TSTP Solution File: HWV008-1.002 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HWV008-1.002 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 18:29:35 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 29
% Syntax : Number of clauses : 140 ( 46 unt; 7 nHn; 140 RR)
% Number of literals : 271 ( 0 equ; 128 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 13 con; 0-2 aty)
% Number of variables : 55 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(value_propagation1,axiom,
( ~ connection(P1,P2)
| ~ value(P1,V)
| value(P2,V) ) ).
cnf(value_propagation2,axiom,
( ~ connection(P1,P2)
| ~ value(P2,V)
| value(P1,V) ) ).
cnf(unique_value,axiom,
( ~ value(P,V1)
| ~ value(P,V2)
| equal_value(V1,V2) ) ).
cnf(equal_value1,axiom,
~ equal_value(n0,n1) ).
cnf(ok_or_abnormal,axiom,
( ~ type(K,Any)
| mode(K,ok)
| mode(K,abnormal) ) ).
cnf(and_0x_0,axiom,
( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(in(Any,K),n0)
| value(out(n1,K),n0) ) ).
cnf(or_00_0,axiom,
( ~ mode(K,ok)
| ~ type(K,or)
| ~ value(in(n1,K),n0)
| ~ value(in(n2,K),n0)
| value(out(n1,K),n0) ) ).
cnf(halfadder_and2,axiom,
( ~ type(X,halfadder)
| type(and2(X),and) ) ).
cnf(halfadder_connection_in1_in1and2,axiom,
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,and2(X))) ) ).
cnf(halfadder_connection_outc_out1and2,axiom,
( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) ) ).
cnf(fulladder_halfadder1,axiom,
( ~ type(X,fulladder)
| type(h1(X),halfadder) ) ).
cnf(fulladder_halfadder2,axiom,
( ~ type(X,fulladder)
| type(h2(X),halfadder) ) ).
cnf(fulladder_or1,axiom,
( ~ type(X,fulladder)
| type(or1(X),or) ) ).
cnf(fulladder_connection_outch1_in2or1,axiom,
( ~ type(X,fulladder)
| connection(out(c,h1(X)),in(n2,or1(X))) ) ).
cnf(fulladder_connection_outch2_in1or1,axiom,
( ~ type(X,fulladder)
| connection(out(c,h2(X)),in(n1,or1(X))) ) ).
cnf(fulladder_connection_in1_in1h2,axiom,
( ~ type(X,fulladder)
| connection(in(n1,X),in(n1,h2(X))) ) ).
cnf(fulladder_connection_in2_in1h1,axiom,
( ~ type(X,fulladder)
| connection(in(n2,X),in(n1,h1(X))) ) ).
cnf(fulladder_connection_outc_out1or1,axiom,
( ~ type(X,fulladder)
| connection(out(c,X),out(n1,or1(X))) ) ).
cnf(nbit_adder_fulladder2,axiom,
( ~ type(X,nbit_adder(n2))
| type(f(n2,X),fulladder) ) ).
cnf(nbit_adder_connection_outc_outcf1,axiom,
( ~ type(X,nbit_adder(n2))
| connection(out(c,X),out(c,f(n2,X))) ) ).
cnf(nbit_adder_connection_ina2_in1f2,axiom,
( ~ type(X,nbit_adder(n2))
| connection(in(a2,X),in(n1,f(n2,X))) ) ).
cnf(nbit_adder_connection_inb2_in2f2,axiom,
( ~ type(X,nbit_adder(n2))
| connection(in(b2,X),in(n2,f(n2,X))) ) ).
cnf(a_isa_2bit_adder,hypothesis,
type(a,nbit_adder(n2)) ).
cnf(ina2_0,hypothesis,
value(in(a2,a),n0) ).
cnf(inb2_0,hypothesis,
value(in(b2,a),n0) ).
cnf(outc_1,hypothesis,
value(out(c,a),n1) ).
cnf(diagnosis_or1f2a,negated_conjecture,
~ mode(or1(f(n2,a)),abnormal) ).
cnf(diagnosis_and2h2f2a,negated_conjecture,
~ mode(and2(h1(f(n2,a))),abnormal) ).
cnf(diagnosis_and2h1f2a,negated_conjecture,
~ mode(and2(h2(f(n2,a))),abnormal) ).
