TSTP Solution File: HWV005-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV005-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 02:10:27 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 149
% Syntax : Number of formulae : 299 ( 64 unt; 23 typ; 0 def)
% Number of atoms : 1533 ( 0 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 2240 (1036 ~;1074 |; 0 &)
% ( 130 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 53 ( 53 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 11 >; 7 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 12 con; 0-2 aty)
% Number of variables : 491 ( 454 !; 0 ?; 491 :)
% Comments :
%------------------------------------------------------------------------------
tff(value_type,type,
value: ( $i * $i ) > $o ).
tff(n0_type,type,
n0: $i ).
tff(out_type,type,
out: ( $i * $i ) > $i ).
tff(and1_type,type,
and1: $i > $i ).
tff(h_type,type,
h: $i ).
tff(n1_type,type,
n1: $i ).
tff(in_type,type,
in: ( $i * $i ) > $i ).
tff(or1_type,type,
or1: $i > $i ).
tff(mode_type,type,
mode: ( $i * $i ) > $o ).
tff(ok_type,type,
ok: $i ).
tff(type_type,type,
type: ( $i * $i ) > $o ).
tff(or_type,type,
or: $i ).
tff(halfadder_type,type,
halfadder: $i ).
tff(abnormal_type,type,
abnormal: $i ).
tff(connection_type,type,
connection: ( $i * $i ) > $o ).
tff(equal_value_type,type,
equal_value: ( $i * $i ) > $o ).
tff(and_type,type,
and: $i ).
tff(n2_type,type,
n2: $i ).
tff(not1_type,type,
not1: $i > $i ).
tff(not_type,type,
not: $i ).
tff(and2_type,type,
and2: $i > $i ).
tff(c_type,type,
c: $i ).
tff(s_type,type,
s: $i ).
tff(1,plain,
( type(h,halfadder)
<=> type(h,halfadder) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
type(h,halfadder),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_isa_halfadder) ).
tff(3,plain,
type(h,halfadder),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(
( ( ~ type(X,halfadder)
| type(or1(X),or) )
<=> ( ~ type(X,halfadder)
| type(or1(X),or) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| type(or1(X),or) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| type(or1(X),or) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| type(or1(X),or) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| type(or1(X),or) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [X: $i] :
( ~ type(X,halfadder)
| type(or1(X),or) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-1.ax',halfadder_or1) ).
tff(8,plain,
! [X: $i] :
( ~ type(X,halfadder)
| type(or1(X),or) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X: $i] :
( ~ type(X,halfadder)
| type(or1(X),or) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] :
( ~ type(X,halfadder)
| type(or1(X),or) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| type(or1(X),or) )
| ~ type(h,halfadder)
| type(or1(h),or) )
<=> ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| type(or1(X),or) )
| ~ type(h,halfadder)
| type(or1(h),or) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| type(or1(X),or) )
| ~ type(h,halfadder)
| type(or1(h),or) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| type(or1(X),or) )
| ~ type(h,halfadder)
| type(or1(h),or) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
type(or1(h),or),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ~ mode(or1(h),abnormal)
<=> ~ mode(or1(h),abnormal) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
~ mode(or1(h),abnormal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_or1) ).
tff(17,plain,
~ mode(or1(h),abnormal),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [Any: $i,K: $i] :
refl(
( ( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
<=> ( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
<=> ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
<=> ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [Any: $i,K: $i] :
rewrite(
( ( ~ type(K,Any)
| mode(K,ok)
| mode(K,abnormal) )
<=> ( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [Any: $i,K: $i] :
( ~ type(K,Any)
| mode(K,ok)
| mode(K,abnormal) )
<=> ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [Any: $i,K: $i] :
( ~ type(K,Any)
| mode(K,ok)
| mode(K,abnormal) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-0.ax',ok_or_abnormal) ).
tff(24,plain,
! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
| mode(or1(h),abnormal)
| mode(or1(h),ok)
| ~ type(or1(h),or) )
<=> ( ~ ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
| mode(or1(h),abnormal)
| mode(or1(h),ok)
| ~ type(or1(h),or) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
| mode(or1(h),abnormal)
| mode(or1(h),ok)
| ~ type(or1(h),or) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
| mode(or1(h),abnormal)
| mode(or1(h),ok)
| ~ type(or1(h),or) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
mode(or1(h),ok),
inference(unit_resolution,[status(thm)],[30,27,17,14]) ).
tff(32,plain,
^ [X: $i] :
refl(
( ( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) )
<=> ( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [X: $i] :
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-1.ax',halfadder_connection_in1_in1or1) ).
tff(36,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) )
| ~ type(h,halfadder)
| connection(in(n1,h),in(n1,or1(h))) )
<=> ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) )
| ~ type(h,halfadder)
| connection(in(n1,h),in(n1,or1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) )
| ~ type(h,halfadder)
| connection(in(n1,h),in(n1,or1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) )
| ~ type(h,halfadder)
| connection(in(n1,h),in(n1,or1(h))) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
connection(in(n1,h),in(n1,or1(h))),
inference(unit_resolution,[status(thm)],[41,38,3]) ).
tff(43,plain,
( value(in(n1,h),n1)
<=> value(in(n1,h),n1) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
value(in(n1,h),n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in1_1) ).
tff(45,plain,
value(in(n1,h),n1),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( ~ equal_value(n0,n1)
<=> ~ equal_value(n0,n1) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
~ equal_value(n0,n1),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-0.ax',equal_value1) ).
