
cnf(refute_0_73,plain,
( not(n0) != n1
| ~ output(n0,n1,not(n0),n1)
| output(n0,n1,n1,n1) ),
introduced(tautology,[equality,[$cnf( output(n0,n1,not(n0),n1) ),[2],$fot(n1)]]) ).
cnf(refute_0_74,plain,
( ~ output(n0,n1,not(n0),n1)
| output(n0,n1,n1,n1) ),
inference(resolve,[$cnf( $equal(not(n0),n1) )],[not_definition1,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ output(not(n1),n1,not(n0),n1)
| output(n0,n1,n1,n1) ),
inference(resolve,[$cnf( output(n0,n1,not(n0),n1) )],[refute_0_72,refute_0_74]) ).
cnf(refute_0_76,plain,
output(n0,n1,n1,n1),
inference(resolve,[$cnf( output(not(n1),n1,not(n0),n1) )],[refute_0_70,refute_0_75]) ).
cnf(refute_0_77,plain,
$false,
inference(resolve,[$cnf( output(n0,n1,n1,n1) )],[refute_0_76,prove_cannot_make_or]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : HWC001-1 : TPTP v8.1.0. Bugfixed v1.1.1.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 12:59:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38
%------------------------------------------------------------------------------