%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HWV007-2 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 18:29:34 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 48
% Syntax : Number of clauses : 198 ( 50 unt; 36 nHn; 198 RR)
% Number of literals : 410 ( 0 equ; 175 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-1 aty)
% Number of variables : 41 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(value_propagation_zero1,axiom,
( ~ connection(P1,P2)
| ~ zero(P1)
| zero(P2) ) ).
cnf(value_propagation_one1,axiom,
( ~ connection(P1,P2)
| ~ one(P1)
| one(P2) ) ).
cnf(value_propagation_zero2,axiom,
( ~ connection(P1,P2)
| ~ zero(P2)
| zero(P1) ) ).
cnf(value_propagation_one2,axiom,
( ~ connection(P1,P2)
| ~ one(P2)
| one(P1) ) ).
cnf(unique_value,axiom,
( ~ zero(P)
| ~ one(P) ) ).
cnf(and_11_1,axiom,
( ~ and_ok(K)
| ~ one(in1(K))
| ~ one(in2(K))
| one(out1(K)) ) ).
cnf(and_1_1x,axiom,
( ~ and_ok(K)
| ~ one(out1(K))
| one(in1(K)) ) ).
cnf(and_1_x1,axiom,
( ~ and_ok(K)
| ~ one(out1(K))
| one(in2(K)) ) ).
cnf(and_ok_or_abnormal,axiom,
( ~ logic_and(K)
| and_ok(K)
| abnormal(K) ) ).
cnf(or_1_11,axiom,
( ~ or_ok(K)
| ~ one(out1(K))
| one(in1(K))
| one(in2(K)) ) ).
cnf(or_0_01,axiom,
( ~ or_ok(K)
| ~ zero(out1(K))
| zero(in2(K)) ) ).
cnf(or_ok_or_abnormal,axiom,
( ~ logic_or(K)
| or_ok(K)
| abnormal(K) ) ).
cnf(not_1_0_fw,axiom,
( ~ not_ok(K)
| ~ one(in1(K))
| zero(out1(K)) ) ).
cnf(not_ok_or_abnormal,axiom,
( ~ logic_not(K)
| not_ok(K)
| abnormal(K) ) ).
cnf(halfadder_and1,axiom,
( ~ halfadder(X)
| logic_and(and1(X)) ) ).
cnf(halfadder_and2,axiom,
( ~ halfadder(X)
| logic_and(and2(X)) ) ).
cnf(halfadder_not1,axiom,
( ~ halfadder(X)
| logic_not(not1(X)) ) ).
cnf(halfadder_or1,axiom,
( ~ halfadder(X)
| logic_or(or1(X)) ) ).
cnf(halfadder_connection_in1_in1or1,axiom,
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) ) ).
cnf(halfadder_connection_in2_in2or1,axiom,
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) ) ).
cnf(halfadder_connection_in1_in1and2,axiom,
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ) ).
cnf(halfadder_connection_in2_in2and2,axiom,
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) ) ).
cnf(halfadder_connection_outs_out1and1,axiom,
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ) ).
cnf(halfadder_connection_outc_out1and2,axiom,
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ) ).
cnf(halfadder_connection_out1or1_in1_and1,axiom,
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ) ).
cnf(halfadder_connection_out1and2_in1not1,axiom,
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ) ).
cnf(halfadder_connection_out1not1_in2and1,axiom,
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ) ).
cnf(fulladder_halfadder1,axiom,
( ~ fulladder(X)
| halfadder(h1(X)) ) ).
cnf(fulladder_halfadder2,axiom,
( ~ fulladder(X)
| halfadder(h2(X)) ) ).
cnf(fulladder_or1,axiom,
( ~ fulladder(X)
| logic_or(or1(X)) ) ).
cnf(fulladder_connection_outsh1_in2h2,axiom,
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) ) ).
cnf(fulladder_connection_outch1_in2or1,axiom,
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ) ).
cnf(fulladder_connection_in1_in1h2,axiom,
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ) ).
cnf(fulladder_connection_in2_in1h1,axiom,
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ) ).
cnf(fulladder_connection_inc_in2h1,axiom,
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) ) ).
cnf(fulladder_connection_outs_outsh2,axiom,
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) ) ).
cnf(fulladder_connection_outc_out1or1,axiom,
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ) ).
cnf(f_isa_fulladder,hypothesis,
fulladder(f) ).
cnf(in1_1,hypothesis,
zero(in1(f)) ).
cnf(in2_0,hypothesis,
one(in2(f)) ).
cnf(inc_1,hypothesis,
one(inc(f)) ).
cnf(outs_1,hypothesis,
one(outs(f)) ).
cnf(outc_0,hypothesis,
zero(outc(f)) ).
cnf(diagnosis_and2h1,negated_conjecture,
~ abnormal(and2(h1(f))) ).
cnf(diagnosis_or1_and1h1,negated_conjecture,
( ~ abnormal(or1(f))
| ~ abnormal(and1(h1(f))) ) ).