cnf(refute_0_0,plain,
( ~ type(a,nbit_adder(n2))
| type(f(n2,a),fulladder) ),
inference(subst,[],[nbit_adder_fulladder2:[bind(X,$fot(a))]]) ).
cnf(refute_0_1,plain,
type(f(n2,a),fulladder),
inference(resolve,[$cnf( type(a,nbit_adder(n2)) )],[a_isa_2bit_adder,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ type(f(n2,a),fulladder)
| connection(out(c,f(n2,a)),out(n1,or1(f(n2,a)))) ),
inference(subst,[],[fulladder_connection_outc_out1or1:[bind(X,$fot(f(n2,a)))]]) ).
cnf(refute_0_3,plain,
connection(out(c,f(n2,a)),out(n1,or1(f(n2,a)))),
inference(resolve,[$cnf( type(f(n2,a),fulladder) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ connection(out(c,f(n2,a)),P2)
| ~ value(out(c,f(n2,a)),n1)
| value(P2,n1) ),
inference(subst,[],[value_propagation1:[bind(P1,$fot(out(c,f(n2,a)))),bind(V,$fot(n1))]]) ).
cnf(refute_0_5,plain,
( ~ type(a,nbit_adder(n2))
| connection(out(c,a),out(c,f(n2,a))) ),
inference(subst,[],[nbit_adder_connection_outc_outcf1:[bind(X,$fot(a))]]) ).
cnf(refute_0_6,plain,
connection(out(c,a),out(c,f(n2,a))),
inference(resolve,[$cnf( type(a,nbit_adder(n2)) )],[a_isa_2bit_adder,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ connection(out(c,a),X_41)
| ~ value(out(c,a),n1)
| value(X_41,n1) ),
inference(subst,[],[value_propagation1:[bind(P1,$fot(out(c,a))),bind(P2,$fot(X_41)),bind(V,$fot(n1))]]) ).
cnf(refute_0_8,plain,
( ~ connection(out(c,a),X_41)
| value(X_41,n1) ),
inference(resolve,[$cnf( value(out(c,a),n1) )],[outc_1,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ connection(out(c,a),out(c,f(n2,a)))
| value(out(c,f(n2,a)),n1) ),
inference(subst,[],[refute_0_8:[bind(X_41,$fot(out(c,f(n2,a))))]]) ).
cnf(refute_0_10,plain,
value(out(c,f(n2,a)),n1),
inference(resolve,[$cnf( connection(out(c,a),out(c,f(n2,a))) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ connection(out(c,f(n2,a)),P2)
| value(P2,n1) ),
inference(resolve,[$cnf( value(out(c,f(n2,a)),n1) )],[refute_0_10,refute_0_4]) ).
cnf(refute_0_12,plain,
( ~ connection(out(c,f(n2,a)),out(n1,or1(f(n2,a))))
| value(out(n1,or1(f(n2,a))),n1) ),
inference(subst,[],[refute_0_11:[bind(P2,$fot(out(n1,or1(f(n2,a)))))]]) ).
cnf(refute_0_13,plain,
value(out(n1,or1(f(n2,a))),n1),
inference(resolve,[$cnf( connection(out(c,f(n2,a)),out(n1,or1(f(n2,a)))) )],[refute_0_3,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ value(out(n1,or1(f(n2,a))),X_148)
| ~ value(out(n1,or1(f(n2,a))),n1)
| equal_value(X_148,n1) ),
inference(subst,[],[unique_value:[bind(P,$fot(out(n1,or1(f(n2,a))))),bind(V1,$fot(X_148)),bind(V2,$fot(n1))]]) ).
cnf(refute_0_15,plain,
( ~ value(out(n1,or1(f(n2,a))),X_148)
| equal_value(X_148,n1) ),
inference(resolve,[$cnf( value(out(n1,or1(f(n2,a))),n1) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ value(out(n1,or1(f(n2,a))),n0)
| equal_value(n0,n1) ),
inference(subst,[],[refute_0_15:[bind(X_148,$fot(n0))]]) ).
cnf(refute_0_17,plain,
( ~ type(f(n2,a),fulladder)
| connection(out(c,h1(f(n2,a))),in(n2,or1(f(n2,a)))) ),
inference(subst,[],[fulladder_connection_outch1_in2or1:[bind(X,$fot(f(n2,a)))]]) ).
