%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV007-2 : TPTP v9.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 Jun 21 05:08:53 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 291
% Syntax : Number of formulae : 666 ( 133 unt; 0 typ; 0 def)
% Number of atoms : 3399 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 4868 (2242 ~;2329 |; 0 &)
% ( 297 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 107 ( 107 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 872 ( 813 !; 0 ?; 872 :)
% Comments :
%------------------------------------------------------------------------------
tff(zero_type,type,
zero: $i > $o ).
tff(outs_type,type,
outs: $i > $i ).
tff(h1_type,type,
h1: $i > $i ).
tff(f_type,type,
f: $i ).
tff(out1_type,type,
out1: $i > $i ).
tff(and1_type,type,
and1: $i > $i ).
tff(and_ok_type,type,
and_ok: $i > $o ).
tff(logic_and_type,type,
logic_and: $i > $o ).
tff(halfadder_type,type,
halfadder: $i > $o ).
tff(fulladder_type,type,
fulladder: $i > $o ).
tff(abnormal_type,type,
abnormal: $i > $o ).
tff(or1_type,type,
or1: $i > $i ).
tff(or_ok_type,type,
or_ok: $i > $o ).
tff(in2_type,type,
in2: $i > $i ).
tff(outc_type,type,
outc: $i > $i ).
tff(and2_type,type,
and2: $i > $i ).
tff(in1_type,type,
in1: $i > $i ).
tff(connection_type,type,
connection: ( $i * $i ) > $o ).
tff(one_type,type,
one: $i > $o ).
tff(inc_type,type,
inc: $i > $i ).
tff(logic_or_type,type,
logic_or: $i > $o ).
tff(not1_type,type,
not1: $i > $i ).
tff(not_ok_type,type,
not_ok: $i > $o ).
tff(logic_not_type,type,
logic_not: $i > $o ).
tff(h2_type,type,
h2: $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(( ( halfadder(h1(X))
| ~ fulladder(X) )
<=> ( halfadder(h1(X))
| ~ fulladder(X) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
<=> ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
<=> ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [X: $i] :
rewrite(( ( ~ fulladder(X)
| halfadder(h1(X)) )
<=> ( halfadder(h1(X))
| ~ fulladder(X) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X: $i] :
( ~ fulladder(X)
| halfadder(h1(X)) )
<=> ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h1(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_halfadder1) ).
tff(10,plain,
! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,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(15,plain,
( ~ ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
| halfadder(h1(f))
| ~ fulladder(f) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
| halfadder(h1(f))
| ~ fulladder(f) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
halfadder(h1(f)),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [X: $i] :
refl(( ( logic_and(and1(X))
| ~ halfadder(X) )
<=> ( logic_and(and1(X))
| ~ halfadder(X) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
<=> ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
<=> ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [X: $i] :
rewrite(( ( ~ halfadder(X)
| logic_and(and1(X)) )
<=> ( logic_and(and1(X))
| ~ halfadder(X) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_and(and1(X)) )
<=> ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and1(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_and1) ).
tff(24,plain,
! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,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(29,plain,
( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h1(f)))
| ~ halfadder(h1(f)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h1(f)))
| ~ halfadder(h1(f)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
logic_and(and1(h1(f))),
inference(unit_resolution,[status(thm)],[30,27,17]) ).
tff(32,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(33,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)],[32]) ).
tff(34,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(35,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(36,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,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(40,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(41,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
| ~ fulladder(f)
| connection(in2(f),in1(h1(f))) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
connection(in2(f),in1(h1(f))),
inference(unit_resolution,[status(thm)],[41,38,3]) ).
tff(43,plain,
( one(in2(f))
<=> one(in2(f)) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
one(in2(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in2_0) ).
tff(45,plain,
one(in2(f)),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
^ [P: $i] :
refl(( ( ~ zero(P)
| ~ one(P) )
<=> ( ~ zero(P)
| ~ one(P) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
<=> ! [P: $i] :
( ~ zero(P)
| ~ one(P) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
<=> ! [P: $i] :
( ~ zero(P)
| ~ one(P) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
! [P: $i] :
( ~ zero(P)
| ~ one(P) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',unique_value) ).
tff(50,plain,
! [P: $i] :
( ~ zero(P)
| ~ one(P) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [P: $i] :
( ~ zero(P)
| ~ one(P) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [P: $i] :
( ~ zero(P)
| ~ one(P) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,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(54,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(in2(f))
| ~ one(in2(f)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(in2(f))
| ~ one(in2(f)) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
~ zero(in2(f)),
inference(unit_resolution,[status(thm)],[55,52,45]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,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(61,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)],[60]) ).
tff(62,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(63,plain,
! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| ~ zero(in1(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| ~ zero(in1(h1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| ~ zero(in1(h1(f))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| ~ zero(in1(h1(f))) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
~ zero(in1(h1(f))),
inference(unit_resolution,[status(thm)],[69,66,56,42]) ).
tff(71,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(72,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)],[71]) ).
tff(73,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(74,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(75,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,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(79,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(80,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)],[79,78]) ).
tff(81,plain,
( ~ halfadder(h1(f))
| connection(in1(h1(f)),in1(and2(h1(f)))) ),
inference(unit_resolution,[status(thm)],[80,77]) ).
tff(82,plain,
connection(in1(h1(f)),in1(and2(h1(f)))),
inference(unit_resolution,[status(thm)],[81,17]) ).
tff(83,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(h1(f)))
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| ~ zero(in1(and2(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(h1(f)))
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| ~ zero(in1(and2(h1(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(h1(f)))
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| ~ zero(in1(and2(h1(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(h1(f)))
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| ~ zero(in1(and2(h1(f)))) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
~ zero(in1(and2(h1(f)))),
inference(unit_resolution,[status(thm)],[85,66,82,70]) ).
tff(87,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(88,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)],[87]) ).
tff(89,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(90,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(91,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,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(95,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(96,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(inc(X),in2(h1(X))) )
| ~ fulladder(f)
| connection(inc(f),in2(h1(f))) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
connection(inc(f),in2(h1(f))),
inference(unit_resolution,[status(thm)],[96,93,3]) ).
tff(98,plain,
( one(inc(f))
<=> one(inc(f)) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,axiom,
one(inc(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inc_1) ).
tff(100,plain,
one(inc(f)),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,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(102,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(inc(f))
| ~ one(inc(f)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(inc(f))
| ~ one(inc(f)) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
~ zero(inc(f)),
inference(unit_resolution,[status(thm)],[103,52,100]) ).
tff(105,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(106,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(107,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)],[106,105]) ).
tff(108,plain,
~ zero(in2(h1(f))),
inference(unit_resolution,[status(thm)],[107,66,104,97]) ).
tff(109,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(110,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)],[109]) ).
tff(111,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(112,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(113,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) )
| ~ halfadder(h1(f))
| connection(in2(h1(f)),in2(and2(h1(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) )
| ~ halfadder(h1(f))
| connection(in2(h1(f)),in2(and2(h1(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) )
| ~ halfadder(h1(f))
| connection(in2(h1(f)),in2(and2(h1(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(and2(X))) )
| ~ halfadder(h1(f))
| connection(in2(h1(f)),in2(and2(h1(f)))) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
( ~ halfadder(h1(f))
| connection(in2(h1(f)),in2(and2(h1(f)))) ),
inference(unit_resolution,[status(thm)],[118,115]) ).
tff(120,plain,
connection(in2(h1(f)),in2(and2(h1(f)))),
inference(unit_resolution,[status(thm)],[119,17]) ).
tff(121,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(h1(f)))
| ~ connection(in2(h1(f)),in2(and2(h1(f))))
| ~ zero(in2(and2(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(h1(f)))
| ~ connection(in2(h1(f)),in2(and2(h1(f))))
| ~ zero(in2(and2(h1(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(h1(f)))
| ~ connection(in2(h1(f)),in2(and2(h1(f))))
| ~ zero(in2(and2(h1(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in2(h1(f)))
| ~ connection(in2(h1(f)),in2(and2(h1(f))))
| ~ zero(in2(and2(h1(f)))) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
~ zero(in2(and2(h1(f)))),
inference(unit_resolution,[status(thm)],[123,66,120,108]) ).