cnf(diagnosis_or1_not1h1,negated_conjecture,
( ~ abnormal(or1(f))
| ~ abnormal(not1(h1(f))) ) ).
cnf(diagnosis_or1_and1h2,negated_conjecture,
( ~ abnormal(or1(f))
| ~ abnormal(and1(h2(f))) ) ).
cnf(diagnosis_or1_or1h2,negated_conjecture,
( ~ abnormal(or1(f))
| ~ abnormal(or1(h2(f))) ) ).
cnf(refute_0_0,plain,
( ~ one(in2(and1(h1(f))))
| ~ zero(in2(and1(h1(f)))) ),
inference(subst,[],[unique_value:[bind(P,$fot(in2(and1(h1(f)))))]]) ).
cnf(refute_0_1,plain,
( ~ fulladder(f)
| halfadder(h1(f)) ),
inference(subst,[],[fulladder_halfadder1:[bind(X,$fot(f))]]) ).
cnf(refute_0_2,plain,
halfadder(h1(f)),
inference(resolve,[$cnf( fulladder(f) )],[f_isa_fulladder,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ halfadder(h1(f))
| connection(out1(not1(h1(f))),in2(and1(h1(f)))) ),
inference(subst,[],[halfadder_connection_out1not1_in2and1:[bind(X,$fot(h1(f)))]]) ).
cnf(refute_0_4,plain,
connection(out1(not1(h1(f))),in2(and1(h1(f)))),
inference(resolve,[$cnf( halfadder(h1(f)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| ~ zero(out1(not1(h1(f))))
| zero(in2(and1(h1(f)))) ),
inference(subst,[],[value_propagation_zero1:[bind(P1,$fot(out1(not1(h1(f))))),bind(P2,$fot(in2(and1(h1(f)))))]]) ).
cnf(refute_0_6,plain,
( ~ zero(out1(not1(h1(f))))
| zero(in2(and1(h1(f)))) ),
inference(resolve,[$cnf( connection(out1(not1(h1(f))),in2(and1(h1(f)))) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ halfadder(h1(f))
| logic_not(not1(h1(f))) ),
inference(subst,[],[halfadder_not1:[bind(X,$fot(h1(f)))]]) ).
cnf(refute_0_8,plain,
logic_not(not1(h1(f))),
inference(resolve,[$cnf( halfadder(h1(f)) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ logic_not(not1(h1(f)))
| abnormal(not1(h1(f)))
| not_ok(not1(h1(f))) ),
inference(subst,[],[not_ok_or_abnormal:[bind(K,$fot(not1(h1(f))))]]) ).
cnf(refute_0_10,plain,
( abnormal(not1(h1(f)))
| not_ok(not1(h1(f))) ),
inference(resolve,[$cnf( logic_not(not1(h1(f))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ not_ok(not1(h1(f)))
| ~ one(in1(not1(h1(f))))
| zero(out1(not1(h1(f)))) ),
inference(subst,[],[not_1_0_fw:[bind(K,$fot(not1(h1(f))))]]) ).
cnf(refute_0_12,plain,
( ~ halfadder(h1(f))
| connection(out1(and2(h1(f))),in1(not1(h1(f)))) ),
inference(subst,[],[halfadder_connection_out1and2_in1not1:[bind(X,$fot(h1(f)))]]) ).
cnf(refute_0_13,plain,
connection(out1(and2(h1(f))),in1(not1(h1(f)))),
inference(resolve,[$cnf( halfadder(h1(f)) )],[refute_0_2,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ connection(out1(and2(h1(f))),in1(not1(h1(f))))
| ~ one(out1(and2(h1(f))))
| one(in1(not1(h1(f)))) ),
inference(subst,[],[value_propagation_one1:[bind(P1,$fot(out1(and2(h1(f))))),bind(P2,$fot(in1(not1(h1(f)))))]]) ).
cnf(refute_0_15,plain,
( ~ one(out1(and2(h1(f))))
| one(in1(not1(h1(f)))) ),
inference(resolve,[$cnf( connection(out1(and2(h1(f))),in1(not1(h1(f)))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ halfadder(h1(f))
| connection(in2(h1(f)),in2(and2(h1(f)))) ),
inference(subst,[],[halfadder_connection_in2_in2and2:[bind(X,$fot(h1(f)))]]) ).
cnf(refute_0_17,plain,
connection(in2(h1(f)),in2(and2(h1(f)))),
inference(resolve,[$cnf( halfadder(h1(f)) )],[refute_0_2,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ connection(in2(h1(f)),in2(and2(h1(f))))
| ~ one(in2(h1(f)))
| one(in2(and2(h1(f)))) ),
inference(subst,[],[value_propagation_one1:[bind(P1,$fot(in2(h1(f)))),bind(P2,$fot(in2(and2(h1(f)))))]]) ).
cnf(refute_0_19,plain,
( ~ one(in2(h1(f)))
| one(in2(and2(h1(f)))) ),
inference(resolve,[$cnf( connection(in2(h1(f)),in2(and2(h1(f)))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ fulladder(f)
| connection(inc(f),in2(h1(f))) ),
inference(subst,[],[fulladder_connection_inc_in2h1:[bind(X,$fot(f))]]) ).