tff(48,plain,
~ equal_value(n0,n1),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
^ [P: $i,V1: $i,V2: $i] :
refl(
( ( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) )
<=> ( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) )
<=> ! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) )
<=> ! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
^ [P: $i,V1: $i,V2: $i] :
trans(
monotonicity(
rewrite(
( ( ~ value(P,V1)
| ~ value(P,V2) )
<=> ( ~ value(P,V2)
| ~ value(P,V1) ) )),
( ( ~ value(P,V1)
| ~ value(P,V2)
| equal_value(V1,V2) )
<=> ( ~ value(P,V2)
| ~ value(P,V1)
| equal_value(V1,V2) ) )),
rewrite(
( ( ~ value(P,V2)
| ~ value(P,V1)
| equal_value(V1,V2) )
<=> ( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) ) )),
( ( ~ value(P,V1)
| ~ value(P,V2)
| equal_value(V1,V2) )
<=> ( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [P: $i,V1: $i,V2: $i] :
( ~ value(P,V1)
| ~ value(P,V2)
| equal_value(V1,V2) )
<=> ! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [P: $i,V1: $i,V2: $i] :
( ~ value(P,V1)
| ~ value(P,V2)
| equal_value(V1,V2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-0.ax',unique_value) ).
tff(55,plain,
! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) )
| equal_value(n0,n1)
| ~ value(in(n1,h),n1)
| ~ value(in(n1,h),n0) )
<=> ( ~ ! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) )
| equal_value(n0,n1)
| ~ value(in(n1,h),n1)
| ~ value(in(n1,h),n0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) )
| equal_value(n0,n1)
| ~ value(in(n1,h),n1)
| ~ value(in(n1,h),n0) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) )
| equal_value(n0,n1)
| ~ value(in(n1,h),n1)
| ~ value(in(n1,h),n0) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
~ value(in(n1,h),n0),
inference(unit_resolution,[status(thm)],[61,58,48,45]) ).
tff(63,plain,
^ [V: $i,P2: $i,P1: $i] :
refl(
( ( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
<=> ( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
<=> ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
<=> ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
^ [V: $i,P2: $i,P1: $i] :
rewrite(
( ( ~ connection(P1,P2)
| ~ value(P2,V)
| value(P1,V) )
<=> ( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [V: $i,P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ value(P2,V)
| value(P1,V) )
<=> ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,axiom,
! [V: $i,P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ value(P2,V)
| value(P1,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-0.ax',value_propagation2) ).
tff(69,plain,
! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) ),
inference(modus_ponens,[status(thm)],[71,64]) ).
tff(73,plain,
( ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(in(n1,h),n0)
| ~ connection(in(n1,h),in(n1,or1(h)))
| ~ value(in(n1,or1(h)),n0) )
<=> ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(in(n1,h),n0)
| ~ connection(in(n1,h),in(n1,or1(h)))
| ~ value(in(n1,or1(h)),n0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(in(n1,h),n0)
| ~ connection(in(n1,h),in(n1,or1(h)))
| ~ value(in(n1,or1(h)),n0) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(in(n1,h),n0)
| ~ connection(in(n1,h),in(n1,or1(h)))
| ~ value(in(n1,or1(h)),n0) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
~ value(in(n1,or1(h)),n0),
inference(unit_resolution,[status(thm)],[75,72,62,42]) ).
tff(77,plain,
^ [K: $i] :
refl(
( ( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) )
<=> ( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) ) )),
inference(bind,[status(th)],]) ).
tff(78,plain,
( ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) )
<=> ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
( ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) )
<=> ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
^ [K: $i] :
trans(
monotonicity(
rewrite(
( ( ~ mode(K,ok)
| ~ type(K,or)
| ~ value(out(n1,K),n0) )
<=> ( ~ mode(K,ok)
| ~ value(out(n1,K),n0)
| ~ type(K,or) ) )),
( ( ~ mode(K,ok)
| ~ type(K,or)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n0) )
<=> ( ~ mode(K,ok)
| ~ value(out(n1,K),n0)
| ~ type(K,or)
| value(in(n1,K),n0) ) )),
rewrite(
( ( ~ mode(K,ok)
| ~ value(out(n1,K),n0)
| ~ type(K,or)
| value(in(n1,K),n0) )
<=> ( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) ) )),
( ( ~ mode(K,ok)
| ~ type(K,or)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n0) )
<=> ( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) ) )),
inference(bind,[status(th)],]) ).
tff(81,plain,
( ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,or)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n0) )
<=> ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,axiom,
! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,or)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n0) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-0.ax',or_0_0x) ).
tff(83,plain,
! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) ),
inference(modus_ponens,[status(thm)],[85,78]) ).
tff(87,plain,
( ( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) )
| value(in(n1,or1(h)),n0)
| ~ mode(or1(h),ok)
| ~ value(out(n1,or1(h)),n0)
| ~ type(or1(h),or) )
<=> ( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) )
| value(in(n1,or1(h)),n0)
| ~ mode(or1(h),ok)
| ~ value(out(n1,or1(h)),n0)
| ~ type(or1(h),or) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( ~ mode(or1(h),ok)
| value(in(n1,or1(h)),n0)
| ~ value(out(n1,or1(h)),n0)
| ~ type(or1(h),or) )
<=> ( value(in(n1,or1(h)),n0)
| ~ mode(or1(h),ok)
| ~ value(out(n1,or1(h)),n0)
| ~ type(or1(h),or) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) )
| ~ mode(or1(h),ok)
| value(in(n1,or1(h)),n0)
| ~ value(out(n1,or1(h)),n0)
| ~ type(or1(h),or) )
<=> ( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) )
| value(in(n1,or1(h)),n0)
| ~ mode(or1(h),ok)
| ~ value(out(n1,or1(h)),n0)
| ~ type(or1(h),or) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) )
| ~ mode(or1(h),ok)
| value(in(n1,or1(h)),n0)
| ~ value(out(n1,or1(h)),n0)
| ~ type(or1(h),or) )
<=> ( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) )
| value(in(n1,or1(h)),n0)
| ~ mode(or1(h),ok)
| ~ value(out(n1,or1(h)),n0)
| ~ type(or1(h),or) ) ),
inference(transitivity,[status(thm)],[89,87]) ).
