TSTP Solution File: HWV006-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV006-2 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%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 : 300s
% DateTime : Sat Sep 17 02:10:28 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 399
% Syntax : Number of formulae : 904 ( 171 unt; 25 typ; 0 def)
% Number of atoms : 4645 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 6800 (3150 ~;3258 |; 0 &)
% ( 392 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 116 ( 116 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 24 >; 1 *; 0 +; 0 <<)
% Number of predicates : 17 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-1 aty)
% Number of variables : 1169 (1099 !; 0 ?;1169 :)
% Comments :
%------------------------------------------------------------------------------
tff(zero_type,type,
zero: $i > $o ).
tff(out1_type,type,
out1: $i > $i ).
tff(not1_type,type,
not1: $i > $i ).
tff(h2_type,type,
h2: $i > $i ).
tff(f_type,type,
f: $i ).
tff(one_type,type,
one: $i > $o ).
tff(in1_type,type,
in1: $i > $i ).
tff(and2_type,type,
and2: $i > $i ).
tff(in2_type,type,
in2: $i > $i ).
tff(outs_type,type,
outs: $i > $i ).
tff(h1_type,type,
h1: $i > $i ).
tff(and1_type,type,
and1: $i > $i ).
tff(or1_type,type,
or1: $i > $i ).
tff(connection_type,type,
connection: ( $i * $i ) > $o ).
tff(inc_type,type,
inc: $i > $i ).
tff(fulladder_type,type,
fulladder: $i > $o ).
tff(halfadder_type,type,
halfadder: $i > $o ).
tff(or_ok_type,type,
or_ok: $i > $o ).
tff(logic_or_type,type,
logic_or: $i > $o ).
tff(abnormal_type,type,
abnormal: $i > $o ).
tff(and_ok_type,type,
and_ok: $i > $o ).
tff(logic_and_type,type,
logic_and: $i > $o ).
tff(not_ok_type,type,
not_ok: $i > $o ).
tff(logic_not_type,type,
logic_not: $i > $o ).
tff(outc_type,type,
outc: $i > $i ).
tff(1,plain,
( fulladder(f)
<=> fulladder(f) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
fulladder(f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_isa_fulladder) ).
tff(3,plain,
fulladder(f),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(
( ( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) )
<=> ( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_connection_inc_in2h1) ).
tff(8,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) )
| ~ fulladder(f)
| connection(inc(f),in2(h1(f))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) )
| ~ fulladder(f)
| connection(inc(f),in2(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) )
| ~ fulladder(f)
| connection(inc(f),in2(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) )
| ~ fulladder(f)
| connection(inc(f),in2(h1(f))) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
connection(inc(f),in2(h1(f))),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( one(inc(f))
<=> one(inc(f)) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
one(inc(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inc_1) ).
tff(17,plain,
one(inc(f)),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [P2: $i,P1: $i] :
refl(
( ( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
<=> ( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
<=> ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
<=> ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [P2: $i,P1: $i] :
trans(
monotonicity(
rewrite(
( ( ~ connection(P1,P2)
| ~ one(P1) )
<=> ( ~ connection(P1,P2)
| ~ one(P1) ) )),
( ( ~ connection(P1,P2)
| ~ one(P1)
| one(P2) )
<=> ( ~ connection(P1,P2)
| ~ one(P1)
| one(P2) ) )),
rewrite(
( ( ~ connection(P1,P2)
| ~ one(P1)
| one(P2) )
<=> ( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ) )),
( ( ~ connection(P1,P2)
| ~ one(P1)
| one(P2) )
<=> ( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ one(P1)
| one(P2) )
<=> ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ one(P1)
| one(P2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',value_propagation_one1) ).
tff(24,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(inc(f))
| ~ connection(inc(f),in2(h1(f)))
| one(in2(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(inc(f))
| ~ connection(inc(f),in2(h1(f)))
| one(in2(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( ~ connection(inc(f),in2(h1(f)))
| one(in2(h1(f)))
| ~ one(inc(f)) )
<=> ( ~ one(inc(f))
| ~ connection(inc(f),in2(h1(f)))
| one(in2(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(inc(f),in2(h1(f)))
| one(in2(h1(f)))
| ~ one(inc(f)) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(inc(f))
| ~ connection(inc(f),in2(h1(f)))
| one(in2(h1(f))) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(inc(f),in2(h1(f)))
| one(in2(h1(f)))
| ~ one(inc(f)) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(inc(f))
| ~ connection(inc(f),in2(h1(f)))
| one(in2(h1(f))) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(inc(f),in2(h1(f)))
| one(in2(h1(f)))
| ~ one(inc(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(inc(f))
| ~ connection(inc(f),in2(h1(f)))
| one(in2(h1(f))) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
one(in2(h1(f))),
inference(unit_resolution,[status(thm)],[33,27,17,14]) ).
tff(35,plain,
^ [X: $i] :
refl(
( ( halfadder(h1(X))
| ~ fulladder(X) )
<=> ( halfadder(h1(X))
| ~ fulladder(X) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
<=> ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
<=> ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
^ [X: $i] :
rewrite(
( ( ~ fulladder(X)
| halfadder(h1(X)) )
<=> ( halfadder(h1(X))
| ~ fulladder(X) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [X: $i] :
( ~ fulladder(X)
| halfadder(h1(X)) )
<=> ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h1(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_halfadder1) ).
tff(41,plain,
! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ( ~ ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
| halfadder(h1(f))
| ~ fulladder(f) )
<=> ( ~ ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
| halfadder(h1(f))
| ~ fulladder(f) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ~ ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
| halfadder(h1(f))
| ~ fulladder(f) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
| halfadder(h1(f))
| ~ fulladder(f) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
halfadder(h1(f)),
inference(unit_resolution,[status(thm)],[47,44,3]) ).
tff(49,plain,
^ [X: $i] :
refl(
( ( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) )
<=> ( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_connection_in2_in2or1) ).
tff(53,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) )
| ~ halfadder(h1(f))
| connection(in2(h1(f)),in2(or1(h1(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) )
| ~ halfadder(h1(f))
| connection(in2(h1(f)),in2(or1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) )
| ~ halfadder(h1(f))
| connection(in2(h1(f)),in2(or1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) )
| ~ halfadder(h1(f))
| connection(in2(h1(f)),in2(or1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
( ~ halfadder(h1(f))
| connection(in2(h1(f)),in2(or1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[58,55]) ).
tff(60,plain,
connection(in2(h1(f)),in2(or1(h1(f)))),
inference(unit_resolution,[status(thm)],[59,48]) ).
tff(61,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(h1(f)))
| ~ connection(in2(h1(f)),in2(or1(h1(f))))
| one(in2(or1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(h1(f)))
| ~ connection(in2(h1(f)),in2(or1(h1(f))))
| one(in2(or1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ( ~ connection(in2(h1(f)),in2(or1(h1(f))))
| one(in2(or1(h1(f))))
| ~ one(in2(h1(f))) )
<=> ( ~ one(in2(h1(f)))
| ~ connection(in2(h1(f)),in2(or1(h1(f))))
| one(in2(or1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in2(h1(f)),in2(or1(h1(f))))
| one(in2(or1(h1(f))))
| ~ one(in2(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(h1(f)))
| ~ connection(in2(h1(f)),in2(or1(h1(f))))
| one(in2(or1(h1(f)))) ) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in2(h1(f)),in2(or1(h1(f))))
| one(in2(or1(h1(f))))
| ~ one(in2(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(h1(f)))
| ~ connection(in2(h1(f)),in2(or1(h1(f))))
| one(in2(or1(h1(f)))) ) ),
inference(transitivity,[status(thm)],[63,61]) ).
tff(65,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in2(h1(f)),in2(or1(h1(f))))
| one(in2(or1(h1(f))))
| ~ one(in2(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(h1(f)))
| ~ connection(in2(h1(f)),in2(or1(h1(f))))
| one(in2(or1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
one(in2(or1(h1(f)))),
inference(unit_resolution,[status(thm)],[66,27,60,34]) ).
tff(68,plain,
^ [X: $i] :
refl(
( ( ~ halfadder(X)
| logic_or(or1(X)) )
<=> ( ~ halfadder(X)
| logic_or(or1(X)) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,axiom,
! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_or1) ).
tff(72,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| logic_or(or1(h1(f)))
| ~ halfadder(h1(f)) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| logic_or(or1(h1(f)))
| ~ halfadder(h1(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( ( ~ halfadder(h1(f))
| logic_or(or1(h1(f))) )
<=> ( logic_or(or1(h1(f)))
| ~ halfadder(h1(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| ~ halfadder(h1(f))
| logic_or(or1(h1(f))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| logic_or(or1(h1(f)))
| ~ halfadder(h1(f)) ) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| ~ halfadder(h1(f))
| logic_or(or1(h1(f))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| logic_or(or1(h1(f)))
| ~ halfadder(h1(f)) ) ),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| ~ halfadder(h1(f))
| logic_or(or1(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| logic_or(or1(h1(f)))
| ~ halfadder(h1(f)) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
( logic_or(or1(h1(f)))
| ~ halfadder(h1(f)) ),
inference(unit_resolution,[status(thm)],[80,74]) ).
tff(82,plain,
logic_or(or1(h1(f))),
inference(unit_resolution,[status(thm)],[81,48]) ).
tff(83,plain,
( ~ abnormal(or1(h1(f)))
<=> ~ abnormal(or1(h1(f))) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
~ abnormal(or1(h1(f))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_or1h1) ).
tff(85,plain,
~ abnormal(or1(h1(f))),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
^ [K: $i] :
refl(
( ( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
<=> ( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
<=> ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
( ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
<=> ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
^ [K: $i] :
trans(
monotonicity(
rewrite(
( ( ~ logic_or(K)
| or_ok(K) )
<=> ( or_ok(K)
| ~ logic_or(K) ) )),
( ( ~ logic_or(K)
| or_ok(K)
| abnormal(K) )
<=> ( or_ok(K)
| ~ logic_or(K)
| abnormal(K) ) )),
rewrite(
( ( or_ok(K)
| ~ logic_or(K)
| abnormal(K) )
<=> ( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ) )),
( ( ~ logic_or(K)
| or_ok(K)
| abnormal(K) )
<=> ( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [K: $i] :
( ~ logic_or(K)
| or_ok(K)
| abnormal(K) )
<=> ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,axiom,
! [K: $i] :
( ~ logic_or(K)
| or_ok(K)
| abnormal(K) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',or_ok_or_abnormal) ).
tff(92,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(modus_ponens,[status(thm)],[94,87]) ).
tff(96,plain,
( ( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(h1(f)))
| or_ok(or1(h1(f)))
| ~ logic_or(or1(h1(f))) )
<=> ( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(h1(f)))
| or_ok(or1(h1(f)))
| ~ logic_or(or1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(h1(f)))
| or_ok(or1(h1(f)))
| ~ logic_or(or1(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(h1(f)))
| or_ok(or1(h1(f)))
| ~ logic_or(or1(h1(f))) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
( or_ok(or1(h1(f)))
| ~ logic_or(or1(h1(f))) ),
inference(unit_resolution,[status(thm)],[98,95,85]) ).
tff(100,plain,
or_ok(or1(h1(f))),
inference(unit_resolution,[status(thm)],[99,82]) ).
tff(101,plain,
^ [K: $i] :
refl(
( ( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) )
<=> ( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) )
<=> ! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) )
<=> ! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
^ [K: $i] :
rewrite(
( ( ~ or_ok(K)
| ~ one(in2(K))
| one(out1(K)) )
<=> ( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(105,plain,
( ! [K: $i] :
( ~ or_ok(K)
| ~ one(in2(K))
| one(out1(K)) )
<=> ! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,axiom,
! [K: $i] :
( ~ or_ok(K)
| ~ one(in2(K))
| one(out1(K)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',or_x1_1) ).
tff(107,plain,
! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[109,102]) ).
tff(111,plain,
( ( ~ ! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) )
| one(out1(or1(h1(f))))
| ~ or_ok(or1(h1(f)))
| ~ one(in2(or1(h1(f)))) )
<=> ( ~ ! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) )
| one(out1(or1(h1(f))))
| ~ or_ok(or1(h1(f)))
| ~ one(in2(or1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ( one(out1(or1(h1(f))))
| ~ one(in2(or1(h1(f))))
| ~ or_ok(or1(h1(f))) )
<=> ( one(out1(or1(h1(f))))
| ~ or_ok(or1(h1(f)))
| ~ one(in2(or1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ( ~ ! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) )
| one(out1(or1(h1(f))))
| ~ one(in2(or1(h1(f))))
| ~ or_ok(or1(h1(f))) )
<=> ( ~ ! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) )
| one(out1(or1(h1(f))))
| ~ or_ok(or1(h1(f)))
| ~ one(in2(or1(h1(f)))) ) ),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ( ~ ! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) )
| one(out1(or1(h1(f))))
| ~ one(in2(or1(h1(f))))
| ~ or_ok(or1(h1(f))) )
<=> ( ~ ! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) )
| one(out1(or1(h1(f))))
| ~ or_ok(or1(h1(f)))
| ~ one(in2(or1(h1(f)))) ) ),
inference(transitivity,[status(thm)],[113,111]) ).
tff(115,plain,
( ~ ! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) )
| one(out1(or1(h1(f))))
| ~ one(in2(or1(h1(f))))
| ~ or_ok(or1(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
( ~ ! [K: $i] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) )
| one(out1(or1(h1(f))))
| ~ or_ok(or1(h1(f)))
| ~ one(in2(or1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
one(out1(or1(h1(f)))),
inference(unit_resolution,[status(thm)],[116,110,100,67]) ).
tff(118,plain,
^ [X: $i] :
refl(
( ( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
<=> ( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ) )),
inference(bind,[status(th)],]) ).
tff(119,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_connection_out1or1_in1_and1) ).
tff(122,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ),
inference(modus_ponens,[status(thm)],[123,119]) ).
tff(125,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
| ~ halfadder(h1(f))
| connection(out1(or1(h1(f))),in1(and1(h1(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
| ~ halfadder(h1(f))
| connection(out1(or1(h1(f))),in1(and1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
| ~ halfadder(h1(f))
| connection(out1(or1(h1(f))),in1(and1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
| ~ halfadder(h1(f))
| connection(out1(or1(h1(f))),in1(and1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
( ~ halfadder(h1(f))
| connection(out1(or1(h1(f))),in1(and1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[127,124]) ).
tff(129,plain,
connection(out1(or1(h1(f))),in1(and1(h1(f)))),
inference(unit_resolution,[status(thm)],[128,48]) ).
tff(130,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(or1(h1(f))),in1(and1(h1(f))))
| one(in1(and1(h1(f))))
| ~ one(out1(or1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(or1(h1(f))),in1(and1(h1(f))))
| one(in1(and1(h1(f))))
| ~ one(out1(or1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(or1(h1(f))),in1(and1(h1(f))))
| one(in1(and1(h1(f))))
| ~ one(out1(or1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(132,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(or1(h1(f))),in1(and1(h1(f))))
| one(in1(and1(h1(f))))
| ~ one(out1(or1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
( one(in1(and1(h1(f))))
| ~ one(out1(or1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[132,27,129]) ).
tff(134,plain,
one(in1(and1(h1(f)))),
inference(unit_resolution,[status(thm)],[133,117]) ).
tff(135,plain,
^ [X: $i] :
refl(
( ( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
<=> ( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ) )),
inference(bind,[status(th)],]) ).
tff(136,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,axiom,
! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_connection_in2_in1h1) ).
tff(139,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ),
inference(skolemize,[status(sab)],[139]) ).
tff(141,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ),
inference(modus_ponens,[status(thm)],[140,136]) ).
tff(142,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
| ~ fulladder(f)
| connection(in2(f),in1(h1(f))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
| ~ fulladder(f)
| connection(in2(f),in1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
| ~ fulladder(f)
| connection(in2(f),in1(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(144,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
| ~ fulladder(f)
| connection(in2(f),in1(h1(f))) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
connection(in2(f),in1(h1(f))),
inference(unit_resolution,[status(thm)],[144,141,3]) ).
