%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWC001-1 : TPTP v9.0.0. Bugfixed v1.1.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:08:50 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 40
% Syntax : Number of formulae : 105 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 309 ( 72 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 366 ( 167 ~; 160 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 344 ( 324 !; 0 ?; 344 :)
% Comments :
%------------------------------------------------------------------------------
tff(output_type,type,
output: ( $i * $i * $i * $i ) > $o ).
tff(nand_type,type,
nand: ( $i * $i ) > $i ).
tff(n0_type,type,
n0: $i ).
tff(n1_type,type,
n1: $i ).
tff(not_type,type,
not: $i > $i ).
tff(and_type,type,
and: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( nand(X,Y) = not(and(X,Y)) )
<=> ( nand(X,Y) = not(and(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( nand(X,Y) = not(and(X,Y)) )
<=> ! [Y: $i,X: $i] : ( nand(X,Y) = not(and(X,Y)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( nand(X,Y) = not(and(X,Y)) )
<=> ! [Y: $i,X: $i] : ( nand(X,Y) = not(and(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( nand(X,Y) = not(and(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nand_definition) ).
tff(5,plain,
! [Y: $i,X: $i] : ( nand(X,Y) = not(and(X,Y)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( nand(X,Y) = not(and(X,Y)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( nand(X,Y) = not(and(X,Y)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( nand(X,Y) = not(and(X,Y)) )
| ( nand(n0,n1) = not(and(n0,n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
nand(n0,n1) = not(and(n0,n1)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
not(and(n0,n1)) = nand(n0,n1),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [X: $i] :
refl(( ( and(X,n1) = X )
<=> ( and(X,n1) = X ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [X: $i] : ( and(X,n1) = X )
<=> ! [X: $i] : ( and(X,n1) = X ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [X: $i] : ( and(X,n1) = X )
<=> ! [X: $i] : ( and(X,n1) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [X: $i] : ( and(X,n1) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_definition2) ).
tff(15,plain,
! [X: $i] : ( and(X,n1) = X ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [X: $i] : ( and(X,n1) = X ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [X: $i] : ( and(X,n1) = X ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [X: $i] : ( and(X,n1) = X )
| ( and(n0,n1) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
and(n0,n1) = n0,
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
not(and(n0,n1)) = not(n0),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
not(n0) = not(and(n0,n1)),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
^ [X: $i] :
refl(( ( and(X,n0) = n0 )
<=> ( and(X,n0) = n0 ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [X: $i] : ( and(X,n0) = n0 )
<=> ! [X: $i] : ( and(X,n0) = n0 ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [X: $i] : ( and(X,n0) = n0 )
<=> ! [X: $i] : ( and(X,n0) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
! [X: $i] : ( and(X,n0) = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_definition1) ).
tff(26,plain,
! [X: $i] : ( and(X,n0) = n0 ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [X: $i] : ( and(X,n0) = n0 ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X: $i] : ( and(X,n0) = n0 ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [X: $i] : ( and(X,n0) = n0 )
| ( and(n1,n0) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
and(n1,n0) = n0,
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
not(and(n1,n0)) = not(n0),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ~ ! [Y: $i,X: $i] : ( nand(X,Y) = not(and(X,Y)) )
| ( nand(n1,n0) = not(and(n1,n0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
nand(n1,n0) = not(and(n1,n0)),
inference(unit_resolution,[status(thm)],[32,7]) ).
tff(34,plain,
nand(n1,n0) = nand(n0,n1),
inference(transitivity,[status(thm)],[33,31,21,10]) ).
tff(35,plain,
( output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0))
<=> output(nand(n1,n1),nand(n0,n1),nand(n0,n1),nand(n0,n0)) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( output(nand(n1,n1),nand(n0,n1),nand(n0,n1),nand(n0,n0))
<=> output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0)) ),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
( ( not(n0) = n1 )
<=> ( not(n0) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
not(n0) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_definition1) ).