tff(91,plain,
( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) )
| ~ mode(or1(h),ok)
| value(in(n1,or1(h)),n0)
| ~ value(out(n1,or1(h)),n0)
| ~ type(or1(h),or) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or) )
| value(in(n1,or1(h)),n0)
| ~ mode(or1(h),ok)
| ~ value(out(n1,or1(h)),n0)
| ~ type(or1(h),or) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
( ~ mode(or1(h),ok)
| ~ value(out(n1,or1(h)),n0) ),
inference(unit_resolution,[status(thm)],[92,86,14,76]) ).
tff(94,plain,
~ value(out(n1,or1(h)),n0),
inference(unit_resolution,[status(thm)],[93,31]) ).
tff(95,plain,
^ [X: $i] :
refl(
( ( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) )
<=> ( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,axiom,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-1.ax',halfadder_connection_out1or1_in1_and1) ).
tff(99,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
( ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) )
| ~ type(h,halfadder)
| connection(out(n1,or1(h)),in(n1,and1(h))) )
<=> ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) )
| ~ type(h,halfadder)
| connection(out(n1,or1(h)),in(n1,and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) )
| ~ type(h,halfadder)
| connection(out(n1,or1(h)),in(n1,and1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) )
| ~ type(h,halfadder)
| connection(out(n1,or1(h)),in(n1,and1(h))) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
connection(out(n1,or1(h)),in(n1,and1(h))),
inference(unit_resolution,[status(thm)],[104,101,3]) ).
tff(106,plain,
( ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| ~ value(in(n1,and1(h)),n0)
| value(out(n1,or1(h)),n0)
| ~ connection(out(n1,or1(h)),in(n1,and1(h))) )
<=> ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| ~ value(in(n1,and1(h)),n0)
| value(out(n1,or1(h)),n0)
| ~ connection(out(n1,or1(h)),in(n1,and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ( value(out(n1,or1(h)),n0)
| ~ connection(out(n1,or1(h)),in(n1,and1(h)))
| ~ value(in(n1,and1(h)),n0) )
<=> ( ~ value(in(n1,and1(h)),n0)
| value(out(n1,or1(h)),n0)
| ~ connection(out(n1,or1(h)),in(n1,and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(n1,or1(h)),n0)
| ~ connection(out(n1,or1(h)),in(n1,and1(h)))
| ~ value(in(n1,and1(h)),n0) )
<=> ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| ~ value(in(n1,and1(h)),n0)
| value(out(n1,or1(h)),n0)
| ~ connection(out(n1,or1(h)),in(n1,and1(h))) ) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(n1,or1(h)),n0)
| ~ connection(out(n1,or1(h)),in(n1,and1(h)))
| ~ value(in(n1,and1(h)),n0) )
<=> ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| ~ value(in(n1,and1(h)),n0)
| value(out(n1,or1(h)),n0)
| ~ connection(out(n1,or1(h)),in(n1,and1(h))) ) ),
inference(transitivity,[status(thm)],[108,106]) ).
tff(110,plain,
( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(n1,or1(h)),n0)
| ~ connection(out(n1,or1(h)),in(n1,and1(h)))
| ~ value(in(n1,and1(h)),n0) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| ~ value(in(n1,and1(h)),n0)
| value(out(n1,or1(h)),n0)
| ~ connection(out(n1,or1(h)),in(n1,and1(h))) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
~ value(in(n1,and1(h)),n0),
inference(unit_resolution,[status(thm)],[111,72,105,94]) ).
tff(113,plain,
^ [X: $i] :
refl(
( ( ~ type(X,halfadder)
| type(and1(X),and) )
<=> ( ~ type(X,halfadder)
| type(and1(X),and) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| type(and1(X),and) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| type(and1(X),and) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| type(and1(X),and) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| type(and1(X),and) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,axiom,
! [X: $i] :
( ~ type(X,halfadder)
| type(and1(X),and) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-1.ax',halfadder_and1) ).
tff(117,plain,
! [X: $i] :
( ~ type(X,halfadder)
| type(and1(X),and) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [X: $i] :
( ~ type(X,halfadder)
| type(and1(X),and) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [X: $i] :
( ~ type(X,halfadder)
| type(and1(X),and) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
( ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| type(and1(X),and) )
| ~ type(h,halfadder)
| type(and1(h),and) )
<=> ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| type(and1(X),and) )
| ~ type(h,halfadder)
| type(and1(h),and) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| type(and1(X),and) )
| ~ type(h,halfadder)
| type(and1(h),and) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| type(and1(X),and) )
| ~ type(h,halfadder)
| type(and1(h),and) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
type(and1(h),and),
inference(unit_resolution,[status(thm)],[122,119,3]) ).
tff(124,plain,
( ~ mode(and1(h),abnormal)
<=> ~ mode(and1(h),abnormal) ),
inference(rewrite,[status(thm)],]) ).
tff(125,axiom,
~ mode(and1(h),abnormal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_and1) ).
