%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV004-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:08:51 AM UTC 2025
% Result : Unsatisfiable 16.22s 16.41s
% Output : Proof 16.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 120
% Syntax : Number of formulae : 374 ( 273 unt; 0 typ; 0 def)
% Number of atoms : 507 ( 475 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 184 ( 67 ~; 60 |; 0 &)
% ( 57 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 447 ( 412 !; 0 ?; 447 :)
% Comments :
%------------------------------------------------------------------------------
tff(circuit_type,type,
circuit: ( $i * $i * $i ) > $o ).
tff(overflow_type,type,
overflow: $i ).
tff(s1_type,type,
s1: $i ).
tff(s0_type,type,
s0: $i ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(and_type,type,
and: ( $i * $i ) > $i ).
tff(b1_type,type,
b1: $i ).
tff(a1_type,type,
a1: $i ).
tff(b0_type,type,
b0: $i ).
tff(a0_type,type,
a0: $i ).
tff(xor_type,type,
xor: ( $i * $i ) > $i ).
tff(carryout_type,type,
carryout: ( $i * $i * $i ) > $i ).
tff(n0_type,type,
n0: $i ).
tff(not_type,type,
not: $i > $i ).
tff(n1_type,type,
n1: $i ).
tff(sum_type,type,
sum: ( $i * $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( or(X,Y) = or(Y,X) )
<=> ( or(X,Y) = or(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
<=> ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
<=> ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_symmetry) ).
tff(5,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(and(a0,b0),or(a1,b1)),and(a1,b1)) = or(and(a1,b1),and(and(a0,b0),or(a1,b1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
or(and(and(a0,b0),or(a1,b1)),and(a1,b1)) = or(and(a1,b1),and(and(a0,b0),or(a1,b1))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( and(X,Y) = and(Y,X) )
<=> ( and(X,Y) = and(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
<=> ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
<=> ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_symmetry) ).
tff(14,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(or(a1,b1),and(a0,b0)) = and(and(a0,b0),or(a1,b1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
and(or(a1,b1),and(a0,b0)) = and(and(a0,b0),or(a1,b1)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
<=> ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_simplification) ).
tff(23,plain,
! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(a1,b1),and(a0,b0)) = or(and(a1,and(a0,b0)),and(b1,and(a0,b0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
and(or(a1,b1),and(a0,b0)) = or(and(a1,and(a0,b0)),and(b1,and(a0,b0))),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
or(and(a1,and(a0,b0)),and(b1,and(a0,b0))) = and(or(a1,b1),and(a0,b0)),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( carryout(X,Y,Z) = or(and(X,or(Y,Z)),and(not(X),and(Y,Z))) )
<=> ( carryout(X,Y,Z) = or(and(X,or(Y,Z)),and(not(X),and(Y,Z))) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [Z: $i,Y: $i,X: $i] : ( carryout(X,Y,Z) = or(and(X,or(Y,Z)),and(not(X),and(Y,Z))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( carryout(X,Y,Z) = or(and(X,or(Y,Z)),and(not(X),and(Y,Z))) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [Z: $i,Y: $i,X: $i] : ( carryout(X,Y,Z) = or(and(X,or(Y,Z)),and(not(X),and(Y,Z))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( carryout(X,Y,Z) = or(and(X,or(Y,Z)),and(not(X),and(Y,Z))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [Z: $i,Y: $i,X: $i] : ( carryout(X,Y,Z) = or(and(X,or(Y,Z)),and(not(X),and(Y,Z))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',carryout_definition) ).
tff(33,plain,
! [Z: $i,Y: $i,X: $i] : ( carryout(X,Y,Z) = or(and(X,or(Y,Z)),and(not(X),and(Y,Z))) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] : ( carryout(X,Y,Z) = or(and(X,or(Y,Z)),and(not(X),and(Y,Z))) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( carryout(X,Y,Z) = or(and(X,or(Y,Z)),and(not(X),and(Y,Z))) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( carryout(X,Y,Z) = or(and(X,or(Y,Z)),and(not(X),and(Y,Z))) )
| ( carryout(a0,b0,n0) = or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
carryout(a0,b0,n0) = or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0))),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0))) = carryout(a0,b0,n0),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(not(a0),and(b0,n0)),and(a0,or(b0,n0))) = or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
or(and(not(a0),and(b0,n0)),and(a0,or(b0,n0))) = or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0))),
inference(unit_resolution,[status(thm)],[39,7]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(b0,a0) = and(a0,b0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
and(b0,a0) = and(a0,b0),
inference(unit_resolution,[status(thm)],[41,16]) ).
