%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV008-2.002 : TPTP v9.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:53 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 182
% Syntax : Number of formulae : 427 ( 82 unt; 0 typ; 0 def)
% Number of atoms : 2136 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 3038 (1389 ~;1453 |; 0 &)
% ( 196 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 60 ( 60 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-1 aty)
% Number of variables : 564 ( 530 !; 0 ?; 564 :)
% Comments :
%------------------------------------------------------------------------------
tff(one_type,type,
one: $i > $o ).
tff(in2_type,type,
in2: $i > $i ).
tff(or1_type,type,
or1: $i > $i ).
tff(f2_type,type,
f2: $i > $i ).
tff(a_type,type,
a: $i ).
tff(outc_type,type,
outc: $i > $i ).
tff(h1_type,type,
h1: $i > $i ).
tff(out1_type,type,
out1: $i > $i ).
tff(and2_type,type,
and2: $i > $i ).
tff(in1_type,type,
in1: $i > $i ).
tff(connection_type,type,
connection: ( $i * $i ) > $o ).
tff(inb2_type,type,
inb2: $i > $i ).
tff(nbit_adder2_type,type,
nbit_adder2: $i > $o ).
tff(zero_type,type,
zero: $i > $o ).
tff(fulladder_type,type,
fulladder: $i > $o ).
tff(halfadder_type,type,
halfadder: $i > $o ).
tff(and_ok_type,type,
and_ok: $i > $o ).
tff(logic_and_type,type,
logic_and: $i > $o ).
tff(abnormal_type,type,
abnormal: $i > $o ).
tff(h2_type,type,
h2: $i > $i ).
tff(ina2_type,type,
ina2: $i > $i ).
tff(or_ok_type,type,
or_ok: $i > $o ).
tff(logic_or_type,type,
logic_or: $i > $o ).
tff(1,plain,
( nbit_adder2(a)
<=> nbit_adder2(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
nbit_adder2(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_isa_2bit_adder) ).
tff(3,plain,
nbit_adder2(a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(( ( ~ nbit_adder2(X)
| connection(inb2(X),in2(f2(X))) )
<=> ( ~ nbit_adder2(X)
| connection(inb2(X),in2(f2(X))) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X: $i] :
( ~ nbit_adder2(X)
| connection(inb2(X),in2(f2(X))) )
<=> ! [X: $i] :
( ~ nbit_adder2(X)
| connection(inb2(X),in2(f2(X))) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] :
( ~ nbit_adder2(X)
| connection(inb2(X),in2(f2(X))) )
<=> ! [X: $i] :
( ~ nbit_adder2(X)
| connection(inb2(X),in2(f2(X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [X: $i] :
( ~ nbit_adder2(X)
| connection(inb2(X),in2(f2(X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nbit_adder_connection_inb2_in2f2) ).
tff(8,plain,
! [X: $i] :
( ~ nbit_adder2(X)
| connection(inb2(X),in2(f2(X))) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X: $i] :
( ~ nbit_adder2(X)
| connection(inb2(X),in2(f2(X))) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] :
( ~ nbit_adder2(X)
| connection(inb2(X),in2(f2(X))) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| connection(inb2(X),in2(f2(X))) )
| ~ nbit_adder2(a)
| connection(inb2(a),in2(f2(a))) )
<=> ( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| connection(inb2(X),in2(f2(X))) )
| ~ nbit_adder2(a)
| connection(inb2(a),in2(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| connection(inb2(X),in2(f2(X))) )
| ~ nbit_adder2(a)
| connection(inb2(a),in2(f2(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| connection(inb2(X),in2(f2(X))) )
| ~ nbit_adder2(a)
| connection(inb2(a),in2(f2(a))) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
connection(inb2(a),in2(f2(a))),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( zero(inb2(a))
<=> zero(inb2(a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
zero(inb2(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inb2_0) ).
tff(17,plain,
zero(inb2(a)),
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/sandbox/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(inb2(a))
| ~ one(inb2(a)) )
<=> ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(inb2(a))
| ~ one(inb2(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(inb2(a))
| ~ one(inb2(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(inb2(a))
| ~ one(inb2(a)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
~ one(inb2(a)),
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/sandbox/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(inb2(a))
| ~ connection(inb2(a),in2(f2(a)))
| ~ one(in2(f2(a))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(inb2(a))
| ~ connection(inb2(a),in2(f2(a)))
| ~ one(in2(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( ~ connection(inb2(a),in2(f2(a)))
| one(inb2(a))
| ~ one(in2(f2(a))) )
<=> ( one(inb2(a))
| ~ connection(inb2(a),in2(f2(a)))
| ~ one(in2(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(inb2(a),in2(f2(a)))
| one(inb2(a))
| ~ one(in2(f2(a))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(inb2(a))
| ~ connection(inb2(a),in2(f2(a)))
| ~ one(in2(f2(a))) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(inb2(a),in2(f2(a)))
| one(inb2(a))
| ~ one(in2(f2(a))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(inb2(a))
| ~ connection(inb2(a),in2(f2(a)))
| ~ one(in2(f2(a))) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(inb2(a),in2(f2(a)))
| one(inb2(a))
| ~ one(in2(f2(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(inb2(a))
| ~ connection(inb2(a),in2(f2(a)))
| ~ one(in2(f2(a))) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ one(in2(f2(a))),
inference(unit_resolution,[status(thm)],[44,38,28,14]) ).
tff(46,plain,
^ [X: $i] :
refl(( ( ~ nbit_adder2(X)
| fulladder(f2(X)) )
<=> ( ~ nbit_adder2(X)
| fulladder(f2(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) )
<=> ! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) )
<=> ! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nbit_adder_fulladder2) ).
tff(50,plain,
! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) )
| fulladder(f2(a))
| ~ nbit_adder2(a) )
<=> ( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) )
| fulladder(f2(a))
| ~ nbit_adder2(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ( ~ nbit_adder2(a)
| fulladder(f2(a)) )
<=> ( fulladder(f2(a))
| ~ nbit_adder2(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) )
| ~ nbit_adder2(a)
| fulladder(f2(a)) )
<=> ( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) )
| fulladder(f2(a))
| ~ nbit_adder2(a) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) )
| ~ nbit_adder2(a)
| fulladder(f2(a)) )
<=> ( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) )
| fulladder(f2(a))
| ~ nbit_adder2(a) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) )
| ~ nbit_adder2(a)
| fulladder(f2(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| fulladder(f2(X)) )
| fulladder(f2(a))
| ~ nbit_adder2(a) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
fulladder(f2(a)),
inference(unit_resolution,[status(thm)],[58,52,3]) ).
tff(60,plain,
^ [X: $i] :
refl(( ( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
<=> ( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_connection_in2_in1h1) ).
tff(64,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
| ~ fulladder(f2(a))
| connection(in2(f2(a)),in1(h1(f2(a)))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
| ~ fulladder(f2(a))
| connection(in2(f2(a)),in1(h1(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
| ~ fulladder(f2(a))
| connection(in2(f2(a)),in1(h1(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in2(X),in1(h1(X))) )
| ~ fulladder(f2(a))
| connection(in2(f2(a)),in1(h1(f2(a)))) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( ~ fulladder(f2(a))
| connection(in2(f2(a)),in1(h1(f2(a)))) ),
inference(unit_resolution,[status(thm)],[69,66]) ).
tff(71,plain,
connection(in2(f2(a)),in1(h1(f2(a)))),
inference(unit_resolution,[status(thm)],[70,59]) ).
tff(72,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in2(f2(a)))
| ~ connection(in2(f2(a)),in1(h1(f2(a))))
| ~ one(in1(h1(f2(a)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in2(f2(a)))
| ~ connection(in2(f2(a)),in1(h1(f2(a))))
| ~ one(in1(h1(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( ~ connection(in2(f2(a)),in1(h1(f2(a))))
| one(in2(f2(a)))
| ~ one(in1(h1(f2(a)))) )
<=> ( one(in2(f2(a)))
| ~ connection(in2(f2(a)),in1(h1(f2(a))))
| ~ one(in1(h1(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in2(f2(a)),in1(h1(f2(a))))
| one(in2(f2(a)))
| ~ one(in1(h1(f2(a)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in2(f2(a)))
| ~ connection(in2(f2(a)),in1(h1(f2(a))))
| ~ one(in1(h1(f2(a)))) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in2(f2(a)),in1(h1(f2(a))))
| one(in2(f2(a)))
| ~ one(in1(h1(f2(a)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in2(f2(a)))
| ~ connection(in2(f2(a)),in1(h1(f2(a))))
| ~ one(in1(h1(f2(a)))) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in2(f2(a)),in1(h1(f2(a))))
| one(in2(f2(a)))
| ~ one(in1(h1(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in2(f2(a)))
| ~ connection(in2(f2(a)),in1(h1(f2(a))))
| ~ one(in1(h1(f2(a)))) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
~ one(in1(h1(f2(a)))),
inference(unit_resolution,[status(thm)],[77,38,71,45]) ).