cnf(refute_0_21,plain,
connection(inc(f),in2(h1(f))),
inference(resolve,[$cnf( fulladder(f) )],[f_isa_fulladder,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ connection(inc(f),in2(h1(f)))
| ~ one(inc(f))
| one(in2(h1(f))) ),
inference(subst,[],[value_propagation_one1:[bind(P1,$fot(inc(f))),bind(P2,$fot(in2(h1(f))))]]) ).
cnf(refute_0_23,plain,
( ~ one(inc(f))
| one(in2(h1(f))) ),
inference(resolve,[$cnf( connection(inc(f),in2(h1(f))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
one(in2(h1(f))),
inference(resolve,[$cnf( one(inc(f)) )],[inc_1,refute_0_23]) ).
cnf(refute_0_25,plain,
one(in2(and2(h1(f)))),
inference(resolve,[$cnf( one(in2(h1(f))) )],[refute_0_24,refute_0_19]) ).
cnf(refute_0_26,plain,
( ~ and_ok(and2(h1(f)))
| ~ one(in1(and2(h1(f))))
| ~ one(in2(and2(h1(f))))
| one(out1(and2(h1(f)))) ),
inference(subst,[],[and_11_1:[bind(K,$fot(and2(h1(f))))]]) ).
cnf(refute_0_27,plain,
( ~ and_ok(and2(h1(f)))
| ~ one(in1(and2(h1(f))))
| one(out1(and2(h1(f)))) ),
inference(resolve,[$cnf( one(in2(and2(h1(f)))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ halfadder(h1(f))
| logic_and(and2(h1(f))) ),
inference(subst,[],[halfadder_and2:[bind(X,$fot(h1(f)))]]) ).
cnf(refute_0_29,plain,
logic_and(and2(h1(f))),
inference(resolve,[$cnf( halfadder(h1(f)) )],[refute_0_2,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ logic_and(and2(h1(f)))
| abnormal(and2(h1(f)))
| and_ok(and2(h1(f))) ),
inference(subst,[],[and_ok_or_abnormal:[bind(K,$fot(and2(h1(f))))]]) ).
cnf(refute_0_31,plain,
( abnormal(and2(h1(f)))
| and_ok(and2(h1(f))) ),
inference(resolve,[$cnf( logic_and(and2(h1(f))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
and_ok(and2(h1(f))),
inference(resolve,[$cnf( abnormal(and2(h1(f))) )],[refute_0_31,diagnosis_and2h1]) ).
cnf(refute_0_33,plain,
( ~ one(in1(and2(h1(f))))
| one(out1(and2(h1(f)))) ),
inference(resolve,[$cnf( and_ok(and2(h1(f))) )],[refute_0_32,refute_0_27]) ).
cnf(refute_0_34,plain,
( ~ halfadder(h1(f))
| connection(in1(h1(f)),in1(and2(h1(f)))) ),
inference(subst,[],[halfadder_connection_in1_in1and2:[bind(X,$fot(h1(f)))]]) ).
cnf(refute_0_35,plain,
connection(in1(h1(f)),in1(and2(h1(f)))),
inference(resolve,[$cnf( halfadder(h1(f)) )],[refute_0_2,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ connection(in1(h1(f)),in1(and2(h1(f))))
| ~ one(in1(h1(f)))
| one(in1(and2(h1(f)))) ),
inference(subst,[],[value_propagation_one1:[bind(P1,$fot(in1(h1(f)))),bind(P2,$fot(in1(and2(h1(f)))))]]) ).
cnf(refute_0_37,plain,
( ~ one(in1(h1(f)))
| one(in1(and2(h1(f)))) ),
inference(resolve,[$cnf( connection(in1(h1(f)),in1(and2(h1(f)))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ fulladder(f)
| connection(in2(f),in1(h1(f))) ),
inference(subst,[],[fulladder_connection_in2_in1h1:[bind(X,$fot(f))]]) ).
cnf(refute_0_39,plain,
connection(in2(f),in1(h1(f))),
inference(resolve,[$cnf( fulladder(f) )],[f_isa_fulladder,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ connection(in2(f),in1(h1(f)))
| ~ one(in2(f))
| one(in1(h1(f))) ),
inference(subst,[],[value_propagation_one1:[bind(P1,$fot(in2(f))),bind(P2,$fot(in1(h1(f))))]]) ).
cnf(refute_0_41,plain,
( ~ one(in2(f))
| one(in1(h1(f))) ),
inference(resolve,[$cnf( connection(in2(f),in1(h1(f))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
one(in1(h1(f))),
inference(resolve,[$cnf( one(in2(f)) )],[in2_0,refute_0_41]) ).
cnf(refute_0_43,plain,
one(in1(and2(h1(f)))),
inference(resolve,[$cnf( one(in1(h1(f))) )],[refute_0_42,refute_0_37]) ).