tff(43,plain,
and(a0,b0) = and(b0,a0),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
^ [X: $i] :
refl(( ( or(X,n0) = X )
<=> ( or(X,n0) = X ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [X: $i] : ( or(X,n0) = X )
<=> ! [X: $i] : ( or(X,n0) = X ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [X: $i] : ( or(X,n0) = X )
<=> ! [X: $i] : ( or(X,n0) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
! [X: $i] : ( or(X,n0) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',or_definition1) ).
tff(48,plain,
! [X: $i] : ( or(X,n0) = X ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [X: $i] : ( or(X,n0) = X ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [X: $i] : ( or(X,n0) = X ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ! [X: $i] : ( or(X,n0) = X )
| ( or(b0,n0) = b0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
or(b0,n0) = b0,
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
and(a0,or(b0,n0)) = and(a0,b0),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
and(a0,or(b0,n0)) = and(b0,a0),
inference(transitivity,[status(thm)],[53,43]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(and(b0,n0),not(a0)) = and(not(a0),and(b0,n0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
and(and(b0,n0),not(a0)) = and(not(a0),and(b0,n0)),
inference(unit_resolution,[status(thm)],[55,16]) ).
tff(57,plain,
and(not(a0),and(b0,n0)) = and(and(b0,n0),not(a0)),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
or(and(not(a0),and(b0,n0)),and(a0,or(b0,n0))) = or(and(and(b0,n0),not(a0)),and(b0,a0)),
inference(monotonicity,[status(thm)],[57,54]) ).
tff(59,plain,
or(and(and(b0,n0),not(a0)),and(b0,a0)) = or(and(not(a0),and(b0,n0)),and(a0,or(b0,n0))),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) )
<=> ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',karnaugh3) ).
tff(64,plain,
! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) )
| ( or(and(and(b0,n0),not(a0)),and(b0,a0)) = or(and(b0,n0),and(b0,a0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
or(and(and(b0,n0),not(a0)),and(b0,a0)) = or(and(b0,n0),and(b0,a0)),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
or(and(b0,n0),and(b0,a0)) = or(and(and(b0,n0),not(a0)),and(b0,a0)),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
^ [X: $i] :
refl(( ( and(X,n0) = n0 )
<=> ( and(X,n0) = n0 ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [X: $i] : ( and(X,n0) = n0 )
<=> ! [X: $i] : ( and(X,n0) = n0 ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [X: $i] : ( and(X,n0) = n0 )
<=> ! [X: $i] : ( and(X,n0) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
! [X: $i] : ( and(X,n0) = n0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',and_definition1) ).
tff(74,plain,
! [X: $i] : ( and(X,n0) = n0 ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [X: $i] : ( and(X,n0) = n0 ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [X: $i] : ( and(X,n0) = n0 ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ~ ! [X: $i] : ( and(X,n0) = n0 )
| ( and(a0,n0) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
and(a0,n0) = n0,
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
n0 = and(a0,n0),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
( ~ ! [X: $i] : ( and(X,n0) = n0 )
| ( and(b0,n0) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
and(b0,n0) = n0,
inference(unit_resolution,[status(thm)],[80,76]) ).
tff(82,plain,
and(b0,n0) = and(a0,n0),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,plain,
or(and(b0,n0),and(b0,a0)) = or(and(a0,n0),and(a0,b0)),
inference(monotonicity,[status(thm)],[82,42]) ).
tff(84,plain,
or(and(a0,n0),and(a0,b0)) = or(and(b0,n0),and(b0,a0)),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(a0,n0),and(a0,b0)) = or(and(a0,b0),and(a0,n0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
or(and(a0,n0),and(a0,b0)) = or(and(a0,b0),and(a0,n0)),
inference(unit_resolution,[status(thm)],[85,7]) ).
tff(87,plain,
or(and(a0,b0),and(a0,n0)) = or(and(a0,n0),and(a0,b0)),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) )
| ( or(and(and(a0,b0),not(n0)),and(a0,n0)) = or(and(a0,b0),and(a0,n0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
or(and(and(a0,b0),not(n0)),and(a0,n0)) = or(and(a0,b0),and(a0,n0)),
inference(unit_resolution,[status(thm)],[88,66]) ).