tff(79,plain,
^ [X: $i] :
refl(( ( halfadder(h1(X))
| ~ fulladder(X) )
<=> ( halfadder(h1(X))
| ~ fulladder(X) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
<=> ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
<=> ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
^ [X: $i] :
rewrite(( ( ~ fulladder(X)
| halfadder(h1(X)) )
<=> ( halfadder(h1(X))
| ~ fulladder(X) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [X: $i] :
( ~ fulladder(X)
| halfadder(h1(X)) )
<=> ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,axiom,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h1(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_halfadder1) ).
tff(85,plain,
! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[87,80]) ).
tff(89,plain,
( ( ~ ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
| halfadder(h1(f2(a)))
| ~ fulladder(f2(a)) )
<=> ( ~ ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
| halfadder(h1(f2(a)))
| ~ fulladder(f2(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
( ~ ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
| halfadder(h1(f2(a)))
| ~ fulladder(f2(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [X: $i] :
( halfadder(h1(X))
| ~ fulladder(X) )
| halfadder(h1(f2(a)))
| ~ fulladder(f2(a)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
( halfadder(h1(f2(a)))
| ~ fulladder(f2(a)) ),
inference(unit_resolution,[status(thm)],[91,88]) ).
tff(93,plain,
halfadder(h1(f2(a))),
inference(unit_resolution,[status(thm)],[92,59]) ).
tff(94,plain,
^ [X: $i] :
refl(( ( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
<=> ( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
<=> ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_connection_in1_in1and2) ).
tff(98,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h1(f2(a)))
| connection(in1(h1(f2(a))),in1(and2(h1(f2(a))))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h1(f2(a)))
| connection(in1(h1(f2(a))),in1(and2(h1(f2(a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h1(f2(a)))
| connection(in1(h1(f2(a))),in1(and2(h1(f2(a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h1(f2(a)))
| connection(in1(h1(f2(a))),in1(and2(h1(f2(a))))) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
( ~ halfadder(h1(f2(a)))
| connection(in1(h1(f2(a))),in1(and2(h1(f2(a))))) ),
inference(unit_resolution,[status(thm)],[103,100]) ).
tff(105,plain,
connection(in1(h1(f2(a))),in1(and2(h1(f2(a))))),
inference(unit_resolution,[status(thm)],[104,93]) ).
tff(106,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h1(f2(a))))
| ~ connection(in1(h1(f2(a))),in1(and2(h1(f2(a)))))
| ~ one(in1(and2(h1(f2(a))))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h1(f2(a))))
| ~ connection(in1(h1(f2(a))),in1(and2(h1(f2(a)))))
| ~ one(in1(and2(h1(f2(a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ( ~ connection(in1(h1(f2(a))),in1(and2(h1(f2(a)))))
| one(in1(h1(f2(a))))
| ~ one(in1(and2(h1(f2(a))))) )
<=> ( one(in1(h1(f2(a))))
| ~ connection(in1(h1(f2(a))),in1(and2(h1(f2(a)))))
| ~ one(in1(and2(h1(f2(a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in1(h1(f2(a))),in1(and2(h1(f2(a)))))
| one(in1(h1(f2(a))))
| ~ one(in1(and2(h1(f2(a))))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h1(f2(a))))
| ~ connection(in1(h1(f2(a))),in1(and2(h1(f2(a)))))
| ~ one(in1(and2(h1(f2(a))))) ) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in1(h1(f2(a))),in1(and2(h1(f2(a)))))
| one(in1(h1(f2(a))))
| ~ one(in1(and2(h1(f2(a))))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h1(f2(a))))
| ~ connection(in1(h1(f2(a))),in1(and2(h1(f2(a)))))
| ~ one(in1(and2(h1(f2(a))))) ) ),
inference(transitivity,[status(thm)],[108,106]) ).
tff(110,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in1(h1(f2(a))),in1(and2(h1(f2(a)))))
| one(in1(h1(f2(a))))
| ~ one(in1(and2(h1(f2(a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h1(f2(a))))
| ~ connection(in1(h1(f2(a))),in1(and2(h1(f2(a)))))
| ~ one(in1(and2(h1(f2(a))))) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
~ one(in1(and2(h1(f2(a))))),
inference(unit_resolution,[status(thm)],[111,38,105,78]) ).
tff(113,plain,
^ [X: $i] :
refl(( ( ~ halfadder(X)
| logic_and(and2(X)) )
<=> ( ~ halfadder(X)
| logic_and(and2(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
<=> ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,axiom,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_and2) ).
tff(117,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h1(f2(a))))
| ~ halfadder(h1(f2(a))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h1(f2(a))))
| ~ halfadder(h1(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
( ( ~ halfadder(h1(f2(a)))
| logic_and(and2(h1(f2(a)))) )
<=> ( logic_and(and2(h1(f2(a))))
| ~ halfadder(h1(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| ~ halfadder(h1(f2(a)))
| logic_and(and2(h1(f2(a)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h1(f2(a))))
| ~ halfadder(h1(f2(a))) ) ),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| ~ halfadder(h1(f2(a)))
| logic_and(and2(h1(f2(a)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h1(f2(a))))
| ~ halfadder(h1(f2(a))) ) ),
inference(transitivity,[status(thm)],[122,120]) ).
tff(124,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| ~ halfadder(h1(f2(a)))
| logic_and(and2(h1(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h1(f2(a))))
| ~ halfadder(h1(f2(a))) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
( logic_and(and2(h1(f2(a))))
| ~ halfadder(h1(f2(a))) ),
inference(unit_resolution,[status(thm)],[125,119]) ).
tff(127,plain,
logic_and(and2(h1(f2(a)))),
inference(unit_resolution,[status(thm)],[126,93]) ).
tff(128,plain,
( ~ abnormal(and2(h1(f2(a))))
<=> ~ abnormal(and2(h1(f2(a)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,axiom,
~ abnormal(and2(h1(f2(a)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_and2h1f2a) ).
tff(130,plain,
~ abnormal(and2(h1(f2(a)))),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,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(132,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)],[131]) ).
tff(133,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(134,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(135,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)],[134]) ).
tff(136,axiom,
! [K: $i] :
( ~ logic_and(K)
| and_ok(K)
| abnormal(K) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',and_ok_or_abnormal) ).
tff(137,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(modus_ponens,[status(thm)],[137,133]) ).
tff(139,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(skolemize,[status(sab)],[138]) ).
tff(140,plain,
! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) ),
inference(modus_ponens,[status(thm)],[139,132]) ).
tff(141,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h1(f2(a))))
| and_ok(and2(h1(f2(a))))
| ~ logic_and(and2(h1(f2(a)))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h1(f2(a))))
| and_ok(and2(h1(f2(a))))
| ~ logic_and(and2(h1(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
( ( and_ok(and2(h1(f2(a))))
| abnormal(and2(h1(f2(a))))
| ~ logic_and(and2(h1(f2(a)))) )
<=> ( abnormal(and2(h1(f2(a))))
| and_ok(and2(h1(f2(a))))
| ~ logic_and(and2(h1(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and2(h1(f2(a))))
| abnormal(and2(h1(f2(a))))
| ~ logic_and(and2(h1(f2(a)))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h1(f2(a))))
| and_ok(and2(h1(f2(a))))
| ~ logic_and(and2(h1(f2(a)))) ) ),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and2(h1(f2(a))))
| abnormal(and2(h1(f2(a))))
| ~ logic_and(and2(h1(f2(a)))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h1(f2(a))))
| and_ok(and2(h1(f2(a))))
| ~ logic_and(and2(h1(f2(a)))) ) ),
inference(transitivity,[status(thm)],[143,141]) ).
tff(145,plain,
( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and2(h1(f2(a))))
| abnormal(and2(h1(f2(a))))
| ~ logic_and(and2(h1(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(146,plain,
( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h1(f2(a))))
| and_ok(and2(h1(f2(a))))
| ~ logic_and(and2(h1(f2(a)))) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
( and_ok(and2(h1(f2(a))))
| ~ logic_and(and2(h1(f2(a)))) ),
inference(unit_resolution,[status(thm)],[146,140,130]) ).