cnf(refute_0_18,plain,
connection(out(c,h1(f(n2,a))),in(n2,or1(f(n2,a)))),
inference(resolve,[$cnf( type(f(n2,a),fulladder) )],[refute_0_1,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ connection(out(c,h1(f(n2,a))),in(n2,or1(f(n2,a))))
| ~ value(out(c,h1(f(n2,a))),X_42)
| value(in(n2,or1(f(n2,a))),X_42) ),
inference(subst,[],[value_propagation1:[bind(P1,$fot(out(c,h1(f(n2,a))))),bind(P2,$fot(in(n2,or1(f(n2,a))))),bind(V,$fot(X_42))]]) ).
cnf(refute_0_20,plain,
( ~ value(out(c,h1(f(n2,a))),X_42)
| value(in(n2,or1(f(n2,a))),X_42) ),
inference(resolve,[$cnf( connection(out(c,h1(f(n2,a))),in(n2,or1(f(n2,a)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ value(out(c,h1(f(n2,a))),n0)
| value(in(n2,or1(f(n2,a))),n0) ),
inference(subst,[],[refute_0_20:[bind(X_42,$fot(n0))]]) ).
cnf(refute_0_22,plain,
( ~ type(f(n2,a),fulladder)
| type(h1(f(n2,a)),halfadder) ),
inference(subst,[],[fulladder_halfadder1:[bind(X,$fot(f(n2,a)))]]) ).
cnf(refute_0_23,plain,
type(h1(f(n2,a)),halfadder),
inference(resolve,[$cnf( type(f(n2,a),fulladder) )],[refute_0_1,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ type(h1(f(n2,a)),halfadder)
| connection(out(c,h1(f(n2,a))),out(n1,and2(h1(f(n2,a))))) ),
inference(subst,[],[halfadder_connection_outc_out1and2:[bind(X,$fot(h1(f(n2,a))))]]) ).
cnf(refute_0_25,plain,
connection(out(c,h1(f(n2,a))),out(n1,and2(h1(f(n2,a))))),
inference(resolve,[$cnf( type(h1(f(n2,a)),halfadder) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ connection(out(c,h1(f(n2,a))),out(n1,and2(h1(f(n2,a)))))
| ~ value(out(n1,and2(h1(f(n2,a)))),X_98)
| value(out(c,h1(f(n2,a))),X_98) ),
inference(subst,[],[value_propagation2:[bind(P1,$fot(out(c,h1(f(n2,a))))),bind(P2,$fot(out(n1,and2(h1(f(n2,a)))))),bind(V,$fot(X_98))]]) ).
cnf(refute_0_27,plain,
( ~ value(out(n1,and2(h1(f(n2,a)))),X_98)
| value(out(c,h1(f(n2,a))),X_98) ),
inference(resolve,[$cnf( connection(out(c,h1(f(n2,a))),out(n1,and2(h1(f(n2,a))))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ value(out(n1,and2(h1(f(n2,a)))),n0)
| value(out(c,h1(f(n2,a))),n0) ),
inference(subst,[],[refute_0_27:[bind(X_98,$fot(n0))]]) ).
cnf(refute_0_29,plain,
( ~ type(h1(f(n2,a)),halfadder)
| connection(in(n1,h1(f(n2,a))),in(n1,and2(h1(f(n2,a))))) ),
inference(subst,[],[halfadder_connection_in1_in1and2:[bind(X,$fot(h1(f(n2,a))))]]) ).
cnf(refute_0_30,plain,
connection(in(n1,h1(f(n2,a))),in(n1,and2(h1(f(n2,a))))),
inference(resolve,[$cnf( type(h1(f(n2,a)),halfadder) )],[refute_0_23,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ connection(in(n1,h1(f(n2,a))),P2)
| ~ value(in(n1,h1(f(n2,a))),n0)
| value(P2,n0) ),
inference(subst,[],[value_propagation1:[bind(P1,$fot(in(n1,h1(f(n2,a))))),bind(V,$fot(n0))]]) ).
cnf(refute_0_32,plain,
( ~ type(f(n2,a),fulladder)
| connection(in(n2,f(n2,a)),in(n1,h1(f(n2,a)))) ),
inference(subst,[],[fulladder_connection_in2_in1h1:[bind(X,$fot(f(n2,a)))]]) ).