tff(90,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(a0,n0),and(and(a0,b0),not(n0))) = or(and(and(a0,b0),not(n0)),and(a0,n0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
or(and(a0,n0),and(and(a0,b0),not(n0))) = or(and(and(a0,b0),not(n0)),and(a0,n0)),
inference(unit_resolution,[status(thm)],[90,7]) ).
tff(92,plain,
( ( not(n0) = n1 )
<=> ( not(n0) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,axiom,
not(n0) = n1,
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',not_definition1) ).
tff(94,plain,
not(n0) = n1,
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
and(and(a0,b0),not(n0)) = and(and(a0,b0),n1),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
^ [Y: $i,X: $i] :
refl(( ( and(and(X,Y),not(Y)) = n0 )
<=> ( and(and(X,Y),not(Y)) = n0 ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 )
<=> ! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 )
<=> ! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,axiom,
! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_not_evaluation2) ).
tff(100,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 ),
inference(modus_ponens,[status(thm)],[101,97]) ).
tff(103,plain,
( ~ ! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 )
| ( and(and(and(a0,b0),n1),not(n1)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
and(and(and(a0,b0),n1),not(n1)) = n0,
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
n0 = and(and(and(a0,b0),n1),not(n1)),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
and(a0,n0) = and(and(and(a0,b0),n1),not(n1)),
inference(transitivity,[status(thm)],[78,105]) ).
tff(107,plain,
or(and(a0,n0),and(and(a0,b0),not(n0))) = or(and(and(and(a0,b0),n1),not(n1)),and(and(a0,b0),n1)),
inference(monotonicity,[status(thm)],[106,95]) ).
tff(108,plain,
or(and(and(and(a0,b0),n1),not(n1)),and(and(a0,b0),n1)) = or(and(a0,n0),and(and(a0,b0),not(n0))),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) )
| ( or(and(and(and(a0,b0),n1),not(n1)),and(and(a0,b0),n1)) = or(and(and(a0,b0),n1),and(and(a0,b0),n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
or(and(and(and(a0,b0),n1),not(n1)),and(and(a0,b0),n1)) = or(and(and(a0,b0),n1),and(and(a0,b0),n1)),
inference(unit_resolution,[status(thm)],[109,66]) ).
tff(111,plain,
or(and(and(a0,b0),n1),and(and(a0,b0),n1)) = or(and(and(and(a0,b0),n1),not(n1)),and(and(a0,b0),n1)),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
^ [X: $i] :
refl(( ( and(X,n1) = X )
<=> ( and(X,n1) = X ) )),
inference(bind,[status(th)],[]) ).
tff(113,plain,
( ! [X: $i] : ( and(X,n1) = X )
<=> ! [X: $i] : ( and(X,n1) = X ) ),
inference(quant_intro,[status(thm)],[112]) ).
tff(114,plain,
( ! [X: $i] : ( and(X,n1) = X )
<=> ! [X: $i] : ( and(X,n1) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,axiom,
! [X: $i] : ( and(X,n1) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',and_definition2) ).
tff(116,plain,
! [X: $i] : ( and(X,n1) = X ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
! [X: $i] : ( and(X,n1) = X ),
inference(skolemize,[status(sab)],[116]) ).
tff(118,plain,
! [X: $i] : ( and(X,n1) = X ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
( ~ ! [X: $i] : ( and(X,n1) = X )
| ( and(and(a0,b0),n1) = and(a0,b0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
and(and(a0,b0),n1) = and(a0,b0),
inference(unit_resolution,[status(thm)],[119,118]) ).
tff(121,plain,
or(and(and(a0,b0),n1),and(and(a0,b0),n1)) = or(and(a0,b0),and(a0,b0)),
inference(monotonicity,[status(thm)],[120,120]) ).
tff(122,plain,
or(and(a0,b0),and(a0,b0)) = or(and(and(a0,b0),n1),and(and(a0,b0),n1)),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
and(and(a0,b0),n1) = and(and(a0,b0),not(n0)),
inference(symmetry,[status(thm)],[95]) ).
tff(124,plain,
and(a0,b0) = and(and(a0,b0),n1),
inference(symmetry,[status(thm)],[120]) ).
tff(125,plain,
and(a0,b0) = and(and(a0,b0),not(n0)),
inference(transitivity,[status(thm)],[124,123]) ).
tff(126,plain,
or(and(a0,b0),and(a0,b0)) = or(and(and(a0,b0),not(n0)),and(a0,b0)),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
or(and(and(a0,b0),not(n0)),and(a0,b0)) = or(and(a0,b0),and(a0,b0)),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
or(and(and(a0,b0),not(n0)),and(a0,b0)) = or(and(and(a0,b0),n1),and(a0,b0)),
inference(monotonicity,[status(thm)],[95]) ).
