TSTP Solution File: HWV005-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV005-2 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 02:10:28 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 157
% Syntax : Number of formulae : 332 ( 66 unt; 21 typ; 0 def)
% Number of atoms : 1597 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 2198 ( 983 ~;1060 |; 0 &)
% ( 155 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 71 ( 71 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 20 >; 1 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-1 aty)
% Number of variables : 418 ( 383 !; 0 ?; 418 :)
% Comments :
%------------------------------------------------------------------------------
tff(zero_type,type,
zero: $i > $o ).
tff(out1_type,type,
out1: $i > $i ).
tff(not1_type,type,
not1: $i > $i ).
tff(h_type,type,
h: $i ).
tff(one_type,type,
one: $i > $o ).
tff(in1_type,type,
in1: $i > $i ).
tff(and2_type,type,
and2: $i > $i ).
tff(connection_type,type,
connection: ( $i * $i ) > $o ).
tff(outc_type,type,
outc: $i > $i ).
tff(halfadder_type,type,
halfadder: $i > $o ).
tff(not_ok_type,type,
not_ok: $i > $o ).
tff(logic_not_type,type,
logic_not: $i > $o ).
tff(abnormal_type,type,
abnormal: $i > $o ).
tff(in2_type,type,
in2: $i > $i ).
tff(and1_type,type,
and1: $i > $i ).
tff(or1_type,type,
or1: $i > $i ).
tff(or_ok_type,type,
or_ok: $i > $o ).
tff(logic_or_type,type,
logic_or: $i > $o ).
tff(outs_type,type,
outs: $i > $i ).
tff(and_ok_type,type,
and_ok: $i > $o ).
tff(logic_and_type,type,
logic_and: $i > $o ).
tff(1,plain,
( halfadder(h)
<=> halfadder(h) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
halfadder(h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_isa_halfadder) ).
tff(3,plain,
halfadder(h),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,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)],[4]) ).
tff(6,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(7,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_connection_outc_out1and2) ).
tff(8,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h)
| connection(outc(h),out1(and2(h))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h)
| connection(outc(h),out1(and2(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h)
| connection(outc(h),out1(and2(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h)
| connection(outc(h),out1(and2(h))) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
connection(outc(h),out1(and2(h))),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( zero(outc(h))
<=> zero(outc(h)) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
zero(outc(h)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outc_0) ).
tff(17,plain,
zero(outc(h)),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [P: $i] :
refl(
( ( ~ zero(P)
| ~ one(P) )
<=> ( ~ zero(P)
| ~ one(P) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
<=> ! [P: $i] :
( ~ zero(P)
| ~ one(P) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
<=> ! [P: $i] :
( ~ zero(P)
| ~ one(P) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [P: $i] :
( ~ zero(P)
| ~ one(P) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',unique_value) ).
tff(22,plain,
! [P: $i] :
( ~ zero(P)
| ~ one(P) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [P: $i] :
( ~ zero(P)
| ~ one(P) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [P: $i] :
( ~ zero(P)
| ~ one(P) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(outc(h))
| ~ one(outc(h)) )
<=> ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(outc(h))
| ~ one(outc(h)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(outc(h))
| ~ one(outc(h)) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(outc(h))
| ~ one(outc(h)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
~ one(outc(h)),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
^ [P2: $i,P1: $i] :
refl(
( ( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
<=> ( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
<=> ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
<=> ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [P2: $i,P1: $i] :
trans(
monotonicity(
rewrite(
( ( ~ connection(P1,P2)
| ~ one(P2) )
<=> ( ~ connection(P1,P2)
| ~ one(P2) ) )),
( ( ~ connection(P1,P2)
| ~ one(P2)
| one(P1) )
<=> ( ~ connection(P1,P2)
| ~ one(P2)
| one(P1) ) )),
rewrite(
( ( ~ connection(P1,P2)
| ~ one(P2)
| one(P1) )
<=> ( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ) )),
( ( ~ connection(P1,P2)
| ~ one(P2)
| one(P1) )
<=> ( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ one(P2)
| one(P1) )
<=> ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ one(P2)
| one(P1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',value_propagation_one2) ).