tff(125,plain,
^ [X: $i] :
refl(( ( ~ halfadder(X)
| logic_and(and2(X)) )
<=> ( ~ halfadder(X)
| logic_and(and2(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(126,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,axiom,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_and2) ).
tff(129,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ),
inference(skolemize,[status(sab)],[129]) ).
tff(131,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ),
inference(modus_ponens,[status(thm)],[130,126]) ).
tff(132,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(133,plain,
( ( ~ halfadder(h1(f))
| logic_and(and2(h1(f))) )
<=> ( logic_and(and2(h1(f)))
| ~ halfadder(h1(f)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,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)],[133]) ).
tff(135,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)],[134,132]) ).
tff(136,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| ~ halfadder(h1(f))
| logic_and(and2(h1(f))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h1(f)))
| ~ halfadder(h1(f)) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( logic_and(and2(h1(f)))
| ~ halfadder(h1(f)) ),
inference(unit_resolution,[status(thm)],[137,131]) ).
tff(139,plain,
logic_and(and2(h1(f))),
inference(unit_resolution,[status(thm)],[138,17]) ).
tff(140,plain,
( ~ abnormal(and2(h1(f)))
<=> ~ abnormal(and2(h1(f))) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,axiom,
~ abnormal(and2(h1(f))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_and2h1) ).
tff(142,plain,
~ abnormal(and2(h1(f))),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,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(144,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)],[143]) ).
tff(145,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(146,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(147,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)],[146]) ).
tff(148,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(149,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(modus_ponens,[status(thm)],[149,145]) ).
tff(151,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(skolemize,[status(sab)],[150]) ).
tff(152,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(modus_ponens,[status(thm)],[151,144]) ).
tff(153,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(154,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(155,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)],[154]) ).
tff(156,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)],[155,153]) ).
tff(157,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(158,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)],[157,156]) ).
tff(159,plain,
( and_ok(and2(h1(f)))
| ~ logic_and(and2(h1(f))) ),
inference(unit_resolution,[status(thm)],[158,152,142]) ).
tff(160,plain,
and_ok(and2(h1(f))),
inference(unit_resolution,[status(thm)],[159,139]) ).
tff(161,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(162,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)],[161]) ).
tff(163,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(164,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(165,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)],[164]) ).
tff(166,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(167,plain,
! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ),
inference(modus_ponens,[status(thm)],[167,163]) ).
tff(169,plain,
! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ),
inference(skolemize,[status(sab)],[168]) ).
tff(170,plain,
! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ),
inference(modus_ponens,[status(thm)],[169,162]) ).
tff(171,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| ~ zero(out1(and2(h1(f))))
| zero(in2(and2(h1(f))))
| zero(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| ~ zero(out1(and2(h1(f))))
| zero(in2(and2(h1(f))))
| zero(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,plain,
( ( zero(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f)))
| zero(in2(and2(h1(f))))
| ~ zero(out1(and2(h1(f)))) )
<=> ( ~ zero(out1(and2(h1(f))))
| zero(in2(and2(h1(f))))
| zero(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(173,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f)))
| zero(in2(and2(h1(f))))
| ~ zero(out1(and2(h1(f)))) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| ~ zero(out1(and2(h1(f))))
| zero(in2(and2(h1(f))))
| zero(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) ) ),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f)))
| zero(in2(and2(h1(f))))
| ~ zero(out1(and2(h1(f)))) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| ~ zero(out1(and2(h1(f))))
| zero(in2(and2(h1(f))))
| zero(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) ) ),
inference(transitivity,[status(thm)],[173,171]) ).
tff(175,plain,
( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f)))
| zero(in2(and2(h1(f))))
| ~ zero(out1(and2(h1(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| ~ zero(out1(and2(h1(f))))
| zero(in2(and2(h1(f))))
| zero(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
~ zero(out1(and2(h1(f)))),
inference(unit_resolution,[status(thm)],[176,170,160,124,86]) ).
tff(178,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(179,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)],[178]) ).
tff(180,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(181,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(182,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
inference(skolemize,[status(sab)],[182]) ).
tff(184,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
inference(modus_ponens,[status(thm)],[183,179]) ).
tff(185,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h1(f))
| connection(outc(h1(f)),out1(and2(h1(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h1(f))
| connection(outc(h1(f)),out1(and2(h1(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h1(f))
| connection(outc(h1(f)),out1(and2(h1(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(187,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h1(f))
| connection(outc(h1(f)),out1(and2(h1(f)))) ),
inference(modus_ponens,[status(thm)],[186,185]) ).
tff(188,plain,
( ~ halfadder(h1(f))
| connection(outc(h1(f)),out1(and2(h1(f)))) ),
inference(unit_resolution,[status(thm)],[187,184]) ).
tff(189,plain,
connection(outc(h1(f)),out1(and2(h1(f)))),
inference(unit_resolution,[status(thm)],[188,17]) ).
tff(190,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(191,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)],[190]) ).
tff(192,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(193,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(194,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)],[193]) ).
tff(195,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(196,plain,
! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
inference(modus_ponens,[status(thm)],[195,194]) ).
tff(197,plain,
! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
inference(modus_ponens,[status(thm)],[196,192]) ).
tff(198,plain,
! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
inference(skolemize,[status(sab)],[197]) ).
tff(199,plain,
! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
inference(modus_ponens,[status(thm)],[198,191]) ).
tff(200,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(h1(f)))
| zero(out1(and2(h1(f))))
| ~ connection(outc(h1(f)),out1(and2(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(h1(f)))
| zero(out1(and2(h1(f))))
| ~ connection(outc(h1(f)),out1(and2(h1(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,plain,
( ( zero(out1(and2(h1(f))))
| ~ zero(outc(h1(f)))
| ~ connection(outc(h1(f)),out1(and2(h1(f)))) )
<=> ( ~ zero(outc(h1(f)))
| zero(out1(and2(h1(f))))
| ~ connection(outc(h1(f)),out1(and2(h1(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(202,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(and2(h1(f))))
| ~ zero(outc(h1(f)))
| ~ connection(outc(h1(f)),out1(and2(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(h1(f)))
| zero(out1(and2(h1(f))))
| ~ connection(outc(h1(f)),out1(and2(h1(f)))) ) ),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(and2(h1(f))))
| ~ zero(outc(h1(f)))
| ~ connection(outc(h1(f)),out1(and2(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(h1(f)))
| zero(out1(and2(h1(f))))
| ~ connection(outc(h1(f)),out1(and2(h1(f)))) ) ),
inference(transitivity,[status(thm)],[202,200]) ).
tff(204,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(and2(h1(f))))
| ~ zero(outc(h1(f)))
| ~ connection(outc(h1(f)),out1(and2(h1(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(205,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outc(h1(f)))
| zero(out1(and2(h1(f))))
| ~ connection(outc(h1(f)),out1(and2(h1(f)))) ),
inference(modus_ponens,[status(thm)],[204,203]) ).
tff(206,plain,
( ~ zero(outc(h1(f)))
| zero(out1(and2(h1(f)))) ),
inference(unit_resolution,[status(thm)],[205,199,189]) ).
tff(207,plain,
~ zero(outc(h1(f))),
inference(unit_resolution,[status(thm)],[206,177]) ).
tff(208,plain,
^ [X: $i] :
refl(( ( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) )
<=> ( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ) )),
inference(bind,[status(th)],[]) ).
tff(209,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ) ),
inference(quant_intro,[status(thm)],[208]) ).
tff(210,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(211,axiom,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_connection_outch1_in2or1) ).
tff(212,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ),
inference(modus_ponens,[status(thm)],[211,210]) ).
tff(213,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ),
inference(skolemize,[status(sab)],[212]) ).
tff(214,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ),
inference(modus_ponens,[status(thm)],[213,209]) ).