tff(126,plain,
~ mode(and1(h),abnormal),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
( ( ~ ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
| mode(and1(h),abnormal)
| mode(and1(h),ok)
| ~ type(and1(h),and) )
<=> ( ~ ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
| mode(and1(h),abnormal)
| mode(and1(h),ok)
| ~ type(and1(h),and) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,plain,
( ~ ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
| mode(and1(h),abnormal)
| mode(and1(h),ok)
| ~ type(and1(h),and) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
( ~ ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
| mode(and1(h),abnormal)
| mode(and1(h),ok)
| ~ type(and1(h),and) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
mode(and1(h),ok),
inference(unit_resolution,[status(thm)],[129,27,126,123]) ).
tff(131,plain,
^ [X: $i] :
refl(
( ( ~ type(X,halfadder)
| type(not1(X),not) )
<=> ( ~ type(X,halfadder)
| type(not1(X),not) ) )),
inference(bind,[status(th)],]) ).
tff(132,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| type(not1(X),not) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| type(not1(X),not) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| type(not1(X),not) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| type(not1(X),not) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,axiom,
! [X: $i] :
( ~ type(X,halfadder)
| type(not1(X),not) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-1.ax',halfadder_not1) ).
tff(135,plain,
! [X: $i] :
( ~ type(X,halfadder)
| type(not1(X),not) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [X: $i] :
( ~ type(X,halfadder)
| type(not1(X),not) ),
inference(skolemize,[status(sab)],[135]) ).
tff(137,plain,
! [X: $i] :
( ~ type(X,halfadder)
| type(not1(X),not) ),
inference(modus_ponens,[status(thm)],[136,132]) ).
tff(138,plain,
( ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| type(not1(X),not) )
| ~ type(h,halfadder)
| type(not1(h),not) )
<=> ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| type(not1(X),not) )
| ~ type(h,halfadder)
| type(not1(h),not) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| type(not1(X),not) )
| ~ type(h,halfadder)
| type(not1(h),not) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| type(not1(X),not) )
| ~ type(h,halfadder)
| type(not1(h),not) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
type(not1(h),not),
inference(unit_resolution,[status(thm)],[140,137,3]) ).
tff(142,plain,
( ~ mode(not1(h),abnormal)
<=> ~ mode(not1(h),abnormal) ),
inference(rewrite,[status(thm)],]) ).
tff(143,axiom,
~ mode(not1(h),abnormal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_not1) ).
tff(144,plain,
~ mode(not1(h),abnormal),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
( ( ~ ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
| mode(not1(h),abnormal)
| mode(not1(h),ok)
| ~ type(not1(h),not) )
<=> ( ~ ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
| mode(not1(h),abnormal)
| mode(not1(h),ok)
| ~ type(not1(h),not) ) ),
inference(rewrite,[status(thm)],]) ).
tff(146,plain,
( ~ ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
| mode(not1(h),abnormal)
| mode(not1(h),ok)
| ~ type(not1(h),not) ),
inference(quant_inst,[status(thm)],]) ).
tff(147,plain,
( ~ ! [Any: $i,K: $i] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) )
| mode(not1(h),abnormal)
| mode(not1(h),ok)
| ~ type(not1(h),not) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
mode(not1(h),ok),
inference(unit_resolution,[status(thm)],[147,27,144,141]) ).
tff(149,plain,
^ [X: $i] :
refl(
( ( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) )
<=> ( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) ) )),
inference(bind,[status(th)],]) ).
tff(150,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,axiom,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-1.ax',halfadder_connection_outc_out1and2) ).
tff(153,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) ),
inference(skolemize,[status(sab)],[153]) ).
tff(155,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) ),
inference(modus_ponens,[status(thm)],[154,150]) ).
tff(156,plain,
( ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) )
| ~ type(h,halfadder)
| connection(out(c,h),out(n1,and2(h))) )
<=> ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) )
| ~ type(h,halfadder)
| connection(out(c,h),out(n1,and2(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) )
| ~ type(h,halfadder)
| connection(out(c,h),out(n1,and2(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) )
| ~ type(h,halfadder)
| connection(out(c,h),out(n1,and2(h))) ),
inference(modus_ponens,[status(thm)],[157,156]) ).
tff(159,plain,
connection(out(c,h),out(n1,and2(h))),
inference(unit_resolution,[status(thm)],[158,155,3]) ).
tff(160,plain,
( value(out(c,h),n0)
<=> value(out(c,h),n0) ),
inference(rewrite,[status(thm)],]) ).
tff(161,axiom,
value(out(c,h),n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outc_0) ).
tff(162,plain,
value(out(c,h),n0),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
( ~ equal_value(n1,n0)
<=> ~ equal_value(n1,n0) ),
inference(rewrite,[status(thm)],]) ).
tff(164,axiom,
~ equal_value(n1,n0),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-0.ax',equal_value2) ).
tff(165,plain,
~ equal_value(n1,n0),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
( ( ~ ! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) )
| equal_value(n1,n0)
| ~ value(out(c,h),n0)
| ~ value(out(c,h),n1) )
<=> ( ~ ! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) )
| equal_value(n1,n0)
| ~ value(out(c,h),n0)
| ~ value(out(c,h),n1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(167,plain,
( ~ ! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) )
| equal_value(n1,n0)
| ~ value(out(c,h),n0)
| ~ value(out(c,h),n1) ),
inference(quant_inst,[status(thm)],]) ).
tff(168,plain,
( ~ ! [P: $i,V1: $i,V2: $i] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) )
| equal_value(n1,n0)
| ~ value(out(c,h),n0)
| ~ value(out(c,h),n1) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
~ value(out(c,h),n1),
inference(unit_resolution,[status(thm)],[168,58,165,162]) ).