tff(35,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(outc(h))
| ~ one(out1(and2(h)))
| ~ connection(outc(h),out1(and2(h))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(outc(h))
| ~ one(out1(and2(h)))
| ~ connection(outc(h),out1(and2(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( ~ connection(outc(h),out1(and2(h)))
| one(outc(h))
| ~ one(out1(and2(h))) )
<=> ( one(outc(h))
| ~ one(out1(and2(h)))
| ~ connection(outc(h),out1(and2(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(outc(h),out1(and2(h)))
| one(outc(h))
| ~ one(out1(and2(h))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(outc(h))
| ~ one(out1(and2(h)))
| ~ connection(outc(h),out1(and2(h))) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(outc(h),out1(and2(h)))
| one(outc(h))
| ~ one(out1(and2(h))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(outc(h))
| ~ one(out1(and2(h)))
| ~ connection(outc(h),out1(and2(h))) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(outc(h),out1(and2(h)))
| one(outc(h))
| ~ one(out1(and2(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(outc(h))
| ~ one(out1(and2(h)))
| ~ connection(outc(h),out1(and2(h))) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ one(out1(and2(h))),
inference(unit_resolution,[status(thm)],[44,38,28,14]) ).
tff(46,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(47,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)],[46]) ).
tff(48,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(49,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_connection_out1and2_in1not1) ).
tff(50,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
| ~ halfadder(h)
| connection(out1(and2(h)),in1(not1(h))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
| ~ halfadder(h)
| connection(out1(and2(h)),in1(not1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
| ~ halfadder(h)
| connection(out1(and2(h)),in1(not1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(and2(X)),in1(not1(X))) )
| ~ halfadder(h)
| connection(out1(and2(h)),in1(not1(h))) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
connection(out1(and2(h)),in1(not1(h))),
inference(unit_resolution,[status(thm)],[55,52,3]) ).
tff(57,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(out1(and2(h)),in1(not1(h)))
| one(out1(and2(h)))
| ~ one(in1(not1(h))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(out1(and2(h)),in1(not1(h)))
| one(out1(and2(h)))
| ~ one(in1(not1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(out1(and2(h)),in1(not1(h)))
| one(out1(and2(h)))
| ~ one(in1(not1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(out1(and2(h)),in1(not1(h)))
| one(out1(and2(h)))
| ~ one(in1(not1(h))) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( one(out1(and2(h)))
| ~ one(in1(not1(h))) ),
inference(unit_resolution,[status(thm)],[59,38,56]) ).
tff(61,plain,
~ one(in1(not1(h))),
inference(unit_resolution,[status(thm)],[60,45]) ).
tff(62,plain,
^ [X: $i] :
refl(
( ( ~ halfadder(X)
| logic_not(not1(X)) )
<=> ( ~ halfadder(X)
| logic_not(not1(X)) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,axiom,
! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_not1) ).
tff(66,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| logic_not(not1(h))
| ~ halfadder(h) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| logic_not(not1(h))
| ~ halfadder(h) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( ~ halfadder(h)
| logic_not(not1(h)) )
<=> ( logic_not(not1(h))
| ~ halfadder(h) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| ~ halfadder(h)
| logic_not(not1(h)) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| logic_not(not1(h))
| ~ halfadder(h) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| ~ halfadder(h)
| logic_not(not1(h)) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| logic_not(not1(h))
| ~ halfadder(h) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| ~ halfadder(h)
| logic_not(not1(h)) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_not(not1(X)) )
| logic_not(not1(h))
| ~ halfadder(h) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
logic_not(not1(h)),
inference(unit_resolution,[status(thm)],[74,68,3]) ).
tff(76,plain,
( ~ abnormal(not1(h))
<=> ~ abnormal(not1(h)) ),
inference(rewrite,[status(thm)],]) ).
tff(77,axiom,
~ abnormal(not1(h)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_not1) ).
tff(78,plain,
~ abnormal(not1(h)),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,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(80,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)],[79]) ).
tff(81,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(82,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(83,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)],[82]) ).
tff(84,axiom,
! [K: $i] :
( ~ logic_not(K)
| not_ok(K)
| abnormal(K) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',not_ok_or_abnormal) ).
tff(85,plain,
! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
inference(modus_ponens,[status(thm)],[87,80]) ).
tff(89,plain,
( ( ~ ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
| abnormal(not1(h))
| not_ok(not1(h))
| ~ logic_not(not1(h)) )
<=> ( ~ ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
| abnormal(not1(h))
| not_ok(not1(h))
| ~ logic_not(not1(h)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ~ ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
| abnormal(not1(h))
| not_ok(not1(h))
| ~ logic_not(not1(h)) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
( ~ ! [K: $i] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) )
| abnormal(not1(h))
| not_ok(not1(h))
| ~ logic_not(not1(h)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
( not_ok(not1(h))
| ~ logic_not(not1(h)) ),
inference(unit_resolution,[status(thm)],[91,88,78]) ).