cnf(refute_0_33,plain,
connection(in(n2,f(n2,a)),in(n1,h1(f(n2,a)))),
inference(resolve,[$cnf( type(f(n2,a),fulladder) )],[refute_0_1,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ connection(in(n2,f(n2,a)),P2)
| ~ value(in(n2,f(n2,a)),n0)
| value(P2,n0) ),
inference(subst,[],[value_propagation1:[bind(P1,$fot(in(n2,f(n2,a)))),bind(V,$fot(n0))]]) ).
cnf(refute_0_35,plain,
( ~ type(a,nbit_adder(n2))
| connection(in(b2,a),in(n2,f(n2,a))) ),
inference(subst,[],[nbit_adder_connection_inb2_in2f2:[bind(X,$fot(a))]]) ).
cnf(refute_0_36,plain,
connection(in(b2,a),in(n2,f(n2,a))),
inference(resolve,[$cnf( type(a,nbit_adder(n2)) )],[a_isa_2bit_adder,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ connection(in(b2,a),X_41)
| ~ value(in(b2,a),n0)
| value(X_41,n0) ),
inference(subst,[],[value_propagation1:[bind(P1,$fot(in(b2,a))),bind(P2,$fot(X_41)),bind(V,$fot(n0))]]) ).
cnf(refute_0_38,plain,
( ~ connection(in(b2,a),X_41)
| value(X_41,n0) ),
inference(resolve,[$cnf( value(in(b2,a),n0) )],[inb2_0,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ connection(in(b2,a),in(n2,f(n2,a)))
| value(in(n2,f(n2,a)),n0) ),
inference(subst,[],[refute_0_38:[bind(X_41,$fot(in(n2,f(n2,a))))]]) ).
cnf(refute_0_40,plain,
value(in(n2,f(n2,a)),n0),
inference(resolve,[$cnf( connection(in(b2,a),in(n2,f(n2,a))) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ connection(in(n2,f(n2,a)),P2)
| value(P2,n0) ),
inference(resolve,[$cnf( value(in(n2,f(n2,a)),n0) )],[refute_0_40,refute_0_34]) ).
cnf(refute_0_42,plain,
( ~ connection(in(n2,f(n2,a)),in(n1,h1(f(n2,a))))
| value(in(n1,h1(f(n2,a))),n0) ),
inference(subst,[],[refute_0_41:[bind(P2,$fot(in(n1,h1(f(n2,a)))))]]) ).
cnf(refute_0_43,plain,
value(in(n1,h1(f(n2,a))),n0),
inference(resolve,[$cnf( connection(in(n2,f(n2,a)),in(n1,h1(f(n2,a)))) )],[refute_0_33,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ connection(in(n1,h1(f(n2,a))),P2)
| value(P2,n0) ),
inference(resolve,[$cnf( value(in(n1,h1(f(n2,a))),n0) )],[refute_0_43,refute_0_31]) ).
cnf(refute_0_45,plain,
( ~ connection(in(n1,h1(f(n2,a))),in(n1,and2(h1(f(n2,a)))))
| value(in(n1,and2(h1(f(n2,a)))),n0) ),
inference(subst,[],[refute_0_44:[bind(P2,$fot(in(n1,and2(h1(f(n2,a))))))]]) ).
cnf(refute_0_46,plain,
value(in(n1,and2(h1(f(n2,a)))),n0),
inference(resolve,[$cnf( connection(in(n1,h1(f(n2,a))),in(n1,and2(h1(f(n2,a))))) )],[refute_0_30,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ mode(and2(h1(f(n2,a))),ok)
| ~ type(and2(h1(f(n2,a))),and)
| ~ value(in(n1,and2(h1(f(n2,a)))),n0)
| value(out(n1,and2(h1(f(n2,a)))),n0) ),
inference(subst,[],[and_0x_0:[bind(Any,$fot(n1)),bind(K,$fot(and2(h1(f(n2,a)))))]]) ).