tff(215,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) )
| ~ fulladder(f)
| connection(outc(h1(f)),in2(or1(f))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) )
| ~ fulladder(f)
| connection(outc(h1(f)),in2(or1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(216,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) )
| ~ fulladder(f)
| connection(outc(h1(f)),in2(or1(f))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) )
| ~ fulladder(f)
| connection(outc(h1(f)),in2(or1(f))) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
connection(outc(h1(f)),in2(or1(f))),
inference(unit_resolution,[status(thm)],[217,214,3]) ).
tff(219,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outc(h1(f)),in2(or1(f)))
| zero(outc(h1(f)))
| ~ zero(in2(or1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outc(h1(f)),in2(or1(f)))
| zero(outc(h1(f)))
| ~ zero(in2(or1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(220,plain,
( ( zero(outc(h1(f)))
| ~ connection(outc(h1(f)),in2(or1(f)))
| ~ zero(in2(or1(f))) )
<=> ( ~ connection(outc(h1(f)),in2(or1(f)))
| zero(outc(h1(f)))
| ~ zero(in2(or1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(221,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outc(h1(f)))
| ~ connection(outc(h1(f)),in2(or1(f)))
| ~ zero(in2(or1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outc(h1(f)),in2(or1(f)))
| zero(outc(h1(f)))
| ~ zero(in2(or1(f))) ) ),
inference(monotonicity,[status(thm)],[220]) ).
tff(222,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outc(h1(f)))
| ~ connection(outc(h1(f)),in2(or1(f)))
| ~ zero(in2(or1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outc(h1(f)),in2(or1(f)))
| zero(outc(h1(f)))
| ~ zero(in2(or1(f))) ) ),
inference(transitivity,[status(thm)],[221,219]) ).
tff(223,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outc(h1(f)))
| ~ connection(outc(h1(f)),in2(or1(f)))
| ~ zero(in2(or1(f))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(224,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(outc(h1(f)),in2(or1(f)))
| zero(outc(h1(f)))
| ~ zero(in2(or1(f))) ),
inference(modus_ponens,[status(thm)],[223,222]) ).
tff(225,plain,
( zero(outc(h1(f)))
| ~ zero(in2(or1(f))) ),
inference(unit_resolution,[status(thm)],[224,66,218]) ).
tff(226,plain,
~ zero(in2(or1(f))),
inference(unit_resolution,[status(thm)],[225,207]) ).
tff(227,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(228,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)],[227]) ).
tff(229,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(230,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(231,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ),
inference(modus_ponens,[status(thm)],[230,229]) ).
tff(232,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ),
inference(skolemize,[status(sab)],[231]) ).
tff(233,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ),
inference(modus_ponens,[status(thm)],[232,228]) ).
tff(234,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(235,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(236,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
| ~ fulladder(f)
| connection(outc(f),out1(or1(f))) ),
inference(modus_ponens,[status(thm)],[235,234]) ).
tff(237,plain,
connection(outc(f),out1(or1(f))),
inference(unit_resolution,[status(thm)],[236,233,3]) ).
tff(238,plain,
( zero(outc(f))
<=> zero(outc(f)) ),
inference(rewrite,[status(thm)],[]) ).
tff(239,axiom,
zero(outc(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outc_0) ).
tff(240,plain,
zero(outc(f)),
inference(modus_ponens,[status(thm)],[239,238]) ).
tff(241,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(242,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(243,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)],[242]) ).
tff(244,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)],[243,241]) ).
tff(245,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(246,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)],[245,244]) ).
tff(247,plain,
zero(out1(or1(f))),
inference(unit_resolution,[status(thm)],[246,199,240,237]) ).
tff(248,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(249,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)],[248]) ).
tff(250,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(251,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(252,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)],[251]) ).
tff(253,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(254,plain,
! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[253,252]) ).
tff(255,plain,
! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[254,250]) ).
tff(256,plain,
! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(skolemize,[status(sab)],[255]) ).
tff(257,plain,
! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[256,249]) ).
tff(258,plain,
( ( ~ ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| zero(in2(or1(f)))
| ~ zero(out1(or1(f)))
| ~ or_ok(or1(f)) )
<=> ( ~ ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| zero(in2(or1(f)))
| ~ zero(out1(or1(f)))
| ~ or_ok(or1(f)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(259,plain,
( ~ ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| zero(in2(or1(f)))
| ~ zero(out1(or1(f)))
| ~ or_ok(or1(f)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(260,plain,
( ~ ! [K: $i] :
( zero(in2(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| zero(in2(or1(f)))
| ~ zero(out1(or1(f)))
| ~ or_ok(or1(f)) ),
inference(modus_ponens,[status(thm)],[259,258]) ).
tff(261,plain,
( zero(in2(or1(f)))
| ~ or_ok(or1(f)) ),
inference(unit_resolution,[status(thm)],[260,257,247]) ).
tff(262,plain,
~ or_ok(or1(f)),
inference(unit_resolution,[status(thm)],[261,226]) ).
tff(263,plain,
^ [X: $i] :
refl(( ( logic_or(or1(X))
| ~ fulladder(X) )
<=> ( logic_or(or1(X))
| ~ fulladder(X) ) )),
inference(bind,[status(th)],[]) ).
tff(264,plain,
( ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
<=> ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ) ),
inference(quant_intro,[status(thm)],[263]) ).
tff(265,plain,
( ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
<=> ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(266,plain,
^ [X: $i] :
rewrite(( ( ~ fulladder(X)
| logic_or(or1(X)) )
<=> ( logic_or(or1(X))
| ~ fulladder(X) ) )),
inference(bind,[status(th)],[]) ).
tff(267,plain,
( ! [X: $i] :
( ~ fulladder(X)
| logic_or(or1(X)) )
<=> ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ) ),
inference(quant_intro,[status(thm)],[266]) ).
tff(268,axiom,
! [X: $i] :
( ~ fulladder(X)
| logic_or(or1(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_or1) ).
tff(269,plain,
! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[268,267]) ).
tff(270,plain,
! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[269,265]) ).
tff(271,plain,
! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ),
inference(skolemize,[status(sab)],[270]) ).
tff(272,plain,
! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[271,264]) ).
tff(273,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(274,plain,
( ~ ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
| logic_or(or1(f))
| ~ fulladder(f) ),
inference(quant_inst,[status(thm)],[]) ).
tff(275,plain,
( ~ ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
| logic_or(or1(f))
| ~ fulladder(f) ),
inference(modus_ponens,[status(thm)],[274,273]) ).
tff(276,plain,
logic_or(or1(f)),
inference(unit_resolution,[status(thm)],[275,272,3]) ).
tff(277,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(278,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)],[277]) ).
tff(279,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(280,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(281,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)],[280]) ).
tff(282,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(283,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(modus_ponens,[status(thm)],[282,281]) ).
tff(284,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(modus_ponens,[status(thm)],[283,279]) ).
tff(285,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(skolemize,[status(sab)],[284]) ).
tff(286,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(modus_ponens,[status(thm)],[285,278]) ).
tff(287,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(288,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(289,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)],[288,287]) ).
tff(290,plain,
( abnormal(or1(f))
| or_ok(or1(f)) ),
inference(unit_resolution,[status(thm)],[289,286,276]) ).
tff(291,plain,
abnormal(or1(f)),
inference(unit_resolution,[status(thm)],[290,262]) ).
tff(292,plain,
( ( ~ abnormal(or1(f))
| ~ abnormal(and1(h1(f))) )
<=> ( ~ abnormal(or1(f))
| ~ abnormal(and1(h1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(293,axiom,
( ~ abnormal(or1(f))
| ~ abnormal(and1(h1(f))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_or1_and1h1) ).
tff(294,plain,
( ~ abnormal(or1(f))
| ~ abnormal(and1(h1(f))) ),
inference(modus_ponens,[status(thm)],[293,292]) ).
tff(295,plain,
~ abnormal(and1(h1(f))),
inference(unit_resolution,[status(thm)],[294,291]) ).
tff(296,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(297,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(298,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)],[297]) ).
tff(299,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)],[298,296]) ).