tff(93,plain,
not_ok(not1(h)),
inference(unit_resolution,[status(thm)],[92,75]) ).
tff(94,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(95,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)],[94]) ).
tff(96,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(97,plain,
^ [K: $i] :
rewrite(
( ( ~ not_ok(K)
| ~ zero(out1(K))
| one(in1(K)) )
<=> ( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [K: $i] :
( ~ not_ok(K)
| ~ zero(out1(K))
| one(in1(K)) )
<=> ! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,axiom,
! [K: $i] :
( ~ not_ok(K)
| ~ zero(out1(K))
| one(in1(K)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',not_0_1_bw) ).
tff(100,plain,
! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) ),
inference(modus_ponens,[status(thm)],[102,95]) ).
tff(104,plain,
( ( ~ ! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) )
| ~ zero(out1(not1(h)))
| one(in1(not1(h)))
| ~ not_ok(not1(h)) )
<=> ( ~ ! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) )
| ~ zero(out1(not1(h)))
| one(in1(not1(h)))
| ~ not_ok(not1(h)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ~ ! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) )
| ~ zero(out1(not1(h)))
| one(in1(not1(h)))
| ~ not_ok(not1(h)) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
( ~ ! [K: $i] :
( ~ zero(out1(K))
| one(in1(K))
| ~ not_ok(K) )
| ~ zero(out1(not1(h)))
| one(in1(not1(h)))
| ~ not_ok(not1(h)) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
( ~ zero(out1(not1(h)))
| one(in1(not1(h))) ),
inference(unit_resolution,[status(thm)],[106,103,93]) ).
tff(108,plain,
~ zero(out1(not1(h))),
inference(unit_resolution,[status(thm)],[107,61]) ).
tff(109,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(110,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)],[109]) ).
tff(111,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(112,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_connection_in1_in1or1) ).
tff(113,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) )
| ~ halfadder(h)
| connection(in1(h),in1(or1(h))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) )
| ~ halfadder(h)
| connection(in1(h),in1(or1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) )
| ~ halfadder(h)
| connection(in1(h),in1(or1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(or1(X))) )
| ~ halfadder(h)
| connection(in1(h),in1(or1(h))) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
connection(in1(h),in1(or1(h))),
inference(unit_resolution,[status(thm)],[118,115,3]) ).
tff(120,plain,
( one(in1(h))
<=> one(in1(h)) ),
inference(rewrite,[status(thm)],]) ).
tff(121,axiom,
one(in1(h)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in1_1) ).
tff(122,plain,
one(in1(h)),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
( ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(in1(h))
| ~ one(in1(h)) )
<=> ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(in1(h))
| ~ one(in1(h)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(in1(h))
| ~ one(in1(h)) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(in1(h))
| ~ one(in1(h)) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
~ zero(in1(h)),
inference(unit_resolution,[status(thm)],[125,24,122]) ).
tff(127,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(128,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)],[127]) ).
tff(129,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(130,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(131,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)],[130]) ).
tff(132,axiom,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ zero(P2)
| zero(P1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',value_propagation_zero2) ).
tff(133,plain,
! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ),
inference(modus_ponens,[status(thm)],[133,129]) ).
tff(135,plain,
! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) ),
inference(modus_ponens,[status(thm)],[135,128]) ).
tff(137,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(h))
| ~ connection(in1(h),in1(or1(h)))
| ~ zero(in1(or1(h))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(h))
| ~ connection(in1(h),in1(or1(h)))
| ~ zero(in1(or1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(h))
| ~ connection(in1(h),in1(or1(h)))
| ~ zero(in1(or1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(139,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(in1(h))
| ~ connection(in1(h),in1(or1(h)))
| ~ zero(in1(or1(h))) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
~ zero(in1(or1(h))),
inference(unit_resolution,[status(thm)],[139,136,126,119]) ).
tff(141,plain,
^ [X: $i] :
refl(
( ( ~ halfadder(X)
| logic_or(or1(X)) )
<=> ( ~ halfadder(X)
| logic_or(or1(X)) ) )),
inference(bind,[status(th)],]) ).