cnf(refute_0_44,plain,
one(out1(and2(h1(f)))),
inference(resolve,[$cnf( one(in1(and2(h1(f)))) )],[refute_0_43,refute_0_33]) ).
cnf(refute_0_45,plain,
one(in1(not1(h1(f)))),
inference(resolve,[$cnf( one(out1(and2(h1(f)))) )],[refute_0_44,refute_0_15]) ).
cnf(refute_0_46,plain,
( ~ not_ok(not1(h1(f)))
| zero(out1(not1(h1(f)))) ),
inference(resolve,[$cnf( one(in1(not1(h1(f)))) )],[refute_0_45,refute_0_11]) ).
cnf(refute_0_47,plain,
( abnormal(not1(h1(f)))
| zero(out1(not1(h1(f)))) ),
inference(resolve,[$cnf( not_ok(not1(h1(f))) )],[refute_0_10,refute_0_46]) ).
cnf(refute_0_48,plain,
( abnormal(not1(h1(f)))
| zero(in2(and1(h1(f)))) ),
inference(resolve,[$cnf( zero(out1(not1(h1(f)))) )],[refute_0_47,refute_0_6]) ).
cnf(refute_0_49,plain,
( ~ one(in2(and1(h1(f))))
| abnormal(not1(h1(f))) ),
inference(resolve,[$cnf( zero(in2(and1(h1(f)))) )],[refute_0_48,refute_0_0]) ).
cnf(refute_0_50,plain,
( ~ halfadder(h1(f))
| logic_and(and1(h1(f))) ),
inference(subst,[],[halfadder_and1:[bind(X,$fot(h1(f)))]]) ).
cnf(refute_0_51,plain,
logic_and(and1(h1(f))),
inference(resolve,[$cnf( halfadder(h1(f)) )],[refute_0_2,refute_0_50]) ).
cnf(refute_0_52,plain,
( ~ logic_and(and1(h1(f)))
| abnormal(and1(h1(f)))
| and_ok(and1(h1(f))) ),
inference(subst,[],[and_ok_or_abnormal:[bind(K,$fot(and1(h1(f))))]]) ).
cnf(refute_0_53,plain,
( abnormal(and1(h1(f)))
| and_ok(and1(h1(f))) ),
inference(resolve,[$cnf( logic_and(and1(h1(f))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ and_ok(and1(h1(f)))
| ~ one(out1(and1(h1(f))))
| one(in2(and1(h1(f)))) ),
inference(subst,[],[and_1_x1:[bind(K,$fot(and1(h1(f))))]]) ).
cnf(refute_0_55,plain,
( ~ halfadder(h1(f))
| connection(outs(h1(f)),out1(and1(h1(f)))) ),
inference(subst,[],[halfadder_connection_outs_out1and1:[bind(X,$fot(h1(f)))]]) ).
cnf(refute_0_56,plain,
connection(outs(h1(f)),out1(and1(h1(f)))),
inference(resolve,[$cnf( halfadder(h1(f)) )],[refute_0_2,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ connection(outs(h1(f)),out1(and1(h1(f))))
| ~ one(outs(h1(f)))
| one(out1(and1(h1(f)))) ),
inference(subst,[],[value_propagation_one1:[bind(P1,$fot(outs(h1(f)))),bind(P2,$fot(out1(and1(h1(f)))))]]) ).
cnf(refute_0_58,plain,
( ~ one(outs(h1(f)))
| one(out1(and1(h1(f)))) ),
inference(resolve,[$cnf( connection(outs(h1(f)),out1(and1(h1(f)))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ fulladder(f)
| connection(outs(h1(f)),in2(h2(f))) ),
inference(subst,[],[fulladder_connection_outsh1_in2h2:[bind(X,$fot(f))]]) ).
cnf(refute_0_60,plain,
connection(outs(h1(f)),in2(h2(f))),
inference(resolve,[$cnf( fulladder(f) )],[f_isa_fulladder,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ connection(outs(h1(f)),in2(h2(f)))
| ~ one(in2(h2(f)))
| one(outs(h1(f))) ),
inference(subst,[],[value_propagation_one2:[bind(P1,$fot(outs(h1(f)))),bind(P2,$fot(in2(h2(f))))]]) ).
cnf(refute_0_62,plain,
( ~ one(in2(h2(f)))
| one(outs(h1(f))) ),
inference(resolve,[$cnf( connection(outs(h1(f)),in2(h2(f))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( ~ fulladder(f)
| halfadder(h2(f)) ),
inference(subst,[],[fulladder_halfadder2:[bind(X,$fot(f))]]) ).
cnf(refute_0_64,plain,
halfadder(h2(f)),
inference(resolve,[$cnf( fulladder(f) )],[f_isa_fulladder,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ halfadder(h2(f))
| connection(in2(h2(f)),in2(or1(h2(f)))) ),
inference(subst,[],[halfadder_connection_in2_in2or1:[bind(X,$fot(h2(f)))]]) ).