tff(146,plain,
( zero(in2(f))
<=> zero(in2(f)) ),
inference(rewrite,[status(thm)],]) ).
tff(147,axiom,
zero(in2(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in2_0) ).
tff(148,plain,
zero(in2(f)),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
^ [P2: $i,P1: $i] :
refl(
( ( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
<=> ( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ) )),
inference(bind,[status(th)],]) ).
tff(150,plain,
( ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
<=> ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,plain,
( ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
<=> ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
^ [P2: $i,P1: $i] :
trans(
monotonicity(
rewrite(
( ( ~ connection(P1,P2)
| ~ zero(P1) )
<=> ( ~ zero(P1)
| ~ connection(P1,P2) ) )),
( ( ~ connection(P1,P2)
| ~ zero(P1)
| zero(P2) )
<=> ( ~ zero(P1)
| ~ connection(P1,P2)
| zero(P2) ) )),
rewrite(
( ( ~ zero(P1)
| ~ connection(P1,P2)
| zero(P2) )
<=> ( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ) )),
( ( ~ connection(P1,P2)
| ~ zero(P1)
| zero(P2) )
<=> ( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ) )),
inference(bind,[status(th)],]) ).
tff(153,plain,
( ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ zero(P1)
| zero(P2) )
<=> ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ) ),
inference(quant_intro,[status(thm)],[152]) ).
tff(154,axiom,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ zero(P1)
| zero(P2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',value_propagation_zero1) ).
tff(155,plain,
! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
inference(modus_ponens,[status(thm)],[155,151]) ).
tff(157,plain,
! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
inference(skolemize,[status(sab)],[156]) ).
tff(158,plain,
! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
inference(modus_ponens,[status(thm)],[157,150]) ).
tff(159,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| zero(in1(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| zero(in1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,plain,
( ( zero(in1(h1(f)))
| ~ zero(in2(f))
| ~ connection(in2(f),in1(h1(f))) )
<=> ( ~ zero(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| zero(in1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(161,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(h1(f)))
| ~ zero(in2(f))
| ~ connection(in2(f),in1(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| zero(in1(h1(f))) ) ),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(h1(f)))
| ~ zero(in2(f))
| ~ connection(in2(f),in1(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| zero(in1(h1(f))) ) ),
inference(transitivity,[status(thm)],[161,159]) ).
tff(163,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(h1(f)))
| ~ zero(in2(f))
| ~ connection(in2(f),in1(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(164,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| zero(in1(h1(f))) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
zero(in1(h1(f))),
inference(unit_resolution,[status(thm)],[164,158,148,145]) ).
tff(166,plain,
^ [X: $i] :
refl(
( ( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
<=> ( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ) )),
inference(bind,[status(th)],]) ).
tff(167,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ) ),
inference(quant_intro,[status(thm)],[166]) ).
tff(168,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(169,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_connection_in1_in1and2) ).
tff(170,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ),
inference(skolemize,[status(sab)],[170]) ).
tff(172,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ),
inference(modus_ponens,[status(thm)],[171,167]) ).
tff(173,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h1(f))
| connection(in1(h1(f)),in1(and2(h1(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h1(f))
| connection(in1(h1(f)),in1(and2(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(174,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h1(f))
| connection(in1(h1(f)),in1(and2(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(175,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h1(f))
| connection(in1(h1(f)),in1(and2(h1(f)))) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
( ~ halfadder(h1(f))
| connection(in1(h1(f)),in1(and2(h1(f)))) ),
inference(unit_resolution,[status(thm)],[175,172]) ).
tff(177,plain,
connection(in1(h1(f)),in1(and2(h1(f)))),
inference(unit_resolution,[status(thm)],[176,48]) ).
tff(178,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| zero(in1(and2(h1(f))))
| ~ zero(in1(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| zero(in1(and2(h1(f))))
| ~ zero(in1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(179,plain,
( ( zero(in1(and2(h1(f))))
| ~ zero(in1(h1(f)))
| ~ connection(in1(h1(f)),in1(and2(h1(f)))) )
<=> ( ~ connection(in1(h1(f)),in1(and2(h1(f))))
| zero(in1(and2(h1(f))))
| ~ zero(in1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(180,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(and2(h1(f))))
| ~ zero(in1(h1(f)))
| ~ connection(in1(h1(f)),in1(and2(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| zero(in1(and2(h1(f))))
| ~ zero(in1(h1(f))) ) ),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(and2(h1(f))))
| ~ zero(in1(h1(f)))
| ~ connection(in1(h1(f)),in1(and2(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| zero(in1(and2(h1(f))))
| ~ zero(in1(h1(f))) ) ),
inference(transitivity,[status(thm)],[180,178]) ).
tff(182,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(and2(h1(f))))
| ~ zero(in1(h1(f)))
| ~ connection(in1(h1(f)),in1(and2(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| zero(in1(and2(h1(f))))
| ~ zero(in1(h1(f))) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
zero(in1(and2(h1(f)))),
inference(unit_resolution,[status(thm)],[183,158,177,165]) ).
tff(185,plain,
^ [X: $i] :
refl(
( ( ~ halfadder(X)
| logic_and(and2(X)) )
<=> ( ~ halfadder(X)
| logic_and(and2(X)) ) )),
inference(bind,[status(th)],]) ).
tff(186,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ) ),
inference(quant_intro,[status(thm)],[185]) ).
tff(187,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(188,axiom,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_and2) ).
tff(189,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ),
inference(skolemize,[status(sab)],[189]) ).
tff(191,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ),
inference(modus_ponens,[status(thm)],[190,186]) ).
tff(192,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h1(f)))
| ~ halfadder(h1(f)) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h1(f)))
| ~ halfadder(h1(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(193,plain,
( ( ~ halfadder(h1(f))
| logic_and(and2(h1(f))) )
<=> ( logic_and(and2(h1(f)))
| ~ halfadder(h1(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(194,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| ~ halfadder(h1(f))
| logic_and(and2(h1(f))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h1(f)))
| ~ halfadder(h1(f)) ) ),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| ~ halfadder(h1(f))
| logic_and(and2(h1(f))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h1(f)))
| ~ halfadder(h1(f)) ) ),
inference(transitivity,[status(thm)],[194,192]) ).
tff(196,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| ~ halfadder(h1(f))
| logic_and(and2(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(197,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h1(f)))
| ~ halfadder(h1(f)) ),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
( logic_and(and2(h1(f)))
| ~ halfadder(h1(f)) ),
inference(unit_resolution,[status(thm)],[197,191]) ).
tff(199,plain,
logic_and(and2(h1(f))),
inference(unit_resolution,[status(thm)],[198,48]) ).
tff(200,plain,
( ~ abnormal(and2(h1(f)))
<=> ~ abnormal(and2(h1(f))) ),
inference(rewrite,[status(thm)],]) ).
tff(201,axiom,
~ abnormal(and2(h1(f))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_and2h1) ).
tff(202,plain,
~ abnormal(and2(h1(f))),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
^ [K: $i] :
refl(
( ( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
<=> ( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ) )),
inference(bind,[status(th)],]) ).
tff(204,plain,
( ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
<=> ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ) ),
inference(quant_intro,[status(thm)],[203]) ).
tff(205,plain,
( ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
<=> ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ) ),
inference(rewrite,[status(thm)],]) ).
tff(206,plain,
^ [K: $i] :
trans(
monotonicity(
rewrite(
( ( ~ logic_and(K)
| and_ok(K) )
<=> ( and_ok(K)
| ~ logic_and(K) ) )),
( ( ~ logic_and(K)
| and_ok(K)
| abnormal(K) )
<=> ( and_ok(K)
| ~ logic_and(K)
| abnormal(K) ) )),
rewrite(
( ( and_ok(K)
| ~ logic_and(K)
| abnormal(K) )
<=> ( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ) )),
( ( ~ logic_and(K)
| and_ok(K)
| abnormal(K) )
<=> ( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ) )),
inference(bind,[status(th)],]) ).
tff(207,plain,
( ! [K: $i] :
( ~ logic_and(K)
| and_ok(K)
| abnormal(K) )
<=> ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ) ),
inference(quant_intro,[status(thm)],[206]) ).
tff(208,axiom,
! [K: $i] :
( ~ logic_and(K)
| and_ok(K)
| abnormal(K) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',and_ok_or_abnormal) ).
tff(209,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(modus_ponens,[status(thm)],[209,205]) ).
tff(211,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(skolemize,[status(sab)],[210]) ).
tff(212,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(modus_ponens,[status(thm)],[211,204]) ).
tff(213,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h1(f)))
| and_ok(and2(h1(f)))
| ~ logic_and(and2(h1(f))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h1(f)))
| and_ok(and2(h1(f)))
| ~ logic_and(and2(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(214,plain,
( ( and_ok(and2(h1(f)))
| abnormal(and2(h1(f)))
| ~ logic_and(and2(h1(f))) )
<=> ( abnormal(and2(h1(f)))
| and_ok(and2(h1(f)))
| ~ logic_and(and2(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(215,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and2(h1(f)))
| abnormal(and2(h1(f)))
| ~ logic_and(and2(h1(f))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h1(f)))
| and_ok(and2(h1(f)))
| ~ logic_and(and2(h1(f))) ) ),
inference(monotonicity,[status(thm)],[214]) ).
tff(216,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and2(h1(f)))
| abnormal(and2(h1(f)))
| ~ logic_and(and2(h1(f))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h1(f)))
| and_ok(and2(h1(f)))
| ~ logic_and(and2(h1(f))) ) ),
inference(transitivity,[status(thm)],[215,213]) ).
tff(217,plain,
( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and2(h1(f)))
| abnormal(and2(h1(f)))
| ~ logic_and(and2(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(218,plain,
( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h1(f)))
| and_ok(and2(h1(f)))
| ~ logic_and(and2(h1(f))) ),
inference(modus_ponens,[status(thm)],[217,216]) ).
tff(219,plain,
( and_ok(and2(h1(f)))
| ~ logic_and(and2(h1(f))) ),
inference(unit_resolution,[status(thm)],[218,212,202]) ).
tff(220,plain,
and_ok(and2(h1(f))),
inference(unit_resolution,[status(thm)],[219,199]) ).
tff(221,plain,
^ [K: $i] :
refl(
( ( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
<=> ( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(222,plain,
( ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
<=> ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ) ),
inference(quant_intro,[status(thm)],[221]) ).
tff(223,plain,
( ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
<=> ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ) ),
inference(rewrite,[status(thm)],]) ).
tff(224,plain,
^ [K: $i] :
rewrite(
( ( ~ and_ok(K)
| ~ zero(in1(K))
| zero(out1(K)) )
<=> ( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(225,plain,
( ! [K: $i] :
( ~ and_ok(K)
| ~ zero(in1(K))
| zero(out1(K)) )
<=> ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ) ),
inference(quant_intro,[status(thm)],[224]) ).
tff(226,axiom,
! [K: $i] :
( ~ and_ok(K)
| ~ zero(in1(K))
| zero(out1(K)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',and_0x_0) ).
tff(227,plain,
! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ),
inference(modus_ponens,[status(thm)],[226,225]) ).
tff(228,plain,
! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ),
inference(modus_ponens,[status(thm)],[227,223]) ).
tff(229,plain,
! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ),
inference(skolemize,[status(sab)],[228]) ).
tff(230,plain,
! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ),
inference(modus_ponens,[status(thm)],[229,222]) ).
tff(231,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
| zero(out1(and2(h1(f))))
| ~ zero(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
| zero(out1(and2(h1(f))))
| ~ zero(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(232,plain,
( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
| zero(out1(and2(h1(f))))
| ~ zero(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(233,plain,
( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
| zero(out1(and2(h1(f))))
| ~ zero(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) ),
inference(modus_ponens,[status(thm)],[232,231]) ).
tff(234,plain,
zero(out1(and2(h1(f)))),
inference(unit_resolution,[status(thm)],[233,230,220,184]) ).
tff(235,plain,
^ [X: $i] :
refl(
( ( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
<=> ( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ) )),
inference(bind,[status(th)],]) ).
tff(236,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ) ),
inference(quant_intro,[status(thm)],[235]) ).
tff(237,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(238,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_connection_out1and2_in1not1) ).
tff(239,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ),
inference(modus_ponens,[status(thm)],[238,237]) ).
tff(240,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ),
inference(skolemize,[status(sab)],[239]) ).
tff(241,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ),
inference(modus_ponens,[status(thm)],[240,236]) ).
tff(242,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
| ~ halfadder(h1(f))
| connection(out1(and2(h1(f))),in1(not1(h1(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
| ~ halfadder(h1(f))
| connection(out1(and2(h1(f))),in1(not1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(243,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
| ~ halfadder(h1(f))
| connection(out1(and2(h1(f))),in1(not1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(244,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
| ~ halfadder(h1(f))
| connection(out1(and2(h1(f))),in1(not1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[243,242]) ).
tff(245,plain,
( ~ halfadder(h1(f))
| connection(out1(and2(h1(f))),in1(not1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[244,241]) ).
tff(246,plain,
connection(out1(and2(h1(f))),in1(not1(h1(f)))),
inference(unit_resolution,[status(thm)],[245,48]) ).
tff(247,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(not1(h1(f))))
| ~ zero(out1(and2(h1(f))))
| ~ connection(out1(and2(h1(f))),in1(not1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(not1(h1(f))))
| ~ zero(out1(and2(h1(f))))
| ~ connection(out1(and2(h1(f))),in1(not1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(248,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(not1(h1(f))))
| ~ zero(out1(and2(h1(f))))
| ~ connection(out1(and2(h1(f))),in1(not1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(249,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(not1(h1(f))))
| ~ zero(out1(and2(h1(f))))
| ~ connection(out1(and2(h1(f))),in1(not1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[248,247]) ).
tff(250,plain,
( zero(in1(not1(h1(f))))
| ~ zero(out1(and2(h1(f)))) ),
inference(unit_resolution,[status(thm)],[249,158,246]) ).
tff(251,plain,
zero(in1(not1(h1(f)))),
inference(unit_resolution,[status(thm)],[250,234]) ).
tff(252,plain,
^ [X: $i] :
refl(
( ( ~ halfadder(X)
| logic_not(not1(X)) )
<=> ( ~ halfadder(X)
| logic_not(not1(X)) ) )),
inference(bind,[status(th)],]) ).
tff(253,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ) ),
inference(quant_intro,[status(thm)],[252]) ).
tff(254,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(255,axiom,
! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_not1) ).
tff(256,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ),
inference(modus_ponens,[status(thm)],[255,254]) ).
tff(257,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ),
inference(skolemize,[status(sab)],[256]) ).
tff(258,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ),
inference(modus_ponens,[status(thm)],[257,253]) ).
tff(259,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| logic_not(not1(h1(f)))
| ~ halfadder(h1(f)) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| logic_not(not1(h1(f)))
| ~ halfadder(h1(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(260,plain,
( ( ~ halfadder(h1(f))
| logic_not(not1(h1(f))) )
<=> ( logic_not(not1(h1(f)))
| ~ halfadder(h1(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(261,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| ~ halfadder(h1(f))
| logic_not(not1(h1(f))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| logic_not(not1(h1(f)))
| ~ halfadder(h1(f)) ) ),
inference(monotonicity,[status(thm)],[260]) ).
tff(262,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| ~ halfadder(h1(f))
| logic_not(not1(h1(f))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| logic_not(not1(h1(f)))
| ~ halfadder(h1(f)) ) ),
inference(transitivity,[status(thm)],[261,259]) ).
tff(263,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| ~ halfadder(h1(f))
| logic_not(not1(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(264,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| logic_not(not1(h1(f)))
| ~ halfadder(h1(f)) ),
inference(modus_ponens,[status(thm)],[263,262]) ).