tff(142,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(144,axiom,
! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_or1) ).
tff(145,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ),
inference(skolemize,[status(sab)],[145]) ).
tff(147,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) ),
inference(modus_ponens,[status(thm)],[146,142]) ).
tff(148,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| logic_or(or1(h))
| ~ halfadder(h) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| logic_or(or1(h))
| ~ halfadder(h) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,plain,
( ( ~ halfadder(h)
| logic_or(or1(h)) )
<=> ( logic_or(or1(h))
| ~ halfadder(h) ) ),
inference(rewrite,[status(thm)],]) ).
tff(150,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| ~ halfadder(h)
| logic_or(or1(h)) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| logic_or(or1(h))
| ~ halfadder(h) ) ),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| ~ halfadder(h)
| logic_or(or1(h)) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| logic_or(or1(h))
| ~ halfadder(h) ) ),
inference(transitivity,[status(thm)],[150,148]) ).
tff(152,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| ~ halfadder(h)
| logic_or(or1(h)) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_or(or1(X)) )
| logic_or(or1(h))
| ~ halfadder(h) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
logic_or(or1(h)),
inference(unit_resolution,[status(thm)],[153,147,3]) ).
tff(155,plain,
( ~ abnormal(or1(h))
<=> ~ abnormal(or1(h)) ),
inference(rewrite,[status(thm)],]) ).
tff(156,axiom,
~ abnormal(or1(h)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_or1) ).
tff(157,plain,
~ abnormal(or1(h)),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,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(159,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)],[158]) ).
tff(160,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(161,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(162,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)],[161]) ).
tff(163,axiom,
! [K: $i] :
( ~ logic_or(K)
| or_ok(K)
| abnormal(K) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',or_ok_or_abnormal) ).
tff(164,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(modus_ponens,[status(thm)],[164,160]) ).
tff(166,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(skolemize,[status(sab)],[165]) ).
tff(167,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(modus_ponens,[status(thm)],[166,159]) ).
tff(168,plain,
( ( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(h))
| or_ok(or1(h))
| ~ logic_or(or1(h)) )
<=> ( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(h))
| or_ok(or1(h))
| ~ logic_or(or1(h)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(169,plain,
( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(h))
| or_ok(or1(h))
| ~ logic_or(or1(h)) ),
inference(quant_inst,[status(thm)],]) ).
tff(170,plain,
( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(h))
| or_ok(or1(h))
| ~ logic_or(or1(h)) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
( or_ok(or1(h))
| ~ logic_or(or1(h)) ),
inference(unit_resolution,[status(thm)],[170,167,157]) ).
tff(172,plain,
or_ok(or1(h)),
inference(unit_resolution,[status(thm)],[171,154]) ).
tff(173,plain,
^ [K: $i] :
refl(
( ( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
<=> ( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(174,plain,
( ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
<=> ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) ),
inference(quant_intro,[status(thm)],[173]) ).
tff(175,plain,
( ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
<=> ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) ),
inference(rewrite,[status(thm)],]) ).
tff(176,plain,
^ [K: $i] :
rewrite(
( ( ~ or_ok(K)
| ~ zero(out1(K))
| zero(in1(K)) )
<=> ( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) )),
inference(bind,[status(th)],]) ).
tff(177,plain,
( ! [K: $i] :
( ~ or_ok(K)
| ~ zero(out1(K))
| zero(in1(K)) )
<=> ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ) ),
inference(quant_intro,[status(thm)],[176]) ).
tff(178,axiom,
! [K: $i] :
( ~ or_ok(K)
| ~ zero(out1(K))
| zero(in1(K)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',or_0_0x) ).
tff(179,plain,
! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[179,175]) ).
tff(181,plain,
! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(skolemize,[status(sab)],[180]) ).
tff(182,plain,
! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[181,174]) ).
tff(183,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| ~ zero(out1(or1(h)))
| zero(in1(or1(h)))
| ~ or_ok(or1(h)) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| ~ zero(out1(or1(h)))
| zero(in1(or1(h)))
| ~ or_ok(or1(h)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(184,plain,
( ( zero(in1(or1(h)))
| ~ zero(out1(or1(h)))
| ~ or_ok(or1(h)) )
<=> ( ~ zero(out1(or1(h)))
| zero(in1(or1(h)))
| ~ or_ok(or1(h)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(185,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| zero(in1(or1(h)))
| ~ zero(out1(or1(h)))
| ~ or_ok(or1(h)) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| ~ zero(out1(or1(h)))
| zero(in1(or1(h)))
| ~ or_ok(or1(h)) ) ),
inference(monotonicity,[status(thm)],[184]) ).