cnf(refute_0_66,plain,
connection(in2(h2(f)),in2(or1(h2(f)))),
inference(resolve,[$cnf( halfadder(h2(f)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ connection(in2(h2(f)),in2(or1(h2(f))))
| ~ one(in2(or1(h2(f))))
| one(in2(h2(f))) ),
inference(subst,[],[value_propagation_one2:[bind(P1,$fot(in2(h2(f)))),bind(P2,$fot(in2(or1(h2(f)))))]]) ).
cnf(refute_0_68,plain,
( ~ one(in2(or1(h2(f))))
| one(in2(h2(f))) ),
inference(resolve,[$cnf( connection(in2(h2(f)),in2(or1(h2(f)))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( ~ halfadder(h2(f))
| logic_or(or1(h2(f))) ),
inference(subst,[],[halfadder_or1:[bind(X,$fot(h2(f)))]]) ).
cnf(refute_0_70,plain,
logic_or(or1(h2(f))),
inference(resolve,[$cnf( halfadder(h2(f)) )],[refute_0_64,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ logic_or(or1(h2(f)))
| abnormal(or1(h2(f)))
| or_ok(or1(h2(f))) ),
inference(subst,[],[or_ok_or_abnormal:[bind(K,$fot(or1(h2(f))))]]) ).
cnf(refute_0_72,plain,
( abnormal(or1(h2(f)))
| or_ok(or1(h2(f))) ),
inference(resolve,[$cnf( logic_or(or1(h2(f))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ halfadder(h2(f))
| logic_and(and1(h2(f))) ),
inference(subst,[],[halfadder_and1:[bind(X,$fot(h2(f)))]]) ).
cnf(refute_0_74,plain,
logic_and(and1(h2(f))),
inference(resolve,[$cnf( halfadder(h2(f)) )],[refute_0_64,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ logic_and(and1(h2(f)))
| abnormal(and1(h2(f)))
| and_ok(and1(h2(f))) ),
inference(subst,[],[and_ok_or_abnormal:[bind(K,$fot(and1(h2(f))))]]) ).
cnf(refute_0_76,plain,
( abnormal(and1(h2(f)))
| and_ok(and1(h2(f))) ),
inference(resolve,[$cnf( logic_and(and1(h2(f))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( ~ and_ok(and1(h2(f)))
| ~ one(out1(and1(h2(f))))
| one(in1(and1(h2(f)))) ),
inference(subst,[],[and_1_1x:[bind(K,$fot(and1(h2(f))))]]) ).
cnf(refute_0_78,plain,
( ~ halfadder(h2(f))
| connection(outs(h2(f)),out1(and1(h2(f)))) ),
inference(subst,[],[halfadder_connection_outs_out1and1:[bind(X,$fot(h2(f)))]]) ).
cnf(refute_0_79,plain,
connection(outs(h2(f)),out1(and1(h2(f)))),
inference(resolve,[$cnf( halfadder(h2(f)) )],[refute_0_64,refute_0_78]) ).
cnf(refute_0_80,plain,
( ~ connection(outs(h2(f)),out1(and1(h2(f))))
| ~ one(outs(h2(f)))
| one(out1(and1(h2(f)))) ),
inference(subst,[],[value_propagation_one1:[bind(P1,$fot(outs(h2(f)))),bind(P2,$fot(out1(and1(h2(f)))))]]) ).
cnf(refute_0_81,plain,
( ~ one(outs(h2(f)))
| one(out1(and1(h2(f)))) ),
inference(resolve,[$cnf( connection(outs(h2(f)),out1(and1(h2(f)))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( ~ fulladder(f)
| connection(outs(f),outs(h2(f))) ),
inference(subst,[],[fulladder_connection_outs_outsh2:[bind(X,$fot(f))]]) ).
cnf(refute_0_83,plain,
connection(outs(f),outs(h2(f))),
inference(resolve,[$cnf( fulladder(f) )],[f_isa_fulladder,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ connection(outs(f),outs(h2(f)))
| ~ one(outs(f))
| one(outs(h2(f))) ),
inference(subst,[],[value_propagation_one1:[bind(P1,$fot(outs(f))),bind(P2,$fot(outs(h2(f))))]]) ).
cnf(refute_0_85,plain,
( ~ one(outs(f))
| one(outs(h2(f))) ),
inference(resolve,[$cnf( connection(outs(f),outs(h2(f))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
one(outs(h2(f))),
inference(resolve,[$cnf( one(outs(f)) )],[outs_1,refute_0_85]) ).
cnf(refute_0_87,plain,
one(out1(and1(h2(f)))),
inference(resolve,[$cnf( one(outs(h2(f))) )],[refute_0_86,refute_0_81]) ).
cnf(refute_0_88,plain,
( ~ and_ok(and1(h2(f)))
| one(in1(and1(h2(f)))) ),
inference(resolve,[$cnf( one(out1(and1(h2(f)))) )],[refute_0_87,refute_0_77]) ).