tff(39,plain,
not(n0) = n1,
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ ! [X: $i] : ( and(X,n0) = n0 )
| ( and(n0,n0) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
and(n0,n0) = n0,
inference(unit_resolution,[status(thm)],[40,28]) ).
tff(42,plain,
not(and(n0,n0)) = not(n0),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] : ( nand(X,Y) = not(and(X,Y)) )
| ( nand(n0,n0) = not(and(n0,n0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
nand(n0,n0) = not(and(n0,n0)),
inference(unit_resolution,[status(thm)],[43,7]) ).
tff(45,plain,
nand(n0,n0) = n1,
inference(transitivity,[status(thm)],[44,42,39]) ).
tff(46,plain,
nand(n0,n1) = n1,
inference(transitivity,[status(thm)],[9,20,39]) ).
tff(47,plain,
( ( not(n1) = n0 )
<=> ( not(n1) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
not(n1) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_definition2) ).
tff(49,plain,
not(n1) = n0,
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( ~ ! [X: $i] : ( and(X,n1) = X )
| ( and(n1,n1) = n1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
and(n1,n1) = n1,
inference(unit_resolution,[status(thm)],[50,17]) ).
tff(52,plain,
not(and(n1,n1)) = not(n1),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ~ ! [Y: $i,X: $i] : ( nand(X,Y) = not(and(X,Y)) )
| ( nand(n1,n1) = not(and(n1,n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
nand(n1,n1) = not(and(n1,n1)),
inference(unit_resolution,[status(thm)],[53,7]) ).
tff(55,plain,
nand(n1,n1) = n0,
inference(transitivity,[status(thm)],[54,52,49]) ).
tff(56,plain,
( output(nand(n1,n1),nand(n0,n1),nand(n0,n1),nand(n0,n0))
<=> output(n0,n1,n1,n1) ),
inference(monotonicity,[status(thm)],[55,46,46,45]) ).
tff(57,plain,
( output(n0,n1,n1,n1)
<=> output(nand(n1,n1),nand(n0,n1),nand(n0,n1),nand(n0,n0)) ),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( output(n0,n1,n1,n1)
<=> output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0)) ),
inference(transitivity,[status(thm)],[57,36]) ).
tff(59,plain,
( ~ output(n0,n1,n1,n1)
<=> ~ output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0)) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ~ output(n0,n1,n1,n1)
<=> ~ output(n0,n1,n1,n1) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
~ output(n0,n1,n1,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cannot_make_or) ).
tff(62,plain,
~ output(n0,n1,n1,n1),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
~ output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0)),
inference(modus_ponens,[status(thm)],[62,59]) ).
tff(64,plain,
( output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1))
<=> output(n1,n0,n1,n0) ),
inference(monotonicity,[status(thm)],[45,55,45,55]) ).
tff(65,plain,
( output(n0,n1,n0,n1)
<=> output(n0,n1,n0,n1) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
output(n0,n1,n0,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',input2) ).
tff(67,plain,
output(n0,n1,n0,n1),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
^ [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
<=> ( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
<=> ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
<=> ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
^ [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
rewrite(( ( ~ output(X1,X2,X3,X4)
| ~ output(Y1,Y2,Y3,Y4)
| output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4)) )
<=> ( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ output(X1,X2,X3,X4)
| ~ output(Y1,Y2,Y3,Y4)
| output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4)) )
<=> ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( ~ output(X1,X2,X3,X4)
| ~ output(Y1,Y2,Y3,Y4)
| output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nand_table_definition) ).
tff(74,plain,
! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n0,n1,n0,n1)
| output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1)) )
<=> ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n0,n1,n0,n1)
| output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ( output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1))
| ~ output(n0,n1,n0,n1)
| ~ output(n0,n1,n0,n1) )
<=> ( ~ output(n0,n1,n0,n1)
| output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1))
| ~ output(n0,n1,n0,n1)
| ~ output(n0,n1,n0,n1) )
<=> ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n0,n1,n0,n1)
| output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1)) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1))
| ~ output(n0,n1,n0,n1)
| ~ output(n0,n1,n0,n1) )
<=> ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n0,n1,n0,n1)
| output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1)) ) ),
inference(transitivity,[status(thm)],[80,78]) ).