tff(186,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| zero(in1(or1(h)))
| ~ zero(out1(or1(h)))
| ~ or_ok(or1(h)) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| ~ zero(out1(or1(h)))
| zero(in1(or1(h)))
| ~ or_ok(or1(h)) ) ),
inference(transitivity,[status(thm)],[185,183]) ).
tff(187,plain,
( ~ ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| zero(in1(or1(h)))
| ~ zero(out1(or1(h)))
| ~ or_ok(or1(h)) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
( ~ ! [K: $i] :
( zero(in1(K))
| ~ zero(out1(K))
| ~ or_ok(K) )
| ~ zero(out1(or1(h)))
| zero(in1(or1(h)))
| ~ or_ok(or1(h)) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
~ zero(out1(or1(h))),
inference(unit_resolution,[status(thm)],[188,182,172,140]) ).
tff(190,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(191,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)],[190]) ).
tff(192,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(193,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_connection_out1or1_in1_and1) ).
tff(194,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ),
inference(modus_ponens,[status(thm)],[193,192]) ).
tff(195,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ),
inference(skolemize,[status(sab)],[194]) ).
tff(196,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) ),
inference(modus_ponens,[status(thm)],[195,191]) ).
tff(197,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
| ~ halfadder(h)
| connection(out1(or1(h)),in1(and1(h))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
| ~ halfadder(h)
| connection(out1(or1(h)),in1(and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(198,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
| ~ halfadder(h)
| connection(out1(or1(h)),in1(and1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(199,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(or1(X)),in1(and1(X))) )
| ~ halfadder(h)
| connection(out1(or1(h)),in1(and1(h))) ),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
connection(out1(or1(h)),in1(and1(h))),
inference(unit_resolution,[status(thm)],[199,196,3]) ).
tff(201,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(or1(h)),in1(and1(h)))
| zero(out1(or1(h)))
| ~ zero(in1(and1(h))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(or1(h)),in1(and1(h)))
| zero(out1(or1(h)))
| ~ zero(in1(and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(202,plain,
( ( zero(out1(or1(h)))
| ~ connection(out1(or1(h)),in1(and1(h)))
| ~ zero(in1(and1(h))) )
<=> ( ~ connection(out1(or1(h)),in1(and1(h)))
| zero(out1(or1(h)))
| ~ zero(in1(and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(203,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(out1(or1(h)))
| ~ connection(out1(or1(h)),in1(and1(h)))
| ~ zero(in1(and1(h))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(or1(h)),in1(and1(h)))
| zero(out1(or1(h)))
| ~ zero(in1(and1(h))) ) ),
inference(monotonicity,[status(thm)],[202]) ).
tff(204,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(out1(or1(h)))
| ~ connection(out1(or1(h)),in1(and1(h)))
| ~ zero(in1(and1(h))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(or1(h)),in1(and1(h)))
| zero(out1(or1(h)))
| ~ zero(in1(and1(h))) ) ),
inference(transitivity,[status(thm)],[203,201]) ).
tff(205,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(out1(or1(h)))
| ~ connection(out1(or1(h)),in1(and1(h)))
| ~ zero(in1(and1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(206,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(or1(h)),in1(and1(h)))
| zero(out1(or1(h)))
| ~ zero(in1(and1(h))) ),
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
( zero(out1(or1(h)))
| ~ zero(in1(and1(h))) ),
inference(unit_resolution,[status(thm)],[206,136,200]) ).
tff(208,plain,
~ zero(in1(and1(h))),
inference(unit_resolution,[status(thm)],[207,189]) ).
tff(209,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(210,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)],[209]) ).
tff(211,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(212,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_connection_outs_out1and1) ).
tff(213,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ),
inference(modus_ponens,[status(thm)],[212,211]) ).
tff(214,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ),
inference(skolemize,[status(sab)],[213]) ).
tff(215,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) ),
inference(modus_ponens,[status(thm)],[214,210]) ).
tff(216,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
| ~ halfadder(h)
| connection(outs(h),out1(and1(h))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
| ~ halfadder(h)
| connection(outs(h),out1(and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(217,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
| ~ halfadder(h)
| connection(outs(h),out1(and1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(218,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outs(X),out1(and1(X))) )
| ~ halfadder(h)
| connection(outs(h),out1(and1(h))) ),
inference(modus_ponens,[status(thm)],[217,216]) ).