tff(265,plain,
( logic_not(not1(h1(f)))
| ~ halfadder(h1(f)) ),
inference(unit_resolution,[status(thm)],[264,258]) ).
tff(266,plain,
logic_not(not1(h1(f))),
inference(unit_resolution,[status(thm)],[265,48]) ).
tff(267,plain,
( ~ abnormal(not1(h1(f)))
<=> ~ abnormal(not1(h1(f))) ),
inference(rewrite,[status(thm)],]) ).
tff(268,axiom,
~ abnormal(not1(h1(f))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_not1h1) ).
tff(269,plain,
~ abnormal(not1(h1(f))),
inference(modus_ponens,[status(thm)],[268,267]) ).
tff(270,plain,
^ [K: $i] :
refl(
( ( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
<=> ( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ) )),
inference(bind,[status(th)],]) ).
tff(271,plain,
( ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
<=> ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ) ),
inference(quant_intro,[status(thm)],[270]) ).
tff(272,plain,
( ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
<=> ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ) ),
inference(rewrite,[status(thm)],]) ).
tff(273,plain,
^ [K: $i] :
trans(
monotonicity(
rewrite(
( ( ~ logic_not(K)
| not_ok(K) )
<=> ( not_ok(K)
| ~ logic_not(K) ) )),
( ( ~ logic_not(K)
| not_ok(K)
| abnormal(K) )
<=> ( not_ok(K)
| ~ logic_not(K)
| abnormal(K) ) )),
rewrite(
( ( not_ok(K)
| ~ logic_not(K)
| abnormal(K) )
<=> ( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ) )),
( ( ~ logic_not(K)
| not_ok(K)
| abnormal(K) )
<=> ( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ) )),
inference(bind,[status(th)],]) ).
tff(274,plain,
( ! [K: $i] :
( ~ logic_not(K)
| not_ok(K)
| abnormal(K) )
<=> ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ) ),
inference(quant_intro,[status(thm)],[273]) ).
tff(275,axiom,
! [K: $i] :
( ~ logic_not(K)
| not_ok(K)
| abnormal(K) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',not_ok_or_abnormal) ).
tff(276,plain,
! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
inference(modus_ponens,[status(thm)],[275,274]) ).
tff(277,plain,
! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
inference(modus_ponens,[status(thm)],[276,272]) ).
tff(278,plain,
! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
inference(skolemize,[status(sab)],[277]) ).
tff(279,plain,
! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
inference(modus_ponens,[status(thm)],[278,271]) ).
tff(280,plain,
( ( ~ ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
| abnormal(not1(h1(f)))
| not_ok(not1(h1(f)))
| ~ logic_not(not1(h1(f))) )
<=> ( ~ ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
| abnormal(not1(h1(f)))
| not_ok(not1(h1(f)))
| ~ logic_not(not1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(281,plain,
( ~ ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
| abnormal(not1(h1(f)))
| not_ok(not1(h1(f)))
| ~ logic_not(not1(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(282,plain,
( ~ ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
| abnormal(not1(h1(f)))
| not_ok(not1(h1(f)))
| ~ logic_not(not1(h1(f))) ),
inference(modus_ponens,[status(thm)],[281,280]) ).
tff(283,plain,
( not_ok(not1(h1(f)))
| ~ logic_not(not1(h1(f))) ),
inference(unit_resolution,[status(thm)],[282,279,269]) ).
tff(284,plain,
not_ok(not1(h1(f))),
inference(unit_resolution,[status(thm)],[283,266]) ).
tff(285,plain,
^ [K: $i] :
refl(
( ( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) )
<=> ( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(286,plain,
( ! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) )
<=> ! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) ) ),
inference(quant_intro,[status(thm)],[285]) ).
tff(287,plain,
( ! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) )
<=> ! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) ) ),
inference(rewrite,[status(thm)],]) ).
tff(288,plain,
^ [K: $i] :
rewrite(
( ( ~ not_ok(K)
| ~ zero(in1(K))
| one(out1(K)) )
<=> ( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(289,plain,
( ! [K: $i] :
( ~ not_ok(K)
| ~ zero(in1(K))
| one(out1(K)) )
<=> ! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) ) ),
inference(quant_intro,[status(thm)],[288]) ).
tff(290,axiom,
! [K: $i] :
( ~ not_ok(K)
| ~ zero(in1(K))
| one(out1(K)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',not_0_1_fw) ).
tff(291,plain,
! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[290,289]) ).
tff(292,plain,
! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[291,287]) ).
tff(293,plain,
! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) ),
inference(skolemize,[status(sab)],[292]) ).
tff(294,plain,
! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[293,286]) ).
tff(295,plain,
( ( ~ ! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) )
| one(out1(not1(h1(f))))
| ~ zero(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) )
<=> ( ~ ! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) )
| one(out1(not1(h1(f))))
| ~ zero(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(296,plain,
( ( ~ zero(in1(not1(h1(f))))
| one(out1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) )
<=> ( one(out1(not1(h1(f))))
| ~ zero(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(297,plain,
( ( ~ ! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) )
| ~ zero(in1(not1(h1(f))))
| one(out1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) )
<=> ( ~ ! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) )
| one(out1(not1(h1(f))))
| ~ zero(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) ) ),
inference(monotonicity,[status(thm)],[296]) ).
tff(298,plain,
( ( ~ ! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) )
| ~ zero(in1(not1(h1(f))))
| one(out1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) )
<=> ( ~ ! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) )
| one(out1(not1(h1(f))))
| ~ zero(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) ) ),
inference(transitivity,[status(thm)],[297,295]) ).
tff(299,plain,
( ~ ! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) )
| ~ zero(in1(not1(h1(f))))
| one(out1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(300,plain,
( ~ ! [K: $i] :
( ~ zero(in1(K))
| one(out1(K))
| ~ not_ok(K) )
| one(out1(not1(h1(f))))
| ~ zero(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) ),
inference(modus_ponens,[status(thm)],[299,298]) ).
tff(301,plain,
( one(out1(not1(h1(f))))
| ~ zero(in1(not1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[300,294,284]) ).
tff(302,plain,
one(out1(not1(h1(f)))),
inference(unit_resolution,[status(thm)],[301,251]) ).
tff(303,plain,
^ [X: $i] :
refl(
( ( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
<=> ( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ) )),
inference(bind,[status(th)],]) ).
tff(304,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ) ),
inference(quant_intro,[status(thm)],[303]) ).
tff(305,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(306,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_connection_out1not1_in2and1) ).
tff(307,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ),
inference(modus_ponens,[status(thm)],[306,305]) ).
tff(308,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ),
inference(skolemize,[status(sab)],[307]) ).
tff(309,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ),
inference(modus_ponens,[status(thm)],[308,304]) ).
tff(310,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
| ~ halfadder(h1(f))
| connection(out1(not1(h1(f))),in2(and1(h1(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
| ~ halfadder(h1(f))
| connection(out1(not1(h1(f))),in2(and1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(311,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
| ~ halfadder(h1(f))
| connection(out1(not1(h1(f))),in2(and1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(312,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
| ~ halfadder(h1(f))
| connection(out1(not1(h1(f))),in2(and1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[311,310]) ).
tff(313,plain,
( ~ halfadder(h1(f))
| connection(out1(not1(h1(f))),in2(and1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[312,309]) ).
tff(314,plain,
connection(out1(not1(h1(f))),in2(and1(h1(f)))),
inference(unit_resolution,[status(thm)],[313,48]) ).
tff(315,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| one(in2(and1(h1(f))))
| ~ one(out1(not1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| one(in2(and1(h1(f))))
| ~ one(out1(not1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(316,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| one(in2(and1(h1(f))))
| ~ one(out1(not1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(317,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| one(in2(and1(h1(f))))
| ~ one(out1(not1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[316,315]) ).
tff(318,plain,
( one(in2(and1(h1(f))))
| ~ one(out1(not1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[317,27,314]) ).
tff(319,plain,
one(in2(and1(h1(f)))),
inference(unit_resolution,[status(thm)],[318,302]) ).
tff(320,plain,
^ [X: $i] :
refl(
( ( logic_and(and1(X))
| ~ halfadder(X) )
<=> ( logic_and(and1(X))
| ~ halfadder(X) ) )),
inference(bind,[status(th)],]) ).
tff(321,plain,
( ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
<=> ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ) ),
inference(quant_intro,[status(thm)],[320]) ).
tff(322,plain,
( ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
<=> ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(323,plain,
^ [X: $i] :
rewrite(
( ( ~ halfadder(X)
| logic_and(and1(X)) )
<=> ( logic_and(and1(X))
| ~ halfadder(X) ) )),
inference(bind,[status(th)],]) ).
tff(324,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_and(and1(X)) )
<=> ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ) ),
inference(quant_intro,[status(thm)],[323]) ).
tff(325,axiom,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and1(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_and1) ).
tff(326,plain,
! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ),
inference(modus_ponens,[status(thm)],[325,324]) ).
tff(327,plain,
! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ),
inference(modus_ponens,[status(thm)],[326,322]) ).
tff(328,plain,
! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ),
inference(skolemize,[status(sab)],[327]) ).
tff(329,plain,
! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ),
inference(modus_ponens,[status(thm)],[328,321]) ).
tff(330,plain,
( ( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h1(f)))
| ~ halfadder(h1(f)) )
<=> ( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h1(f)))
| ~ halfadder(h1(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(331,plain,
( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h1(f)))
| ~ halfadder(h1(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(332,plain,
( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h1(f)))
| ~ halfadder(h1(f)) ),
inference(modus_ponens,[status(thm)],[331,330]) ).
tff(333,plain,
( logic_and(and1(h1(f)))
| ~ halfadder(h1(f)) ),
inference(unit_resolution,[status(thm)],[332,329]) ).
tff(334,plain,
logic_and(and1(h1(f))),
inference(unit_resolution,[status(thm)],[333,48]) ).
tff(335,plain,
( ~ abnormal(and1(h1(f)))
<=> ~ abnormal(and1(h1(f))) ),
inference(rewrite,[status(thm)],]) ).
tff(336,axiom,
~ abnormal(and1(h1(f))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_and1h1) ).
tff(337,plain,
~ abnormal(and1(h1(f))),
inference(modus_ponens,[status(thm)],[336,335]) ).
tff(338,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h1(f)))
| and_ok(and1(h1(f)))
| ~ logic_and(and1(h1(f))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h1(f)))
| and_ok(and1(h1(f)))
| ~ logic_and(and1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(339,plain,
( ( and_ok(and1(h1(f)))
| abnormal(and1(h1(f)))
| ~ logic_and(and1(h1(f))) )
<=> ( abnormal(and1(h1(f)))
| and_ok(and1(h1(f)))
| ~ logic_and(and1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(340,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and1(h1(f)))
| abnormal(and1(h1(f)))
| ~ logic_and(and1(h1(f))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h1(f)))
| and_ok(and1(h1(f)))
| ~ logic_and(and1(h1(f))) ) ),
inference(monotonicity,[status(thm)],[339]) ).
tff(341,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and1(h1(f)))
| abnormal(and1(h1(f)))
| ~ logic_and(and1(h1(f))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h1(f)))
| and_ok(and1(h1(f)))
| ~ logic_and(and1(h1(f))) ) ),
inference(transitivity,[status(thm)],[340,338]) ).
tff(342,plain,
( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and1(h1(f)))
| abnormal(and1(h1(f)))
| ~ logic_and(and1(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(343,plain,
( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h1(f)))
| and_ok(and1(h1(f)))
| ~ logic_and(and1(h1(f))) ),
inference(modus_ponens,[status(thm)],[342,341]) ).
tff(344,plain,
( and_ok(and1(h1(f)))
| ~ logic_and(and1(h1(f))) ),
inference(unit_resolution,[status(thm)],[343,212,337]) ).
tff(345,plain,
and_ok(and1(h1(f))),
inference(unit_resolution,[status(thm)],[344,334]) ).
tff(346,plain,
^ [K: $i] :
refl(
( ( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
<=> ( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) ) )),
inference(bind,[status(th)],]) ).
tff(347,plain,
( ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
<=> ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) ) ),
inference(quant_intro,[status(thm)],[346]) ).
tff(348,plain,
( ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
<=> ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(349,plain,
^ [K: $i] :
trans(
monotonicity(
rewrite(
( ( ~ and_ok(K)
| ~ one(in1(K))
| ~ one(in2(K)) )
<=> ( ~ and_ok(K)
| ~ one(in2(K))
| ~ one(in1(K)) ) )),
( ( ~ and_ok(K)
| ~ one(in1(K))
| ~ one(in2(K))
| one(out1(K)) )
<=> ( ~ and_ok(K)
| ~ one(in2(K))
| ~ one(in1(K))
| one(out1(K)) ) )),
rewrite(
( ( ~ and_ok(K)
| ~ one(in2(K))
| ~ one(in1(K))
| one(out1(K)) )
<=> ( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) ) )),
( ( ~ and_ok(K)
| ~ one(in1(K))
| ~ one(in2(K))
| one(out1(K)) )
<=> ( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) ) )),
inference(bind,[status(th)],]) ).
tff(350,plain,
( ! [K: $i] :
( ~ and_ok(K)
| ~ one(in1(K))
| ~ one(in2(K))
| one(out1(K)) )
<=> ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) ) ),
inference(quant_intro,[status(thm)],[349]) ).
tff(351,axiom,
! [K: $i] :
( ~ and_ok(K)
| ~ one(in1(K))
| ~ one(in2(K))
| one(out1(K)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',and_11_1) ).
tff(352,plain,
! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) ),
inference(modus_ponens,[status(thm)],[351,350]) ).
tff(353,plain,
! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) ),
inference(modus_ponens,[status(thm)],[352,348]) ).
tff(354,plain,
! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) ),
inference(skolemize,[status(sab)],[353]) ).
tff(355,plain,
! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) ),
inference(modus_ponens,[status(thm)],[354,347]) ).
tff(356,plain,
( ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| ~ one(in2(and1(h1(f))))
| ~ one(in1(and1(h1(f))))
| one(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) )
<=> ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| ~ one(in2(and1(h1(f))))
| ~ one(in1(and1(h1(f))))
| one(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(357,plain,
( ( ~ and_ok(and1(h1(f)))
| one(out1(and1(h1(f))))
| ~ one(in2(and1(h1(f))))
| ~ one(in1(and1(h1(f)))) )
<=> ( ~ one(in2(and1(h1(f))))
| ~ one(in1(and1(h1(f))))
| one(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(358,plain,
( ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| ~ and_ok(and1(h1(f)))
| one(out1(and1(h1(f))))
| ~ one(in2(and1(h1(f))))
| ~ one(in1(and1(h1(f)))) )
<=> ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| ~ one(in2(and1(h1(f))))
| ~ one(in1(and1(h1(f))))
| one(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ) ),
inference(monotonicity,[status(thm)],[357]) ).
tff(359,plain,
( ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| ~ and_ok(and1(h1(f)))
| one(out1(and1(h1(f))))
| ~ one(in2(and1(h1(f))))
| ~ one(in1(and1(h1(f)))) )
<=> ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| ~ one(in2(and1(h1(f))))
| ~ one(in1(and1(h1(f))))
| one(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ) ),
inference(transitivity,[status(thm)],[358,356]) ).
tff(360,plain,
( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| ~ and_ok(and1(h1(f)))
| one(out1(and1(h1(f))))
| ~ one(in2(and1(h1(f))))
| ~ one(in1(and1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(361,plain,
( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| ~ one(in2(and1(h1(f))))
| ~ one(in1(and1(h1(f))))
| one(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ),
inference(modus_ponens,[status(thm)],[360,359]) ).
tff(362,plain,
( ~ one(in2(and1(h1(f))))
| ~ one(in1(and1(h1(f))))
| one(out1(and1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[361,355,345]) ).
tff(363,plain,
one(out1(and1(h1(f)))),
inference(unit_resolution,[status(thm)],[362,319,134]) ).