tff(170,plain,
( ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(c,h),n1)
| ~ connection(out(c,h),out(n1,and2(h)))
| ~ value(out(n1,and2(h)),n1) )
<=> ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(c,h),n1)
| ~ connection(out(c,h),out(n1,and2(h)))
| ~ value(out(n1,and2(h)),n1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(171,plain,
( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(c,h),n1)
| ~ connection(out(c,h),out(n1,and2(h)))
| ~ value(out(n1,and2(h)),n1) ),
inference(quant_inst,[status(thm)],]) ).
tff(172,plain,
( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(c,h),n1)
| ~ connection(out(c,h),out(n1,and2(h)))
| ~ value(out(n1,and2(h)),n1) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
~ value(out(n1,and2(h)),n1),
inference(unit_resolution,[status(thm)],[172,72,169,159]) ).
tff(174,plain,
^ [X: $i] :
refl(
( ( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) )
<=> ( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) ) )),
inference(bind,[status(th)],]) ).
tff(175,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) ) ),
inference(quant_intro,[status(thm)],[174]) ).
tff(176,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(177,axiom,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-1.ax',halfadder_connection_out1and2_in1not1) ).
tff(178,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) ),
inference(modus_ponens,[status(thm)],[177,176]) ).
tff(179,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) ),
inference(skolemize,[status(sab)],[178]) ).
tff(180,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) ),
inference(modus_ponens,[status(thm)],[179,175]) ).
tff(181,plain,
( ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) )
| ~ type(h,halfadder)
| connection(out(n1,and2(h)),in(n1,not1(h))) )
<=> ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) )
| ~ type(h,halfadder)
| connection(out(n1,and2(h)),in(n1,not1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(182,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) )
| ~ type(h,halfadder)
| connection(out(n1,and2(h)),in(n1,not1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) )
| ~ type(h,halfadder)
| connection(out(n1,and2(h)),in(n1,not1(h))) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
connection(out(n1,and2(h)),in(n1,not1(h))),
inference(unit_resolution,[status(thm)],[183,180,3]) ).
tff(185,plain,
( ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(n1,and2(h)),n1)
| ~ value(in(n1,not1(h)),n1)
| ~ connection(out(n1,and2(h)),in(n1,not1(h))) )
<=> ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(n1,and2(h)),n1)
| ~ value(in(n1,not1(h)),n1)
| ~ connection(out(n1,and2(h)),in(n1,not1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(186,plain,
( ( value(out(n1,and2(h)),n1)
| ~ connection(out(n1,and2(h)),in(n1,not1(h)))
| ~ value(in(n1,not1(h)),n1) )
<=> ( value(out(n1,and2(h)),n1)
| ~ value(in(n1,not1(h)),n1)
| ~ connection(out(n1,and2(h)),in(n1,not1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(187,plain,
( ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(n1,and2(h)),n1)
| ~ connection(out(n1,and2(h)),in(n1,not1(h)))
| ~ value(in(n1,not1(h)),n1) )
<=> ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(n1,and2(h)),n1)
| ~ value(in(n1,not1(h)),n1)
| ~ connection(out(n1,and2(h)),in(n1,not1(h))) ) ),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
( ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(n1,and2(h)),n1)
| ~ connection(out(n1,and2(h)),in(n1,not1(h)))
| ~ value(in(n1,not1(h)),n1) )
<=> ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(n1,and2(h)),n1)
| ~ value(in(n1,not1(h)),n1)
| ~ connection(out(n1,and2(h)),in(n1,not1(h))) ) ),
inference(transitivity,[status(thm)],[187,185]) ).
tff(189,plain,
( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(n1,and2(h)),n1)
| ~ connection(out(n1,and2(h)),in(n1,not1(h)))
| ~ value(in(n1,not1(h)),n1) ),
inference(quant_inst,[status(thm)],]) ).
tff(190,plain,
( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(n1,and2(h)),n1)
| ~ value(in(n1,not1(h)),n1)
| ~ connection(out(n1,and2(h)),in(n1,not1(h))) ),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,plain,
~ value(in(n1,not1(h)),n1),
inference(unit_resolution,[status(thm)],[190,72,184,173]) ).
tff(192,plain,
^ [K: $i] :
refl(
( ( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) )
<=> ( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) ) )),
inference(bind,[status(th)],]) ).
tff(193,plain,
( ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) )
<=> ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) ) ),
inference(quant_intro,[status(thm)],[192]) ).
tff(194,plain,
( ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) )
<=> ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) ) ),
inference(rewrite,[status(thm)],]) ).
tff(195,plain,
^ [K: $i] :
trans(
monotonicity(
rewrite(
( ( ~ mode(K,ok)
| ~ type(K,not)
| ~ value(out(n1,K),n0) )
<=> ( ~ mode(K,ok)
| ~ value(out(n1,K),n0)
| ~ type(K,not) ) )),
( ( ~ mode(K,ok)
| ~ type(K,not)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n1) )
<=> ( ~ mode(K,ok)
| ~ value(out(n1,K),n0)
| ~ type(K,not)
| value(in(n1,K),n1) ) )),
rewrite(
( ( ~ mode(K,ok)
| ~ value(out(n1,K),n0)
| ~ type(K,not)
| value(in(n1,K),n1) )
<=> ( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) ) )),
( ( ~ mode(K,ok)
| ~ type(K,not)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n1) )
<=> ( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) ) )),
inference(bind,[status(th)],]) ).
tff(196,plain,
( ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,not)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n1) )
<=> ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) ) ),
inference(quant_intro,[status(thm)],[195]) ).
tff(197,axiom,
! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,not)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-0.ax',not_0_1_bw) ).
tff(198,plain,
! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) ),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) ),
inference(modus_ponens,[status(thm)],[198,194]) ).