cnf(refute_0_48,plain,
( ~ mode(and2(h1(f(n2,a))),ok)
| ~ type(and2(h1(f(n2,a))),and)
| value(out(n1,and2(h1(f(n2,a)))),n0) ),
inference(resolve,[$cnf( value(in(n1,and2(h1(f(n2,a)))),n0) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ type(h1(f(n2,a)),halfadder)
| type(and2(h1(f(n2,a))),and) ),
inference(subst,[],[halfadder_and2:[bind(X,$fot(h1(f(n2,a))))]]) ).
cnf(refute_0_50,plain,
type(and2(h1(f(n2,a))),and),
inference(resolve,[$cnf( type(h1(f(n2,a)),halfadder) )],[refute_0_23,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ type(and2(h1(f(n2,a))),and)
| mode(and2(h1(f(n2,a))),abnormal)
| mode(and2(h1(f(n2,a))),ok) ),
inference(subst,[],[ok_or_abnormal:[bind(Any,$fot(and)),bind(K,$fot(and2(h1(f(n2,a)))))]]) ).
cnf(refute_0_52,plain,
( mode(and2(h1(f(n2,a))),abnormal)
| mode(and2(h1(f(n2,a))),ok) ),
inference(resolve,[$cnf( type(and2(h1(f(n2,a))),and) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
mode(and2(h1(f(n2,a))),ok),
inference(resolve,[$cnf( mode(and2(h1(f(n2,a))),abnormal) )],[refute_0_52,diagnosis_and2h2f2a]) ).
cnf(refute_0_54,plain,
( ~ type(and2(h1(f(n2,a))),and)
| value(out(n1,and2(h1(f(n2,a)))),n0) ),
inference(resolve,[$cnf( mode(and2(h1(f(n2,a))),ok) )],[refute_0_53,refute_0_48]) ).
cnf(refute_0_55,plain,
value(out(n1,and2(h1(f(n2,a)))),n0),
inference(resolve,[$cnf( type(and2(h1(f(n2,a))),and) )],[refute_0_50,refute_0_54]) ).
cnf(refute_0_56,plain,
value(out(c,h1(f(n2,a))),n0),
inference(resolve,[$cnf( value(out(n1,and2(h1(f(n2,a)))),n0) )],[refute_0_55,refute_0_28]) ).
cnf(refute_0_57,plain,
value(in(n2,or1(f(n2,a))),n0),
inference(resolve,[$cnf( value(out(c,h1(f(n2,a))),n0) )],[refute_0_56,refute_0_21]) ).
cnf(refute_0_58,plain,
( ~ mode(or1(f(n2,a)),ok)
| ~ type(or1(f(n2,a)),or)
| ~ value(in(n1,or1(f(n2,a))),n0)
| ~ value(in(n2,or1(f(n2,a))),n0)
| value(out(n1,or1(f(n2,a))),n0) ),
inference(subst,[],[or_00_0:[bind(K,$fot(or1(f(n2,a))))]]) ).
cnf(refute_0_59,plain,
( ~ mode(or1(f(n2,a)),ok)
| ~ type(or1(f(n2,a)),or)
| ~ value(in(n1,or1(f(n2,a))),n0)
| value(out(n1,or1(f(n2,a))),n0) ),
inference(resolve,[$cnf( value(in(n2,or1(f(n2,a))),n0) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ type(f(n2,a),fulladder)
| type(or1(f(n2,a)),or) ),
inference(subst,[],[fulladder_or1:[bind(X,$fot(f(n2,a)))]]) ).
cnf(refute_0_61,plain,
type(or1(f(n2,a)),or),
inference(resolve,[$cnf( type(f(n2,a),fulladder) )],[refute_0_1,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ type(or1(f(n2,a)),or)
| mode(or1(f(n2,a)),abnormal)
| mode(or1(f(n2,a)),ok) ),
inference(subst,[],[ok_or_abnormal:[bind(Any,$fot(or)),bind(K,$fot(or1(f(n2,a))))]]) ).
cnf(refute_0_63,plain,
( mode(or1(f(n2,a)),abnormal)
| mode(or1(f(n2,a)),ok) ),
inference(resolve,[$cnf( type(or1(f(n2,a)),or) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
mode(or1(f(n2,a)),ok),
inference(resolve,[$cnf( mode(or1(f(n2,a)),abnormal) )],[refute_0_63,diagnosis_or1f2a]) ).