tff(364,plain,
^ [X: $i] :
refl(
( ( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
<=> ( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ) )),
inference(bind,[status(th)],]) ).
tff(365,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ) ),
inference(quant_intro,[status(thm)],[364]) ).
tff(366,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(367,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_connection_outs_out1and1) ).
tff(368,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ),
inference(modus_ponens,[status(thm)],[367,366]) ).
tff(369,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ),
inference(skolemize,[status(sab)],[368]) ).
tff(370,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ),
inference(modus_ponens,[status(thm)],[369,365]) ).
tff(371,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
| ~ halfadder(h1(f))
| connection(outs(h1(f)),out1(and1(h1(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
| ~ halfadder(h1(f))
| connection(outs(h1(f)),out1(and1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(372,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
| ~ halfadder(h1(f))
| connection(outs(h1(f)),out1(and1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(373,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
| ~ halfadder(h1(f))
| connection(outs(h1(f)),out1(and1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[372,371]) ).
tff(374,plain,
( ~ halfadder(h1(f))
| connection(outs(h1(f)),out1(and1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[373,370]) ).
tff(375,plain,
connection(outs(h1(f)),out1(and1(h1(f)))),
inference(unit_resolution,[status(thm)],[374,48]) ).
tff(376,plain,
^ [P2: $i,P1: $i] :
refl(
( ( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
<=> ( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ) )),
inference(bind,[status(th)],]) ).
tff(377,plain,
( ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
<=> ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ) ),
inference(quant_intro,[status(thm)],[376]) ).
tff(378,plain,
( ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
<=> ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(379,plain,
^ [P2: $i,P1: $i] :
trans(
monotonicity(
rewrite(
( ( ~ connection(P1,P2)
| ~ one(P2) )
<=> ( ~ connection(P1,P2)
| ~ one(P2) ) )),
( ( ~ connection(P1,P2)
| ~ one(P2)
| one(P1) )
<=> ( ~ connection(P1,P2)
| ~ one(P2)
| one(P1) ) )),
rewrite(
( ( ~ connection(P1,P2)
| ~ one(P2)
| one(P1) )
<=> ( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ) )),
( ( ~ connection(P1,P2)
| ~ one(P2)
| one(P1) )
<=> ( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ) )),
inference(bind,[status(th)],]) ).
tff(380,plain,
( ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ one(P2)
| one(P1) )
<=> ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ) ),
inference(quant_intro,[status(thm)],[379]) ).
tff(381,axiom,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ one(P2)
| one(P1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',value_propagation_one2) ).
tff(382,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ),
inference(modus_ponens,[status(thm)],[381,380]) ).
tff(383,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ),
inference(modus_ponens,[status(thm)],[382,378]) ).
tff(384,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ),
inference(skolemize,[status(sab)],[383]) ).
tff(385,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ),
inference(modus_ponens,[status(thm)],[384,377]) ).
tff(386,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| ~ one(out1(and1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| ~ one(out1(and1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(387,plain,
( ( ~ connection(outs(h1(f)),out1(and1(h1(f))))
| one(outs(h1(f)))
| ~ one(out1(and1(h1(f)))) )
<=> ( one(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| ~ one(out1(and1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(388,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| one(outs(h1(f)))
| ~ one(out1(and1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| ~ one(out1(and1(h1(f)))) ) ),
inference(monotonicity,[status(thm)],[387]) ).
tff(389,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| one(outs(h1(f)))
| ~ one(out1(and1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| ~ one(out1(and1(h1(f)))) ) ),
inference(transitivity,[status(thm)],[388,386]) ).
tff(390,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| one(outs(h1(f)))
| ~ one(out1(and1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(391,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| ~ one(out1(and1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[390,389]) ).
tff(392,plain,
( one(outs(h1(f)))
| ~ one(out1(and1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[391,385,375]) ).
tff(393,plain,
one(outs(h1(f))),
inference(unit_resolution,[status(thm)],[392,363]) ).
tff(394,plain,
^ [X: $i] :
refl(
( ( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) )
<=> ( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) ) )),
inference(bind,[status(th)],]) ).
tff(395,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) ) ),
inference(quant_intro,[status(thm)],[394]) ).
tff(396,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(397,axiom,
! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_connection_outsh1_in2h2) ).
tff(398,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) ),
inference(modus_ponens,[status(thm)],[397,396]) ).
tff(399,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) ),
inference(skolemize,[status(sab)],[398]) ).
tff(400,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) ),
inference(modus_ponens,[status(thm)],[399,395]) ).
tff(401,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) )
| ~ fulladder(f)
| connection(outs(h1(f)),in2(h2(f))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) )
| ~ fulladder(f)
| connection(outs(h1(f)),in2(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(402,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) )
| ~ fulladder(f)
| connection(outs(h1(f)),in2(h2(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(403,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) )
| ~ fulladder(f)
| connection(outs(h1(f)),in2(h2(f))) ),
inference(modus_ponens,[status(thm)],[402,401]) ).
tff(404,plain,
connection(outs(h1(f)),in2(h2(f))),
inference(unit_resolution,[status(thm)],[403,400,3]) ).
tff(405,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outs(h1(f)),in2(h2(f)))
| one(in2(h2(f)))
| ~ one(outs(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outs(h1(f)),in2(h2(f)))
| one(in2(h2(f)))
| ~ one(outs(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(406,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outs(h1(f)),in2(h2(f)))
| one(in2(h2(f)))
| ~ one(outs(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(407,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outs(h1(f)),in2(h2(f)))
| one(in2(h2(f)))
| ~ one(outs(h1(f))) ),
inference(modus_ponens,[status(thm)],[406,405]) ).
tff(408,plain,
( one(in2(h2(f)))
| ~ one(outs(h1(f))) ),
inference(unit_resolution,[status(thm)],[407,27,404]) ).
tff(409,plain,
one(in2(h2(f))),
inference(unit_resolution,[status(thm)],[408,393]) ).
tff(410,plain,
^ [X: $i] :
refl(
( ( ~ fulladder(X)
| halfadder(h2(X)) )
<=> ( ~ fulladder(X)
| halfadder(h2(X)) ) )),
inference(bind,[status(th)],]) ).
tff(411,plain,
( ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
<=> ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ) ),
inference(quant_intro,[status(thm)],[410]) ).
tff(412,plain,
( ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
<=> ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(413,axiom,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_halfadder2) ).
tff(414,plain,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ),
inference(modus_ponens,[status(thm)],[413,412]) ).
tff(415,plain,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ),
inference(skolemize,[status(sab)],[414]) ).
tff(416,plain,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ),
inference(modus_ponens,[status(thm)],[415,411]) ).
tff(417,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
| ~ fulladder(f)
| halfadder(h2(f)) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
| ~ fulladder(f)
| halfadder(h2(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(418,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
| ~ fulladder(f)
| halfadder(h2(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(419,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
| ~ fulladder(f)
| halfadder(h2(f)) ),
inference(modus_ponens,[status(thm)],[418,417]) ).
tff(420,plain,
halfadder(h2(f)),
inference(unit_resolution,[status(thm)],[419,416,3]) ).
tff(421,plain,
^ [X: $i] :
refl(
( ( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) )
<=> ( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) ) )),
inference(bind,[status(th)],]) ).
tff(422,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) ) ),
inference(quant_intro,[status(thm)],[421]) ).
tff(423,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(424,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_connection_in2_in2and2) ).
tff(425,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) ),
inference(modus_ponens,[status(thm)],[424,423]) ).
tff(426,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) ),
inference(skolemize,[status(sab)],[425]) ).
tff(427,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) ),
inference(modus_ponens,[status(thm)],[426,422]) ).
tff(428,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) )
| ~ halfadder(h2(f))
| connection(in2(h2(f)),in2(and2(h2(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) )
| ~ halfadder(h2(f))
| connection(in2(h2(f)),in2(and2(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(429,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) )
| ~ halfadder(h2(f))
| connection(in2(h2(f)),in2(and2(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(430,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) )
| ~ halfadder(h2(f))
| connection(in2(h2(f)),in2(and2(h2(f)))) ),
inference(modus_ponens,[status(thm)],[429,428]) ).
tff(431,plain,
( ~ halfadder(h2(f))
| connection(in2(h2(f)),in2(and2(h2(f)))) ),
inference(unit_resolution,[status(thm)],[430,427]) ).
tff(432,plain,
connection(in2(h2(f)),in2(and2(h2(f)))),
inference(unit_resolution,[status(thm)],[431,420]) ).
tff(433,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(and2(h2(f))))
| one(in2(and2(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(and2(h2(f))))
| one(in2(and2(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(434,plain,
( ( ~ connection(in2(h2(f)),in2(and2(h2(f))))
| one(in2(and2(h2(f))))
| ~ one(in2(h2(f))) )
<=> ( ~ one(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(and2(h2(f))))
| one(in2(and2(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(435,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in2(h2(f)),in2(and2(h2(f))))
| one(in2(and2(h2(f))))
| ~ one(in2(h2(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(and2(h2(f))))
| one(in2(and2(h2(f)))) ) ),
inference(monotonicity,[status(thm)],[434]) ).
tff(436,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in2(h2(f)),in2(and2(h2(f))))
| one(in2(and2(h2(f))))
| ~ one(in2(h2(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(and2(h2(f))))
| one(in2(and2(h2(f)))) ) ),
inference(transitivity,[status(thm)],[435,433]) ).
tff(437,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in2(h2(f)),in2(and2(h2(f))))
| one(in2(and2(h2(f))))
| ~ one(in2(h2(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(438,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(and2(h2(f))))
| one(in2(and2(h2(f)))) ),
inference(modus_ponens,[status(thm)],[437,436]) ).
tff(439,plain,
( ~ one(in2(h2(f)))
| one(in2(and2(h2(f)))) ),
inference(unit_resolution,[status(thm)],[438,27,432]) ).
tff(440,plain,
one(in2(and2(h2(f)))),
inference(unit_resolution,[status(thm)],[439,409]) ).
tff(441,plain,
^ [X: $i] :
refl(
( ( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
<=> ( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ) )),
inference(bind,[status(th)],]) ).
tff(442,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ) ),
inference(quant_intro,[status(thm)],[441]) ).
tff(443,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(444,axiom,
! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_connection_in1_in1h2) ).
tff(445,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ),
inference(modus_ponens,[status(thm)],[444,443]) ).
tff(446,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ),
inference(skolemize,[status(sab)],[445]) ).
tff(447,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ),
inference(modus_ponens,[status(thm)],[446,442]) ).
tff(448,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
| ~ fulladder(f)
| connection(in1(f),in1(h2(f))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
| ~ fulladder(f)
| connection(in1(f),in1(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(449,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
| ~ fulladder(f)
| connection(in1(f),in1(h2(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(450,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
| ~ fulladder(f)
| connection(in1(f),in1(h2(f))) ),
inference(modus_ponens,[status(thm)],[449,448]) ).
tff(451,plain,
connection(in1(f),in1(h2(f))),
inference(unit_resolution,[status(thm)],[450,447,3]) ).
tff(452,plain,
( one(in1(f))
<=> one(in1(f)) ),
inference(rewrite,[status(thm)],]) ).
tff(453,axiom,
one(in1(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in1_1) ).
tff(454,plain,
one(in1(f)),
inference(modus_ponens,[status(thm)],[453,452]) ).
tff(455,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| one(in1(h2(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| one(in1(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(456,plain,
( ( ~ connection(in1(f),in1(h2(f)))
| one(in1(h2(f)))
| ~ one(in1(f)) )
<=> ( ~ one(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| one(in1(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(457,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in1(f),in1(h2(f)))
| one(in1(h2(f)))
| ~ one(in1(f)) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| one(in1(h2(f))) ) ),
inference(monotonicity,[status(thm)],[456]) ).
tff(458,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in1(f),in1(h2(f)))
| one(in1(h2(f)))
| ~ one(in1(f)) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| one(in1(h2(f))) ) ),
inference(transitivity,[status(thm)],[457,455]) ).
tff(459,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in1(f),in1(h2(f)))
| one(in1(h2(f)))
| ~ one(in1(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(460,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| one(in1(h2(f))) ),
inference(modus_ponens,[status(thm)],[459,458]) ).
tff(461,plain,
one(in1(h2(f))),
inference(unit_resolution,[status(thm)],[460,27,454,451]) ).
tff(462,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h2(f))
| connection(in1(h2(f)),in1(and2(h2(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h2(f))
| connection(in1(h2(f)),in1(and2(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(463,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h2(f))
| connection(in1(h2(f)),in1(and2(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(464,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h2(f))
| connection(in1(h2(f)),in1(and2(h2(f)))) ),
inference(modus_ponens,[status(thm)],[463,462]) ).
tff(465,plain,
( ~ halfadder(h2(f))
| connection(in1(h2(f)),in1(and2(h2(f)))) ),
inference(unit_resolution,[status(thm)],[464,172]) ).
tff(466,plain,
connection(in1(h2(f)),in1(and2(h2(f)))),
inference(unit_resolution,[status(thm)],[465,420]) ).
tff(467,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in1(h2(f)),in1(and2(h2(f))))
| one(in1(and2(h2(f))))
| ~ one(in1(h2(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in1(h2(f)),in1(and2(h2(f))))
| one(in1(and2(h2(f))))
| ~ one(in1(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(468,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in1(h2(f)),in1(and2(h2(f))))
| one(in1(and2(h2(f))))
| ~ one(in1(h2(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(469,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in1(h2(f)),in1(and2(h2(f))))
| one(in1(and2(h2(f))))
| ~ one(in1(h2(f))) ),
inference(modus_ponens,[status(thm)],[468,467]) ).
tff(470,plain,
one(in1(and2(h2(f)))),
inference(unit_resolution,[status(thm)],[469,27,466,461]) ).
tff(471,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h2(f)))
| ~ halfadder(h2(f)) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h2(f)))
| ~ halfadder(h2(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(472,plain,
( ( ~ halfadder(h2(f))
| logic_and(and2(h2(f))) )
<=> ( logic_and(and2(h2(f)))
| ~ halfadder(h2(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(473,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| ~ halfadder(h2(f))
| logic_and(and2(h2(f))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h2(f)))
| ~ halfadder(h2(f)) ) ),
inference(monotonicity,[status(thm)],[472]) ).
tff(474,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| ~ halfadder(h2(f))
| logic_and(and2(h2(f))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h2(f)))
| ~ halfadder(h2(f)) ) ),
inference(transitivity,[status(thm)],[473,471]) ).
tff(475,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| ~ halfadder(h2(f))
| logic_and(and2(h2(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(476,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h2(f)))
| ~ halfadder(h2(f)) ),
inference(modus_ponens,[status(thm)],[475,474]) ).
tff(477,plain,
( logic_and(and2(h2(f)))
| ~ halfadder(h2(f)) ),
inference(unit_resolution,[status(thm)],[476,191]) ).
tff(478,plain,
logic_and(and2(h2(f))),
inference(unit_resolution,[status(thm)],[477,420]) ).
tff(479,plain,
( ~ abnormal(and2(h2(f)))
<=> ~ abnormal(and2(h2(f))) ),
inference(rewrite,[status(thm)],]) ).
tff(480,axiom,
~ abnormal(and2(h2(f))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_and2) ).
tff(481,plain,
~ abnormal(and2(h2(f))),
inference(modus_ponens,[status(thm)],[480,479]) ).
tff(482,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h2(f)))
| and_ok(and2(h2(f)))
| ~ logic_and(and2(h2(f))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h2(f)))
| and_ok(and2(h2(f)))
| ~ logic_and(and2(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(483,plain,
( ( and_ok(and2(h2(f)))
| abnormal(and2(h2(f)))
| ~ logic_and(and2(h2(f))) )
<=> ( abnormal(and2(h2(f)))
| and_ok(and2(h2(f)))
| ~ logic_and(and2(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(484,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and2(h2(f)))
| abnormal(and2(h2(f)))
| ~ logic_and(and2(h2(f))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h2(f)))
| and_ok(and2(h2(f)))
| ~ logic_and(and2(h2(f))) ) ),
inference(monotonicity,[status(thm)],[483]) ).