tff(300,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(301,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)],[300,299]) ).
tff(302,plain,
and_ok(and1(h1(f))),
inference(unit_resolution,[status(thm)],[301,152,295,31]) ).
tff(303,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(304,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)],[303]) ).
tff(305,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(306,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(307,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)],[306]) ).
tff(308,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(309,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ),
inference(modus_ponens,[status(thm)],[308,307]) ).
tff(310,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ),
inference(modus_ponens,[status(thm)],[309,305]) ).
tff(311,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ),
inference(skolemize,[status(sab)],[310]) ).
tff(312,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ),
inference(modus_ponens,[status(thm)],[311,304]) ).
tff(313,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| one(in1(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| one(in1(h1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(314,plain,
( ( ~ connection(in2(f),in1(h1(f)))
| one(in1(h1(f)))
| ~ one(in2(f)) )
<=> ( ~ one(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| one(in1(h1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(315,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in2(f),in1(h1(f)))
| one(in1(h1(f)))
| ~ one(in2(f)) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| one(in1(h1(f))) ) ),
inference(monotonicity,[status(thm)],[314]) ).
tff(316,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in2(f),in1(h1(f)))
| one(in1(h1(f)))
| ~ one(in2(f)) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| one(in1(h1(f))) ) ),
inference(transitivity,[status(thm)],[315,313]) ).
tff(317,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in2(f),in1(h1(f)))
| one(in1(h1(f)))
| ~ one(in2(f)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(318,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(in2(f))
| ~ connection(in2(f),in1(h1(f)))
| one(in1(h1(f))) ),
inference(modus_ponens,[status(thm)],[317,316]) ).
tff(319,plain,
one(in1(h1(f))),
inference(unit_resolution,[status(thm)],[318,312,45,42]) ).
tff(320,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| one(in1(and2(h1(f))))
| ~ one(in1(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| one(in1(and2(h1(f))))
| ~ one(in1(h1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(321,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| one(in1(and2(h1(f))))
| ~ one(in1(h1(f))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(322,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in1(h1(f)),in1(and2(h1(f))))
| one(in1(and2(h1(f))))
| ~ one(in1(h1(f))) ),
inference(modus_ponens,[status(thm)],[321,320]) ).
tff(323,plain,
one(in1(and2(h1(f)))),
inference(unit_resolution,[status(thm)],[322,312,82,319]) ).
tff(324,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(325,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(326,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)],[325]) ).
tff(327,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)],[326,324]) ).
tff(328,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(329,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)],[328,327]) ).
tff(330,plain,
one(in2(h1(f))),
inference(unit_resolution,[status(thm)],[329,312,100,97]) ).
tff(331,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in2(h1(f)),in2(and2(h1(f))))
| one(in2(and2(h1(f))))
| ~ one(in2(h1(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in2(h1(f)),in2(and2(h1(f))))
| one(in2(and2(h1(f))))
| ~ one(in2(h1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(332,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in2(h1(f)),in2(and2(h1(f))))
| one(in2(and2(h1(f))))
| ~ one(in2(h1(f))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(in2(h1(f)),in2(and2(h1(f))))
| one(in2(and2(h1(f))))
| ~ one(in2(h1(f))) ),
inference(modus_ponens,[status(thm)],[332,331]) ).
tff(334,plain,
one(in2(and2(h1(f)))),
inference(unit_resolution,[status(thm)],[333,312,120,330]) ).
tff(335,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(336,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)],[335]) ).
tff(337,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(338,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(339,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)],[338]) ).
tff(340,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(341,plain,
! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) ),
inference(modus_ponens,[status(thm)],[340,339]) ).
tff(342,plain,
! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) ),
inference(modus_ponens,[status(thm)],[341,337]) ).
tff(343,plain,
! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) ),
inference(skolemize,[status(sab)],[342]) ).
tff(344,plain,
! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) ),
inference(modus_ponens,[status(thm)],[343,336]) ).
tff(345,plain,
( ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| one(out1(and2(h1(f))))
| ~ one(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f)))
| ~ one(in2(and2(h1(f)))) )
<=> ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| one(out1(and2(h1(f))))
| ~ one(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f)))
| ~ one(in2(and2(h1(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(346,plain,
( ( ~ and_ok(and2(h1(f)))
| one(out1(and2(h1(f))))
| ~ one(in2(and2(h1(f))))
| ~ one(in1(and2(h1(f)))) )
<=> ( one(out1(and2(h1(f))))
| ~ one(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f)))
| ~ one(in2(and2(h1(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(347,plain,
( ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| ~ and_ok(and2(h1(f)))
| one(out1(and2(h1(f))))
| ~ one(in2(and2(h1(f))))
| ~ one(in1(and2(h1(f)))) )
<=> ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| one(out1(and2(h1(f))))
| ~ one(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f)))
| ~ one(in2(and2(h1(f)))) ) ),
inference(monotonicity,[status(thm)],[346]) ).
tff(348,plain,
( ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| ~ and_ok(and2(h1(f)))
| one(out1(and2(h1(f))))
| ~ one(in2(and2(h1(f))))
| ~ one(in1(and2(h1(f)))) )
<=> ( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| one(out1(and2(h1(f))))
| ~ one(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f)))
| ~ one(in2(and2(h1(f)))) ) ),
inference(transitivity,[status(thm)],[347,345]) ).
tff(349,plain,
( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| ~ and_ok(and2(h1(f)))
| one(out1(and2(h1(f))))
| ~ one(in2(and2(h1(f))))
| ~ one(in1(and2(h1(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(350,plain,
( ~ ! [K: $i] :
( ~ and_ok(K)
| one(out1(K))
| ~ one(in2(K))
| ~ one(in1(K)) )
| one(out1(and2(h1(f))))
| ~ one(in1(and2(h1(f))))
| ~ and_ok(and2(h1(f)))
| ~ one(in2(and2(h1(f)))) ),
inference(modus_ponens,[status(thm)],[349,348]) ).
tff(351,plain,
one(out1(and2(h1(f)))),
inference(unit_resolution,[status(thm)],[350,344,160,334,323]) ).
tff(352,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(353,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)],[352]) ).
tff(354,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(355,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(356,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ),
inference(modus_ponens,[status(thm)],[355,354]) ).
tff(357,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ),
inference(skolemize,[status(sab)],[356]) ).
tff(358,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ),
inference(modus_ponens,[status(thm)],[357,353]) ).
tff(359,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(360,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(361,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)],[360,359]) ).
tff(362,plain,
( ~ halfadder(h1(f))
| connection(out1(and2(h1(f))),in1(not1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[361,358]) ).
tff(363,plain,
connection(out1(and2(h1(f))),in1(not1(h1(f)))),
inference(unit_resolution,[status(thm)],[362,17]) ).
tff(364,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(and2(h1(f))),in1(not1(h1(f))))
| one(in1(not1(h1(f))))
| ~ one(out1(and2(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(and2(h1(f))),in1(not1(h1(f))))
| one(in1(not1(h1(f))))
| ~ one(out1(and2(h1(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(365,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(and2(h1(f))),in1(not1(h1(f))))
| one(in1(not1(h1(f))))
| ~ one(out1(and2(h1(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(366,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(out1(and2(h1(f))),in1(not1(h1(f))))
| one(in1(not1(h1(f))))
| ~ one(out1(and2(h1(f)))) ),
inference(modus_ponens,[status(thm)],[365,364]) ).
tff(367,plain,
( one(in1(not1(h1(f))))
| ~ one(out1(and2(h1(f)))) ),
inference(unit_resolution,[status(thm)],[366,312,363]) ).
tff(368,plain,
one(in1(not1(h1(f)))),
inference(unit_resolution,[status(thm)],[367,351]) ).
tff(369,plain,
^ [X: $i] :
refl(( ( ~ halfadder(X)
| logic_not(not1(X)) )
<=> ( ~ halfadder(X)
| logic_not(not1(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(370,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ) ),
inference(quant_intro,[status(thm)],[369]) ).
tff(371,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(372,axiom,
! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_not1) ).