cnf(refute_0_65,plain,
( ~ type(or1(f(n2,a)),or)
| ~ value(in(n1,or1(f(n2,a))),n0)
| value(out(n1,or1(f(n2,a))),n0) ),
inference(resolve,[$cnf( mode(or1(f(n2,a)),ok) )],[refute_0_64,refute_0_59]) ).
cnf(refute_0_66,plain,
( ~ value(in(n1,or1(f(n2,a))),n0)
| value(out(n1,or1(f(n2,a))),n0) ),
inference(resolve,[$cnf( type(or1(f(n2,a)),or) )],[refute_0_61,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ type(f(n2,a),fulladder)
| connection(out(c,h2(f(n2,a))),in(n1,or1(f(n2,a)))) ),
inference(subst,[],[fulladder_connection_outch2_in1or1:[bind(X,$fot(f(n2,a)))]]) ).
cnf(refute_0_68,plain,
connection(out(c,h2(f(n2,a))),in(n1,or1(f(n2,a)))),
inference(resolve,[$cnf( type(f(n2,a),fulladder) )],[refute_0_1,refute_0_67]) ).
cnf(refute_0_69,plain,
( ~ connection(out(c,h2(f(n2,a))),in(n1,or1(f(n2,a))))
| ~ value(out(c,h2(f(n2,a))),X_42)
| value(in(n1,or1(f(n2,a))),X_42) ),
inference(subst,[],[value_propagation1:[bind(P1,$fot(out(c,h2(f(n2,a))))),bind(P2,$fot(in(n1,or1(f(n2,a))))),bind(V,$fot(X_42))]]) ).
cnf(refute_0_70,plain,
( ~ value(out(c,h2(f(n2,a))),X_42)
| value(in(n1,or1(f(n2,a))),X_42) ),
inference(resolve,[$cnf( connection(out(c,h2(f(n2,a))),in(n1,or1(f(n2,a)))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ value(out(c,h2(f(n2,a))),n0)
| value(in(n1,or1(f(n2,a))),n0) ),
inference(subst,[],[refute_0_70:[bind(X_42,$fot(n0))]]) ).
cnf(refute_0_72,plain,
( ~ type(f(n2,a),fulladder)
| type(h2(f(n2,a)),halfadder) ),
inference(subst,[],[fulladder_halfadder2:[bind(X,$fot(f(n2,a)))]]) ).
cnf(refute_0_73,plain,
type(h2(f(n2,a)),halfadder),
inference(resolve,[$cnf( type(f(n2,a),fulladder) )],[refute_0_1,refute_0_72]) ).
cnf(refute_0_74,plain,
( ~ type(h2(f(n2,a)),halfadder)
| connection(out(c,h2(f(n2,a))),out(n1,and2(h2(f(n2,a))))) ),
inference(subst,[],[halfadder_connection_outc_out1and2:[bind(X,$fot(h2(f(n2,a))))]]) ).
cnf(refute_0_75,plain,
connection(out(c,h2(f(n2,a))),out(n1,and2(h2(f(n2,a))))),
inference(resolve,[$cnf( type(h2(f(n2,a)),halfadder) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ connection(out(c,h2(f(n2,a))),out(n1,and2(h2(f(n2,a)))))
| ~ value(out(n1,and2(h2(f(n2,a)))),X_98)
| value(out(c,h2(f(n2,a))),X_98) ),
inference(subst,[],[value_propagation2:[bind(P1,$fot(out(c,h2(f(n2,a))))),bind(P2,$fot(out(n1,and2(h2(f(n2,a)))))),bind(V,$fot(X_98))]]) ).
cnf(refute_0_77,plain,
( ~ value(out(n1,and2(h2(f(n2,a)))),X_98)
| value(out(c,h2(f(n2,a))),X_98) ),
inference(resolve,[$cnf( connection(out(c,h2(f(n2,a))),out(n1,and2(h2(f(n2,a))))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ value(out(n1,and2(h2(f(n2,a)))),n0)
| value(out(c,h2(f(n2,a))),n0) ),
inference(subst,[],[refute_0_77:[bind(X_98,$fot(n0))]]) ).
cnf(refute_0_79,plain,
( ~ type(h2(f(n2,a)),halfadder)
| connection(in(n1,h2(f(n2,a))),in(n1,and2(h2(f(n2,a))))) ),
inference(subst,[],[halfadder_connection_in1_in1and2:[bind(X,$fot(h2(f(n2,a))))]]) ).