tff(485,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and2(h2(f)))
| abnormal(and2(h2(f)))
| ~ logic_and(and2(h2(f))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h2(f)))
| and_ok(and2(h2(f)))
| ~ logic_and(and2(h2(f))) ) ),
inference(transitivity,[status(thm)],[484,482]) ).
tff(486,plain,
( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and2(h2(f)))
| abnormal(and2(h2(f)))
| ~ logic_and(and2(h2(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(487,plain,
( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h2(f)))
| and_ok(and2(h2(f)))
| ~ logic_and(and2(h2(f))) ),
inference(modus_ponens,[status(thm)],[486,485]) ).
tff(488,plain,
( and_ok(and2(h2(f)))
| ~ logic_and(and2(h2(f))) ),
inference(unit_resolution,[status(thm)],[487,212,481]) ).
tff(489,plain,
and_ok(and2(h2(f))),
inference(unit_resolution,[status(thm)],[488,478]) ).
tff(490,plain,
( ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| one(out1(and2(h2(f))))
| ~ one(in2(and2(h2(f))))
| ~ one(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f))) )
<=> ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| one(out1(and2(h2(f))))
| ~ one(in2(and2(h2(f))))
| ~ one(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(491,plain,
( ( ~ and_ok(and2(h2(f)))
| one(out1(and2(h2(f))))
| ~ one(in2(and2(h2(f))))
| ~ one(in1(and2(h2(f)))) )
<=> ( one(out1(and2(h2(f))))
| ~ one(in2(and2(h2(f))))
| ~ one(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(492,plain,
( ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| ~ and_ok(and2(h2(f)))
| one(out1(and2(h2(f))))
| ~ one(in2(and2(h2(f))))
| ~ one(in1(and2(h2(f)))) )
<=> ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| one(out1(and2(h2(f))))
| ~ one(in2(and2(h2(f))))
| ~ one(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f))) ) ),
inference(monotonicity,[status(thm)],[491]) ).
tff(493,plain,
( ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| ~ and_ok(and2(h2(f)))
| one(out1(and2(h2(f))))
| ~ one(in2(and2(h2(f))))
| ~ one(in1(and2(h2(f)))) )
<=> ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| one(out1(and2(h2(f))))
| ~ one(in2(and2(h2(f))))
| ~ one(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f))) ) ),
inference(transitivity,[status(thm)],[492,490]) ).
tff(494,plain,
( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| ~ and_ok(and2(h2(f)))
| one(out1(and2(h2(f))))
| ~ one(in2(and2(h2(f))))
| ~ one(in1(and2(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(495,plain,
( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| one(out1(and2(h2(f))))
| ~ one(in2(and2(h2(f))))
| ~ one(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f))) ),
inference(modus_ponens,[status(thm)],[494,493]) ).
tff(496,plain,
( one(out1(and2(h2(f))))
| ~ one(in2(and2(h2(f)))) ),
inference(unit_resolution,[status(thm)],[495,355,489,470]) ).
tff(497,plain,
one(out1(and2(h2(f)))),
inference(unit_resolution,[status(thm)],[496,440]) ).
tff(498,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
| ~ halfadder(h2(f))
| connection(out1(and2(h2(f))),in1(not1(h2(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
| ~ halfadder(h2(f))
| connection(out1(and2(h2(f))),in1(not1(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(499,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
| ~ halfadder(h2(f))
| connection(out1(and2(h2(f))),in1(not1(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(500,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
| ~ halfadder(h2(f))
| connection(out1(and2(h2(f))),in1(not1(h2(f)))) ),
inference(modus_ponens,[status(thm)],[499,498]) ).
tff(501,plain,
( ~ halfadder(h2(f))
| connection(out1(and2(h2(f))),in1(not1(h2(f)))) ),
inference(unit_resolution,[status(thm)],[500,241]) ).
tff(502,plain,
connection(out1(and2(h2(f))),in1(not1(h2(f)))),
inference(unit_resolution,[status(thm)],[501,420]) ).
tff(503,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(and2(h2(f))),in1(not1(h2(f))))
| one(in1(not1(h2(f))))
| ~ one(out1(and2(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(and2(h2(f))),in1(not1(h2(f))))
| one(in1(not1(h2(f))))
| ~ one(out1(and2(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(504,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(and2(h2(f))),in1(not1(h2(f))))
| one(in1(not1(h2(f))))
| ~ one(out1(and2(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(505,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(and2(h2(f))),in1(not1(h2(f))))
| one(in1(not1(h2(f))))
| ~ one(out1(and2(h2(f)))) ),
inference(modus_ponens,[status(thm)],[504,503]) ).
tff(506,plain,
( one(in1(not1(h2(f))))
| ~ one(out1(and2(h2(f)))) ),
inference(unit_resolution,[status(thm)],[505,27,502]) ).
tff(507,plain,
one(in1(not1(h2(f)))),
inference(unit_resolution,[status(thm)],[506,497]) ).
tff(508,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| ~ halfadder(h2(f))
| logic_not(not1(h2(f))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| ~ halfadder(h2(f))
| logic_not(not1(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(509,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| ~ halfadder(h2(f))
| logic_not(not1(h2(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(510,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| ~ halfadder(h2(f))
| logic_not(not1(h2(f))) ),
inference(modus_ponens,[status(thm)],[509,508]) ).
tff(511,plain,
logic_not(not1(h2(f))),
inference(unit_resolution,[status(thm)],[510,258,420]) ).
tff(512,plain,
^ [P: $i] :
refl(
( ( ~ zero(P)
| ~ one(P) )
<=> ( ~ zero(P)
| ~ one(P) ) )),
inference(bind,[status(th)],]) ).
tff(513,plain,
( ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
<=> ! [P: $i] :
( ~ zero(P)
| ~ one(P) ) ),
inference(quant_intro,[status(thm)],[512]) ).
tff(514,plain,
( ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
<=> ! [P: $i] :
( ~ zero(P)
| ~ one(P) ) ),
inference(rewrite,[status(thm)],]) ).
tff(515,axiom,
! [P: $i] :
( ~ zero(P)
| ~ one(P) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',unique_value) ).
tff(516,plain,
! [P: $i] :
( ~ zero(P)
| ~ one(P) ),
inference(modus_ponens,[status(thm)],[515,514]) ).
tff(517,plain,
! [P: $i] :
( ~ zero(P)
| ~ one(P) ),
inference(skolemize,[status(sab)],[516]) ).
tff(518,plain,
! [P: $i] :
( ~ zero(P)
| ~ one(P) ),
inference(modus_ponens,[status(thm)],[517,513]) ).
tff(519,plain,
( ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(inc(f))
| ~ one(inc(f)) )
<=> ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(inc(f))
| ~ one(inc(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(520,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(inc(f))
| ~ one(inc(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(521,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(inc(f))
| ~ one(inc(f)) ),
inference(modus_ponens,[status(thm)],[520,519]) ).
tff(522,plain,
~ zero(inc(f)),
inference(unit_resolution,[status(thm)],[521,518,17]) ).
tff(523,plain,
^ [P2: $i,P1: $i] :
refl(
( ( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
<=> ( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ) )),
inference(bind,[status(th)],]) ).
tff(524,plain,
( ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
<=> ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ) ),
inference(quant_intro,[status(thm)],[523]) ).
tff(525,plain,
( ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
<=> ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(526,plain,
^ [P2: $i,P1: $i] :
trans(
monotonicity(
rewrite(
( ( ~ connection(P1,P2)
| ~ zero(P2) )
<=> ( ~ connection(P1,P2)
| ~ zero(P2) ) )),
( ( ~ connection(P1,P2)
| ~ zero(P2)
| zero(P1) )
<=> ( ~ connection(P1,P2)
| ~ zero(P2)
| zero(P1) ) )),
rewrite(
( ( ~ connection(P1,P2)
| ~ zero(P2)
| zero(P1) )
<=> ( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ) )),
( ( ~ connection(P1,P2)
| ~ zero(P2)
| zero(P1) )
<=> ( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ) )),
inference(bind,[status(th)],]) ).
tff(527,plain,
( ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ zero(P2)
| zero(P1) )
<=> ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ) ),
inference(quant_intro,[status(thm)],[526]) ).
tff(528,axiom,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ zero(P2)
| zero(P1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',value_propagation_zero2) ).
tff(529,plain,
! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ),
inference(modus_ponens,[status(thm)],[528,527]) ).
tff(530,plain,
! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ),
inference(modus_ponens,[status(thm)],[529,525]) ).
tff(531,plain,
! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ),
inference(skolemize,[status(sab)],[530]) ).
tff(532,plain,
! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ),
inference(modus_ponens,[status(thm)],[531,524]) ).
tff(533,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(inc(f))
| ~ connection(inc(f),in2(h1(f)))
| ~ zero(in2(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(inc(f))
| ~ connection(inc(f),in2(h1(f)))
| ~ zero(in2(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(534,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(inc(f))
| ~ connection(inc(f),in2(h1(f)))
| ~ zero(in2(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(535,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(inc(f))
| ~ connection(inc(f),in2(h1(f)))
| ~ zero(in2(h1(f))) ),
inference(modus_ponens,[status(thm)],[534,533]) ).
tff(536,plain,
~ zero(in2(h1(f))),
inference(unit_resolution,[status(thm)],[535,532,522,14]) ).
tff(537,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(h1(f)))
| ~ connection(in2(h1(f)),in2(or1(h1(f))))
| ~ zero(in2(or1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(h1(f)))
| ~ connection(in2(h1(f)),in2(or1(h1(f))))
| ~ zero(in2(or1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(538,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(h1(f)))
| ~ connection(in2(h1(f)),in2(or1(h1(f))))
| ~ zero(in2(or1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(539,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(h1(f)))
| ~ connection(in2(h1(f)),in2(or1(h1(f))))
| ~ zero(in2(or1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[538,537]) ).
tff(540,plain,
~ zero(in2(or1(h1(f)))),
inference(unit_resolution,[status(thm)],[539,532,60,536]) ).
tff(541,plain,
^ [K: $i] :
refl(
( ( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
<=> ( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(542,plain,
( ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
<=> ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) ),
inference(quant_intro,[status(thm)],[541]) ).
tff(543,plain,
( ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
<=> ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) ),
inference(rewrite,[status(thm)],]) ).
tff(544,plain,
^ [K: $i] :
rewrite(
( ( ~ or_ok(K)
| ~ zero(out1(K))
| zero(in2(K)) )
<=> ( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(545,plain,
( ! [K: $i] :
( ~ or_ok(K)
| ~ zero(out1(K))
| zero(in2(K)) )
<=> ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) ),
inference(quant_intro,[status(thm)],[544]) ).
tff(546,axiom,
! [K: $i] :
( ~ or_ok(K)
| ~ zero(out1(K))
| zero(in2(K)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',or_0_01) ).
tff(547,plain,
! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[546,545]) ).
tff(548,plain,
! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[547,543]) ).
tff(549,plain,
! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(skolemize,[status(sab)],[548]) ).
tff(550,plain,
! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[549,542]) ).
tff(551,plain,
( ( ~ ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| ~ zero(out1(or1(h1(f))))
| zero(in2(or1(h1(f))))
| ~ or_ok(or1(h1(f))) )
<=> ( ~ ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| ~ zero(out1(or1(h1(f))))
| zero(in2(or1(h1(f))))
| ~ or_ok(or1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(552,plain,
( ( zero(in2(or1(h1(f))))
| ~ zero(out1(or1(h1(f))))
| ~ or_ok(or1(h1(f))) )
<=> ( ~ zero(out1(or1(h1(f))))
| zero(in2(or1(h1(f))))
| ~ or_ok(or1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(553,plain,
( ( ~ ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| zero(in2(or1(h1(f))))
| ~ zero(out1(or1(h1(f))))
| ~ or_ok(or1(h1(f))) )
<=> ( ~ ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| ~ zero(out1(or1(h1(f))))
| zero(in2(or1(h1(f))))
| ~ or_ok(or1(h1(f))) ) ),
inference(monotonicity,[status(thm)],[552]) ).
tff(554,plain,
( ( ~ ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| zero(in2(or1(h1(f))))
| ~ zero(out1(or1(h1(f))))
| ~ or_ok(or1(h1(f))) )
<=> ( ~ ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| ~ zero(out1(or1(h1(f))))
| zero(in2(or1(h1(f))))
| ~ or_ok(or1(h1(f))) ) ),
inference(transitivity,[status(thm)],[553,551]) ).
tff(555,plain,
( ~ ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| zero(in2(or1(h1(f))))
| ~ zero(out1(or1(h1(f))))
| ~ or_ok(or1(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(556,plain,
( ~ ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| ~ zero(out1(or1(h1(f))))
| zero(in2(or1(h1(f))))
| ~ or_ok(or1(h1(f))) ),
inference(modus_ponens,[status(thm)],[555,554]) ).
tff(557,plain,
~ zero(out1(or1(h1(f)))),
inference(unit_resolution,[status(thm)],[556,550,100,540]) ).
tff(558,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(or1(h1(f))),in1(and1(h1(f))))
| zero(out1(or1(h1(f))))
| ~ zero(in1(and1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(or1(h1(f))),in1(and1(h1(f))))
| zero(out1(or1(h1(f))))
| ~ zero(in1(and1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(559,plain,
( ( zero(out1(or1(h1(f))))
| ~ connection(out1(or1(h1(f))),in1(and1(h1(f))))
| ~ zero(in1(and1(h1(f)))) )
<=> ( ~ connection(out1(or1(h1(f))),in1(and1(h1(f))))
| zero(out1(or1(h1(f))))
| ~ zero(in1(and1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(560,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(out1(or1(h1(f))))
| ~ connection(out1(or1(h1(f))),in1(and1(h1(f))))
| ~ zero(in1(and1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(or1(h1(f))),in1(and1(h1(f))))
| zero(out1(or1(h1(f))))
| ~ zero(in1(and1(h1(f)))) ) ),
inference(monotonicity,[status(thm)],[559]) ).
tff(561,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(out1(or1(h1(f))))
| ~ connection(out1(or1(h1(f))),in1(and1(h1(f))))
| ~ zero(in1(and1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(or1(h1(f))),in1(and1(h1(f))))
| zero(out1(or1(h1(f))))
| ~ zero(in1(and1(h1(f)))) ) ),
inference(transitivity,[status(thm)],[560,558]) ).
tff(562,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(out1(or1(h1(f))))
| ~ connection(out1(or1(h1(f))),in1(and1(h1(f))))
| ~ zero(in1(and1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(563,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(or1(h1(f))),in1(and1(h1(f))))
| zero(out1(or1(h1(f))))
| ~ zero(in1(and1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[562,561]) ).
tff(564,plain,
( zero(out1(or1(h1(f))))
| ~ zero(in1(and1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[563,532,129]) ).
tff(565,plain,
~ zero(in1(and1(h1(f)))),
inference(unit_resolution,[status(thm)],[564,557]) ).
tff(566,plain,
( ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(in2(f))
| ~ one(in2(f)) )
<=> ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(in2(f))
| ~ one(in2(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(567,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(in2(f))
| ~ one(in2(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(568,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(in2(f))
| ~ one(in2(f)) ),
inference(modus_ponens,[status(thm)],[567,566]) ).
tff(569,plain,
~ one(in2(f)),
inference(unit_resolution,[status(thm)],[568,518,148]) ).
tff(570,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| ~ one(in1(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| ~ one(in1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(571,plain,
( ( ~ connection(in2(f),in1(h1(f)))
| one(in2(f))
| ~ one(in1(h1(f))) )
<=> ( one(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| ~ one(in1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(572,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in2(f),in1(h1(f)))
| one(in2(f))
| ~ one(in1(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| ~ one(in1(h1(f))) ) ),
inference(monotonicity,[status(thm)],[571]) ).