tff(373,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ),
inference(modus_ponens,[status(thm)],[372,371]) ).
tff(374,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ),
inference(skolemize,[status(sab)],[373]) ).
tff(375,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ),
inference(modus_ponens,[status(thm)],[374,370]) ).
tff(376,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)) )
| ~ halfadder(h1(f))
| logic_not(not1(h1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(377,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| ~ halfadder(h1(f))
| logic_not(not1(h1(f))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(378,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| ~ halfadder(h1(f))
| logic_not(not1(h1(f))) ),
inference(modus_ponens,[status(thm)],[377,376]) ).
tff(379,plain,
logic_not(not1(h1(f))),
inference(unit_resolution,[status(thm)],[378,375,17]) ).
tff(380,plain,
( ( ~ abnormal(or1(f))
| ~ abnormal(not1(h1(f))) )
<=> ( ~ abnormal(or1(f))
| ~ abnormal(not1(h1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(381,axiom,
( ~ abnormal(or1(f))
| ~ abnormal(not1(h1(f))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_or1_not1h1) ).
tff(382,plain,
( ~ abnormal(or1(f))
| ~ abnormal(not1(h1(f))) ),
inference(modus_ponens,[status(thm)],[381,380]) ).
tff(383,plain,
~ abnormal(not1(h1(f))),
inference(unit_resolution,[status(thm)],[382,291]) ).
tff(384,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(385,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)],[384]) ).
tff(386,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(387,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(388,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)],[387]) ).
tff(389,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(390,plain,
! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
inference(modus_ponens,[status(thm)],[389,388]) ).
tff(391,plain,
! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
inference(modus_ponens,[status(thm)],[390,386]) ).
tff(392,plain,
! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
inference(skolemize,[status(sab)],[391]) ).
tff(393,plain,
! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
inference(modus_ponens,[status(thm)],[392,385]) ).
tff(394,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(395,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(396,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)],[395,394]) ).
tff(397,plain,
not_ok(not1(h1(f))),
inference(unit_resolution,[status(thm)],[396,393,383,379]) ).
tff(398,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(399,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)],[398]) ).
tff(400,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(401,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(402,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)],[401]) ).
tff(403,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(404,plain,
! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[403,402]) ).
tff(405,plain,
! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[404,400]) ).
tff(406,plain,
! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) ),
inference(skolemize,[status(sab)],[405]) ).
tff(407,plain,
! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[406,399]) ).
tff(408,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) )
| ~ one(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f)))
| zero(out1(not1(h1(f)))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) )
| ~ one(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f)))
| zero(out1(not1(h1(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(409,plain,
( ( zero(out1(not1(h1(f))))
| ~ one(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f))) )
<=> ( ~ one(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f)))
| zero(out1(not1(h1(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(410,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) )
| ~ one(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f)))
| zero(out1(not1(h1(f)))) ) ),
inference(monotonicity,[status(thm)],[409]) ).
tff(411,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) )
| ~ one(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f)))
| zero(out1(not1(h1(f)))) ) ),
inference(transitivity,[status(thm)],[410,408]) ).
tff(412,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(413,plain,
( ~ ! [K: $i] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) )
| ~ one(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f)))
| zero(out1(not1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[412,411]) ).
tff(414,plain,
( ~ one(in1(not1(h1(f))))
| ~ not_ok(not1(h1(f)))
| zero(out1(not1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[413,407]) ).
tff(415,plain,
zero(out1(not1(h1(f)))),
inference(unit_resolution,[status(thm)],[414,397,368]) ).
tff(416,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(417,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)],[416]) ).
tff(418,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(419,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(420,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ),
inference(modus_ponens,[status(thm)],[419,418]) ).
tff(421,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ),
inference(skolemize,[status(sab)],[420]) ).
tff(422,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ),
inference(modus_ponens,[status(thm)],[421,417]) ).
tff(423,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(424,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(425,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)],[424,423]) ).
tff(426,plain,
connection(out1(not1(h1(f))),in2(and1(h1(f)))),
inference(unit_resolution,[status(thm)],[425,422,17]) ).
tff(427,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(and1(h1(f))))
| ~ zero(out1(not1(h1(f))))
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(and1(h1(f))))
| ~ zero(out1(not1(h1(f))))
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(428,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(and1(h1(f))))
| ~ zero(out1(not1(h1(f))))
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(429,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(and1(h1(f))))
| ~ zero(out1(not1(h1(f))))
| ~ connection(out1(not1(h1(f))),in2(and1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[428,427]) ).
tff(430,plain,
( zero(in2(and1(h1(f))))
| ~ zero(out1(not1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[429,199,426]) ).
tff(431,plain,
zero(in2(and1(h1(f)))),
inference(unit_resolution,[status(thm)],[430,415]) ).
tff(432,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(433,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)],[432]) ).
tff(434,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(435,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(436,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)],[435]) ).
tff(437,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(438,plain,
! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) ),
inference(modus_ponens,[status(thm)],[437,436]) ).
tff(439,plain,
! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) ),
inference(modus_ponens,[status(thm)],[438,434]) ).
tff(440,plain,
! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) ),
inference(skolemize,[status(sab)],[439]) ).
tff(441,plain,
! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) ),
inference(modus_ponens,[status(thm)],[440,433]) ).
tff(442,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| ~ zero(in2(and1(h1(f))))
| zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| ~ zero(in2(and1(h1(f))))
| zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(443,plain,
( ( zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f)))
| ~ zero(in2(and1(h1(f)))) )
<=> ( ~ zero(in2(and1(h1(f))))
| zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(444,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f)))
| ~ zero(in2(and1(h1(f)))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| ~ zero(in2(and1(h1(f))))
| zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ) ),
inference(monotonicity,[status(thm)],[443]) ).
tff(445,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f)))
| ~ zero(in2(and1(h1(f)))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| ~ zero(in2(and1(h1(f))))
| zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ) ),
inference(transitivity,[status(thm)],[444,442]) ).
tff(446,plain,
( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f)))
| ~ zero(in2(and1(h1(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(447,plain,
( ~ ! [K: $i] :
( zero(out1(K))
| ~ and_ok(K)
| ~ zero(in2(K)) )
| ~ zero(in2(and1(h1(f))))
| zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ),
inference(modus_ponens,[status(thm)],[446,445]) ).
tff(448,plain,
( ~ zero(in2(and1(h1(f))))
| zero(out1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ),
inference(unit_resolution,[status(thm)],[447,441]) ).
tff(449,plain,
zero(out1(and1(h1(f)))),
inference(unit_resolution,[status(thm)],[448,431,302]) ).
tff(450,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(451,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)],[450]) ).
tff(452,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(453,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(454,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ),
inference(modus_ponens,[status(thm)],[453,452]) ).
tff(455,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ),
inference(skolemize,[status(sab)],[454]) ).
tff(456,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ),
inference(modus_ponens,[status(thm)],[455,451]) ).
tff(457,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(458,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(459,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)],[458,457]) ).
tff(460,plain,
connection(outs(h1(f)),out1(and1(h1(f)))),
inference(unit_resolution,[status(thm)],[459,456,17]) ).
tff(461,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| ~ zero(out1(and1(h1(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| ~ zero(out1(and1(h1(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(462,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| ~ zero(out1(and1(h1(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(463,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(outs(h1(f)))
| ~ connection(outs(h1(f)),out1(and1(h1(f))))
| ~ zero(out1(and1(h1(f)))) ),
inference(modus_ponens,[status(thm)],[462,461]) ).
tff(464,plain,
( zero(outs(h1(f)))
| ~ zero(out1(and1(h1(f)))) ),
inference(unit_resolution,[status(thm)],[463,66,460]) ).
tff(465,plain,
zero(outs(h1(f))),
inference(unit_resolution,[status(thm)],[464,449]) ).
tff(466,plain,
^ [X: $i] :
refl(( ( ~ fulladder(X)
| halfadder(h2(X)) )
<=> ( ~ fulladder(X)
| halfadder(h2(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(467,plain,
( ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
<=> ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ) ),
inference(quant_intro,[status(thm)],[466]) ).