tff(200,plain,
! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) ),
inference(skolemize,[status(sab)],[199]) ).
tff(201,plain,
! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) ),
inference(modus_ponens,[status(thm)],[200,193]) ).
tff(202,plain,
( ( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) )
| ~ mode(not1(h),ok)
| value(in(n1,not1(h)),n1)
| ~ type(not1(h),not)
| ~ value(out(n1,not1(h)),n0) )
<=> ( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) )
| ~ mode(not1(h),ok)
| value(in(n1,not1(h)),n1)
| ~ type(not1(h),not)
| ~ value(out(n1,not1(h)),n0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(203,plain,
( ( ~ mode(not1(h),ok)
| value(in(n1,not1(h)),n1)
| ~ value(out(n1,not1(h)),n0)
| ~ type(not1(h),not) )
<=> ( ~ mode(not1(h),ok)
| value(in(n1,not1(h)),n1)
| ~ type(not1(h),not)
| ~ value(out(n1,not1(h)),n0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(204,plain,
( ( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) )
| ~ mode(not1(h),ok)
| value(in(n1,not1(h)),n1)
| ~ value(out(n1,not1(h)),n0)
| ~ type(not1(h),not) )
<=> ( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) )
| ~ mode(not1(h),ok)
| value(in(n1,not1(h)),n1)
| ~ type(not1(h),not)
| ~ value(out(n1,not1(h)),n0) ) ),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
( ( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) )
| ~ mode(not1(h),ok)
| value(in(n1,not1(h)),n1)
| ~ value(out(n1,not1(h)),n0)
| ~ type(not1(h),not) )
<=> ( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) )
| ~ mode(not1(h),ok)
| value(in(n1,not1(h)),n1)
| ~ type(not1(h),not)
| ~ value(out(n1,not1(h)),n0) ) ),
inference(transitivity,[status(thm)],[204,202]) ).
tff(206,plain,
( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) )
| ~ mode(not1(h),ok)
| value(in(n1,not1(h)),n1)
| ~ value(out(n1,not1(h)),n0)
| ~ type(not1(h),not) ),
inference(quant_inst,[status(thm)],]) ).
tff(207,plain,
( ~ ! [K: $i] :
( ~ mode(K,ok)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n0)
| ~ type(K,not) )
| ~ mode(not1(h),ok)
| value(in(n1,not1(h)),n1)
| ~ type(not1(h),not)
| ~ value(out(n1,not1(h)),n0) ),
inference(modus_ponens,[status(thm)],[206,205]) ).
tff(208,plain,
( ~ mode(not1(h),ok)
| value(in(n1,not1(h)),n1)
| ~ value(out(n1,not1(h)),n0) ),
inference(unit_resolution,[status(thm)],[207,201,141]) ).
tff(209,plain,
~ value(out(n1,not1(h)),n0),
inference(unit_resolution,[status(thm)],[208,191,148]) ).
tff(210,plain,
^ [X: $i] :
refl(
( ( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) )
<=> ( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) ) )),
inference(bind,[status(th)],]) ).
tff(211,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) ) ),
inference(quant_intro,[status(thm)],[210]) ).
tff(212,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(213,axiom,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-1.ax',halfadder_connection_out1not1_in2and1) ).
tff(214,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) ),
inference(modus_ponens,[status(thm)],[213,212]) ).
tff(215,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) ),
inference(skolemize,[status(sab)],[214]) ).
tff(216,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) ),
inference(modus_ponens,[status(thm)],[215,211]) ).
tff(217,plain,
( ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) )
| ~ type(h,halfadder)
| connection(out(n1,not1(h)),in(n2,and1(h))) )
<=> ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) )
| ~ type(h,halfadder)
| connection(out(n1,not1(h)),in(n2,and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(218,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) )
| ~ type(h,halfadder)
| connection(out(n1,not1(h)),in(n2,and1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(219,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) )
| ~ type(h,halfadder)
| connection(out(n1,not1(h)),in(n2,and1(h))) ),
inference(modus_ponens,[status(thm)],[218,217]) ).
tff(220,plain,
connection(out(n1,not1(h)),in(n2,and1(h))),
inference(unit_resolution,[status(thm)],[219,216,3]) ).
tff(221,plain,
( ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| ~ value(in(n2,and1(h)),n0)
| value(out(n1,not1(h)),n0)
| ~ connection(out(n1,not1(h)),in(n2,and1(h))) )
<=> ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| ~ value(in(n2,and1(h)),n0)
| value(out(n1,not1(h)),n0)
| ~ connection(out(n1,not1(h)),in(n2,and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(222,plain,
( ( value(out(n1,not1(h)),n0)
| ~ connection(out(n1,not1(h)),in(n2,and1(h)))
| ~ value(in(n2,and1(h)),n0) )
<=> ( ~ value(in(n2,and1(h)),n0)
| value(out(n1,not1(h)),n0)
| ~ connection(out(n1,not1(h)),in(n2,and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(223,plain,
( ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(n1,not1(h)),n0)
| ~ connection(out(n1,not1(h)),in(n2,and1(h)))
| ~ value(in(n2,and1(h)),n0) )
<=> ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| ~ value(in(n2,and1(h)),n0)
| value(out(n1,not1(h)),n0)
| ~ connection(out(n1,not1(h)),in(n2,and1(h))) ) ),
inference(monotonicity,[status(thm)],[222]) ).
tff(224,plain,
( ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(n1,not1(h)),n0)
| ~ connection(out(n1,not1(h)),in(n2,and1(h)))
| ~ value(in(n2,and1(h)),n0) )
<=> ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| ~ value(in(n2,and1(h)),n0)
| value(out(n1,not1(h)),n0)
| ~ connection(out(n1,not1(h)),in(n2,and1(h))) ) ),
inference(transitivity,[status(thm)],[223,221]) ).