tff(148,plain,
and_ok(and2(h1(f2(a)))),
inference(unit_resolution,[status(thm)],[147,127]) ).
tff(149,plain,
^ [K: $i] :
refl(( ( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
<=> ( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ) )),
inference(bind,[status(th)],[]) ).
tff(150,plain,
( ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
<=> ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,plain,
( ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
<=> ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
^ [K: $i] :
rewrite(( ( ~ and_ok(K)
| ~ one(out1(K))
| one(in1(K)) )
<=> ( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ) )),
inference(bind,[status(th)],[]) ).
tff(153,plain,
( ! [K: $i] :
( ~ and_ok(K)
| ~ one(out1(K))
| one(in1(K)) )
<=> ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ) ),
inference(quant_intro,[status(thm)],[152]) ).
tff(154,axiom,
! [K: $i] :
( ~ and_ok(K)
| ~ one(out1(K))
| one(in1(K)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',and_1_1x) ).
tff(155,plain,
! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ),
inference(modus_ponens,[status(thm)],[155,151]) ).
tff(157,plain,
! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ),
inference(skolemize,[status(sab)],[156]) ).
tff(158,plain,
! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) ),
inference(modus_ponens,[status(thm)],[157,150]) ).
tff(159,plain,
( ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f2(a)))))
| one(in1(and2(h1(f2(a)))))
| ~ and_ok(and2(h1(f2(a)))) )
<=> ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f2(a)))))
| one(in1(and2(h1(f2(a)))))
| ~ and_ok(and2(h1(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,plain,
( ( ~ one(out1(and2(h1(f2(a)))))
| ~ and_ok(and2(h1(f2(a))))
| one(in1(and2(h1(f2(a))))) )
<=> ( ~ one(out1(and2(h1(f2(a)))))
| one(in1(and2(h1(f2(a)))))
| ~ and_ok(and2(h1(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(161,plain,
( ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f2(a)))))
| ~ and_ok(and2(h1(f2(a))))
| one(in1(and2(h1(f2(a))))) )
<=> ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f2(a)))))
| one(in1(and2(h1(f2(a)))))
| ~ and_ok(and2(h1(f2(a)))) ) ),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
( ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f2(a)))))
| ~ and_ok(and2(h1(f2(a))))
| one(in1(and2(h1(f2(a))))) )
<=> ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f2(a)))))
| one(in1(and2(h1(f2(a)))))
| ~ and_ok(and2(h1(f2(a)))) ) ),
inference(transitivity,[status(thm)],[161,159]) ).
tff(163,plain,
( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f2(a)))))
| ~ and_ok(and2(h1(f2(a))))
| one(in1(and2(h1(f2(a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h1(f2(a)))))
| one(in1(and2(h1(f2(a)))))
| ~ and_ok(and2(h1(f2(a)))) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
~ one(out1(and2(h1(f2(a))))),
inference(unit_resolution,[status(thm)],[164,158,148,112]) ).
tff(166,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(167,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)],[166]) ).
tff(168,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(169,axiom,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-1.ax',halfadder_connection_outc_out1and2) ).
tff(170,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
inference(skolemize,[status(sab)],[170]) ).
tff(172,plain,
! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) ),
inference(modus_ponens,[status(thm)],[171,167]) ).
tff(173,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h1(f2(a)))
| connection(outc(h1(f2(a))),out1(and2(h1(f2(a))))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h1(f2(a)))
| connection(outc(h1(f2(a))),out1(and2(h1(f2(a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(174,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h1(f2(a)))
| connection(outc(h1(f2(a))),out1(and2(h1(f2(a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h1(f2(a)))
| connection(outc(h1(f2(a))),out1(and2(h1(f2(a))))) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
( ~ halfadder(h1(f2(a)))
| connection(outc(h1(f2(a))),out1(and2(h1(f2(a))))) ),
inference(unit_resolution,[status(thm)],[175,172]) ).
tff(177,plain,
connection(outc(h1(f2(a))),out1(and2(h1(f2(a))))),
inference(unit_resolution,[status(thm)],[176,93]) ).
tff(178,plain,
^ [P2: $i,P1: $i] :
refl(( ( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
<=> ( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ) )),
inference(bind,[status(th)],[]) ).
tff(179,plain,
( ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
<=> ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ) ),
inference(quant_intro,[status(thm)],[178]) ).
tff(180,plain,
( ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
<=> ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(181,plain,
^ [P2: $i,P1: $i] :
trans(monotonicity(rewrite(( ( ~ connection(P1,P2)
| ~ one(P1) )
<=> ( ~ connection(P1,P2)
| ~ one(P1) ) )),
( ( ~ connection(P1,P2)
| ~ one(P1)
| one(P2) )
<=> ( ~ connection(P1,P2)
| ~ one(P1)
| one(P2) ) )),
rewrite(( ( ~ connection(P1,P2)
| ~ one(P1)
| one(P2) )
<=> ( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ) )),
( ( ~ connection(P1,P2)
| ~ one(P1)
| one(P2) )
<=> ( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ) )),
inference(bind,[status(th)],[]) ).
tff(182,plain,
( ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ one(P1)
| one(P2) )
<=> ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ) ),
inference(quant_intro,[status(thm)],[181]) ).
tff(183,axiom,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| ~ one(P1)
| one(P2) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',value_propagation_one1) ).
tff(184,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ),
inference(modus_ponens,[status(thm)],[184,180]) ).
tff(186,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ),
inference(skolemize,[status(sab)],[185]) ).
tff(187,plain,
! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) ),
inference(modus_ponens,[status(thm)],[186,179]) ).
tff(188,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(h1(f2(a))))
| one(out1(and2(h1(f2(a)))))
| ~ connection(outc(h1(f2(a))),out1(and2(h1(f2(a))))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(h1(f2(a))))
| one(out1(and2(h1(f2(a)))))
| ~ connection(outc(h1(f2(a))),out1(and2(h1(f2(a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(189,plain,
( ( ~ connection(outc(h1(f2(a))),out1(and2(h1(f2(a)))))
| one(out1(and2(h1(f2(a)))))
| ~ one(outc(h1(f2(a)))) )
<=> ( ~ one(outc(h1(f2(a))))
| one(out1(and2(h1(f2(a)))))
| ~ connection(outc(h1(f2(a))),out1(and2(h1(f2(a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(190,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outc(h1(f2(a))),out1(and2(h1(f2(a)))))
| one(out1(and2(h1(f2(a)))))
| ~ one(outc(h1(f2(a)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(h1(f2(a))))
| one(out1(and2(h1(f2(a)))))
| ~ connection(outc(h1(f2(a))),out1(and2(h1(f2(a))))) ) ),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outc(h1(f2(a))),out1(and2(h1(f2(a)))))
| one(out1(and2(h1(f2(a)))))
| ~ one(outc(h1(f2(a)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(h1(f2(a))))
| one(out1(and2(h1(f2(a)))))
| ~ connection(outc(h1(f2(a))),out1(and2(h1(f2(a))))) ) ),
inference(transitivity,[status(thm)],[190,188]) ).
tff(192,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outc(h1(f2(a))),out1(and2(h1(f2(a)))))
| one(out1(and2(h1(f2(a)))))
| ~ one(outc(h1(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(193,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(h1(f2(a))))
| one(out1(and2(h1(f2(a)))))
| ~ connection(outc(h1(f2(a))),out1(and2(h1(f2(a))))) ),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
( ~ one(outc(h1(f2(a))))
| one(out1(and2(h1(f2(a))))) ),
inference(unit_resolution,[status(thm)],[193,187,177]) ).
tff(195,plain,
~ one(outc(h1(f2(a)))),
inference(unit_resolution,[status(thm)],[194,165]) ).
tff(196,plain,
^ [X: $i] :
refl(( ( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) )
<=> ( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ) )),
inference(bind,[status(th)],[]) ).
tff(197,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ) ),
inference(quant_intro,[status(thm)],[196]) ).
tff(198,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(199,axiom,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_connection_outch1_in2or1) ).
tff(200,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ),
inference(modus_ponens,[status(thm)],[199,198]) ).
tff(201,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ),
inference(skolemize,[status(sab)],[200]) ).
tff(202,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) ),
inference(modus_ponens,[status(thm)],[201,197]) ).