tff(219,plain,
connection(outs(h),out1(and1(h))),
inference(unit_resolution,[status(thm)],[218,215,3]) ).
tff(220,plain,
( zero(outs(h))
<=> zero(outs(h)) ),
inference(rewrite,[status(thm)],]) ).
tff(221,axiom,
zero(outs(h)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outs_0) ).
tff(222,plain,
zero(outs(h)),
inference(modus_ponens,[status(thm)],[221,220]) ).
tff(223,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(224,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)],[223]) ).
tff(225,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(226,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(227,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)],[226]) ).
tff(228,axiom,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ zero(P1)
| zero(P2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',value_propagation_zero1) ).
tff(229,plain,
! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
inference(modus_ponens,[status(thm)],[228,227]) ).
tff(230,plain,
! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
inference(modus_ponens,[status(thm)],[229,225]) ).
tff(231,plain,
! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
inference(skolemize,[status(sab)],[230]) ).
tff(232,plain,
! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
inference(modus_ponens,[status(thm)],[231,224]) ).
tff(233,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outs(h))
| ~ connection(outs(h),out1(and1(h)))
| zero(out1(and1(h))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outs(h))
| ~ connection(outs(h),out1(and1(h)))
| zero(out1(and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(234,plain,
( ( zero(out1(and1(h)))
| ~ zero(outs(h))
| ~ connection(outs(h),out1(and1(h))) )
<=> ( ~ zero(outs(h))
| ~ connection(outs(h),out1(and1(h)))
| zero(out1(and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(235,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(and1(h)))
| ~ zero(outs(h))
| ~ connection(outs(h),out1(and1(h))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outs(h))
| ~ connection(outs(h),out1(and1(h)))
| zero(out1(and1(h))) ) ),
inference(monotonicity,[status(thm)],[234]) ).
tff(236,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(and1(h)))
| ~ zero(outs(h))
| ~ connection(outs(h),out1(and1(h))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outs(h))
| ~ connection(outs(h),out1(and1(h)))
| zero(out1(and1(h))) ) ),
inference(transitivity,[status(thm)],[235,233]) ).
tff(237,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| zero(out1(and1(h)))
| ~ zero(outs(h))
| ~ connection(outs(h),out1(and1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(238,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) )
| ~ zero(outs(h))
| ~ connection(outs(h),out1(and1(h)))
| zero(out1(and1(h))) ),
inference(modus_ponens,[status(thm)],[237,236]) ).
tff(239,plain,
zero(out1(and1(h))),
inference(unit_resolution,[status(thm)],[238,232,222,219]) ).
tff(240,plain,
^ [X: $i] :
refl(
( ( logic_and(and1(X))
| ~ halfadder(X) )
<=> ( logic_and(and1(X))
| ~ halfadder(X) ) )),
inference(bind,[status(th)],]) ).
tff(241,plain,
( ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
<=> ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ) ),
inference(quant_intro,[status(thm)],[240]) ).
tff(242,plain,
( ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
<=> ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(243,plain,
^ [X: $i] :
rewrite(
( ( ~ halfadder(X)
| logic_and(and1(X)) )
<=> ( logic_and(and1(X))
| ~ halfadder(X) ) )),
inference(bind,[status(th)],]) ).
tff(244,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_and(and1(X)) )
<=> ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ) ),
inference(quant_intro,[status(thm)],[243]) ).
tff(245,axiom,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and1(X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_and1) ).
tff(246,plain,
! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ),
inference(modus_ponens,[status(thm)],[245,244]) ).
tff(247,plain,
! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ),
inference(modus_ponens,[status(thm)],[246,242]) ).
tff(248,plain,
! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ),
inference(skolemize,[status(sab)],[247]) ).
tff(249,plain,
! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) ),
inference(modus_ponens,[status(thm)],[248,241]) ).
tff(250,plain,
( ( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h))
| ~ halfadder(h) )
<=> ( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h))
| ~ halfadder(h) ) ),
inference(rewrite,[status(thm)],]) ).
tff(251,plain,
( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h))
| ~ halfadder(h) ),
inference(quant_inst,[status(thm)],]) ).