tff(225,plain,
( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| value(out(n1,not1(h)),n0)
| ~ connection(out(n1,not1(h)),in(n2,and1(h)))
| ~ value(in(n2,and1(h)),n0) ),
inference(quant_inst,[status(thm)],]) ).
tff(226,plain,
( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P1,V)
| ~ connection(P1,P2)
| ~ value(P2,V) )
| ~ value(in(n2,and1(h)),n0)
| value(out(n1,not1(h)),n0)
| ~ connection(out(n1,not1(h)),in(n2,and1(h))) ),
inference(modus_ponens,[status(thm)],[225,224]) ).
tff(227,plain,
~ value(in(n2,and1(h)),n0),
inference(unit_resolution,[status(thm)],[226,72,220,209]) ).
tff(228,plain,
^ [K: $i] :
refl(
( ( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) )
<=> ( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) ) )),
inference(bind,[status(th)],]) ).
tff(229,plain,
( ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) )
<=> ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) ) ),
inference(quant_intro,[status(thm)],[228]) ).
tff(230,plain,
( ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) )
<=> ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(231,plain,
^ [K: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(out(n1,K),n0) )
<=> ( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(out(n1,K),n0) ) )),
( ( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n0) )
<=> ( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n0) ) )),
rewrite(
( ( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n0) )
<=> ( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) ) )),
( ( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n0) )
<=> ( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) ) )),
( ( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n0)
| value(in(n2,K),n0) )
<=> ( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| value(in(n2,K),n0) ) )),
rewrite(
( ( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| value(in(n2,K),n0) )
<=> ( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) ) )),
( ( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n0)
| value(in(n2,K),n0) )
<=> ( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) ) )),
inference(bind,[status(th)],]) ).
tff(232,plain,
( ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n0)
| value(in(n2,K),n0) )
<=> ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) ) ),
inference(quant_intro,[status(thm)],[231]) ).
tff(233,axiom,
! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n0)
| value(in(n2,K),n0) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-0.ax',and_0_00) ).
tff(234,plain,
! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) ),
inference(modus_ponens,[status(thm)],[233,232]) ).
tff(235,plain,
! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) ),
inference(modus_ponens,[status(thm)],[234,230]) ).
tff(236,plain,
! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) ),
inference(skolemize,[status(sab)],[235]) ).
tff(237,plain,
! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) ),
inference(modus_ponens,[status(thm)],[236,229]) ).
tff(238,plain,
( ( ~ ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) )
| ~ mode(and1(h),ok)
| value(in(n2,and1(h)),n0)
| ~ type(and1(h),and)
| ~ value(out(n1,and1(h)),n0)
| value(in(n1,and1(h)),n0) )
<=> ( ~ ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) )
| ~ mode(and1(h),ok)
| value(in(n2,and1(h)),n0)
| ~ type(and1(h),and)
| ~ value(out(n1,and1(h)),n0)
| value(in(n1,and1(h)),n0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(239,plain,
( ( ~ mode(and1(h),ok)
| ~ type(and1(h),and)
| value(in(n2,and1(h)),n0)
| value(in(n1,and1(h)),n0)
| ~ value(out(n1,and1(h)),n0) )
<=> ( ~ mode(and1(h),ok)
| value(in(n2,and1(h)),n0)
| ~ type(and1(h),and)
| ~ value(out(n1,and1(h)),n0)
| value(in(n1,and1(h)),n0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(240,plain,
( ( ~ ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) )
| ~ mode(and1(h),ok)
| ~ type(and1(h),and)
| value(in(n2,and1(h)),n0)
| value(in(n1,and1(h)),n0)
| ~ value(out(n1,and1(h)),n0) )
<=> ( ~ ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) )
| ~ mode(and1(h),ok)
| value(in(n2,and1(h)),n0)
| ~ type(and1(h),and)
| ~ value(out(n1,and1(h)),n0)
| value(in(n1,and1(h)),n0) ) ),
inference(monotonicity,[status(thm)],[239]) ).
tff(241,plain,
( ( ~ ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) )
| ~ mode(and1(h),ok)
| ~ type(and1(h),and)
| value(in(n2,and1(h)),n0)
| value(in(n1,and1(h)),n0)
| ~ value(out(n1,and1(h)),n0) )
<=> ( ~ ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) )
| ~ mode(and1(h),ok)
| value(in(n2,and1(h)),n0)
| ~ type(and1(h),and)
| ~ value(out(n1,and1(h)),n0)
| value(in(n1,and1(h)),n0) ) ),
inference(transitivity,[status(thm)],[240,238]) ).
tff(242,plain,
( ~ ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) )
| ~ mode(and1(h),ok)
| ~ type(and1(h),and)
| value(in(n2,and1(h)),n0)
| value(in(n1,and1(h)),n0)
| ~ value(out(n1,and1(h)),n0) ),
inference(quant_inst,[status(thm)],]) ).
tff(243,plain,
( ~ ! [K: $i] :
( ~ mode(K,ok)
| ~ type(K,and)
| value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0) )
| ~ mode(and1(h),ok)
| value(in(n2,and1(h)),n0)
| ~ type(and1(h),and)
| ~ value(out(n1,and1(h)),n0)
| value(in(n1,and1(h)),n0) ),
inference(modus_ponens,[status(thm)],[242,241]) ).