tff(468,plain,
( ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
<=> ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(469,axiom,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_halfadder2) ).
tff(470,plain,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ),
inference(modus_ponens,[status(thm)],[469,468]) ).
tff(471,plain,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ),
inference(skolemize,[status(sab)],[470]) ).
tff(472,plain,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ),
inference(modus_ponens,[status(thm)],[471,467]) ).
tff(473,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(474,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
| ~ fulladder(f)
| halfadder(h2(f)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(475,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
| ~ fulladder(f)
| halfadder(h2(f)) ),
inference(modus_ponens,[status(thm)],[474,473]) ).
tff(476,plain,
halfadder(h2(f)),
inference(unit_resolution,[status(thm)],[475,472,3]) ).
tff(477,plain,
^ [X: $i] :
refl(( ( ~ halfadder(X)
| logic_or(or1(X)) )
<=> ( ~ halfadder(X)
| logic_or(or1(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(478,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ) ),
inference(quant_intro,[status(thm)],[477]) ).
tff(479,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(480,axiom,
! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_or1) ).
tff(481,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ),
inference(modus_ponens,[status(thm)],[480,479]) ).
tff(482,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ),
inference(skolemize,[status(sab)],[481]) ).
tff(483,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ),
inference(modus_ponens,[status(thm)],[482,478]) ).
tff(484,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| ~ halfadder(h2(f))
| logic_or(or1(h2(f))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| ~ halfadder(h2(f))
| logic_or(or1(h2(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(485,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| ~ halfadder(h2(f))
| logic_or(or1(h2(f))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(486,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| ~ halfadder(h2(f))
| logic_or(or1(h2(f))) ),
inference(modus_ponens,[status(thm)],[485,484]) ).
tff(487,plain,
logic_or(or1(h2(f))),
inference(unit_resolution,[status(thm)],[486,483,476]) ).
tff(488,plain,
( ( ~ abnormal(or1(f))
| ~ abnormal(or1(h2(f))) )
<=> ( ~ abnormal(or1(f))
| ~ abnormal(or1(h2(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(489,axiom,
( ~ abnormal(or1(f))
| ~ abnormal(or1(h2(f))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_or1_or1h2) ).
tff(490,plain,
( ~ abnormal(or1(f))
| ~ abnormal(or1(h2(f))) ),
inference(modus_ponens,[status(thm)],[489,488]) ).
tff(491,plain,
~ abnormal(or1(h2(f))),
inference(unit_resolution,[status(thm)],[490,291]) ).
tff(492,plain,
( ( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(h2(f)))
| or_ok(or1(h2(f)))
| ~ logic_or(or1(h2(f))) )
<=> ( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(h2(f)))
| or_ok(or1(h2(f)))
| ~ logic_or(or1(h2(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(493,plain,
( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(h2(f)))
| or_ok(or1(h2(f)))
| ~ logic_or(or1(h2(f))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(494,plain,
( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(h2(f)))
| or_ok(or1(h2(f)))
| ~ logic_or(or1(h2(f))) ),
inference(modus_ponens,[status(thm)],[493,492]) ).
tff(495,plain,
or_ok(or1(h2(f))),
inference(unit_resolution,[status(thm)],[494,286,491,487]) ).
tff(496,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(497,plain,
( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h2(f)))
| ~ halfadder(h2(f)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(498,plain,
( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h2(f)))
| ~ halfadder(h2(f)) ),
inference(modus_ponens,[status(thm)],[497,496]) ).
tff(499,plain,
logic_and(and1(h2(f))),
inference(unit_resolution,[status(thm)],[498,27,476]) ).
tff(500,plain,
( ( ~ abnormal(or1(f))
| ~ abnormal(and1(h2(f))) )
<=> ( ~ abnormal(or1(f))
| ~ abnormal(and1(h2(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(501,axiom,
( ~ abnormal(or1(f))
| ~ abnormal(and1(h2(f))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_or1_and1h2) ).
tff(502,plain,
( ~ abnormal(or1(f))
| ~ abnormal(and1(h2(f))) ),
inference(modus_ponens,[status(thm)],[501,500]) ).
tff(503,plain,
~ abnormal(and1(h2(f))),
inference(unit_resolution,[status(thm)],[502,291]) ).
tff(504,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(505,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(506,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)],[505]) ).
tff(507,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)],[506,504]) ).
tff(508,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(509,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)],[508,507]) ).
tff(510,plain,
and_ok(and1(h2(f))),
inference(unit_resolution,[status(thm)],[509,152,503,499]) ).
tff(511,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(512,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(513,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)],[512,511]) ).
tff(514,plain,
connection(outs(h2(f)),out1(and1(h2(f)))),
inference(unit_resolution,[status(thm)],[513,456,476]) ).
tff(515,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(516,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)],[515]) ).
tff(517,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(518,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(519,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) ),
inference(modus_ponens,[status(thm)],[518,517]) ).
tff(520,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) ),
inference(skolemize,[status(sab)],[519]) ).
tff(521,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) ),
inference(modus_ponens,[status(thm)],[520,516]) ).
tff(522,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(523,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(524,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outs(X),outs(h2(X))) )
| ~ fulladder(f)
| connection(outs(f),outs(h2(f))) ),
inference(modus_ponens,[status(thm)],[523,522]) ).
tff(525,plain,
connection(outs(f),outs(h2(f))),
inference(unit_resolution,[status(thm)],[524,521,3]) ).
tff(526,plain,
( one(outs(f))
<=> one(outs(f)) ),
inference(rewrite,[status(thm)],[]) ).
tff(527,axiom,
one(outs(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outs_1) ).
tff(528,plain,
one(outs(f)),
inference(modus_ponens,[status(thm)],[527,526]) ).
tff(529,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(530,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(outs(f))
| ~ one(outs(f)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(531,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(outs(f))
| ~ one(outs(f)) ),
inference(modus_ponens,[status(thm)],[530,529]) ).
tff(532,plain,
~ zero(outs(f)),
inference(unit_resolution,[status(thm)],[531,52,528]) ).
tff(533,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(534,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(535,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)],[534,533]) ).
tff(536,plain,
~ zero(outs(h2(f))),
inference(unit_resolution,[status(thm)],[535,66,532,525]) ).
tff(537,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(538,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(539,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)],[538,537]) ).
tff(540,plain,
~ zero(out1(and1(h2(f)))),
inference(unit_resolution,[status(thm)],[539,66,536,514]) ).
tff(541,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(542,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)],[541]) ).
tff(543,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(544,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(545,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)],[544]) ).
tff(546,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(547,plain,
! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ),
inference(modus_ponens,[status(thm)],[546,545]) ).
tff(548,plain,
! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ),
inference(modus_ponens,[status(thm)],[547,543]) ).
tff(549,plain,
! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ),
inference(skolemize,[status(sab)],[548]) ).
tff(550,plain,
! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ),
inference(modus_ponens,[status(thm)],[549,542]) ).
tff(551,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
| ~ zero(in1(and1(h2(f))))
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
| ~ zero(in1(and1(h2(f))))
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(552,plain,
( ( zero(out1(and1(h2(f))))
| ~ zero(in1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) )
<=> ( ~ zero(in1(and1(h2(f))))
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(553,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
| zero(out1(and1(h2(f))))
| ~ zero(in1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
| ~ zero(in1(and1(h2(f))))
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) ) ),
inference(monotonicity,[status(thm)],[552]) ).
tff(554,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
| zero(out1(and1(h2(f))))
| ~ zero(in1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
| ~ zero(in1(and1(h2(f))))
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) ) ),
inference(transitivity,[status(thm)],[553,551]) ).
tff(555,plain,
( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
| zero(out1(and1(h2(f))))
| ~ zero(in1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(556,plain,
( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) )
| ~ zero(in1(and1(h2(f))))
| zero(out1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) ),
inference(modus_ponens,[status(thm)],[555,554]) ).