tff(252,plain,
( ~ ! [X: $i] :
( logic_and(and1(X))
| ~ halfadder(X) )
| logic_and(and1(h))
| ~ halfadder(h) ),
inference(modus_ponens,[status(thm)],[251,250]) ).
tff(253,plain,
logic_and(and1(h)),
inference(unit_resolution,[status(thm)],[252,249,3]) ).
tff(254,plain,
( ~ abnormal(and1(h))
<=> ~ abnormal(and1(h)) ),
inference(rewrite,[status(thm)],]) ).
tff(255,axiom,
~ abnormal(and1(h)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diagnosis_and1) ).
tff(256,plain,
~ abnormal(and1(h)),
inference(modus_ponens,[status(thm)],[255,254]) ).
tff(257,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(258,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)],[257]) ).
tff(259,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(260,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(261,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)],[260]) ).
tff(262,axiom,
! [K: $i] :
( ~ logic_and(K)
| and_ok(K)
| abnormal(K) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',and_ok_or_abnormal) ).
tff(263,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(modus_ponens,[status(thm)],[262,261]) ).
tff(264,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(modus_ponens,[status(thm)],[263,259]) ).
tff(265,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(skolemize,[status(sab)],[264]) ).
tff(266,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(modus_ponens,[status(thm)],[265,258]) ).
tff(267,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h))
| and_ok(and1(h))
| ~ logic_and(and1(h)) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h))
| and_ok(and1(h))
| ~ logic_and(and1(h)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(268,plain,
( ( and_ok(and1(h))
| abnormal(and1(h))
| ~ logic_and(and1(h)) )
<=> ( abnormal(and1(h))
| and_ok(and1(h))
| ~ logic_and(and1(h)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(269,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and1(h))
| abnormal(and1(h))
| ~ logic_and(and1(h)) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h))
| and_ok(and1(h))
| ~ logic_and(and1(h)) ) ),
inference(monotonicity,[status(thm)],[268]) ).
tff(270,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and1(h))
| abnormal(and1(h))
| ~ logic_and(and1(h)) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h))
| and_ok(and1(h))
| ~ logic_and(and1(h)) ) ),
inference(transitivity,[status(thm)],[269,267]) ).
tff(271,plain,
( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and1(h))
| abnormal(and1(h))
| ~ logic_and(and1(h)) ),
inference(quant_inst,[status(thm)],]) ).
tff(272,plain,
( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and1(h))
| and_ok(and1(h))
| ~ logic_and(and1(h)) ),
inference(modus_ponens,[status(thm)],[271,270]) ).
tff(273,plain,
( and_ok(and1(h))
| ~ logic_and(and1(h)) ),
inference(unit_resolution,[status(thm)],[272,266,256]) ).
tff(274,plain,
and_ok(and1(h)),
inference(unit_resolution,[status(thm)],[273,253]) ).
tff(275,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(276,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)],[275]) ).
tff(277,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(278,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(279,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)],[278]) ).
tff(280,axiom,
! [K: $i] :
( ~ and_ok(K)
| ~ zero(out1(K))
| zero(in1(K))
| zero(in2(K)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-0.ax',and_0_00) ).
tff(281,plain,
! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ),
inference(modus_ponens,[status(thm)],[280,279]) ).
tff(282,plain,
! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ),
inference(modus_ponens,[status(thm)],[281,277]) ).
tff(283,plain,
! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ),
inference(skolemize,[status(sab)],[282]) ).
tff(284,plain,
! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) ),
inference(modus_ponens,[status(thm)],[283,276]) ).
tff(285,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in2(and1(h)))
| zero(in1(and1(h)))
| ~ zero(out1(and1(h)))
| ~ and_ok(and1(h)) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in2(and1(h)))
| zero(in1(and1(h)))
| ~ zero(out1(and1(h)))
| ~ and_ok(and1(h)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(286,plain,
( ( zero(in1(and1(h)))
| ~ and_ok(and1(h))
| zero(in2(and1(h)))
| ~ zero(out1(and1(h))) )
<=> ( zero(in2(and1(h)))
| zero(in1(and1(h)))
| ~ zero(out1(and1(h)))
| ~ and_ok(and1(h)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(287,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in1(and1(h)))
| ~ and_ok(and1(h))
| zero(in2(and1(h)))
| ~ zero(out1(and1(h))) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in2(and1(h)))
| zero(in1(and1(h)))
| ~ zero(out1(and1(h)))
| ~ and_ok(and1(h)) ) ),
inference(monotonicity,[status(thm)],[286]) ).