tff(203,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) )
| ~ fulladder(f2(a))
| connection(outc(h1(f2(a))),in2(or1(f2(a)))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) )
| ~ fulladder(f2(a))
| connection(outc(h1(f2(a))),in2(or1(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(204,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) )
| ~ fulladder(f2(a))
| connection(outc(h1(f2(a))),in2(or1(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(205,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h1(X)),in2(or1(X))) )
| ~ fulladder(f2(a))
| connection(outc(h1(f2(a))),in2(or1(f2(a)))) ),
inference(modus_ponens,[status(thm)],[204,203]) ).
tff(206,plain,
( ~ fulladder(f2(a))
| connection(outc(h1(f2(a))),in2(or1(f2(a)))) ),
inference(unit_resolution,[status(thm)],[205,202]) ).
tff(207,plain,
connection(outc(h1(f2(a))),in2(or1(f2(a)))),
inference(unit_resolution,[status(thm)],[206,59]) ).
tff(208,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(outc(h1(f2(a))),in2(or1(f2(a))))
| one(outc(h1(f2(a))))
| ~ one(in2(or1(f2(a)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(outc(h1(f2(a))),in2(or1(f2(a))))
| one(outc(h1(f2(a))))
| ~ one(in2(or1(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(209,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(outc(h1(f2(a))),in2(or1(f2(a))))
| one(outc(h1(f2(a))))
| ~ one(in2(or1(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(210,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(outc(h1(f2(a))),in2(or1(f2(a))))
| one(outc(h1(f2(a))))
| ~ one(in2(or1(f2(a)))) ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
( one(outc(h1(f2(a))))
| ~ one(in2(or1(f2(a)))) ),
inference(unit_resolution,[status(thm)],[210,38,207]) ).
tff(212,plain,
~ one(in2(or1(f2(a)))),
inference(unit_resolution,[status(thm)],[211,195]) ).
tff(213,plain,
^ [X: $i] :
refl(( ( ~ nbit_adder2(X)
| connection(ina2(X),in1(f2(X))) )
<=> ( ~ nbit_adder2(X)
| connection(ina2(X),in1(f2(X))) ) )),
inference(bind,[status(th)],[]) ).
tff(214,plain,
( ! [X: $i] :
( ~ nbit_adder2(X)
| connection(ina2(X),in1(f2(X))) )
<=> ! [X: $i] :
( ~ nbit_adder2(X)
| connection(ina2(X),in1(f2(X))) ) ),
inference(quant_intro,[status(thm)],[213]) ).
tff(215,plain,
( ! [X: $i] :
( ~ nbit_adder2(X)
| connection(ina2(X),in1(f2(X))) )
<=> ! [X: $i] :
( ~ nbit_adder2(X)
| connection(ina2(X),in1(f2(X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(216,axiom,
! [X: $i] :
( ~ nbit_adder2(X)
| connection(ina2(X),in1(f2(X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nbit_adder_connection_ina2_in1f2) ).
tff(217,plain,
! [X: $i] :
( ~ nbit_adder2(X)
| connection(ina2(X),in1(f2(X))) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
! [X: $i] :
( ~ nbit_adder2(X)
| connection(ina2(X),in1(f2(X))) ),
inference(skolemize,[status(sab)],[217]) ).
tff(219,plain,
! [X: $i] :
( ~ nbit_adder2(X)
| connection(ina2(X),in1(f2(X))) ),
inference(modus_ponens,[status(thm)],[218,214]) ).
tff(220,plain,
( ( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| connection(ina2(X),in1(f2(X))) )
| ~ nbit_adder2(a)
| connection(ina2(a),in1(f2(a))) )
<=> ( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| connection(ina2(X),in1(f2(X))) )
| ~ nbit_adder2(a)
| connection(ina2(a),in1(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(221,plain,
( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| connection(ina2(X),in1(f2(X))) )
| ~ nbit_adder2(a)
| connection(ina2(a),in1(f2(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(222,plain,
( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| connection(ina2(X),in1(f2(X))) )
| ~ nbit_adder2(a)
| connection(ina2(a),in1(f2(a))) ),
inference(modus_ponens,[status(thm)],[221,220]) ).
tff(223,plain,
connection(ina2(a),in1(f2(a))),
inference(unit_resolution,[status(thm)],[222,219,3]) ).
tff(224,plain,
( zero(ina2(a))
<=> zero(ina2(a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(225,axiom,
zero(ina2(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ina2_0) ).
tff(226,plain,
zero(ina2(a)),
inference(modus_ponens,[status(thm)],[225,224]) ).
tff(227,plain,
( ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(ina2(a))
| ~ one(ina2(a)) )
<=> ( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(ina2(a))
| ~ one(ina2(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(228,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(ina2(a))
| ~ one(ina2(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(229,plain,
( ~ ! [P: $i] :
( ~ zero(P)
| ~ one(P) )
| ~ zero(ina2(a))
| ~ one(ina2(a)) ),
inference(modus_ponens,[status(thm)],[228,227]) ).
tff(230,plain,
~ one(ina2(a)),
inference(unit_resolution,[status(thm)],[229,24,226]) ).
tff(231,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(ina2(a))
| ~ connection(ina2(a),in1(f2(a)))
| ~ one(in1(f2(a))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(ina2(a))
| ~ connection(ina2(a),in1(f2(a)))
| ~ one(in1(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(232,plain,
( ( ~ connection(ina2(a),in1(f2(a)))
| one(ina2(a))
| ~ one(in1(f2(a))) )
<=> ( one(ina2(a))
| ~ connection(ina2(a),in1(f2(a)))
| ~ one(in1(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(233,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(ina2(a),in1(f2(a)))
| one(ina2(a))
| ~ one(in1(f2(a))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(ina2(a))
| ~ connection(ina2(a),in1(f2(a)))
| ~ one(in1(f2(a))) ) ),
inference(monotonicity,[status(thm)],[232]) ).
tff(234,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(ina2(a),in1(f2(a)))
| one(ina2(a))
| ~ one(in1(f2(a))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(ina2(a))
| ~ connection(ina2(a),in1(f2(a)))
| ~ one(in1(f2(a))) ) ),
inference(transitivity,[status(thm)],[233,231]) ).
tff(235,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(ina2(a),in1(f2(a)))
| one(ina2(a))
| ~ one(in1(f2(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(236,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(ina2(a))
| ~ connection(ina2(a),in1(f2(a)))
| ~ one(in1(f2(a))) ),
inference(modus_ponens,[status(thm)],[235,234]) ).
tff(237,plain,
~ one(in1(f2(a))),
inference(unit_resolution,[status(thm)],[236,38,230,223]) ).
tff(238,plain,
^ [X: $i] :
refl(( ( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
<=> ( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ) )),
inference(bind,[status(th)],[]) ).
tff(239,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ) ),
inference(quant_intro,[status(thm)],[238]) ).
tff(240,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(241,axiom,
! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_connection_in1_in1h2) ).
tff(242,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ),
inference(modus_ponens,[status(thm)],[241,240]) ).
tff(243,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ),
inference(skolemize,[status(sab)],[242]) ).
tff(244,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) ),
inference(modus_ponens,[status(thm)],[243,239]) ).
tff(245,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
| ~ fulladder(f2(a))
| connection(in1(f2(a)),in1(h2(f2(a)))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
| ~ fulladder(f2(a))
| connection(in1(f2(a)),in1(h2(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(246,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
| ~ fulladder(f2(a))
| connection(in1(f2(a)),in1(h2(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(247,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(in1(X),in1(h2(X))) )
| ~ fulladder(f2(a))
| connection(in1(f2(a)),in1(h2(f2(a)))) ),
inference(modus_ponens,[status(thm)],[246,245]) ).
tff(248,plain,
( ~ fulladder(f2(a))
| connection(in1(f2(a)),in1(h2(f2(a)))) ),
inference(unit_resolution,[status(thm)],[247,244]) ).
tff(249,plain,
connection(in1(f2(a)),in1(h2(f2(a)))),
inference(unit_resolution,[status(thm)],[248,59]) ).
tff(250,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(f2(a)))
| ~ connection(in1(f2(a)),in1(h2(f2(a))))
| ~ one(in1(h2(f2(a)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(f2(a)))
| ~ connection(in1(f2(a)),in1(h2(f2(a))))
| ~ one(in1(h2(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(251,plain,
( ( ~ connection(in1(f2(a)),in1(h2(f2(a))))
| one(in1(f2(a)))
| ~ one(in1(h2(f2(a)))) )
<=> ( one(in1(f2(a)))
| ~ connection(in1(f2(a)),in1(h2(f2(a))))
| ~ one(in1(h2(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(252,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in1(f2(a)),in1(h2(f2(a))))
| one(in1(f2(a)))
| ~ one(in1(h2(f2(a)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(f2(a)))
| ~ connection(in1(f2(a)),in1(h2(f2(a))))
| ~ one(in1(h2(f2(a)))) ) ),
inference(monotonicity,[status(thm)],[251]) ).