tff(573,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in2(f),in1(h1(f)))
| one(in2(f))
| ~ one(in1(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| ~ one(in1(h1(f))) ) ),
inference(transitivity,[status(thm)],[572,570]) ).
tff(574,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in2(f),in1(h1(f)))
| one(in2(f))
| ~ one(in1(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(575,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| ~ one(in1(h1(f))) ),
inference(modus_ponens,[status(thm)],[574,573]) ).
tff(576,plain,
~ one(in1(h1(f))),
inference(unit_resolution,[status(thm)],[575,385,569,145]) ).
tff(577,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h1(f)))
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| ~ one(in1(and2(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h1(f)))
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| ~ one(in1(and2(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(578,plain,
( ( ~ connection(in1(h1(f)),in1(and2(h1(f))))
| one(in1(h1(f)))
| ~ one(in1(and2(h1(f)))) )
<=> ( one(in1(h1(f)))
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| ~ one(in1(and2(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(579,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| one(in1(h1(f)))
| ~ one(in1(and2(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h1(f)))
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| ~ one(in1(and2(h1(f)))) ) ),
inference(monotonicity,[status(thm)],[578]) ).
tff(580,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| one(in1(h1(f)))
| ~ one(in1(and2(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h1(f)))
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| ~ one(in1(and2(h1(f)))) ) ),
inference(transitivity,[status(thm)],[579,577]) ).
tff(581,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| one(in1(h1(f)))
| ~ one(in1(and2(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(582,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h1(f)))
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| ~ one(in1(and2(h1(f)))) ),
inference(modus_ponens,[status(thm)],[581,580]) ).
tff(583,plain,
~ one(in1(and2(h1(f)))),
inference(unit_resolution,[status(thm)],[582,385,177,576]) ).
tff(584,plain,
^ [K: $i] :
refl(
( ( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
<=> ( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ) )),
inference(bind,[status(th)],]) ).
tff(585,plain,
( ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
<=> ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ) ),
inference(quant_intro,[status(thm)],[584]) ).
tff(586,plain,
( ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
<=> ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(587,plain,
^ [K: $i] :
rewrite(
( ( ~ and_ok(K)
| ~ one(out1(K))
| one(in1(K)) )
<=> ( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ) )),
inference(bind,[status(th)],]) ).
tff(588,plain,
( ! [K: $i] :
( ~ and_ok(K)
| ~ one(out1(K))
| one(in1(K)) )
<=> ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ) ),
inference(quant_intro,[status(thm)],[587]) ).
tff(589,axiom,
! [K: $i] :
( ~ and_ok(K)
| ~ one(out1(K))
| one(in1(K)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',and_1_1x) ).
tff(590,plain,
! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ),
inference(modus_ponens,[status(thm)],[589,588]) ).
tff(591,plain,
! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ),
inference(modus_ponens,[status(thm)],[590,586]) ).
tff(592,plain,
! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ),
inference(skolemize,[status(sab)],[591]) ).
tff(593,plain,
! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ),
inference(modus_ponens,[status(thm)],[592,585]) ).
tff(594,plain,
( ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f))))
| one(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) )
<=> ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f))))
| one(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(595,plain,
( ( ~ one(out1(and2(h1(f))))
| ~ and_ok(and2(h1(f)))
| one(in1(and2(h1(f)))) )
<=> ( ~ one(out1(and2(h1(f))))
| one(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(596,plain,
( ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f))))
| ~ and_ok(and2(h1(f)))
| one(in1(and2(h1(f)))) )
<=> ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f))))
| one(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) ) ),
inference(monotonicity,[status(thm)],[595]) ).
tff(597,plain,
( ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f))))
| ~ and_ok(and2(h1(f)))
| one(in1(and2(h1(f)))) )
<=> ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f))))
| one(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) ) ),
inference(transitivity,[status(thm)],[596,594]) ).
tff(598,plain,
( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f))))
| ~ and_ok(and2(h1(f)))
| one(in1(and2(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(599,plain,
( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f))))
| one(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) ),
inference(modus_ponens,[status(thm)],[598,597]) ).
tff(600,plain,
~ one(out1(and2(h1(f)))),
inference(unit_resolution,[status(thm)],[599,593,220,583]) ).
tff(601,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(out1(and2(h1(f))),in1(not1(h1(f))))
| one(out1(and2(h1(f))))
| ~ one(in1(not1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(out1(and2(h1(f))),in1(not1(h1(f))))
| one(out1(and2(h1(f))))
| ~ one(in1(not1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(602,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(out1(and2(h1(f))),in1(not1(h1(f))))
| one(out1(and2(h1(f))))
| ~ one(in1(not1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(603,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(out1(and2(h1(f))),in1(not1(h1(f))))
| one(out1(and2(h1(f))))
| ~ one(in1(not1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[602,601]) ).
tff(604,plain,
( one(out1(and2(h1(f))))
| ~ one(in1(not1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[603,385,246]) ).
tff(605,plain,
~ one(in1(not1(h1(f)))),
inference(unit_resolution,[status(thm)],[604,600]) ).
tff(606,plain,
^ [K: $i] :
refl(
( ( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) )
<=> ( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(607,plain,
( ! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) )
<=> ! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ) ),
inference(quant_intro,[status(thm)],[606]) ).
tff(608,plain,
( ! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) )
<=> ! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ) ),
inference(rewrite,[status(thm)],]) ).
tff(609,plain,
^ [K: $i] :
rewrite(
( ( ~ not_ok(K)
| ~ zero(out1(K))
| one(in1(K)) )
<=> ( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(610,plain,
( ! [K: $i] :
( ~ not_ok(K)
| ~ zero(out1(K))
| one(in1(K)) )
<=> ! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ) ),
inference(quant_intro,[status(thm)],[609]) ).
tff(611,axiom,
! [K: $i] :
( ~ not_ok(K)
| ~ zero(out1(K))
| one(in1(K)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',not_0_1_bw) ).
tff(612,plain,
! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[611,610]) ).
tff(613,plain,
! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[612,608]) ).
tff(614,plain,
! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ),
inference(skolemize,[status(sab)],[613]) ).
tff(615,plain,
! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[614,607]) ).
tff(616,plain,
( ( ~ ! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) )
| ~ zero(out1(not1(h1(f))))
| one(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) )
<=> ( ~ ! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) )
| ~ zero(out1(not1(h1(f))))
| one(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(617,plain,
( ~ ! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) )
| ~ zero(out1(not1(h1(f))))
| one(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(618,plain,
( ~ ! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) )
| ~ zero(out1(not1(h1(f))))
| one(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) ),
inference(modus_ponens,[status(thm)],[617,616]) ).
tff(619,plain,
( ~ zero(out1(not1(h1(f))))
| one(in1(not1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[618,615,284]) ).
tff(620,plain,
~ zero(out1(not1(h1(f)))),
inference(unit_resolution,[status(thm)],[619,605]) ).
tff(621,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| zero(out1(not1(h1(f))))
| ~ zero(in2(and1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| zero(out1(not1(h1(f))))
| ~ zero(in2(and1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(622,plain,
( ( zero(out1(not1(h1(f))))
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| ~ zero(in2(and1(h1(f)))) )
<=> ( ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| zero(out1(not1(h1(f))))
| ~ zero(in2(and1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(623,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(out1(not1(h1(f))))
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| ~ zero(in2(and1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| zero(out1(not1(h1(f))))
| ~ zero(in2(and1(h1(f)))) ) ),
inference(monotonicity,[status(thm)],[622]) ).
tff(624,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(out1(not1(h1(f))))
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| ~ zero(in2(and1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| zero(out1(not1(h1(f))))
| ~ zero(in2(and1(h1(f)))) ) ),
inference(transitivity,[status(thm)],[623,621]) ).
tff(625,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(out1(not1(h1(f))))
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| ~ zero(in2(and1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(626,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f))))
| zero(out1(not1(h1(f))))
| ~ zero(in2(and1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[625,624]) ).
tff(627,plain,
( zero(out1(not1(h1(f))))
| ~ zero(in2(and1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[626,532,314]) ).
tff(628,plain,
~ zero(in2(and1(h1(f)))),
inference(unit_resolution,[status(thm)],[627,620]) ).
tff(629,plain,
^ [K: $i] :
refl(
( ( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
<=> ( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ) )),
inference(bind,[status(th)],]) ).
tff(630,plain,
( ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
<=> ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ) ),
inference(quant_intro,[status(thm)],[629]) ).
tff(631,plain,
( ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
<=> ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(632,plain,
^ [K: $i] :
trans(
monotonicity(
rewrite(
( ( ~ and_ok(K)
| ~ zero(out1(K))
| zero(in1(K)) )
<=> ( zero(in1(K))
| ~ and_ok(K)
| ~ zero(out1(K)) ) )),
( ( ~ and_ok(K)
| ~ zero(out1(K))
| zero(in1(K))
| zero(in2(K)) )
<=> ( zero(in1(K))
| ~ and_ok(K)
| ~ zero(out1(K))
| zero(in2(K)) ) )),
rewrite(
( ( zero(in1(K))
| ~ and_ok(K)
| ~ zero(out1(K))
| zero(in2(K)) )
<=> ( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ) )),
( ( ~ and_ok(K)
| ~ zero(out1(K))
| zero(in1(K))
| zero(in2(K)) )
<=> ( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ) )),
inference(bind,[status(th)],]) ).
tff(633,plain,
( ! [K: $i] :
( ~ and_ok(K)
| ~ zero(out1(K))
| zero(in1(K))
| zero(in2(K)) )
<=> ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ) ),
inference(quant_intro,[status(thm)],[632]) ).
tff(634,axiom,
! [K: $i] :
( ~ and_ok(K)
| ~ zero(out1(K))
| zero(in1(K))
| zero(in2(K)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',and_0_00) ).
tff(635,plain,
! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ),
inference(modus_ponens,[status(thm)],[634,633]) ).
tff(636,plain,
! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ),
inference(modus_ponens,[status(thm)],[635,631]) ).
tff(637,plain,
! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ),
inference(skolemize,[status(sab)],[636]) ).
tff(638,plain,
! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ),
inference(modus_ponens,[status(thm)],[637,630]) ).
tff(639,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in2(and1(h1(f))))
| zero(in1(and1(h1(f))))
| ~ zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in2(and1(h1(f))))
| zero(in1(and1(h1(f))))
| ~ zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(640,plain,
( ( zero(in1(and1(h1(f))))
| ~ and_ok(and1(h1(f)))
| zero(in2(and1(h1(f))))
| ~ zero(out1(and1(h1(f)))) )
<=> ( zero(in2(and1(h1(f))))
| zero(in1(and1(h1(f))))
| ~ zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(641,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in1(and1(h1(f))))
| ~ and_ok(and1(h1(f)))
| zero(in2(and1(h1(f))))
| ~ zero(out1(and1(h1(f)))) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in2(and1(h1(f))))
| zero(in1(and1(h1(f))))
| ~ zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ) ),
inference(monotonicity,[status(thm)],[640]) ).
tff(642,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in1(and1(h1(f))))
| ~ and_ok(and1(h1(f)))
| zero(in2(and1(h1(f))))
| ~ zero(out1(and1(h1(f)))) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in2(and1(h1(f))))
| zero(in1(and1(h1(f))))
| ~ zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ) ),
inference(transitivity,[status(thm)],[641,639]) ).
tff(643,plain,
( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in1(and1(h1(f))))
| ~ and_ok(and1(h1(f)))
| zero(in2(and1(h1(f))))
| ~ zero(out1(and1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(644,plain,
( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in2(and1(h1(f))))
| zero(in1(and1(h1(f))))
| ~ zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ),
inference(modus_ponens,[status(thm)],[643,642]) ).
tff(645,plain,
( zero(in2(and1(h1(f))))
| zero(in1(and1(h1(f))))
| ~ zero(out1(and1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[644,638,345]) ).
tff(646,plain,
~ zero(out1(and1(h1(f)))),
inference(unit_resolution,[status(thm)],[645,628,565]) ).
tff(647,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| zero(out1(and1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| zero(out1(and1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(648,plain,
( ( zero(out1(and1(h1(f))))
| ~ zero(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f)))) )
<=> ( ~ zero(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| zero(out1(and1(h1(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(649,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(and1(h1(f))))
| ~ zero(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| zero(out1(and1(h1(f)))) ) ),
inference(monotonicity,[status(thm)],[648]) ).
tff(650,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(and1(h1(f))))
| ~ zero(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| zero(out1(and1(h1(f)))) ) ),
inference(transitivity,[status(thm)],[649,647]) ).
tff(651,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(and1(h1(f))))
| ~ zero(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(652,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| zero(out1(and1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[651,650]) ).
tff(653,plain,
( ~ zero(outs(h1(f)))
| zero(out1(and1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[652,158,375]) ).
tff(654,plain,
~ zero(outs(h1(f))),
inference(unit_resolution,[status(thm)],[653,646]) ).
tff(655,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outs(h1(f)),in2(h2(f)))
| zero(outs(h1(f)))
| ~ zero(in2(h2(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outs(h1(f)),in2(h2(f)))
| zero(outs(h1(f)))
| ~ zero(in2(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(656,plain,
( ( zero(outs(h1(f)))
| ~ connection(outs(h1(f)),in2(h2(f)))
| ~ zero(in2(h2(f))) )
<=> ( ~ connection(outs(h1(f)),in2(h2(f)))
| zero(outs(h1(f)))
| ~ zero(in2(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(657,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(h1(f)))
| ~ connection(outs(h1(f)),in2(h2(f)))
| ~ zero(in2(h2(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outs(h1(f)),in2(h2(f)))
| zero(outs(h1(f)))
| ~ zero(in2(h2(f))) ) ),
inference(monotonicity,[status(thm)],[656]) ).
tff(658,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(h1(f)))
| ~ connection(outs(h1(f)),in2(h2(f)))
| ~ zero(in2(h2(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outs(h1(f)),in2(h2(f)))
| zero(outs(h1(f)))
| ~ zero(in2(h2(f))) ) ),
inference(transitivity,[status(thm)],[657,655]) ).
tff(659,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(h1(f)))
| ~ connection(outs(h1(f)),in2(h2(f)))
| ~ zero(in2(h2(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(660,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outs(h1(f)),in2(h2(f)))
| zero(outs(h1(f)))
| ~ zero(in2(h2(f))) ),
inference(modus_ponens,[status(thm)],[659,658]) ).
tff(661,plain,
( zero(outs(h1(f)))
| ~ zero(in2(h2(f))) ),
inference(unit_resolution,[status(thm)],[660,532,404]) ).
tff(662,plain,
~ zero(in2(h2(f))),
inference(unit_resolution,[status(thm)],[661,654]) ).
tff(663,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(and2(h2(f))))
| ~ zero(in2(and2(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(and2(h2(f))))
| ~ zero(in2(and2(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(664,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(and2(h2(f))))
| ~ zero(in2(and2(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(665,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(and2(h2(f))))
| ~ zero(in2(and2(h2(f)))) ),
inference(modus_ponens,[status(thm)],[664,663]) ).
tff(666,plain,
( zero(in2(h2(f)))
| ~ zero(in2(and2(h2(f)))) ),
inference(unit_resolution,[status(thm)],[665,532,432]) ).
tff(667,plain,
~ zero(in2(and2(h2(f)))),
inference(unit_resolution,[status(thm)],[666,662]) ).
tff(668,plain,
( ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(in1(f))
| ~ one(in1(f)) )
<=> ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(in1(f))
| ~ one(in1(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(669,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(in1(f))
| ~ one(in1(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(670,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(in1(f))
| ~ one(in1(f)) ),
inference(modus_ponens,[status(thm)],[669,668]) ).
tff(671,plain,
~ zero(in1(f)),
inference(unit_resolution,[status(thm)],[670,518,454]) ).