tff(82,plain,
( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1))
| ~ output(n0,n1,n0,n1)
| ~ output(n0,n1,n0,n1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n0,n1,n0,n1)
| output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1)) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1)),
inference(unit_resolution,[status(thm)],[83,77,67]) ).
tff(85,plain,
output(n1,n0,n1,n0),
inference(modus_ponens,[status(thm)],[84,64]) ).
tff(86,plain,
( output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1))
<=> output(n1,n1,n0,n0) ),
inference(monotonicity,[status(thm)],[45,45,55,55]) ).
tff(87,plain,
( output(n0,n0,n1,n1)
<=> output(n0,n0,n1,n1) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,axiom,
output(n0,n0,n1,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',input1) ).
tff(89,plain,
output(n0,n0,n1,n1),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
( ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n0,n0,n1,n1)
| output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1)) )
<=> ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n0,n0,n1,n1)
| output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ( output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1))
| ~ output(n0,n0,n1,n1)
| ~ output(n0,n0,n1,n1) )
<=> ( ~ output(n0,n0,n1,n1)
| output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1))
| ~ output(n0,n0,n1,n1)
| ~ output(n0,n0,n1,n1) )
<=> ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n0,n0,n1,n1)
| output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1)) ) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1))
| ~ output(n0,n0,n1,n1)
| ~ output(n0,n0,n1,n1) )
<=> ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n0,n0,n1,n1)
| output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1)) ) ),
inference(transitivity,[status(thm)],[92,90]) ).
tff(94,plain,
( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1))
| ~ output(n0,n0,n1,n1)
| ~ output(n0,n0,n1,n1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n0,n0,n1,n1)
| output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1)) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1)),
inference(unit_resolution,[status(thm)],[95,77,89]) ).
tff(97,plain,
output(n1,n1,n0,n0),
inference(modus_ponens,[status(thm)],[96,86]) ).
tff(98,plain,
( ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n1,n1,n0,n0)
| ~ output(n1,n0,n1,n0)
| output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0)) )
<=> ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n1,n1,n0,n0)
| ~ output(n1,n0,n1,n0)
| output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ( output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0))
| ~ output(n1,n1,n0,n0)
| ~ output(n1,n0,n1,n0) )
<=> ( ~ output(n1,n1,n0,n0)
| ~ output(n1,n0,n1,n0)
| output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0))
| ~ output(n1,n1,n0,n0)
| ~ output(n1,n0,n1,n0) )
<=> ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n1,n1,n0,n0)
| ~ output(n1,n0,n1,n0)
| output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0)) ) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0))
| ~ output(n1,n1,n0,n0)
| ~ output(n1,n0,n1,n0) )
<=> ( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n1,n1,n0,n0)
| ~ output(n1,n0,n1,n0)
| output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0)) ) ),
inference(transitivity,[status(thm)],[100,98]) ).
tff(102,plain,
( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0))
| ~ output(n1,n1,n0,n0)
| ~ output(n1,n0,n1,n0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
( output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4))
| ~ output(Y1,Y2,Y3,Y4)
| ~ output(X1,X2,X3,X4) )
| ~ output(n1,n1,n0,n0)
| ~ output(n1,n0,n1,n0)
| output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0)) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
( ~ output(n1,n1,n0,n0)
| ~ output(n1,n0,n1,n0)
| output(nand(n1,n1),nand(n0,n1),nand(n1,n0),nand(n0,n0)) ),
inference(unit_resolution,[status(thm)],[103,77]) ).
tff(105,plain,
$false,
inference(unit_resolution,[status(thm)],[104,97,85,63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : HWC001-1 : TPTP v9.0.0. Bugfixed v1.1.1.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n014.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 17:17:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40 % SZS output start Proof
% See solution above
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------