cnf(refute_0_80,plain,
connection(in(n1,h2(f(n2,a))),in(n1,and2(h2(f(n2,a))))),
inference(resolve,[$cnf( type(h2(f(n2,a)),halfadder) )],[refute_0_73,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ connection(in(n1,h2(f(n2,a))),P2)
| ~ value(in(n1,h2(f(n2,a))),n0)
| value(P2,n0) ),
inference(subst,[],[value_propagation1:[bind(P1,$fot(in(n1,h2(f(n2,a))))),bind(V,$fot(n0))]]) ).
cnf(refute_0_82,plain,
( ~ type(f(n2,a),fulladder)
| connection(in(n1,f(n2,a)),in(n1,h2(f(n2,a)))) ),
inference(subst,[],[fulladder_connection_in1_in1h2:[bind(X,$fot(f(n2,a)))]]) ).
cnf(refute_0_83,plain,
connection(in(n1,f(n2,a)),in(n1,h2(f(n2,a)))),
inference(resolve,[$cnf( type(f(n2,a),fulladder) )],[refute_0_1,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ connection(in(n1,f(n2,a)),P2)
| ~ value(in(n1,f(n2,a)),n0)
| value(P2,n0) ),
inference(subst,[],[value_propagation1:[bind(P1,$fot(in(n1,f(n2,a)))),bind(V,$fot(n0))]]) ).
cnf(refute_0_85,plain,
( ~ type(a,nbit_adder(n2))
| connection(in(a2,a),in(n1,f(n2,a))) ),
inference(subst,[],[nbit_adder_connection_ina2_in1f2:[bind(X,$fot(a))]]) ).
cnf(refute_0_86,plain,
connection(in(a2,a),in(n1,f(n2,a))),
inference(resolve,[$cnf( type(a,nbit_adder(n2)) )],[a_isa_2bit_adder,refute_0_85]) ).
cnf(refute_0_87,plain,
( ~ connection(in(a2,a),X_41)
| ~ value(in(a2,a),n0)
| value(X_41,n0) ),
inference(subst,[],[value_propagation1:[bind(P1,$fot(in(a2,a))),bind(P2,$fot(X_41)),bind(V,$fot(n0))]]) ).
cnf(refute_0_88,plain,
( ~ connection(in(a2,a),X_41)
| value(X_41,n0) ),
inference(resolve,[$cnf( value(in(a2,a),n0) )],[ina2_0,refute_0_87]) ).
cnf(refute_0_89,plain,
( ~ connection(in(a2,a),in(n1,f(n2,a)))
| value(in(n1,f(n2,a)),n0) ),
inference(subst,[],[refute_0_88:[bind(X_41,$fot(in(n1,f(n2,a))))]]) ).
cnf(refute_0_90,plain,
value(in(n1,f(n2,a)),n0),
inference(resolve,[$cnf( connection(in(a2,a),in(n1,f(n2,a))) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
( ~ connection(in(n1,f(n2,a)),P2)
| value(P2,n0) ),
inference(resolve,[$cnf( value(in(n1,f(n2,a)),n0) )],[refute_0_90,refute_0_84]) ).
cnf(refute_0_92,plain,
( ~ connection(in(n1,f(n2,a)),in(n1,h2(f(n2,a))))
| value(in(n1,h2(f(n2,a))),n0) ),
inference(subst,[],[refute_0_91:[bind(P2,$fot(in(n1,h2(f(n2,a)))))]]) ).
cnf(refute_0_93,plain,
value(in(n1,h2(f(n2,a))),n0),
inference(resolve,[$cnf( connection(in(n1,f(n2,a)),in(n1,h2(f(n2,a)))) )],[refute_0_83,refute_0_92]) ).
cnf(refute_0_94,plain,
( ~ connection(in(n1,h2(f(n2,a))),P2)
| value(P2,n0) ),
inference(resolve,[$cnf( value(in(n1,h2(f(n2,a))),n0) )],[refute_0_93,refute_0_81]) ).