tff(672,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| ~ zero(in1(h2(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| ~ zero(in1(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(673,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| ~ zero(in1(h2(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(674,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| ~ zero(in1(h2(f))) ),
inference(modus_ponens,[status(thm)],[673,672]) ).
tff(675,plain,
~ zero(in1(h2(f))),
inference(unit_resolution,[status(thm)],[674,532,671,451]) ).
tff(676,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(h2(f)))
| ~ connection(in1(h2(f)),in1(and2(h2(f))))
| ~ zero(in1(and2(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(h2(f)))
| ~ connection(in1(h2(f)),in1(and2(h2(f))))
| ~ zero(in1(and2(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(677,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(h2(f)))
| ~ connection(in1(h2(f)),in1(and2(h2(f))))
| ~ zero(in1(and2(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(678,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(h2(f)))
| ~ connection(in1(h2(f)),in1(and2(h2(f))))
| ~ zero(in1(and2(h2(f)))) ),
inference(modus_ponens,[status(thm)],[677,676]) ).
tff(679,plain,
~ zero(in1(and2(h2(f)))),
inference(unit_resolution,[status(thm)],[678,532,466,675]) ).
tff(680,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| ~ zero(out1(and2(h2(f))))
| zero(in2(and2(h2(f))))
| zero(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f))) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| ~ zero(out1(and2(h2(f))))
| zero(in2(and2(h2(f))))
| zero(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(681,plain,
( ( zero(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f)))
| zero(in2(and2(h2(f))))
| ~ zero(out1(and2(h2(f)))) )
<=> ( ~ zero(out1(and2(h2(f))))
| zero(in2(and2(h2(f))))
| zero(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(682,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f)))
| zero(in2(and2(h2(f))))
| ~ zero(out1(and2(h2(f)))) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| ~ zero(out1(and2(h2(f))))
| zero(in2(and2(h2(f))))
| zero(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f))) ) ),
inference(monotonicity,[status(thm)],[681]) ).
tff(683,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f)))
| zero(in2(and2(h2(f))))
| ~ zero(out1(and2(h2(f)))) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| ~ zero(out1(and2(h2(f))))
| zero(in2(and2(h2(f))))
| zero(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f))) ) ),
inference(transitivity,[status(thm)],[682,680]) ).
tff(684,plain,
( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f)))
| zero(in2(and2(h2(f))))
| ~ zero(out1(and2(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(685,plain,
( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| ~ zero(out1(and2(h2(f))))
| zero(in2(and2(h2(f))))
| zero(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f))) ),
inference(modus_ponens,[status(thm)],[684,683]) ).
tff(686,plain,
( ~ zero(out1(and2(h2(f))))
| zero(in2(and2(h2(f)))) ),
inference(unit_resolution,[status(thm)],[685,638,489,679]) ).
tff(687,plain,
~ zero(out1(and2(h2(f)))),
inference(unit_resolution,[status(thm)],[686,667]) ).
tff(688,plain,
^ [X: $i] :
refl(
( ( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
<=> ( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ) )),
inference(bind,[status(th)],]) ).
tff(689,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ) ),
inference(quant_intro,[status(thm)],[688]) ).
tff(690,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(691,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_connection_outc_out1and2) ).
tff(692,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
inference(modus_ponens,[status(thm)],[691,690]) ).
tff(693,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
inference(skolemize,[status(sab)],[692]) ).
tff(694,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
inference(modus_ponens,[status(thm)],[693,689]) ).
tff(695,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h2(f))
| connection(outc(h2(f)),out1(and2(h2(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h2(f))
| connection(outc(h2(f)),out1(and2(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(696,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h2(f))
| connection(outc(h2(f)),out1(and2(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(697,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h2(f))
| connection(outc(h2(f)),out1(and2(h2(f)))) ),
inference(modus_ponens,[status(thm)],[696,695]) ).
tff(698,plain,
( ~ halfadder(h2(f))
| connection(outc(h2(f)),out1(and2(h2(f)))) ),
inference(unit_resolution,[status(thm)],[697,694]) ).
tff(699,plain,
connection(outc(h2(f)),out1(and2(h2(f)))),
inference(unit_resolution,[status(thm)],[698,420]) ).
tff(700,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(h2(f)))
| zero(out1(and2(h2(f))))
| ~ connection(outc(h2(f)),out1(and2(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(h2(f)))
| zero(out1(and2(h2(f))))
| ~ connection(outc(h2(f)),out1(and2(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(701,plain,
( ( zero(out1(and2(h2(f))))
| ~ zero(outc(h2(f)))
| ~ connection(outc(h2(f)),out1(and2(h2(f)))) )
<=> ( ~ zero(outc(h2(f)))
| zero(out1(and2(h2(f))))
| ~ connection(outc(h2(f)),out1(and2(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(702,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(and2(h2(f))))
| ~ zero(outc(h2(f)))
| ~ connection(outc(h2(f)),out1(and2(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(h2(f)))
| zero(out1(and2(h2(f))))
| ~ connection(outc(h2(f)),out1(and2(h2(f)))) ) ),
inference(monotonicity,[status(thm)],[701]) ).
tff(703,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(and2(h2(f))))
| ~ zero(outc(h2(f)))
| ~ connection(outc(h2(f)),out1(and2(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(h2(f)))
| zero(out1(and2(h2(f))))
| ~ connection(outc(h2(f)),out1(and2(h2(f)))) ) ),
inference(transitivity,[status(thm)],[702,700]) ).
tff(704,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(and2(h2(f))))
| ~ zero(outc(h2(f)))
| ~ connection(outc(h2(f)),out1(and2(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(705,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(h2(f)))
| zero(out1(and2(h2(f))))
| ~ connection(outc(h2(f)),out1(and2(h2(f)))) ),
inference(modus_ponens,[status(thm)],[704,703]) ).
tff(706,plain,
( ~ zero(outc(h2(f)))
| zero(out1(and2(h2(f)))) ),
inference(unit_resolution,[status(thm)],[705,158,699]) ).
tff(707,plain,
~ zero(outc(h2(f))),
inference(unit_resolution,[status(thm)],[706,687]) ).
tff(708,plain,
^ [X: $i] :
refl(
( ( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) )
<=> ( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) ) )),
inference(bind,[status(th)],]) ).
tff(709,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) ) ),
inference(quant_intro,[status(thm)],[708]) ).
tff(710,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(711,axiom,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_connection_outch2_in1or1) ).
tff(712,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) ),
inference(modus_ponens,[status(thm)],[711,710]) ).
tff(713,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) ),
inference(skolemize,[status(sab)],[712]) ).
tff(714,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) ),
inference(modus_ponens,[status(thm)],[713,709]) ).
tff(715,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) )
| ~ fulladder(f)
| connection(outc(h2(f)),in1(or1(f))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) )
| ~ fulladder(f)
| connection(outc(h2(f)),in1(or1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(716,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) )
| ~ fulladder(f)
| connection(outc(h2(f)),in1(or1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(717,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) )
| ~ fulladder(f)
| connection(outc(h2(f)),in1(or1(f))) ),
inference(modus_ponens,[status(thm)],[716,715]) ).
tff(718,plain,
connection(outc(h2(f)),in1(or1(f))),
inference(unit_resolution,[status(thm)],[717,714,3]) ).
tff(719,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outc(h2(f)),in1(or1(f)))
| zero(outc(h2(f)))
| ~ zero(in1(or1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outc(h2(f)),in1(or1(f)))
| zero(outc(h2(f)))
| ~ zero(in1(or1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(720,plain,
( ( zero(outc(h2(f)))
| ~ connection(outc(h2(f)),in1(or1(f)))
| ~ zero(in1(or1(f))) )
<=> ( ~ connection(outc(h2(f)),in1(or1(f)))
| zero(outc(h2(f)))
| ~ zero(in1(or1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(721,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outc(h2(f)))
| ~ connection(outc(h2(f)),in1(or1(f)))
| ~ zero(in1(or1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outc(h2(f)),in1(or1(f)))
| zero(outc(h2(f)))
| ~ zero(in1(or1(f))) ) ),
inference(monotonicity,[status(thm)],[720]) ).
tff(722,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outc(h2(f)))
| ~ connection(outc(h2(f)),in1(or1(f)))
| ~ zero(in1(or1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outc(h2(f)),in1(or1(f)))
| zero(outc(h2(f)))
| ~ zero(in1(or1(f))) ) ),
inference(transitivity,[status(thm)],[721,719]) ).
tff(723,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outc(h2(f)))
| ~ connection(outc(h2(f)),in1(or1(f)))
| ~ zero(in1(or1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(724,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outc(h2(f)),in1(or1(f)))
| zero(outc(h2(f)))
| ~ zero(in1(or1(f))) ),
inference(modus_ponens,[status(thm)],[723,722]) ).
tff(725,plain,
( zero(outc(h2(f)))
| ~ zero(in1(or1(f))) ),
inference(unit_resolution,[status(thm)],[724,532,718]) ).
tff(726,plain,
~ zero(in1(or1(f))),
inference(unit_resolution,[status(thm)],[725,707]) ).
tff(727,plain,
^ [X: $i] :
refl(
( ( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
<=> ( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ) )),
inference(bind,[status(th)],]) ).
tff(728,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ) ),
inference(quant_intro,[status(thm)],[727]) ).
tff(729,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(730,axiom,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_connection_outc_out1or1) ).
tff(731,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ),
inference(modus_ponens,[status(thm)],[730,729]) ).
tff(732,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ),
inference(skolemize,[status(sab)],[731]) ).
tff(733,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ),
inference(modus_ponens,[status(thm)],[732,728]) ).
tff(734,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
| ~ fulladder(f)
| connection(outc(f),out1(or1(f))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
| ~ fulladder(f)
| connection(outc(f),out1(or1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(735,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
| ~ fulladder(f)
| connection(outc(f),out1(or1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(736,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
| ~ fulladder(f)
| connection(outc(f),out1(or1(f))) ),
inference(modus_ponens,[status(thm)],[735,734]) ).
tff(737,plain,
connection(outc(f),out1(or1(f))),
inference(unit_resolution,[status(thm)],[736,733,3]) ).
tff(738,plain,
( zero(outc(f))
<=> zero(outc(f)) ),
inference(rewrite,[status(thm)],]) ).
tff(739,axiom,
zero(outc(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outc_0) ).
tff(740,plain,
zero(outc(f)),
inference(modus_ponens,[status(thm)],[739,738]) ).
tff(741,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(f))
| ~ connection(outc(f),out1(or1(f)))
| zero(out1(or1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(f))
| ~ connection(outc(f),out1(or1(f)))
| zero(out1(or1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(742,plain,
( ( zero(out1(or1(f)))
| ~ zero(outc(f))
| ~ connection(outc(f),out1(or1(f))) )
<=> ( ~ zero(outc(f))
| ~ connection(outc(f),out1(or1(f)))
| zero(out1(or1(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(743,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(or1(f)))
| ~ zero(outc(f))
| ~ connection(outc(f),out1(or1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(f))
| ~ connection(outc(f),out1(or1(f)))
| zero(out1(or1(f))) ) ),
inference(monotonicity,[status(thm)],[742]) ).
tff(744,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(or1(f)))
| ~ zero(outc(f))
| ~ connection(outc(f),out1(or1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(f))
| ~ connection(outc(f),out1(or1(f)))
| zero(out1(or1(f))) ) ),
inference(transitivity,[status(thm)],[743,741]) ).
tff(745,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(or1(f)))
| ~ zero(outc(f))
| ~ connection(outc(f),out1(or1(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(746,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(f))
| ~ connection(outc(f),out1(or1(f)))
| zero(out1(or1(f))) ),
inference(modus_ponens,[status(thm)],[745,744]) ).
tff(747,plain,
zero(out1(or1(f))),
inference(unit_resolution,[status(thm)],[746,158,740,737]) ).
tff(748,plain,
^ [K: $i] :
refl(
( ( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
<=> ( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(749,plain,
( ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
<=> ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) ),
inference(quant_intro,[status(thm)],[748]) ).
tff(750,plain,
( ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
<=> ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) ),
inference(rewrite,[status(thm)],]) ).
tff(751,plain,
^ [K: $i] :
rewrite(
( ( ~ or_ok(K)
| ~ zero(out1(K))
| zero(in1(K)) )
<=> ( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(752,plain,
( ! [K: $i] :
( ~ or_ok(K)
| ~ zero(out1(K))
| zero(in1(K)) )
<=> ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) ),
inference(quant_intro,[status(thm)],[751]) ).
tff(753,axiom,
! [K: $i] :
( ~ or_ok(K)
| ~ zero(out1(K))
| zero(in1(K)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',or_0_0x) ).
tff(754,plain,
! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[753,752]) ).
tff(755,plain,
! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[754,750]) ).
tff(756,plain,
! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(skolemize,[status(sab)],[755]) ).
tff(757,plain,
! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[756,749]) ).
tff(758,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| zero(in1(or1(f)))
| ~ zero(out1(or1(f)))
| ~ or_ok(or1(f)) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| zero(in1(or1(f)))
| ~ zero(out1(or1(f)))
| ~ or_ok(or1(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(759,plain,
( ~ ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| zero(in1(or1(f)))
| ~ zero(out1(or1(f)))
| ~ or_ok(or1(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(760,plain,
( ~ ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| zero(in1(or1(f)))
| ~ zero(out1(or1(f)))
| ~ or_ok(or1(f)) ),
inference(modus_ponens,[status(thm)],[759,758]) ).
tff(761,plain,
( zero(in1(or1(f)))
| ~ or_ok(or1(f)) ),
inference(unit_resolution,[status(thm)],[760,757,747]) ).
tff(762,plain,
~ or_ok(or1(f)),
inference(unit_resolution,[status(thm)],[761,726]) ).
tff(763,plain,
^ [X: $i] :
refl(
( ( logic_or(or1(X))
| ~ fulladder(X) )
<=> ( logic_or(or1(X))
| ~ fulladder(X) ) )),
inference(bind,[status(th)],]) ).
tff(764,plain,
( ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
<=> ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ) ),
inference(quant_intro,[status(thm)],[763]) ).
tff(765,plain,
( ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
<=> ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(766,plain,
^ [X: $i] :
rewrite(
( ( ~ fulladder(X)
| logic_or(or1(X)) )
<=> ( logic_or(or1(X))
| ~ fulladder(X) ) )),
inference(bind,[status(th)],]) ).
tff(767,plain,
( ! [X: $i] :
( ~ fulladder(X)
| logic_or(or1(X)) )
<=> ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ) ),
inference(quant_intro,[status(thm)],[766]) ).
tff(768,axiom,
! [X: $i] :
( ~ fulladder(X)
| logic_or(or1(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_or1) ).
tff(769,plain,
! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[768,767]) ).
tff(770,plain,
! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[769,765]) ).
tff(771,plain,
! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ),
inference(skolemize,[status(sab)],[770]) ).
tff(772,plain,
! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[771,764]) ).
tff(773,plain,
( ( ~ ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
| logic_or(or1(f))
| ~ fulladder(f) )
<=> ( ~ ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
| logic_or(or1(f))
| ~ fulladder(f) ) ),
inference(rewrite,[status(thm)],]) ).
tff(774,plain,
( ~ ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
| logic_or(or1(f))
| ~ fulladder(f) ),
inference(quant_inst,[status(thm)],]) ).
tff(775,plain,
( ~ ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
| logic_or(or1(f))
| ~ fulladder(f) ),
inference(modus_ponens,[status(thm)],[774,773]) ).
tff(776,plain,
logic_or(or1(f)),
inference(unit_resolution,[status(thm)],[775,772,3]) ).
tff(777,plain,
( ( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(f))
| or_ok(or1(f))
| ~ logic_or(or1(f)) )
<=> ( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(f))
| or_ok(or1(f))
| ~ logic_or(or1(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(778,plain,
( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(f))
| or_ok(or1(f))
| ~ logic_or(or1(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(779,plain,
( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(f))
| or_ok(or1(f))
| ~ logic_or(or1(f)) ),
inference(modus_ponens,[status(thm)],[778,777]) ).