tff(244,plain,
( ~ mode(and1(h),ok)
| value(in(n2,and1(h)),n0)
| ~ value(out(n1,and1(h)),n0)
| value(in(n1,and1(h)),n0) ),
inference(unit_resolution,[status(thm)],[243,237,123]) ).
tff(245,plain,
~ value(out(n1,and1(h)),n0),
inference(unit_resolution,[status(thm)],[244,227,130,112]) ).
tff(246,plain,
^ [X: $i] :
refl(
( ( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) )
<=> ( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) ) )),
inference(bind,[status(th)],]) ).
tff(247,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) ) ),
inference(quant_intro,[status(thm)],[246]) ).
tff(248,plain,
( ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) )
<=> ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(249,axiom,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-1.ax',halfadder_connection_outs_out1and1) ).
tff(250,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) ),
inference(modus_ponens,[status(thm)],[249,248]) ).
tff(251,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) ),
inference(skolemize,[status(sab)],[250]) ).
tff(252,plain,
! [X: $i] :
( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) ),
inference(modus_ponens,[status(thm)],[251,247]) ).
tff(253,plain,
( ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) )
| ~ type(h,halfadder)
| connection(out(s,h),out(n1,and1(h))) )
<=> ( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) )
| ~ type(h,halfadder)
| connection(out(s,h),out(n1,and1(h))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(254,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) )
| ~ type(h,halfadder)
| connection(out(s,h),out(n1,and1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(255,plain,
( ~ ! [X: $i] :
( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) )
| ~ type(h,halfadder)
| connection(out(s,h),out(n1,and1(h))) ),
inference(modus_ponens,[status(thm)],[254,253]) ).
tff(256,plain,
connection(out(s,h),out(n1,and1(h))),
inference(unit_resolution,[status(thm)],[255,252,3]) ).
tff(257,plain,
( value(out(s,h),n0)
<=> value(out(s,h),n0) ),
inference(rewrite,[status(thm)],]) ).
tff(258,axiom,
value(out(s,h),n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outs_0) ).
tff(259,plain,
value(out(s,h),n0),
inference(modus_ponens,[status(thm)],[258,257]) ).
tff(260,plain,
^ [V: $i,P2: $i,P1: $i] :
refl(
( ( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) )
<=> ( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) ) )),
inference(bind,[status(th)],]) ).
tff(261,plain,
( ! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) )
<=> ! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) ) ),
inference(quant_intro,[status(thm)],[260]) ).
tff(262,plain,
( ! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) )
<=> ! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(263,plain,
^ [V: $i,P2: $i,P1: $i] :
rewrite(
( ( ~ connection(P1,P2)
| ~ value(P1,V)
| value(P2,V) )
<=> ( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) ) )),
inference(bind,[status(th)],]) ).
tff(264,plain,
( ! [V: $i,P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ value(P1,V)
| value(P2,V) )
<=> ! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) ) ),
inference(quant_intro,[status(thm)],[263]) ).
tff(265,axiom,
! [V: $i,P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ value(P1,V)
| value(P2,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV001-0.ax',value_propagation1) ).
tff(266,plain,
! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) ),
inference(modus_ponens,[status(thm)],[265,264]) ).
tff(267,plain,
! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) ),
inference(modus_ponens,[status(thm)],[266,262]) ).
tff(268,plain,
! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) ),
inference(skolemize,[status(sab)],[267]) ).
tff(269,plain,
! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) ),
inference(modus_ponens,[status(thm)],[268,261]) ).
tff(270,plain,
( ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) )
| ~ value(out(s,h),n0)
| ~ connection(out(s,h),out(n1,and1(h)))
| value(out(n1,and1(h)),n0) )
<=> ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) )
| ~ value(out(s,h),n0)
| ~ connection(out(s,h),out(n1,and1(h)))
| value(out(n1,and1(h)),n0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(271,plain,
( ( value(out(n1,and1(h)),n0)
| ~ value(out(s,h),n0)
| ~ connection(out(s,h),out(n1,and1(h))) )
<=> ( ~ value(out(s,h),n0)
| ~ connection(out(s,h),out(n1,and1(h)))
| value(out(n1,and1(h)),n0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(272,plain,
( ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) )
| value(out(n1,and1(h)),n0)
| ~ value(out(s,h),n0)
| ~ connection(out(s,h),out(n1,and1(h))) )
<=> ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) )
| ~ value(out(s,h),n0)
| ~ connection(out(s,h),out(n1,and1(h)))
| value(out(n1,and1(h)),n0) ) ),
inference(monotonicity,[status(thm)],[271]) ).
tff(273,plain,
( ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) )
| value(out(n1,and1(h)),n0)
| ~ value(out(s,h),n0)
| ~ connection(out(s,h),out(n1,and1(h))) )
<=> ( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) )
| ~ value(out(s,h),n0)
| ~ connection(out(s,h),out(n1,and1(h)))
| value(out(n1,and1(h)),n0) ) ),
inference(transitivity,[status(thm)],[272,270]) ).
tff(274,plain,
( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) )
| value(out(n1,and1(h)),n0)
| ~ value(out(s,h),n0)
| ~ connection(out(s,h),out(n1,and1(h))) ),
inference(quant_inst,[status(thm)],]) ).
tff(275,plain,
( ~ ! [V: $i,P2: $i,P1: $i] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) )
| ~ value(out(s,h),n0)
| ~ connection(out(s,h),out(n1,and1(h)))
| value(out(n1,and1(h)),n0) ),
inference(modus_ponens,[status(thm)],[274,273]) ).
tff(276,plain,
$false,
inference(unit_resolution,[status(thm)],[275,269,259,256,245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HWV005-1 : TPTP v8.1.0. Released v2.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 21:42:02 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
%------------------------------------------------------------------------------