tff(288,plain,
( ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in1(and1(h)))
| ~ and_ok(and1(h))
| zero(in2(and1(h)))
| ~ zero(out1(and1(h))) )
<=> ( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in2(and1(h)))
| zero(in1(and1(h)))
| ~ zero(out1(and1(h)))
| ~ and_ok(and1(h)) ) ),
inference(transitivity,[status(thm)],[287,285]) ).
tff(289,plain,
( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in1(and1(h)))
| ~ and_ok(and1(h))
| zero(in2(and1(h)))
| ~ zero(out1(and1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(290,plain,
( ~ ! [K: $i] :
( zero(in1(K))
| ~ and_ok(K)
| zero(in2(K))
| ~ zero(out1(K)) )
| zero(in2(and1(h)))
| zero(in1(and1(h)))
| ~ zero(out1(and1(h)))
| ~ and_ok(and1(h)) ),
inference(modus_ponens,[status(thm)],[289,288]) ).
tff(291,plain,
( zero(in2(and1(h)))
| zero(in1(and1(h))) ),
inference(unit_resolution,[status(thm)],[290,284,274,239]) ).
tff(292,plain,
zero(in2(and1(h))),
inference(unit_resolution,[status(thm)],[291,208]) ).
tff(293,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(294,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)],[293]) ).
tff(295,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(296,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV002-1.ax',halfadder_connection_out1not1_in2and1) ).
tff(297,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ),
inference(modus_ponens,[status(thm)],[296,295]) ).
tff(298,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ),
inference(skolemize,[status(sab)],[297]) ).
tff(299,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) ),
inference(modus_ponens,[status(thm)],[298,294]) ).
tff(300,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
| ~ halfadder(h)
| connection(out1(not1(h)),in2(and1(h))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
| ~ halfadder(h)
| connection(out1(not1(h)),in2(and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(301,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
| ~ halfadder(h)
| connection(out1(not1(h)),in2(and1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(302,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(out1(not1(X)),in2(and1(X))) )
| ~ halfadder(h)
| connection(out1(not1(h)),in2(and1(h))) ),
inference(modus_ponens,[status(thm)],[301,300]) ).
tff(303,plain,
connection(out1(not1(h)),in2(and1(h))),
inference(unit_resolution,[status(thm)],[302,299,3]) ).
tff(304,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(not1(h)),in2(and1(h)))
| zero(out1(not1(h)))
| ~ zero(in2(and1(h))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(not1(h)),in2(and1(h)))
| zero(out1(not1(h)))
| ~ zero(in2(and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(305,plain,
( ( zero(out1(not1(h)))
| ~ connection(out1(not1(h)),in2(and1(h)))
| ~ zero(in2(and1(h))) )
<=> ( ~ connection(out1(not1(h)),in2(and1(h)))
| zero(out1(not1(h)))
| ~ zero(in2(and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(306,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(out1(not1(h)))
| ~ connection(out1(not1(h)),in2(and1(h)))
| ~ zero(in2(and1(h))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(not1(h)),in2(and1(h)))
| zero(out1(not1(h)))
| ~ zero(in2(and1(h))) ) ),
inference(monotonicity,[status(thm)],[305]) ).
tff(307,plain,
( ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(out1(not1(h)))
| ~ connection(out1(not1(h)),in2(and1(h)))
| ~ zero(in2(and1(h))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(not1(h)),in2(and1(h)))
| zero(out1(not1(h)))
| ~ zero(in2(and1(h))) ) ),
inference(transitivity,[status(thm)],[306,304]) ).
tff(308,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| zero(out1(not1(h)))
| ~ connection(out1(not1(h)),in2(and1(h)))
| ~ zero(in2(and1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(309,plain,
( ~ ! [P2: $i,P1: $i] :
( zero(P1)
| ~ connection(P1,P2)
| ~ zero(P2) )
| ~ connection(out1(not1(h)),in2(and1(h)))
| zero(out1(not1(h)))
| ~ zero(in2(and1(h))) ),
inference(modus_ponens,[status(thm)],[308,307]) ).
tff(310,plain,
( zero(out1(not1(h)))
| ~ zero(in2(and1(h))) ),
inference(unit_resolution,[status(thm)],[309,136,303]) ).
tff(311,plain,
$false,
inference(unit_resolution,[status(thm)],[310,292,108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HWV005-2 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 22:00:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------