cnf(refute_0_89,plain,
( abnormal(and1(h2(f)))
| one(in1(and1(h2(f)))) ),
inference(resolve,[$cnf( and_ok(and1(h2(f))) )],[refute_0_76,refute_0_88]) ).
cnf(refute_0_90,plain,
( ~ halfadder(h2(f))
| connection(out1(or1(h2(f))),in1(and1(h2(f)))) ),
inference(subst,[],[halfadder_connection_out1or1_in1_and1:[bind(X,$fot(h2(f)))]]) ).
cnf(refute_0_91,plain,
connection(out1(or1(h2(f))),in1(and1(h2(f)))),
inference(resolve,[$cnf( halfadder(h2(f)) )],[refute_0_64,refute_0_90]) ).
cnf(refute_0_92,plain,
( ~ connection(out1(or1(h2(f))),in1(and1(h2(f))))
| ~ one(in1(and1(h2(f))))
| one(out1(or1(h2(f)))) ),
inference(subst,[],[value_propagation_one2:[bind(P1,$fot(out1(or1(h2(f))))),bind(P2,$fot(in1(and1(h2(f)))))]]) ).
cnf(refute_0_93,plain,
( ~ one(in1(and1(h2(f))))
| one(out1(or1(h2(f)))) ),
inference(resolve,[$cnf( connection(out1(or1(h2(f))),in1(and1(h2(f)))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
( abnormal(and1(h2(f)))
| one(out1(or1(h2(f)))) ),
inference(resolve,[$cnf( one(in1(and1(h2(f)))) )],[refute_0_89,refute_0_93]) ).
cnf(refute_0_95,plain,
( ~ one(out1(or1(h2(f))))
| ~ or_ok(or1(h2(f)))
| one(in1(or1(h2(f))))
| one(in2(or1(h2(f)))) ),
inference(subst,[],[or_1_11:[bind(K,$fot(or1(h2(f))))]]) ).
cnf(refute_0_96,plain,
( ~ or_ok(or1(h2(f)))
| abnormal(and1(h2(f)))
| one(in1(or1(h2(f))))
| one(in2(or1(h2(f)))) ),
inference(resolve,[$cnf( one(out1(or1(h2(f)))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
( ~ one(in1(or1(h2(f))))
| ~ zero(in1(or1(h2(f)))) ),
inference(subst,[],[unique_value:[bind(P,$fot(in1(or1(h2(f)))))]]) ).
cnf(refute_0_98,plain,
( ~ halfadder(h2(f))
| connection(in1(h2(f)),in1(or1(h2(f)))) ),
inference(subst,[],[halfadder_connection_in1_in1or1:[bind(X,$fot(h2(f)))]]) ).
cnf(refute_0_99,plain,
connection(in1(h2(f)),in1(or1(h2(f)))),
inference(resolve,[$cnf( halfadder(h2(f)) )],[refute_0_64,refute_0_98]) ).
cnf(refute_0_100,plain,
( ~ connection(in1(h2(f)),in1(or1(h2(f))))
| ~ zero(in1(h2(f)))
| zero(in1(or1(h2(f)))) ),
inference(subst,[],[value_propagation_zero1:[bind(P1,$fot(in1(h2(f)))),bind(P2,$fot(in1(or1(h2(f)))))]]) ).
cnf(refute_0_101,plain,
( ~ zero(in1(h2(f)))
| zero(in1(or1(h2(f)))) ),
inference(resolve,[$cnf( connection(in1(h2(f)),in1(or1(h2(f)))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
( ~ fulladder(f)
| connection(in1(f),in1(h2(f))) ),
inference(subst,[],[fulladder_connection_in1_in1h2:[bind(X,$fot(f))]]) ).
cnf(refute_0_103,plain,
connection(in1(f),in1(h2(f))),
inference(resolve,[$cnf( fulladder(f) )],[f_isa_fulladder,refute_0_102]) ).
cnf(refute_0_104,plain,
( ~ connection(in1(f),in1(h2(f)))
| ~ zero(in1(f))
| zero(in1(h2(f))) ),
inference(subst,[],[value_propagation_zero1:[bind(P1,$fot(in1(f))),bind(P2,$fot(in1(h2(f))))]]) ).
cnf(refute_0_105,plain,
( ~ zero(in1(f))
| zero(in1(h2(f))) ),
inference(resolve,[$cnf( connection(in1(f),in1(h2(f))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
zero(in1(h2(f))),
inference(resolve,[$cnf( zero(in1(f)) )],[in1_1,refute_0_105]) ).
cnf(refute_0_107,plain,
zero(in1(or1(h2(f)))),
inference(resolve,[$cnf( zero(in1(h2(f))) )],[refute_0_106,refute_0_101]) ).
cnf(refute_0_108,plain,
~ one(in1(or1(h2(f)))),
inference(resolve,[$cnf( zero(in1(or1(h2(f)))) )],[refute_0_107,refute_0_97]) ).