tff(129,plain,
or(and(and(a0,b0),n1),and(a0,b0)) = or(and(and(a0,b0),not(n0)),and(a0,b0)),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
^ [Y: $i,X: $i] :
refl(( ( or(and(X,Y),X) = X )
<=> ( or(and(X,Y),X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(131,plain,
( ! [Y: $i,X: $i] : ( or(and(X,Y),X) = X )
<=> ! [Y: $i,X: $i] : ( or(and(X,Y),X) = X ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
( ! [Y: $i,X: $i] : ( or(and(X,Y),X) = X )
<=> ! [Y: $i,X: $i] : ( or(and(X,Y),X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,axiom,
! [Y: $i,X: $i] : ( or(and(X,Y),X) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_subsumption2) ).
tff(134,plain,
! [Y: $i,X: $i] : ( or(and(X,Y),X) = X ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [Y: $i,X: $i] : ( or(and(X,Y),X) = X ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [Y: $i,X: $i] : ( or(and(X,Y),X) = X ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,Y),X) = X )
| ( or(and(and(a0,b0),n1),and(a0,b0)) = and(a0,b0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
or(and(and(a0,b0),n1),and(a0,b0)) = and(a0,b0),
inference(unit_resolution,[status(thm)],[137,136]) ).
tff(139,plain,
and(a0,b0) = or(and(and(a0,b0),n1),and(a0,b0)),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
and(a0,b0) = carryout(a0,b0,n0),
inference(transitivity,[status(thm)],[139,129,127,122,111,108,91,89,87,84,69,59,40,38]) ).
tff(141,plain,
and(b1,and(a0,b0)) = and(b1,carryout(a0,b0,n0)),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
and(b1,carryout(a0,b0,n0)) = and(b1,and(a0,b0)),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
or(and(a1,and(a0,b0)),and(b1,carryout(a0,b0,n0))) = or(and(a1,and(a0,b0)),and(b1,and(a0,b0))),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
or(and(a1,and(a0,b0)),and(b1,carryout(a0,b0,n0))) = and(and(a0,b0),or(a1,b1)),
inference(transitivity,[status(thm)],[143,28,18]) ).
tff(145,plain,
or(or(and(a1,and(a0,b0)),and(b1,carryout(a0,b0,n0))),and(a1,b1)) = or(and(and(a0,b0),or(a1,b1)),and(a1,b1)),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( or(or(X,Y),Z) = or(or(X,Z),Y) )
<=> ( or(or(X,Y),Z) = or(or(X,Z),Y) ) )),
inference(bind,[status(th)],[]) ).
tff(147,plain,
( ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) )
<=> ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,plain,
( ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) )
<=> ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(149,axiom,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_commutativity) ).
tff(150,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) ),
inference(skolemize,[status(sab)],[150]) ).
tff(152,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) ),
inference(modus_ponens,[status(thm)],[151,147]) ).
tff(153,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) )
| ( or(or(and(a1,and(a0,b0)),and(b1,carryout(a0,b0,n0))),and(a1,b1)) = or(or(and(a1,and(a0,b0)),and(a1,b1)),and(b1,carryout(a0,b0,n0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
or(or(and(a1,and(a0,b0)),and(b1,carryout(a0,b0,n0))),and(a1,b1)) = or(or(and(a1,and(a0,b0)),and(a1,b1)),and(b1,carryout(a0,b0,n0))),
inference(unit_resolution,[status(thm)],[153,152]) ).
tff(155,plain,
or(or(and(a1,and(a0,b0)),and(a1,b1)),and(b1,carryout(a0,b0,n0))) = or(or(and(a1,and(a0,b0)),and(b1,carryout(a0,b0,n0))),and(a1,b1)),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(a1,and(a0,b0)),and(a1,b1)) = or(and(a1,b1),and(a1,and(a0,b0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
or(and(a1,and(a0,b0)),and(a1,b1)) = or(and(a1,b1),and(a1,and(a0,b0))),
inference(unit_resolution,[status(thm)],[156,7]) ).
tff(158,plain,
or(and(a1,b1),and(a1,and(a0,b0))) = or(and(a1,and(a0,b0)),and(a1,b1)),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(and(a0,b0),a1) = and(a1,and(a0,b0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(160,plain,
and(and(a0,b0),a1) = and(a1,and(a0,b0)),
inference(unit_resolution,[status(thm)],[159,16]) ).