tff(557,plain,
( ~ zero(in1(and1(h2(f))))
| ~ and_ok(and1(h2(f))) ),
inference(unit_resolution,[status(thm)],[556,550,540]) ).
tff(558,plain,
~ zero(in1(and1(h2(f)))),
inference(unit_resolution,[status(thm)],[557,510]) ).
tff(559,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(560,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)],[559]) ).
tff(561,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(562,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(563,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ),
inference(modus_ponens,[status(thm)],[562,561]) ).
tff(564,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ),
inference(skolemize,[status(sab)],[563]) ).
tff(565,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ),
inference(modus_ponens,[status(thm)],[564,560]) ).
tff(566,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
| ~ halfadder(h2(f))
| connection(out1(or1(h2(f))),in1(and1(h2(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
| ~ halfadder(h2(f))
| connection(out1(or1(h2(f))),in1(and1(h2(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(567,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
| ~ halfadder(h2(f))
| connection(out1(or1(h2(f))),in1(and1(h2(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(568,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
| ~ halfadder(h2(f))
| connection(out1(or1(h2(f))),in1(and1(h2(f)))) ),
inference(modus_ponens,[status(thm)],[567,566]) ).
tff(569,plain,
connection(out1(or1(h2(f))),in1(and1(h2(f)))),
inference(unit_resolution,[status(thm)],[568,565,476]) ).
tff(570,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(and1(h2(f))))
| ~ zero(out1(or1(h2(f))))
| ~ connection(out1(or1(h2(f))),in1(and1(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(and1(h2(f))))
| ~ zero(out1(or1(h2(f))))
| ~ connection(out1(or1(h2(f))),in1(and1(h2(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(571,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(and1(h2(f))))
| ~ zero(out1(or1(h2(f))))
| ~ connection(out1(or1(h2(f))),in1(and1(h2(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(572,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(and1(h2(f))))
| ~ zero(out1(or1(h2(f))))
| ~ connection(out1(or1(h2(f))),in1(and1(h2(f)))) ),
inference(modus_ponens,[status(thm)],[571,570]) ).
tff(573,plain,
( zero(in1(and1(h2(f))))
| ~ zero(out1(or1(h2(f)))) ),
inference(unit_resolution,[status(thm)],[572,199,569]) ).
tff(574,plain,
~ zero(out1(or1(h2(f)))),
inference(unit_resolution,[status(thm)],[573,558]) ).
tff(575,plain,
^ [X: $i] :
refl(( ( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) )
<=> ( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) ) )),
inference(bind,[status(th)],[]) ).
tff(576,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) ) ),
inference(quant_intro,[status(thm)],[575]) ).
tff(577,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(578,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_connection_in1_in1or1) ).
tff(579,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) ),
inference(modus_ponens,[status(thm)],[578,577]) ).
tff(580,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) ),
inference(skolemize,[status(sab)],[579]) ).
tff(581,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) ),
inference(modus_ponens,[status(thm)],[580,576]) ).
tff(582,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) )
| ~ halfadder(h2(f))
| connection(in1(h2(f)),in1(or1(h2(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) )
| ~ halfadder(h2(f))
| connection(in1(h2(f)),in1(or1(h2(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(583,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) )
| ~ halfadder(h2(f))
| connection(in1(h2(f)),in1(or1(h2(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(584,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) )
| ~ halfadder(h2(f))
| connection(in1(h2(f)),in1(or1(h2(f)))) ),
inference(modus_ponens,[status(thm)],[583,582]) ).
tff(585,plain,
connection(in1(h2(f)),in1(or1(h2(f)))),
inference(unit_resolution,[status(thm)],[584,581,476]) ).
tff(586,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(587,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)],[586]) ).
tff(588,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(589,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(590,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ),
inference(modus_ponens,[status(thm)],[589,588]) ).
tff(591,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ),
inference(skolemize,[status(sab)],[590]) ).
tff(592,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ),
inference(modus_ponens,[status(thm)],[591,587]) ).
tff(593,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(594,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(595,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
| ~ fulladder(f)
| connection(in1(f),in1(h2(f))) ),
inference(modus_ponens,[status(thm)],[594,593]) ).
tff(596,plain,
connection(in1(f),in1(h2(f))),
inference(unit_resolution,[status(thm)],[595,592,3]) ).
tff(597,plain,
( zero(in1(f))
<=> zero(in1(f)) ),
inference(rewrite,[status(thm)],[]) ).
tff(598,axiom,
zero(in1(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in1_1) ).
tff(599,plain,
zero(in1(f)),
inference(modus_ponens,[status(thm)],[598,597]) ).
tff(600,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| zero(in1(h2(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| zero(in1(h2(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(601,plain,
( ( zero(in1(h2(f)))
| ~ zero(in1(f))
| ~ connection(in1(f),in1(h2(f))) )
<=> ( ~ zero(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| zero(in1(h2(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(602,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(h2(f)))
| ~ zero(in1(f))
| ~ connection(in1(f),in1(h2(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| zero(in1(h2(f))) ) ),
inference(monotonicity,[status(thm)],[601]) ).
tff(603,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(h2(f)))
| ~ zero(in1(f))
| ~ connection(in1(f),in1(h2(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| zero(in1(h2(f))) ) ),
inference(transitivity,[status(thm)],[602,600]) ).
tff(604,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(h2(f)))
| ~ zero(in1(f))
| ~ connection(in1(f),in1(h2(f))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(605,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in1(f))
| ~ connection(in1(f),in1(h2(f)))
| zero(in1(h2(f))) ),
inference(modus_ponens,[status(thm)],[604,603]) ).
tff(606,plain,
zero(in1(h2(f))),
inference(unit_resolution,[status(thm)],[605,199,599,596]) ).
tff(607,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in1(h2(f)))
| ~ connection(in1(h2(f)),in1(or1(h2(f))))
| zero(in1(or1(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in1(h2(f)))
| ~ connection(in1(h2(f)),in1(or1(h2(f))))
| zero(in1(or1(h2(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(608,plain,
( ( zero(in1(or1(h2(f))))
| ~ zero(in1(h2(f)))
| ~ connection(in1(h2(f)),in1(or1(h2(f)))) )
<=> ( ~ zero(in1(h2(f)))
| ~ connection(in1(h2(f)),in1(or1(h2(f))))
| zero(in1(or1(h2(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(609,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(or1(h2(f))))
| ~ zero(in1(h2(f)))
| ~ connection(in1(h2(f)),in1(or1(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in1(h2(f)))
| ~ connection(in1(h2(f)),in1(or1(h2(f))))
| zero(in1(or1(h2(f)))) ) ),
inference(monotonicity,[status(thm)],[608]) ).
tff(610,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(or1(h2(f))))
| ~ zero(in1(h2(f)))
| ~ connection(in1(h2(f)),in1(or1(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in1(h2(f)))
| ~ connection(in1(h2(f)),in1(or1(h2(f))))
| zero(in1(or1(h2(f)))) ) ),
inference(transitivity,[status(thm)],[609,607]) ).
tff(611,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in1(or1(h2(f))))
| ~ zero(in1(h2(f)))
| ~ connection(in1(h2(f)),in1(or1(h2(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(612,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in1(h2(f)))
| ~ connection(in1(h2(f)),in1(or1(h2(f))))
| zero(in1(or1(h2(f)))) ),
inference(modus_ponens,[status(thm)],[611,610]) ).
tff(613,plain,
zero(in1(or1(h2(f)))),
inference(unit_resolution,[status(thm)],[612,199,606,585]) ).
tff(614,plain,
^ [K: $i] :
refl(( ( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) )
<=> ( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) ) )),
inference(bind,[status(th)],[]) ).
tff(615,plain,
( ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) )
<=> ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) ) ),
inference(quant_intro,[status(thm)],[614]) ).