cnf(refute_0_109,plain,
( ~ or_ok(or1(h2(f)))
| abnormal(and1(h2(f)))
| one(in2(or1(h2(f)))) ),
inference(resolve,[$cnf( one(in1(or1(h2(f)))) )],[refute_0_96,refute_0_108]) ).
cnf(refute_0_110,plain,
( abnormal(and1(h2(f)))
| abnormal(or1(h2(f)))
| one(in2(or1(h2(f)))) ),
inference(resolve,[$cnf( or_ok(or1(h2(f))) )],[refute_0_72,refute_0_109]) ).
cnf(refute_0_111,plain,
( abnormal(and1(h2(f)))
| abnormal(or1(h2(f)))
| one(in2(h2(f))) ),
inference(resolve,[$cnf( one(in2(or1(h2(f)))) )],[refute_0_110,refute_0_68]) ).
cnf(refute_0_112,plain,
( abnormal(and1(h2(f)))
| abnormal(or1(h2(f)))
| one(outs(h1(f))) ),
inference(resolve,[$cnf( one(in2(h2(f))) )],[refute_0_111,refute_0_62]) ).
cnf(refute_0_113,plain,
( abnormal(and1(h2(f)))
| abnormal(or1(h2(f)))
| one(out1(and1(h1(f)))) ),
inference(resolve,[$cnf( one(outs(h1(f))) )],[refute_0_112,refute_0_58]) ).
cnf(refute_0_114,plain,
( ~ and_ok(and1(h1(f)))
| abnormal(and1(h2(f)))
| abnormal(or1(h2(f)))
| one(in2(and1(h1(f)))) ),
inference(resolve,[$cnf( one(out1(and1(h1(f)))) )],[refute_0_113,refute_0_54]) ).
cnf(refute_0_115,plain,
( abnormal(and1(h1(f)))
| abnormal(and1(h2(f)))
| abnormal(or1(h2(f)))
| one(in2(and1(h1(f)))) ),
inference(resolve,[$cnf( and_ok(and1(h1(f))) )],[refute_0_53,refute_0_114]) ).
cnf(refute_0_116,plain,
( abnormal(and1(h1(f)))
| abnormal(and1(h2(f)))
| abnormal(not1(h1(f)))
| abnormal(or1(h2(f))) ),
inference(resolve,[$cnf( one(in2(and1(h1(f)))) )],[refute_0_115,refute_0_49]) ).
cnf(refute_0_117,plain,
( ~ abnormal(or1(f))
| abnormal(and1(h1(f)))
| abnormal(and1(h2(f)))
| abnormal(not1(h1(f))) ),
inference(resolve,[$cnf( abnormal(or1(h2(f))) )],[refute_0_116,diagnosis_or1_or1h2]) ).
cnf(refute_0_118,plain,
( ~ one(outc(h1(f)))
| ~ zero(outc(h1(f))) ),
inference(subst,[],[unique_value:[bind(P,$fot(outc(h1(f))))]]) ).
cnf(refute_0_119,plain,
( ~ fulladder(f)
| logic_or(or1(f)) ),
inference(subst,[],[fulladder_or1:[bind(X,$fot(f))]]) ).
cnf(refute_0_120,plain,
logic_or(or1(f)),
inference(resolve,[$cnf( fulladder(f) )],[f_isa_fulladder,refute_0_119]) ).
cnf(refute_0_121,plain,
( ~ logic_or(or1(f))
| abnormal(or1(f))
| or_ok(or1(f)) ),
inference(subst,[],[or_ok_or_abnormal:[bind(K,$fot(or1(f)))]]) ).
cnf(refute_0_122,plain,
( abnormal(or1(f))
| or_ok(or1(f)) ),
inference(resolve,[$cnf( logic_or(or1(f)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
( ~ or_ok(or1(f))
| ~ zero(out1(or1(f)))
| zero(in2(or1(f))) ),
inference(subst,[],[or_0_01:[bind(K,$fot(or1(f)))]]) ).
cnf(refute_0_124,plain,
( ~ fulladder(f)
| connection(outc(f),out1(or1(f))) ),
inference(subst,[],[fulladder_connection_outc_out1or1:[bind(X,$fot(f))]]) ).
cnf(refute_0_125,plain,
connection(outc(f),out1(or1(f))),
inference(resolve,[$cnf( fulladder(f) )],[f_isa_fulladder,refute_0_124]) ).
cnf(refute_0_126,plain,
( ~ connection(outc(f),out1(or1(f)))
| ~ zero(outc(f))
| zero(out1(or1(f))) ),
inference(subst,[],[value_propagation_zero1:[bind(P1,$fot(outc(f))),bind(P2,$fot(out1(or1(f))))]]) ).
cnf(refute_0_127,plain,
( ~ zero(outc(f))
| zero(out1(or1(f))) ),
inference(resolve,[$cnf( connection(outc(f),out1(or1(f))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
zero(out1(or1(f))),
inference(resolve,[$cnf( zero(outc(f)) )],[outc_0,refute_0_127]) ).