tff(161,plain,
and(a1,and(a0,b0)) = and(and(a0,b0),a1),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(b1,a1) = and(a1,b1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
and(b1,a1) = and(a1,b1),
inference(unit_resolution,[status(thm)],[162,16]) ).
tff(164,plain,
and(a1,b1) = and(b1,a1),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
or(and(a1,b1),and(a1,and(a0,b0))) = or(and(b1,a1),and(and(a0,b0),a1)),
inference(monotonicity,[status(thm)],[164,161]) ).
tff(166,plain,
or(and(b1,a1),and(and(a0,b0),a1)) = or(and(a1,b1),and(a1,and(a0,b0))),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(b1,and(a0,b0)),a1) = or(and(b1,a1),and(and(a0,b0),a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
and(or(b1,and(a0,b0)),a1) = or(and(b1,a1),and(and(a0,b0),a1)),
inference(unit_resolution,[status(thm)],[167,25]) ).
tff(169,plain,
or(b1,and(a0,b0)) = or(b1,carryout(a0,b0,n0)),
inference(monotonicity,[status(thm)],[140]) ).
tff(170,plain,
and(or(b1,and(a0,b0)),a1) = and(or(b1,carryout(a0,b0,n0)),a1),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
and(or(b1,carryout(a0,b0,n0)),a1) = and(or(b1,and(a0,b0)),a1),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(or(b1,carryout(a0,b0,n0)),a1) = and(a1,or(b1,carryout(a0,b0,n0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
and(or(b1,carryout(a0,b0,n0)),a1) = and(a1,or(b1,carryout(a0,b0,n0))),
inference(unit_resolution,[status(thm)],[172,16]) ).
tff(174,plain,
and(a1,or(b1,carryout(a0,b0,n0))) = and(or(b1,carryout(a0,b0,n0)),a1),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
and(a1,or(b1,carryout(a0,b0,n0))) = or(and(a1,and(a0,b0)),and(a1,b1)),
inference(transitivity,[status(thm)],[174,171,168,166,158]) ).
tff(176,plain,
or(and(a1,or(b1,carryout(a0,b0,n0))),and(b1,carryout(a0,b0,n0))) = or(or(and(a1,and(a0,b0)),and(a1,b1)),and(b1,carryout(a0,b0,n0))),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,Y),X) = X )
| ( or(and(a1,b1),a1) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(178,plain,
or(and(a1,b1),a1) = a1,
inference(unit_resolution,[status(thm)],[177,136]) ).
tff(179,plain,
and(or(and(a1,b1),a1),or(b1,carryout(a0,b0,n0))) = and(a1,or(b1,carryout(a0,b0,n0))),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(and(a1,b1),a1),or(b1,carryout(a0,b0,n0))) = or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
and(or(and(a1,b1),a1),or(b1,carryout(a0,b0,n0))) = or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))),
inference(unit_resolution,[status(thm)],[180,25]) ).
tff(182,plain,
or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))) = and(or(and(a1,b1),a1),or(b1,carryout(a0,b0,n0))),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))) = and(a1,or(b1,carryout(a0,b0,n0))),
inference(transitivity,[status(thm)],[182,179]) ).
tff(184,plain,
or(or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))),and(b1,carryout(a0,b0,n0))) = or(and(a1,or(b1,carryout(a0,b0,n0))),and(b1,carryout(a0,b0,n0))),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) )
| ( or(or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))),and(b1,carryout(a0,b0,n0))) = or(or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(186,plain,
or(or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))),and(b1,carryout(a0,b0,n0))) = or(or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))),
inference(unit_resolution,[status(thm)],[185,152]) ).
tff(187,plain,
or(or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))) = or(or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))),and(b1,carryout(a0,b0,n0))),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))) = and(b1,carryout(a0,b0,n0)),
inference(monotonicity,[status(thm)],[38]) ).
tff(189,plain,
and(b1,carryout(a0,b0,n0)) = and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
( ~ ! [X: $i] : ( and(X,n1) = X )
| ( and(and(a1,b1),n1) = and(a1,b1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(191,plain,
and(and(a1,b1),n1) = and(a1,b1),
inference(unit_resolution,[status(thm)],[190,118]) ).
tff(192,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(n1,and(a1,b1)) = and(and(a1,b1),n1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(193,plain,
and(n1,and(a1,b1)) = and(and(a1,b1),n1),
inference(unit_resolution,[status(thm)],[192,16]) ).