tff(253,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in1(f2(a)),in1(h2(f2(a))))
| one(in1(f2(a)))
| ~ one(in1(h2(f2(a)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(f2(a)))
| ~ connection(in1(f2(a)),in1(h2(f2(a))))
| ~ one(in1(h2(f2(a)))) ) ),
inference(transitivity,[status(thm)],[252,250]) ).
tff(254,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in1(f2(a)),in1(h2(f2(a))))
| one(in1(f2(a)))
| ~ one(in1(h2(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(255,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(f2(a)))
| ~ connection(in1(f2(a)),in1(h2(f2(a))))
| ~ one(in1(h2(f2(a)))) ),
inference(modus_ponens,[status(thm)],[254,253]) ).
tff(256,plain,
~ one(in1(h2(f2(a)))),
inference(unit_resolution,[status(thm)],[255,38,249,237]) ).
tff(257,plain,
^ [X: $i] :
refl(( ( ~ fulladder(X)
| halfadder(h2(X)) )
<=> ( ~ fulladder(X)
| halfadder(h2(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(258,plain,
( ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
<=> ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ) ),
inference(quant_intro,[status(thm)],[257]) ).
tff(259,plain,
( ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
<=> ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(260,axiom,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_halfadder2) ).
tff(261,plain,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ),
inference(modus_ponens,[status(thm)],[260,259]) ).
tff(262,plain,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ),
inference(skolemize,[status(sab)],[261]) ).
tff(263,plain,
! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) ),
inference(modus_ponens,[status(thm)],[262,258]) ).
tff(264,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
| halfadder(h2(f2(a)))
| ~ fulladder(f2(a)) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
| halfadder(h2(f2(a)))
| ~ fulladder(f2(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(265,plain,
( ( ~ fulladder(f2(a))
| halfadder(h2(f2(a))) )
<=> ( halfadder(h2(f2(a)))
| ~ fulladder(f2(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(266,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
| ~ fulladder(f2(a))
| halfadder(h2(f2(a))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
| halfadder(h2(f2(a)))
| ~ fulladder(f2(a)) ) ),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
| ~ fulladder(f2(a))
| halfadder(h2(f2(a))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
| halfadder(h2(f2(a)))
| ~ fulladder(f2(a)) ) ),
inference(transitivity,[status(thm)],[266,264]) ).
tff(268,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
| ~ fulladder(f2(a))
| halfadder(h2(f2(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(269,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| halfadder(h2(X)) )
| halfadder(h2(f2(a)))
| ~ fulladder(f2(a)) ),
inference(modus_ponens,[status(thm)],[268,267]) ).
tff(270,plain,
( halfadder(h2(f2(a)))
| ~ fulladder(f2(a)) ),
inference(unit_resolution,[status(thm)],[269,263]) ).
tff(271,plain,
halfadder(h2(f2(a))),
inference(unit_resolution,[status(thm)],[270,59]) ).
tff(272,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h2(f2(a)))
| connection(in1(h2(f2(a))),in1(and2(h2(f2(a))))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h2(f2(a)))
| connection(in1(h2(f2(a))),in1(and2(h2(f2(a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(273,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h2(f2(a)))
| connection(in1(h2(f2(a))),in1(and2(h2(f2(a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(274,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(in1(X),in1(and2(X))) )
| ~ halfadder(h2(f2(a)))
| connection(in1(h2(f2(a))),in1(and2(h2(f2(a))))) ),
inference(modus_ponens,[status(thm)],[273,272]) ).
tff(275,plain,
( ~ halfadder(h2(f2(a)))
| connection(in1(h2(f2(a))),in1(and2(h2(f2(a))))) ),
inference(unit_resolution,[status(thm)],[274,100]) ).
tff(276,plain,
connection(in1(h2(f2(a))),in1(and2(h2(f2(a))))),
inference(unit_resolution,[status(thm)],[275,271]) ).
tff(277,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h2(f2(a))))
| ~ connection(in1(h2(f2(a))),in1(and2(h2(f2(a)))))
| ~ one(in1(and2(h2(f2(a))))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h2(f2(a))))
| ~ connection(in1(h2(f2(a))),in1(and2(h2(f2(a)))))
| ~ one(in1(and2(h2(f2(a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(278,plain,
( ( ~ connection(in1(h2(f2(a))),in1(and2(h2(f2(a)))))
| one(in1(h2(f2(a))))
| ~ one(in1(and2(h2(f2(a))))) )
<=> ( one(in1(h2(f2(a))))
| ~ connection(in1(h2(f2(a))),in1(and2(h2(f2(a)))))
| ~ one(in1(and2(h2(f2(a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(279,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in1(h2(f2(a))),in1(and2(h2(f2(a)))))
| one(in1(h2(f2(a))))
| ~ one(in1(and2(h2(f2(a))))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h2(f2(a))))
| ~ connection(in1(h2(f2(a))),in1(and2(h2(f2(a)))))
| ~ one(in1(and2(h2(f2(a))))) ) ),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in1(h2(f2(a))),in1(and2(h2(f2(a)))))
| one(in1(h2(f2(a))))
| ~ one(in1(and2(h2(f2(a))))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h2(f2(a))))
| ~ connection(in1(h2(f2(a))),in1(and2(h2(f2(a)))))
| ~ one(in1(and2(h2(f2(a))))) ) ),
inference(transitivity,[status(thm)],[279,277]) ).
tff(281,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(in1(h2(f2(a))),in1(and2(h2(f2(a)))))
| one(in1(h2(f2(a))))
| ~ one(in1(and2(h2(f2(a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(282,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| one(in1(h2(f2(a))))
| ~ connection(in1(h2(f2(a))),in1(and2(h2(f2(a)))))
| ~ one(in1(and2(h2(f2(a))))) ),
inference(modus_ponens,[status(thm)],[281,280]) ).
tff(283,plain,
~ one(in1(and2(h2(f2(a))))),
inference(unit_resolution,[status(thm)],[282,38,276,256]) ).
tff(284,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h2(f2(a))))
| ~ halfadder(h2(f2(a))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h2(f2(a))))
| ~ halfadder(h2(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(285,plain,
( ( ~ halfadder(h2(f2(a)))
| logic_and(and2(h2(f2(a)))) )
<=> ( logic_and(and2(h2(f2(a))))
| ~ halfadder(h2(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(286,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| ~ halfadder(h2(f2(a)))
| logic_and(and2(h2(f2(a)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h2(f2(a))))
| ~ halfadder(h2(f2(a))) ) ),
inference(monotonicity,[status(thm)],[285]) ).
tff(287,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| ~ halfadder(h2(f2(a)))
| logic_and(and2(h2(f2(a)))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h2(f2(a))))
| ~ halfadder(h2(f2(a))) ) ),
inference(transitivity,[status(thm)],[286,284]) ).
tff(288,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| ~ halfadder(h2(f2(a)))
| logic_and(and2(h2(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(289,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| logic_and(and2(X)) )
| logic_and(and2(h2(f2(a))))
| ~ halfadder(h2(f2(a))) ),
inference(modus_ponens,[status(thm)],[288,287]) ).
tff(290,plain,
( logic_and(and2(h2(f2(a))))
| ~ halfadder(h2(f2(a))) ),
inference(unit_resolution,[status(thm)],[289,119]) ).
tff(291,plain,
logic_and(and2(h2(f2(a)))),
inference(unit_resolution,[status(thm)],[290,271]) ).
tff(292,plain,
( ~ abnormal(and2(h2(f2(a))))
<=> ~ abnormal(and2(h2(f2(a)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(293,axiom,
~ abnormal(and2(h2(f2(a)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_and2h2f2a) ).
tff(294,plain,
~ abnormal(and2(h2(f2(a)))),
inference(modus_ponens,[status(thm)],[293,292]) ).