cnf(refute_0_129,plain,
( ~ or_ok(or1(f))
| zero(in2(or1(f))) ),
inference(resolve,[$cnf( zero(out1(or1(f))) )],[refute_0_128,refute_0_123]) ).
cnf(refute_0_130,plain,
( abnormal(or1(f))
| zero(in2(or1(f))) ),
inference(resolve,[$cnf( or_ok(or1(f)) )],[refute_0_122,refute_0_129]) ).
cnf(refute_0_131,plain,
( ~ fulladder(f)
| connection(outc(h1(f)),in2(or1(f))) ),
inference(subst,[],[fulladder_connection_outch1_in2or1:[bind(X,$fot(f))]]) ).
cnf(refute_0_132,plain,
connection(outc(h1(f)),in2(or1(f))),
inference(resolve,[$cnf( fulladder(f) )],[f_isa_fulladder,refute_0_131]) ).
cnf(refute_0_133,plain,
( ~ connection(outc(h1(f)),in2(or1(f)))
| ~ zero(in2(or1(f)))
| zero(outc(h1(f))) ),
inference(subst,[],[value_propagation_zero2:[bind(P1,$fot(outc(h1(f)))),bind(P2,$fot(in2(or1(f))))]]) ).
cnf(refute_0_134,plain,
( ~ zero(in2(or1(f)))
| zero(outc(h1(f))) ),
inference(resolve,[$cnf( connection(outc(h1(f)),in2(or1(f))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
( abnormal(or1(f))
| zero(outc(h1(f))) ),
inference(resolve,[$cnf( zero(in2(or1(f))) )],[refute_0_130,refute_0_134]) ).
cnf(refute_0_136,plain,
( ~ one(outc(h1(f)))
| abnormal(or1(f)) ),
inference(resolve,[$cnf( zero(outc(h1(f))) )],[refute_0_135,refute_0_118]) ).
cnf(refute_0_137,plain,
( ~ halfadder(h1(f))
| connection(outc(h1(f)),out1(and2(h1(f)))) ),
inference(subst,[],[halfadder_connection_outc_out1and2:[bind(X,$fot(h1(f)))]]) ).
cnf(refute_0_138,plain,
connection(outc(h1(f)),out1(and2(h1(f)))),
inference(resolve,[$cnf( halfadder(h1(f)) )],[refute_0_2,refute_0_137]) ).
cnf(refute_0_139,plain,
( ~ connection(outc(h1(f)),out1(and2(h1(f))))
| ~ one(out1(and2(h1(f))))
| one(outc(h1(f))) ),
inference(subst,[],[value_propagation_one2:[bind(P1,$fot(outc(h1(f)))),bind(P2,$fot(out1(and2(h1(f)))))]]) ).
cnf(refute_0_140,plain,
( ~ one(out1(and2(h1(f))))
| one(outc(h1(f))) ),
inference(resolve,[$cnf( connection(outc(h1(f)),out1(and2(h1(f)))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
one(outc(h1(f))),
inference(resolve,[$cnf( one(out1(and2(h1(f)))) )],[refute_0_44,refute_0_140]) ).
cnf(refute_0_142,plain,
abnormal(or1(f)),
inference(resolve,[$cnf( one(outc(h1(f))) )],[refute_0_141,refute_0_136]) ).
cnf(refute_0_143,plain,
( abnormal(and1(h1(f)))
| abnormal(and1(h2(f)))
| abnormal(not1(h1(f))) ),
inference(resolve,[$cnf( abnormal(or1(f)) )],[refute_0_142,refute_0_117]) ).
cnf(refute_0_144,plain,
( ~ abnormal(or1(f))
| abnormal(and1(h1(f)))
| abnormal(and1(h2(f))) ),
inference(resolve,[$cnf( abnormal(not1(h1(f))) )],[refute_0_143,diagnosis_or1_not1h1]) ).
cnf(refute_0_145,plain,
( abnormal(and1(h1(f)))
| abnormal(and1(h2(f))) ),
inference(resolve,[$cnf( abnormal(or1(f)) )],[refute_0_142,refute_0_144]) ).
cnf(refute_0_146,plain,
( ~ abnormal(or1(f))
| abnormal(and1(h1(f))) ),
inference(resolve,[$cnf( abnormal(and1(h2(f))) )],[refute_0_145,diagnosis_or1_and1h2]) ).
cnf(refute_0_147,plain,
abnormal(and1(h1(f))),
inference(resolve,[$cnf( abnormal(or1(f)) )],[refute_0_142,refute_0_146]) ).
cnf(refute_0_148,plain,
~ abnormal(or1(f)),
inference(resolve,[$cnf( abnormal(and1(h1(f))) )],[refute_0_147,diagnosis_or1_and1h1]) ).
cnf(refute_0_149,plain,
$false,
inference(resolve,[$cnf( abnormal(or1(f)) )],[refute_0_142,refute_0_148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HWV007-2 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n027.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 : Fri Jun 17 02:51:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40
% 0.19/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.42
%------------------------------------------------------------------------------