cnf(refute_0_95,plain,
( ~ connection(in(n1,h2(f(n2,a))),in(n1,and2(h2(f(n2,a)))))
| value(in(n1,and2(h2(f(n2,a)))),n0) ),
inference(subst,[],[refute_0_94:[bind(P2,$fot(in(n1,and2(h2(f(n2,a))))))]]) ).
cnf(refute_0_96,plain,
value(in(n1,and2(h2(f(n2,a)))),n0),
inference(resolve,[$cnf( connection(in(n1,h2(f(n2,a))),in(n1,and2(h2(f(n2,a))))) )],[refute_0_80,refute_0_95]) ).
cnf(refute_0_97,plain,
( ~ mode(and2(h2(f(n2,a))),ok)
| ~ type(and2(h2(f(n2,a))),and)
| ~ value(in(n1,and2(h2(f(n2,a)))),n0)
| value(out(n1,and2(h2(f(n2,a)))),n0) ),
inference(subst,[],[and_0x_0:[bind(Any,$fot(n1)),bind(K,$fot(and2(h2(f(n2,a)))))]]) ).
cnf(refute_0_98,plain,
( ~ mode(and2(h2(f(n2,a))),ok)
| ~ type(and2(h2(f(n2,a))),and)
| value(out(n1,and2(h2(f(n2,a)))),n0) ),
inference(resolve,[$cnf( value(in(n1,and2(h2(f(n2,a)))),n0) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( ~ type(h2(f(n2,a)),halfadder)
| type(and2(h2(f(n2,a))),and) ),
inference(subst,[],[halfadder_and2:[bind(X,$fot(h2(f(n2,a))))]]) ).
cnf(refute_0_100,plain,
type(and2(h2(f(n2,a))),and),
inference(resolve,[$cnf( type(h2(f(n2,a)),halfadder) )],[refute_0_73,refute_0_99]) ).
cnf(refute_0_101,plain,
( ~ type(and2(h2(f(n2,a))),and)
| mode(and2(h2(f(n2,a))),abnormal)
| mode(and2(h2(f(n2,a))),ok) ),
inference(subst,[],[ok_or_abnormal:[bind(Any,$fot(and)),bind(K,$fot(and2(h2(f(n2,a)))))]]) ).
cnf(refute_0_102,plain,
( mode(and2(h2(f(n2,a))),abnormal)
| mode(and2(h2(f(n2,a))),ok) ),
inference(resolve,[$cnf( type(and2(h2(f(n2,a))),and) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
mode(and2(h2(f(n2,a))),ok),
inference(resolve,[$cnf( mode(and2(h2(f(n2,a))),abnormal) )],[refute_0_102,diagnosis_and2h1f2a]) ).
cnf(refute_0_104,plain,
( ~ type(and2(h2(f(n2,a))),and)
| value(out(n1,and2(h2(f(n2,a)))),n0) ),
inference(resolve,[$cnf( mode(and2(h2(f(n2,a))),ok) )],[refute_0_103,refute_0_98]) ).
cnf(refute_0_105,plain,
value(out(n1,and2(h2(f(n2,a)))),n0),
inference(resolve,[$cnf( type(and2(h2(f(n2,a))),and) )],[refute_0_100,refute_0_104]) ).
cnf(refute_0_106,plain,
value(out(c,h2(f(n2,a))),n0),
inference(resolve,[$cnf( value(out(n1,and2(h2(f(n2,a)))),n0) )],[refute_0_105,refute_0_78]) ).
cnf(refute_0_107,plain,
value(in(n1,or1(f(n2,a))),n0),
inference(resolve,[$cnf( value(out(c,h2(f(n2,a))),n0) )],[refute_0_106,refute_0_71]) ).
cnf(refute_0_108,plain,
value(out(n1,or1(f(n2,a))),n0),
inference(resolve,[$cnf( value(in(n1,or1(f(n2,a))),n0) )],[refute_0_107,refute_0_66]) ).
cnf(refute_0_109,plain,
equal_value(n0,n1),
inference(resolve,[$cnf( value(out(n1,or1(f(n2,a))),n0) )],[refute_0_108,refute_0_16]) ).
cnf(refute_0_110,plain,
$false,
inference(resolve,[$cnf( equal_value(n0,n1) )],[refute_0_109,equal_value1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HWV008-1.002 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n005.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 : Thu Jun 16 21:20:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.49
% 0.20/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.50
%------------------------------------------------------------------------------