tff(295,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h2(f2(a))))
| and_ok(and2(h2(f2(a))))
| ~ logic_and(and2(h2(f2(a)))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h2(f2(a))))
| and_ok(and2(h2(f2(a))))
| ~ logic_and(and2(h2(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(296,plain,
( ( and_ok(and2(h2(f2(a))))
| abnormal(and2(h2(f2(a))))
| ~ logic_and(and2(h2(f2(a)))) )
<=> ( abnormal(and2(h2(f2(a))))
| and_ok(and2(h2(f2(a))))
| ~ logic_and(and2(h2(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(297,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and2(h2(f2(a))))
| abnormal(and2(h2(f2(a))))
| ~ logic_and(and2(h2(f2(a)))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h2(f2(a))))
| and_ok(and2(h2(f2(a))))
| ~ logic_and(and2(h2(f2(a)))) ) ),
inference(monotonicity,[status(thm)],[296]) ).
tff(298,plain,
( ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and2(h2(f2(a))))
| abnormal(and2(h2(f2(a))))
| ~ logic_and(and2(h2(f2(a)))) )
<=> ( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h2(f2(a))))
| and_ok(and2(h2(f2(a))))
| ~ logic_and(and2(h2(f2(a)))) ) ),
inference(transitivity,[status(thm)],[297,295]) ).
tff(299,plain,
( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| and_ok(and2(h2(f2(a))))
| abnormal(and2(h2(f2(a))))
| ~ logic_and(and2(h2(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(300,plain,
( ~ ! [K: $i] :
( and_ok(K)
| abnormal(K)
| ~ logic_and(K) )
| abnormal(and2(h2(f2(a))))
| and_ok(and2(h2(f2(a))))
| ~ logic_and(and2(h2(f2(a)))) ),
inference(modus_ponens,[status(thm)],[299,298]) ).
tff(301,plain,
( and_ok(and2(h2(f2(a))))
| ~ logic_and(and2(h2(f2(a)))) ),
inference(unit_resolution,[status(thm)],[300,140,294]) ).
tff(302,plain,
and_ok(and2(h2(f2(a)))),
inference(unit_resolution,[status(thm)],[301,291]) ).
tff(303,plain,
( ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h2(f2(a)))))
| one(in1(and2(h2(f2(a)))))
| ~ and_ok(and2(h2(f2(a)))) )
<=> ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h2(f2(a)))))
| one(in1(and2(h2(f2(a)))))
| ~ and_ok(and2(h2(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(304,plain,
( ( ~ one(out1(and2(h2(f2(a)))))
| ~ and_ok(and2(h2(f2(a))))
| one(in1(and2(h2(f2(a))))) )
<=> ( ~ one(out1(and2(h2(f2(a)))))
| one(in1(and2(h2(f2(a)))))
| ~ and_ok(and2(h2(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(305,plain,
( ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h2(f2(a)))))
| ~ and_ok(and2(h2(f2(a))))
| one(in1(and2(h2(f2(a))))) )
<=> ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h2(f2(a)))))
| one(in1(and2(h2(f2(a)))))
| ~ and_ok(and2(h2(f2(a)))) ) ),
inference(monotonicity,[status(thm)],[304]) ).
tff(306,plain,
( ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h2(f2(a)))))
| ~ and_ok(and2(h2(f2(a))))
| one(in1(and2(h2(f2(a))))) )
<=> ( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h2(f2(a)))))
| one(in1(and2(h2(f2(a)))))
| ~ and_ok(and2(h2(f2(a)))) ) ),
inference(transitivity,[status(thm)],[305,303]) ).
tff(307,plain,
( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h2(f2(a)))))
| ~ and_ok(and2(h2(f2(a))))
| one(in1(and2(h2(f2(a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(308,plain,
( ~ ! [K: $i] :
( ~ one(out1(K))
| ~ and_ok(K)
| one(in1(K)) )
| ~ one(out1(and2(h2(f2(a)))))
| one(in1(and2(h2(f2(a)))))
| ~ and_ok(and2(h2(f2(a)))) ),
inference(modus_ponens,[status(thm)],[307,306]) ).
tff(309,plain,
~ one(out1(and2(h2(f2(a))))),
inference(unit_resolution,[status(thm)],[308,158,302,283]) ).
tff(310,plain,
( ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h2(f2(a)))
| connection(outc(h2(f2(a))),out1(and2(h2(f2(a))))) )
<=> ( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h2(f2(a)))
| connection(outc(h2(f2(a))),out1(and2(h2(f2(a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(311,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h2(f2(a)))
| connection(outc(h2(f2(a))),out1(and2(h2(f2(a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(312,plain,
( ~ ! [X: $i] :
( ~ halfadder(X)
| connection(outc(X),out1(and2(X))) )
| ~ halfadder(h2(f2(a)))
| connection(outc(h2(f2(a))),out1(and2(h2(f2(a))))) ),
inference(modus_ponens,[status(thm)],[311,310]) ).
tff(313,plain,
( ~ halfadder(h2(f2(a)))
| connection(outc(h2(f2(a))),out1(and2(h2(f2(a))))) ),
inference(unit_resolution,[status(thm)],[312,172]) ).
tff(314,plain,
connection(outc(h2(f2(a))),out1(and2(h2(f2(a))))),
inference(unit_resolution,[status(thm)],[313,271]) ).
tff(315,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(h2(f2(a))))
| one(out1(and2(h2(f2(a)))))
| ~ connection(outc(h2(f2(a))),out1(and2(h2(f2(a))))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(h2(f2(a))))
| one(out1(and2(h2(f2(a)))))
| ~ connection(outc(h2(f2(a))),out1(and2(h2(f2(a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(316,plain,
( ( ~ connection(outc(h2(f2(a))),out1(and2(h2(f2(a)))))
| one(out1(and2(h2(f2(a)))))
| ~ one(outc(h2(f2(a)))) )
<=> ( ~ one(outc(h2(f2(a))))
| one(out1(and2(h2(f2(a)))))
| ~ connection(outc(h2(f2(a))),out1(and2(h2(f2(a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(317,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outc(h2(f2(a))),out1(and2(h2(f2(a)))))
| one(out1(and2(h2(f2(a)))))
| ~ one(outc(h2(f2(a)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(h2(f2(a))))
| one(out1(and2(h2(f2(a)))))
| ~ connection(outc(h2(f2(a))),out1(and2(h2(f2(a))))) ) ),
inference(monotonicity,[status(thm)],[316]) ).
tff(318,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outc(h2(f2(a))),out1(and2(h2(f2(a)))))
| one(out1(and2(h2(f2(a)))))
| ~ one(outc(h2(f2(a)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(h2(f2(a))))
| one(out1(and2(h2(f2(a)))))
| ~ connection(outc(h2(f2(a))),out1(and2(h2(f2(a))))) ) ),
inference(transitivity,[status(thm)],[317,315]) ).
tff(319,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outc(h2(f2(a))),out1(and2(h2(f2(a)))))
| one(out1(and2(h2(f2(a)))))
| ~ one(outc(h2(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(320,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(h2(f2(a))))
| one(out1(and2(h2(f2(a)))))
| ~ connection(outc(h2(f2(a))),out1(and2(h2(f2(a))))) ),
inference(modus_ponens,[status(thm)],[319,318]) ).
tff(321,plain,
( ~ one(outc(h2(f2(a))))
| one(out1(and2(h2(f2(a))))) ),
inference(unit_resolution,[status(thm)],[320,187,314]) ).
tff(322,plain,
~ one(outc(h2(f2(a)))),
inference(unit_resolution,[status(thm)],[321,309]) ).
tff(323,plain,
^ [X: $i] :
refl(( ( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) )
<=> ( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) ) )),
inference(bind,[status(th)],[]) ).
tff(324,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) ) ),
inference(quant_intro,[status(thm)],[323]) ).
tff(325,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(326,axiom,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_connection_outch2_in1or1) ).
tff(327,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) ),
inference(modus_ponens,[status(thm)],[326,325]) ).
tff(328,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) ),
inference(skolemize,[status(sab)],[327]) ).
tff(329,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) ),
inference(modus_ponens,[status(thm)],[328,324]) ).
tff(330,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) )
| ~ fulladder(f2(a))
| connection(outc(h2(f2(a))),in1(or1(f2(a)))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) )
| ~ fulladder(f2(a))
| connection(outc(h2(f2(a))),in1(or1(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(331,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) )
| ~ fulladder(f2(a))
| connection(outc(h2(f2(a))),in1(or1(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(332,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(h2(X)),in1(or1(X))) )
| ~ fulladder(f2(a))
| connection(outc(h2(f2(a))),in1(or1(f2(a)))) ),
inference(modus_ponens,[status(thm)],[331,330]) ).