tff(616,plain,
( ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) )
<=> ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(617,plain,
^ [K: $i] :
trans(monotonicity(rewrite(( ( ~ or_ok(K)
| ~ zero(in1(K))
| ~ zero(in2(K)) )
<=> ( ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) ) )),
( ( ~ or_ok(K)
| ~ zero(in1(K))
| ~ zero(in2(K))
| zero(out1(K)) )
<=> ( ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K)
| zero(out1(K)) ) )),
rewrite(( ( ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K)
| zero(out1(K)) )
<=> ( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) ) )),
( ( ~ or_ok(K)
| ~ zero(in1(K))
| ~ zero(in2(K))
| zero(out1(K)) )
<=> ( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) ) )),
inference(bind,[status(th)],[]) ).
tff(618,plain,
( ! [K: $i] :
( ~ or_ok(K)
| ~ zero(in1(K))
| ~ zero(in2(K))
| zero(out1(K)) )
<=> ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) ) ),
inference(quant_intro,[status(thm)],[617]) ).
tff(619,axiom,
! [K: $i] :
( ~ or_ok(K)
| ~ zero(in1(K))
| ~ zero(in2(K))
| zero(out1(K)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',or_00_0) ).
tff(620,plain,
! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[619,618]) ).
tff(621,plain,
! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[620,616]) ).
tff(622,plain,
! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) ),
inference(skolemize,[status(sab)],[621]) ).
tff(623,plain,
! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[622,615]) ).
tff(624,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) )
| zero(out1(or1(h2(f))))
| ~ zero(in2(or1(h2(f))))
| ~ zero(in1(or1(h2(f))))
| ~ or_ok(or1(h2(f))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) )
| zero(out1(or1(h2(f))))
| ~ zero(in2(or1(h2(f))))
| ~ zero(in1(or1(h2(f))))
| ~ or_ok(or1(h2(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(625,plain,
( ( zero(out1(or1(h2(f))))
| ~ zero(in1(or1(h2(f))))
| ~ zero(in2(or1(h2(f))))
| ~ or_ok(or1(h2(f))) )
<=> ( zero(out1(or1(h2(f))))
| ~ zero(in2(or1(h2(f))))
| ~ zero(in1(or1(h2(f))))
| ~ or_ok(or1(h2(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(626,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) )
| zero(out1(or1(h2(f))))
| ~ zero(in1(or1(h2(f))))
| ~ zero(in2(or1(h2(f))))
| ~ or_ok(or1(h2(f))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) )
| zero(out1(or1(h2(f))))
| ~ zero(in2(or1(h2(f))))
| ~ zero(in1(or1(h2(f))))
| ~ or_ok(or1(h2(f))) ) ),
inference(monotonicity,[status(thm)],[625]) ).
tff(627,plain,
( ( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) )
| zero(out1(or1(h2(f))))
| ~ zero(in1(or1(h2(f))))
| ~ zero(in2(or1(h2(f))))
| ~ or_ok(or1(h2(f))) )
<=> ( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) )
| zero(out1(or1(h2(f))))
| ~ zero(in2(or1(h2(f))))
| ~ zero(in1(or1(h2(f))))
| ~ or_ok(or1(h2(f))) ) ),
inference(transitivity,[status(thm)],[626,624]) ).
tff(628,plain,
( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) )
| zero(out1(or1(h2(f))))
| ~ zero(in1(or1(h2(f))))
| ~ zero(in2(or1(h2(f))))
| ~ or_ok(or1(h2(f))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(629,plain,
( ~ ! [K: $i] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ zero(in2(K))
| ~ or_ok(K) )
| zero(out1(or1(h2(f))))
| ~ zero(in2(or1(h2(f))))
| ~ zero(in1(or1(h2(f))))
| ~ or_ok(or1(h2(f))) ),
inference(modus_ponens,[status(thm)],[628,627]) ).
tff(630,plain,
( zero(out1(or1(h2(f))))
| ~ zero(in2(or1(h2(f))))
| ~ or_ok(or1(h2(f))) ),
inference(unit_resolution,[status(thm)],[629,623,613]) ).
tff(631,plain,
~ zero(in2(or1(h2(f)))),
inference(unit_resolution,[status(thm)],[630,574,495]) ).
tff(632,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(633,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)],[632]) ).
tff(634,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(635,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(636,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) ),
inference(modus_ponens,[status(thm)],[635,634]) ).
tff(637,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) ),
inference(skolemize,[status(sab)],[636]) ).
tff(638,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) ),
inference(modus_ponens,[status(thm)],[637,633]) ).
tff(639,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) )
| ~ halfadder(h2(f))
| connection(in2(h2(f)),in2(or1(h2(f)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) )
| ~ halfadder(h2(f))
| connection(in2(h2(f)),in2(or1(h2(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(640,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) )
| ~ halfadder(h2(f))
| connection(in2(h2(f)),in2(or1(h2(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(641,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in2(X),in2(or1(X))) )
| ~ halfadder(h2(f))
| connection(in2(h2(f)),in2(or1(h2(f)))) ),
inference(modus_ponens,[status(thm)],[640,639]) ).
tff(642,plain,
connection(in2(h2(f)),in2(or1(h2(f)))),
inference(unit_resolution,[status(thm)],[641,638,476]) ).
tff(643,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(or1(h2(f))))
| zero(in2(or1(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(or1(h2(f))))
| zero(in2(or1(h2(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(644,plain,
( ( zero(in2(or1(h2(f))))
| ~ zero(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(or1(h2(f)))) )
<=> ( ~ zero(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(or1(h2(f))))
| zero(in2(or1(h2(f)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(645,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(or1(h2(f))))
| ~ zero(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(or1(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(or1(h2(f))))
| zero(in2(or1(h2(f)))) ) ),
inference(monotonicity,[status(thm)],[644]) ).
tff(646,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(or1(h2(f))))
| ~ zero(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(or1(h2(f)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(or1(h2(f))))
| zero(in2(or1(h2(f)))) ) ),
inference(transitivity,[status(thm)],[645,643]) ).
tff(647,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(or1(h2(f))))
| ~ zero(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(or1(h2(f)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(648,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(in2(h2(f)))
| ~ connection(in2(h2(f)),in2(or1(h2(f))))
| zero(in2(or1(h2(f)))) ),
inference(modus_ponens,[status(thm)],[647,646]) ).
tff(649,plain,
( ~ zero(in2(h2(f)))
| zero(in2(or1(h2(f)))) ),
inference(unit_resolution,[status(thm)],[648,199,642]) ).
tff(650,plain,
~ zero(in2(h2(f))),
inference(unit_resolution,[status(thm)],[649,631]) ).
tff(651,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(652,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)],[651]) ).
tff(653,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(654,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(655,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) ),
inference(modus_ponens,[status(thm)],[654,653]) ).
tff(656,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) ),
inference(skolemize,[status(sab)],[655]) ).
tff(657,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outs(h1(X)),in2(h2(X))) ),
inference(modus_ponens,[status(thm)],[656,652]) ).
tff(658,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(659,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(660,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)],[659,658]) ).
tff(661,plain,
connection(outs(h1(f)),in2(h2(f))),
inference(unit_resolution,[status(thm)],[660,657,3]) ).
tff(662,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(h2(f)))
| ~ zero(outs(h1(f)))
| ~ connection(outs(h1(f)),in2(h2(f))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(h2(f)))
| ~ zero(outs(h1(f)))
| ~ connection(outs(h1(f)),in2(h2(f))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(663,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(h2(f)))
| ~ zero(outs(h1(f)))
| ~ connection(outs(h1(f)),in2(h2(f))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(664,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(in2(h2(f)))
| ~ zero(outs(h1(f)))
| ~ connection(outs(h1(f)),in2(h2(f))) ),
inference(modus_ponens,[status(thm)],[663,662]) ).
tff(665,plain,
( zero(in2(h2(f)))
| ~ zero(outs(h1(f))) ),
inference(unit_resolution,[status(thm)],[664,199,661]) ).
tff(666,plain,
$false,
inference(unit_resolution,[status(thm)],[665,650,465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : HWV007-2 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 17:19:32 EDT 2025
% 0.18/0.34 % CPUTime :
% 0.18/0.39 % SZS status Unsatisfiable
% 0.18/0.39 % SZS output start Proof
% See solution above
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------