tff(780,plain,
( abnormal(or1(f))
| or_ok(or1(f)) ),
inference(unit_resolution,[status(thm)],[779,95,776]) ).
tff(781,plain,
abnormal(or1(f)),
inference(unit_resolution,[status(thm)],[780,762]) ).
tff(782,plain,
( ( ~ abnormal(or1(f))
| ~ abnormal(not1(h2(f))) )
<=> ( ~ abnormal(or1(f))
| ~ abnormal(not1(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(783,axiom,
( ~ abnormal(or1(f))
| ~ abnormal(not1(h2(f))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_or1_not1h2) ).
tff(784,plain,
( ~ abnormal(or1(f))
| ~ abnormal(not1(h2(f))) ),
inference(modus_ponens,[status(thm)],[783,782]) ).
tff(785,plain,
~ abnormal(not1(h2(f))),
inference(unit_resolution,[status(thm)],[784,781]) ).
tff(786,plain,
( ( ~ ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
| abnormal(not1(h2(f)))
| not_ok(not1(h2(f)))
| ~ logic_not(not1(h2(f))) )
<=> ( ~ ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
| abnormal(not1(h2(f)))
| not_ok(not1(h2(f)))
| ~ logic_not(not1(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(787,plain,
( ~ ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
| abnormal(not1(h2(f)))
| not_ok(not1(h2(f)))
| ~ logic_not(not1(h2(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(788,plain,
( ~ ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
| abnormal(not1(h2(f)))
| not_ok(not1(h2(f)))
| ~ logic_not(not1(h2(f))) ),
inference(modus_ponens,[status(thm)],[787,786]) ).
tff(789,plain,
not_ok(not1(h2(f))),
inference(unit_resolution,[status(thm)],[788,279,785,511]) ).
tff(790,plain,
^ [K: $i] :
refl(
( ( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) )
<=> ( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(791,plain,
( ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) )
<=> ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) ) ),
inference(quant_intro,[status(thm)],[790]) ).
tff(792,plain,
( ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) )
<=> ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) ) ),
inference(rewrite,[status(thm)],]) ).
tff(793,plain,
^ [K: $i] :
rewrite(
( ( ~ not_ok(K)
| ~ one(in1(K))
| zero(out1(K)) )
<=> ( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(794,plain,
( ! [K: $i] :
( ~ not_ok(K)
| ~ one(in1(K))
| zero(out1(K)) )
<=> ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) ) ),
inference(quant_intro,[status(thm)],[793]) ).
tff(795,axiom,
! [K: $i] :
( ~ not_ok(K)
| ~ one(in1(K))
| zero(out1(K)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',not_1_0_fw) ).
tff(796,plain,
! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[795,794]) ).
tff(797,plain,
! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[796,792]) ).
tff(798,plain,
! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) ),
inference(skolemize,[status(sab)],[797]) ).
tff(799,plain,
! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[798,791]) ).
tff(800,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) )
| ~ one(in1(not1(h2(f))))
| ~ not_ok(not1(h2(f)))
| zero(out1(not1(h2(f)))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) )
| ~ one(in1(not1(h2(f))))
| ~ not_ok(not1(h2(f)))
| zero(out1(not1(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(801,plain,
( ( zero(out1(not1(h2(f))))
| ~ one(in1(not1(h2(f))))
| ~ not_ok(not1(h2(f))) )
<=> ( ~ one(in1(not1(h2(f))))
| ~ not_ok(not1(h2(f)))
| zero(out1(not1(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(802,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) )
| zero(out1(not1(h2(f))))
| ~ one(in1(not1(h2(f))))
| ~ not_ok(not1(h2(f))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) )
| ~ one(in1(not1(h2(f))))
| ~ not_ok(not1(h2(f)))
| zero(out1(not1(h2(f)))) ) ),
inference(monotonicity,[status(thm)],[801]) ).
tff(803,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) )
| zero(out1(not1(h2(f))))
| ~ one(in1(not1(h2(f))))
| ~ not_ok(not1(h2(f))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) )
| ~ one(in1(not1(h2(f))))
| ~ not_ok(not1(h2(f)))
| zero(out1(not1(h2(f)))) ) ),
inference(transitivity,[status(thm)],[802,800]) ).
tff(804,plain,
( ~ ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) )
| zero(out1(not1(h2(f))))
| ~ one(in1(not1(h2(f))))
| ~ not_ok(not1(h2(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(805,plain,
( ~ ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) )
| ~ one(in1(not1(h2(f))))
| ~ not_ok(not1(h2(f)))
| zero(out1(not1(h2(f)))) ),
inference(modus_ponens,[status(thm)],[804,803]) ).
tff(806,plain,
( ~ one(in1(not1(h2(f))))
| ~ not_ok(not1(h2(f)))
| zero(out1(not1(h2(f)))) ),
inference(unit_resolution,[status(thm)],[805,799]) ).
tff(807,plain,
zero(out1(not1(h2(f)))),
inference(unit_resolution,[status(thm)],[806,789,507]) ).
tff(808,plain,
( ( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h2(f)))
| ~ halfadder(h2(f)) )
<=> ( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h2(f)))
| ~ halfadder(h2(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(809,plain,
( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h2(f)))
| ~ halfadder(h2(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(810,plain,
( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h2(f)))
| ~ halfadder(h2(f)) ),
inference(modus_ponens,[status(thm)],[809,808]) ).
tff(811,plain,
logic_and(and1(h2(f))),
inference(unit_resolution,[status(thm)],[810,329,420]) ).
tff(812,plain,
( ( ~ abnormal(or1(f))
| ~ abnormal(and1(h2(f))) )
<=> ( ~ abnormal(or1(f))
| ~ abnormal(and1(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(813,axiom,
( ~ abnormal(or1(f))
| ~ abnormal(and1(h2(f))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_or1_and1h2) ).
tff(814,plain,
( ~ abnormal(or1(f))
| ~ abnormal(and1(h2(f))) ),
inference(modus_ponens,[status(thm)],[813,812]) ).
tff(815,plain,
~ abnormal(and1(h2(f))),
inference(unit_resolution,[status(thm)],[814,781]) ).
tff(816,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h2(f)))
| and_ok(and1(h2(f)))
| ~ logic_and(and1(h2(f))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h2(f)))
| and_ok(and1(h2(f)))
| ~ logic_and(and1(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(817,plain,
( ( and_ok(and1(h2(f)))
| abnormal(and1(h2(f)))
| ~ logic_and(and1(h2(f))) )
<=> ( abnormal(and1(h2(f)))
| and_ok(and1(h2(f)))
| ~ logic_and(and1(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(818,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and1(h2(f)))
| abnormal(and1(h2(f)))
| ~ logic_and(and1(h2(f))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h2(f)))
| and_ok(and1(h2(f)))
| ~ logic_and(and1(h2(f))) ) ),
inference(monotonicity,[status(thm)],[817]) ).
tff(819,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and1(h2(f)))
| abnormal(and1(h2(f)))
| ~ logic_and(and1(h2(f))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h2(f)))
| and_ok(and1(h2(f)))
| ~ logic_and(and1(h2(f))) ) ),
inference(transitivity,[status(thm)],[818,816]) ).
tff(820,plain,
( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and1(h2(f)))
| abnormal(and1(h2(f)))
| ~ logic_and(and1(h2(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(821,plain,
( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h2(f)))
| and_ok(and1(h2(f)))
| ~ logic_and(and1(h2(f))) ),
inference(modus_ponens,[status(thm)],[820,819]) ).
tff(822,plain,
and_ok(and1(h2(f))),
inference(unit_resolution,[status(thm)],[821,212,815,811]) ).
tff(823,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
| ~ halfadder(h2(f))
| connection(outs(h2(f)),out1(and1(h2(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
| ~ halfadder(h2(f))
| connection(outs(h2(f)),out1(and1(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(824,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
| ~ halfadder(h2(f))
| connection(outs(h2(f)),out1(and1(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(825,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
| ~ halfadder(h2(f))
| connection(outs(h2(f)),out1(and1(h2(f)))) ),
inference(modus_ponens,[status(thm)],[824,823]) ).
tff(826,plain,
connection(outs(h2(f)),out1(and1(h2(f)))),
inference(unit_resolution,[status(thm)],[825,370,420]) ).
tff(827,plain,
^ [X: $i] :
refl(
( ( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) )
<=> ( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) ) )),
inference(bind,[status(th)],]) ).
tff(828,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) ) ),
inference(quant_intro,[status(thm)],[827]) ).
tff(829,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(830,axiom,
! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_connection_outs_outsh2) ).
tff(831,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) ),
inference(modus_ponens,[status(thm)],[830,829]) ).
tff(832,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) ),
inference(skolemize,[status(sab)],[831]) ).
tff(833,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) ),
inference(modus_ponens,[status(thm)],[832,828]) ).
tff(834,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) )
| ~ fulladder(f)
| connection(outs(f),outs(h2(f))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) )
| ~ fulladder(f)
| connection(outs(f),outs(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(835,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) )
| ~ fulladder(f)
| connection(outs(f),outs(h2(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(836,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) )
| ~ fulladder(f)
| connection(outs(f),outs(h2(f))) ),
inference(modus_ponens,[status(thm)],[835,834]) ).
tff(837,plain,
connection(outs(f),outs(h2(f))),
inference(unit_resolution,[status(thm)],[836,833,3]) ).
tff(838,plain,
( one(outs(f))
<=> one(outs(f)) ),
inference(rewrite,[status(thm)],]) ).
tff(839,axiom,
one(outs(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outs_1) ).
tff(840,plain,
one(outs(f)),
inference(modus_ponens,[status(thm)],[839,838]) ).
tff(841,plain,
( ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(outs(f))
| ~ one(outs(f)) )
<=> ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(outs(f))
| ~ one(outs(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(842,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(outs(f))
| ~ one(outs(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(843,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(outs(f))
| ~ one(outs(f)) ),
inference(modus_ponens,[status(thm)],[842,841]) ).
tff(844,plain,
~ zero(outs(f)),
inference(unit_resolution,[status(thm)],[843,518,840]) ).
tff(845,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(f))
| ~ connection(outs(f),outs(h2(f)))
| ~ zero(outs(h2(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(f))
| ~ connection(outs(f),outs(h2(f)))
| ~ zero(outs(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(846,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(f))
| ~ connection(outs(f),outs(h2(f)))
| ~ zero(outs(h2(f))) ),
inference(quant_inst,[status(thm)],]) ).
tff(847,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(f))
| ~ connection(outs(f),outs(h2(f)))
| ~ zero(outs(h2(f))) ),
inference(modus_ponens,[status(thm)],[846,845]) ).
tff(848,plain,
~ zero(outs(h2(f))),
inference(unit_resolution,[status(thm)],[847,532,844,837]) ).
tff(849,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(h2(f)))
| ~ connection(outs(h2(f)),out1(and1(h2(f))))
| ~ zero(out1(and1(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(h2(f)))
| ~ connection(outs(h2(f)),out1(and1(h2(f))))
| ~ zero(out1(and1(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(850,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(h2(f)))
| ~ connection(outs(h2(f)),out1(and1(h2(f))))
| ~ zero(out1(and1(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(851,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(h2(f)))
| ~ connection(outs(h2(f)),out1(and1(h2(f))))
| ~ zero(out1(and1(h2(f)))) ),
inference(modus_ponens,[status(thm)],[850,849]) ).
tff(852,plain,
~ zero(out1(and1(h2(f)))),
inference(unit_resolution,[status(thm)],[851,532,848,826]) ).
tff(853,plain,
^ [K: $i] :
refl(
( ( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
<=> ( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) ) )),
inference(bind,[status(th)],]) ).
tff(854,plain,
( ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
<=> ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) ) ),
inference(quant_intro,[status(thm)],[853]) ).
tff(855,plain,
( ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
<=> ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(856,plain,
^ [K: $i] :
rewrite(
( ( ~ and_ok(K)
| ~ zero(in2(K))
| zero(out1(K)) )
<=> ( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) ) )),
inference(bind,[status(th)],]) ).
tff(857,plain,
( ! [K: $i] :
( ~ and_ok(K)
| ~ zero(in2(K))
| zero(out1(K)) )
<=> ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) ) ),
inference(quant_intro,[status(thm)],[856]) ).
tff(858,axiom,
! [K: $i] :
( ~ and_ok(K)
| ~ zero(in2(K))
| zero(out1(K)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',and_x0_0) ).
tff(859,plain,
! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) ),
inference(modus_ponens,[status(thm)],[858,857]) ).
tff(860,plain,
! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) ),
inference(modus_ponens,[status(thm)],[859,855]) ).
tff(861,plain,
! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) ),
inference(skolemize,[status(sab)],[860]) ).
tff(862,plain,
! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) ),
inference(modus_ponens,[status(thm)],[861,854]) ).
tff(863,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| ~ zero(in2(and1(h2(f))))
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| ~ zero(in2(and1(h2(f))))
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(864,plain,
( ( zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f)))
| ~ zero(in2(and1(h2(f)))) )
<=> ( ~ zero(in2(and1(h2(f))))
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(865,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f)))
| ~ zero(in2(and1(h2(f)))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| ~ zero(in2(and1(h2(f))))
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) ) ),
inference(monotonicity,[status(thm)],[864]) ).
tff(866,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f)))
| ~ zero(in2(and1(h2(f)))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| ~ zero(in2(and1(h2(f))))
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) ) ),
inference(transitivity,[status(thm)],[865,863]) ).
tff(867,plain,
( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f)))
| ~ zero(in2(and1(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(868,plain,
( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| ~ zero(in2(and1(h2(f))))
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) ),
inference(modus_ponens,[status(thm)],[867,866]) ).
tff(869,plain,
( ~ zero(in2(and1(h2(f))))
| ~ and_ok(and1(h2(f))) ),
inference(unit_resolution,[status(thm)],[868,862,852]) ).
tff(870,plain,
~ zero(in2(and1(h2(f)))),
inference(unit_resolution,[status(thm)],[869,822]) ).
tff(871,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
| ~ halfadder(h2(f))
| connection(out1(not1(h2(f))),in2(and1(h2(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
| ~ halfadder(h2(f))
| connection(out1(not1(h2(f))),in2(and1(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(872,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
| ~ halfadder(h2(f))
| connection(out1(not1(h2(f))),in2(and1(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(873,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
| ~ halfadder(h2(f))
| connection(out1(not1(h2(f))),in2(and1(h2(f)))) ),
inference(modus_ponens,[status(thm)],[872,871]) ).
tff(874,plain,
connection(out1(not1(h2(f))),in2(and1(h2(f)))),
inference(unit_resolution,[status(thm)],[873,309,420]) ).
tff(875,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(and1(h2(f))))
| ~ zero(out1(not1(h2(f))))
| ~ connection(out1(not1(h2(f))),in2(and1(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(and1(h2(f))))
| ~ zero(out1(not1(h2(f))))
| ~ connection(out1(not1(h2(f))),in2(and1(h2(f)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(876,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(and1(h2(f))))
| ~ zero(out1(not1(h2(f))))
| ~ connection(out1(not1(h2(f))),in2(and1(h2(f)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(877,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(and1(h2(f))))
| ~ zero(out1(not1(h2(f))))
| ~ connection(out1(not1(h2(f))),in2(and1(h2(f)))) ),
inference(modus_ponens,[status(thm)],[876,875]) ).
tff(878,plain,
( zero(in2(and1(h2(f))))
| ~ zero(out1(not1(h2(f)))) ),
inference(unit_resolution,[status(thm)],[877,158,874]) ).
tff(879,plain,
$false,
inference(unit_resolution,[status(thm)],[878,870,807]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HWV006-2 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 22:18:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------