tff(333,plain,
( ~ fulladder(f2(a))
| connection(outc(h2(f2(a))),in1(or1(f2(a)))) ),
inference(unit_resolution,[status(thm)],[332,329]) ).
tff(334,plain,
connection(outc(h2(f2(a))),in1(or1(f2(a)))),
inference(unit_resolution,[status(thm)],[333,59]) ).
tff(335,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(outc(h2(f2(a))),in1(or1(f2(a))))
| one(outc(h2(f2(a))))
| ~ one(in1(or1(f2(a)))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(outc(h2(f2(a))),in1(or1(f2(a))))
| one(outc(h2(f2(a))))
| ~ one(in1(or1(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(336,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(outc(h2(f2(a))),in1(or1(f2(a))))
| one(outc(h2(f2(a))))
| ~ one(in1(or1(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(337,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P1)
| ~ one(P2) )
| ~ connection(outc(h2(f2(a))),in1(or1(f2(a))))
| one(outc(h2(f2(a))))
| ~ one(in1(or1(f2(a)))) ),
inference(modus_ponens,[status(thm)],[336,335]) ).
tff(338,plain,
( one(outc(h2(f2(a))))
| ~ one(in1(or1(f2(a)))) ),
inference(unit_resolution,[status(thm)],[337,38,334]) ).
tff(339,plain,
~ one(in1(or1(f2(a)))),
inference(unit_resolution,[status(thm)],[338,322]) ).
tff(340,plain,
^ [X: $i] :
refl(( ( ~ nbit_adder2(X)
| connection(outc(X),outc(f2(X))) )
<=> ( ~ nbit_adder2(X)
| connection(outc(X),outc(f2(X))) ) )),
inference(bind,[status(th)],[]) ).
tff(341,plain,
( ! [X: $i] :
( ~ nbit_adder2(X)
| connection(outc(X),outc(f2(X))) )
<=> ! [X: $i] :
( ~ nbit_adder2(X)
| connection(outc(X),outc(f2(X))) ) ),
inference(quant_intro,[status(thm)],[340]) ).
tff(342,plain,
( ! [X: $i] :
( ~ nbit_adder2(X)
| connection(outc(X),outc(f2(X))) )
<=> ! [X: $i] :
( ~ nbit_adder2(X)
| connection(outc(X),outc(f2(X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(343,axiom,
! [X: $i] :
( ~ nbit_adder2(X)
| connection(outc(X),outc(f2(X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nbit_adder_connection_outc_outcf1) ).
tff(344,plain,
! [X: $i] :
( ~ nbit_adder2(X)
| connection(outc(X),outc(f2(X))) ),
inference(modus_ponens,[status(thm)],[343,342]) ).
tff(345,plain,
! [X: $i] :
( ~ nbit_adder2(X)
| connection(outc(X),outc(f2(X))) ),
inference(skolemize,[status(sab)],[344]) ).
tff(346,plain,
! [X: $i] :
( ~ nbit_adder2(X)
| connection(outc(X),outc(f2(X))) ),
inference(modus_ponens,[status(thm)],[345,341]) ).
tff(347,plain,
( ( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| connection(outc(X),outc(f2(X))) )
| ~ nbit_adder2(a)
| connection(outc(a),outc(f2(a))) )
<=> ( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| connection(outc(X),outc(f2(X))) )
| ~ nbit_adder2(a)
| connection(outc(a),outc(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(348,plain,
( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| connection(outc(X),outc(f2(X))) )
| ~ nbit_adder2(a)
| connection(outc(a),outc(f2(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(349,plain,
( ~ ! [X: $i] :
( ~ nbit_adder2(X)
| connection(outc(X),outc(f2(X))) )
| ~ nbit_adder2(a)
| connection(outc(a),outc(f2(a))) ),
inference(modus_ponens,[status(thm)],[348,347]) ).
tff(350,plain,
connection(outc(a),outc(f2(a))),
inference(unit_resolution,[status(thm)],[349,346,3]) ).
tff(351,plain,
( one(outc(a))
<=> one(outc(a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(352,axiom,
one(outc(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outc_1) ).
tff(353,plain,
one(outc(a)),
inference(modus_ponens,[status(thm)],[352,351]) ).
tff(354,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(a))
| ~ connection(outc(a),outc(f2(a)))
| one(outc(f2(a))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(a))
| ~ connection(outc(a),outc(f2(a)))
| one(outc(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(355,plain,
( ( ~ connection(outc(a),outc(f2(a)))
| one(outc(f2(a)))
| ~ one(outc(a)) )
<=> ( ~ one(outc(a))
| ~ connection(outc(a),outc(f2(a)))
| one(outc(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(356,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outc(a),outc(f2(a)))
| one(outc(f2(a)))
| ~ one(outc(a)) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(a))
| ~ connection(outc(a),outc(f2(a)))
| one(outc(f2(a))) ) ),
inference(monotonicity,[status(thm)],[355]) ).
tff(357,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outc(a),outc(f2(a)))
| one(outc(f2(a)))
| ~ one(outc(a)) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(a))
| ~ connection(outc(a),outc(f2(a)))
| one(outc(f2(a))) ) ),
inference(transitivity,[status(thm)],[356,354]) ).
tff(358,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outc(a),outc(f2(a)))
| one(outc(f2(a)))
| ~ one(outc(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(359,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ one(outc(a))
| ~ connection(outc(a),outc(f2(a)))
| one(outc(f2(a))) ),
inference(modus_ponens,[status(thm)],[358,357]) ).
tff(360,plain,
one(outc(f2(a))),
inference(unit_resolution,[status(thm)],[359,187,353,350]) ).
tff(361,plain,
^ [X: $i] :
refl(( ( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
<=> ( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ) )),
inference(bind,[status(th)],[]) ).
tff(362,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ) ),
inference(quant_intro,[status(thm)],[361]) ).
tff(363,plain,
( ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
<=> ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(364,axiom,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_connection_outc_out1or1) ).
tff(365,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ),
inference(modus_ponens,[status(thm)],[364,363]) ).
tff(366,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ),
inference(skolemize,[status(sab)],[365]) ).
tff(367,plain,
! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) ),
inference(modus_ponens,[status(thm)],[366,362]) ).
tff(368,plain,
( ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
| ~ fulladder(f2(a))
| connection(outc(f2(a)),out1(or1(f2(a)))) )
<=> ( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
| ~ fulladder(f2(a))
| connection(outc(f2(a)),out1(or1(f2(a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(369,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
| ~ fulladder(f2(a))
| connection(outc(f2(a)),out1(or1(f2(a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(370,plain,
( ~ ! [X: $i] :
( ~ fulladder(X)
| connection(outc(X),out1(or1(X))) )
| ~ fulladder(f2(a))
| connection(outc(f2(a)),out1(or1(f2(a)))) ),
inference(modus_ponens,[status(thm)],[369,368]) ).
tff(371,plain,
( ~ fulladder(f2(a))
| connection(outc(f2(a)),out1(or1(f2(a)))) ),
inference(unit_resolution,[status(thm)],[370,367]) ).
tff(372,plain,
connection(outc(f2(a)),out1(or1(f2(a)))),
inference(unit_resolution,[status(thm)],[371,59]) ).
tff(373,plain,
( ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outc(f2(a)),out1(or1(f2(a))))
| one(out1(or1(f2(a))))
| ~ one(outc(f2(a))) )
<=> ( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outc(f2(a)),out1(or1(f2(a))))
| one(out1(or1(f2(a))))
| ~ one(outc(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(374,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outc(f2(a)),out1(or1(f2(a))))
| one(out1(or1(f2(a))))
| ~ one(outc(f2(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(375,plain,
( ~ ! [P2: $i,P1: $i] :
( ~ connection(P1,P2)
| one(P2)
| ~ one(P1) )
| ~ connection(outc(f2(a)),out1(or1(f2(a))))
| one(out1(or1(f2(a))))
| ~ one(outc(f2(a))) ),
inference(modus_ponens,[status(thm)],[374,373]) ).
tff(376,plain,
one(out1(or1(f2(a)))),
inference(unit_resolution,[status(thm)],[375,187,372,360]) ).
tff(377,plain,
^ [X: $i] :
refl(( ( logic_or(or1(X))
| ~ fulladder(X) )
<=> ( logic_or(or1(X))
| ~ fulladder(X) ) )),
inference(bind,[status(th)],[]) ).
tff(378,plain,
( ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
<=> ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ) ),
inference(quant_intro,[status(thm)],[377]) ).
tff(379,plain,
( ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
<=> ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(380,plain,
^ [X: $i] :
rewrite(( ( ~ fulladder(X)
| logic_or(or1(X)) )
<=> ( logic_or(or1(X))
| ~ fulladder(X) ) )),
inference(bind,[status(th)],[]) ).
tff(381,plain,
( ! [X: $i] :
( ~ fulladder(X)
| logic_or(or1(X)) )
<=> ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ) ),
inference(quant_intro,[status(thm)],[380]) ).
tff(382,axiom,
! [X: $i] :
( ~ fulladder(X)
| logic_or(or1(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-2.ax',fulladder_or1) ).
tff(383,plain,
! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[382,381]) ).
tff(384,plain,
! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[383,379]) ).
tff(385,plain,
! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ),
inference(skolemize,[status(sab)],[384]) ).
tff(386,plain,
! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) ),
inference(modus_ponens,[status(thm)],[385,378]) ).
tff(387,plain,
( ( ~ ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
| logic_or(or1(f2(a)))
| ~ fulladder(f2(a)) )
<=> ( ~ ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
| logic_or(or1(f2(a)))
| ~ fulladder(f2(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(388,plain,
( ~ ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
| logic_or(or1(f2(a)))
| ~ fulladder(f2(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(389,plain,
( ~ ! [X: $i] :
( logic_or(or1(X))
| ~ fulladder(X) )
| logic_or(or1(f2(a)))
| ~ fulladder(f2(a)) ),
inference(modus_ponens,[status(thm)],[388,387]) ).
tff(390,plain,
( logic_or(or1(f2(a)))
| ~ fulladder(f2(a)) ),
inference(unit_resolution,[status(thm)],[389,386]) ).
tff(391,plain,
logic_or(or1(f2(a))),
inference(unit_resolution,[status(thm)],[390,59]) ).
tff(392,plain,
( ~ abnormal(or1(f2(a)))
<=> ~ abnormal(or1(f2(a))) ),
inference(rewrite,[status(thm)],[]) ).
tff(393,axiom,
~ abnormal(or1(f2(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagnosis_or1f2a) ).
tff(394,plain,
~ abnormal(or1(f2(a))),
inference(modus_ponens,[status(thm)],[393,392]) ).
tff(395,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(396,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)],[395]) ).
tff(397,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(398,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(399,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)],[398]) ).
tff(400,axiom,
! [K: $i] :
( ~ logic_or(K)
| or_ok(K)
| abnormal(K) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',or_ok_or_abnormal) ).
tff(401,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(modus_ponens,[status(thm)],[400,399]) ).
tff(402,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(modus_ponens,[status(thm)],[401,397]) ).
tff(403,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(skolemize,[status(sab)],[402]) ).
tff(404,plain,
! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
inference(modus_ponens,[status(thm)],[403,396]) ).
tff(405,plain,
( ( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(f2(a)))
| or_ok(or1(f2(a)))
| ~ logic_or(or1(f2(a))) )
<=> ( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(f2(a)))
| or_ok(or1(f2(a)))
| ~ logic_or(or1(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(406,plain,
( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(f2(a)))
| or_ok(or1(f2(a)))
| ~ logic_or(or1(f2(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(407,plain,
( ~ ! [K: $i] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) )
| abnormal(or1(f2(a)))
| or_ok(or1(f2(a)))
| ~ logic_or(or1(f2(a))) ),
inference(modus_ponens,[status(thm)],[406,405]) ).
tff(408,plain,
( or_ok(or1(f2(a)))
| ~ logic_or(or1(f2(a))) ),
inference(unit_resolution,[status(thm)],[407,404,394]) ).
tff(409,plain,
or_ok(or1(f2(a))),
inference(unit_resolution,[status(thm)],[408,391]) ).
tff(410,plain,
^ [K: $i] :
refl(( ( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) )
<=> ( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) ) )),
inference(bind,[status(th)],[]) ).
tff(411,plain,
( ! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) )
<=> ! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) ) ),
inference(quant_intro,[status(thm)],[410]) ).
tff(412,plain,
( ! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) )
<=> ! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(413,plain,
^ [K: $i] :
trans(monotonicity(rewrite(( ( ~ or_ok(K)
| ~ one(out1(K))
| one(in1(K)) )
<=> ( ~ one(out1(K))
| one(in1(K))
| ~ or_ok(K) ) )),
( ( ~ or_ok(K)
| ~ one(out1(K))
| one(in1(K))
| one(in2(K)) )
<=> ( ~ one(out1(K))
| one(in1(K))
| ~ or_ok(K)
| one(in2(K)) ) )),
rewrite(( ( ~ one(out1(K))
| one(in1(K))
| ~ or_ok(K)
| one(in2(K)) )
<=> ( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) ) )),
( ( ~ or_ok(K)
| ~ one(out1(K))
| one(in1(K))
| one(in2(K)) )
<=> ( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) ) )),
inference(bind,[status(th)],[]) ).
tff(414,plain,
( ! [K: $i] :
( ~ or_ok(K)
| ~ one(out1(K))
| one(in1(K))
| one(in2(K)) )
<=> ! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) ) ),
inference(quant_intro,[status(thm)],[413]) ).
tff(415,axiom,
! [K: $i] :
( ~ or_ok(K)
| ~ one(out1(K))
| one(in1(K))
| one(in2(K)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV002-0.ax',or_1_11) ).
tff(416,plain,
! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[415,414]) ).
tff(417,plain,
! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[416,412]) ).
tff(418,plain,
! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) ),
inference(skolemize,[status(sab)],[417]) ).
tff(419,plain,
! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) ),
inference(modus_ponens,[status(thm)],[418,411]) ).
tff(420,plain,
( ( ~ ! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) )
| one(in1(or1(f2(a))))
| one(in2(or1(f2(a))))
| ~ one(out1(or1(f2(a))))
| ~ or_ok(or1(f2(a))) )
<=> ( ~ ! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) )
| one(in1(or1(f2(a))))
| one(in2(or1(f2(a))))
| ~ one(out1(or1(f2(a))))
| ~ or_ok(or1(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(421,plain,
( ( ~ one(out1(or1(f2(a))))
| one(in2(or1(f2(a))))
| one(in1(or1(f2(a))))
| ~ or_ok(or1(f2(a))) )
<=> ( one(in1(or1(f2(a))))
| one(in2(or1(f2(a))))
| ~ one(out1(or1(f2(a))))
| ~ or_ok(or1(f2(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(422,plain,
( ( ~ ! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) )
| ~ one(out1(or1(f2(a))))
| one(in2(or1(f2(a))))
| one(in1(or1(f2(a))))
| ~ or_ok(or1(f2(a))) )
<=> ( ~ ! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) )
| one(in1(or1(f2(a))))
| one(in2(or1(f2(a))))
| ~ one(out1(or1(f2(a))))
| ~ or_ok(or1(f2(a))) ) ),
inference(monotonicity,[status(thm)],[421]) ).
tff(423,plain,
( ( ~ ! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) )
| ~ one(out1(or1(f2(a))))
| one(in2(or1(f2(a))))
| one(in1(or1(f2(a))))
| ~ or_ok(or1(f2(a))) )
<=> ( ~ ! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) )
| one(in1(or1(f2(a))))
| one(in2(or1(f2(a))))
| ~ one(out1(or1(f2(a))))
| ~ or_ok(or1(f2(a))) ) ),
inference(transitivity,[status(thm)],[422,420]) ).
tff(424,plain,
( ~ ! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) )
| ~ one(out1(or1(f2(a))))
| one(in2(or1(f2(a))))
| one(in1(or1(f2(a))))
| ~ or_ok(or1(f2(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(425,plain,
( ~ ! [K: $i] :
( ~ one(out1(K))
| one(in2(K))
| one(in1(K))
| ~ or_ok(K) )
| one(in1(or1(f2(a))))
| one(in2(or1(f2(a))))
| ~ one(out1(or1(f2(a))))
| ~ or_ok(or1(f2(a))) ),
inference(modus_ponens,[status(thm)],[424,423]) ).
tff(426,plain,
( one(in1(or1(f2(a))))
| one(in2(or1(f2(a)))) ),
inference(unit_resolution,[status(thm)],[425,419,409,376]) ).
tff(427,plain,
$false,
inference(unit_resolution,[status(thm)],[426,339,212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HWV008-2.002 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.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 : Thu Jun 19 17:19:12 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% See solution above
% 0.19/0.45 % E exiting
%------------------------------------------------------------------------------