tff(194,plain,
^ [Y: $i,X: $i] :
refl(( ( or(or(X,Y),not(X)) = n1 )
<=> ( or(or(X,Y),not(X)) = n1 ) )),
inference(bind,[status(th)],[]) ).
tff(195,plain,
( ! [Y: $i,X: $i] : ( or(or(X,Y),not(X)) = n1 )
<=> ! [Y: $i,X: $i] : ( or(or(X,Y),not(X)) = n1 ) ),
inference(quant_intro,[status(thm)],[194]) ).
tff(196,plain,
( ! [Y: $i,X: $i] : ( or(or(X,Y),not(X)) = n1 )
<=> ! [Y: $i,X: $i] : ( or(or(X,Y),not(X)) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(197,axiom,
! [Y: $i,X: $i] : ( or(or(X,Y),not(X)) = n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_not_evaluation3) ).
tff(198,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),not(X)) = n1 ),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),not(X)) = n1 ),
inference(skolemize,[status(sab)],[198]) ).
tff(200,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),not(X)) = n1 ),
inference(modus_ponens,[status(thm)],[199,195]) ).
tff(201,plain,
( ~ ! [Y: $i,X: $i] : ( or(or(X,Y),not(X)) = n1 )
| ( or(or(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))),not(b1)) = n1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,plain,
or(or(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))),not(b1)) = n1,
inference(unit_resolution,[status(thm)],[201,200]) ).
tff(203,plain,
or(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))) = or(b1,carryout(a0,b0,n0)),
inference(monotonicity,[status(thm)],[38]) ).
tff(204,plain,
or(b1,carryout(a0,b0,n0)) = or(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
or(or(b1,carryout(a0,b0,n0)),not(b1)) = or(or(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))),not(b1)),
inference(monotonicity,[status(thm)],[204]) ).
tff(206,plain,
or(or(b1,carryout(a0,b0,n0)),not(b1)) = n1,
inference(transitivity,[status(thm)],[205,202]) ).
tff(207,plain,
and(or(or(b1,carryout(a0,b0,n0)),not(b1)),and(a1,b1)) = and(n1,and(a1,b1)),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(or(b1,carryout(a0,b0,n0)),not(b1)),and(a1,b1)) = or(and(or(b1,carryout(a0,b0,n0)),and(a1,b1)),and(not(b1),and(a1,b1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(209,plain,
and(or(or(b1,carryout(a0,b0,n0)),not(b1)),and(a1,b1)) = or(and(or(b1,carryout(a0,b0,n0)),and(a1,b1)),and(not(b1),and(a1,b1))),
inference(unit_resolution,[status(thm)],[208,25]) ).
tff(210,plain,
or(and(or(b1,carryout(a0,b0,n0)),and(a1,b1)),and(not(b1),and(a1,b1))) = and(or(or(b1,carryout(a0,b0,n0)),not(b1)),and(a1,b1)),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(not(b1),and(a1,b1)) = and(and(a1,b1),not(b1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(212,plain,
and(not(b1),and(a1,b1)) = and(and(a1,b1),not(b1)),
inference(unit_resolution,[status(thm)],[211,16]) ).
tff(213,plain,
and(and(a1,b1),not(b1)) = and(not(b1),and(a1,b1)),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
( ~ ! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 )
| ( and(and(a1,b1),not(b1)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(215,plain,
and(and(a1,b1),not(b1)) = n0,
inference(unit_resolution,[status(thm)],[214,102]) ).
tff(216,plain,
n0 = and(and(a1,b1),not(b1)),
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
n0 = and(not(b1),and(a1,b1)),
inference(transitivity,[status(thm)],[216,213]) ).
tff(218,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(or(b1,carryout(a0,b0,n0)),and(a1,b1)) = and(and(a1,b1),or(b1,carryout(a0,b0,n0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(219,plain,
and(or(b1,carryout(a0,b0,n0)),and(a1,b1)) = and(and(a1,b1),or(b1,carryout(a0,b0,n0))),
inference(unit_resolution,[status(thm)],[218,16]) ).
tff(220,plain,
and(and(a1,b1),or(b1,carryout(a0,b0,n0))) = and(or(b1,carryout(a0,b0,n0)),and(a1,b1)),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),n0) = or(and(or(b1,carryout(a0,b0,n0)),and(a1,b1)),and(not(b1),and(a1,b1))),
inference(monotonicity,[status(thm)],[220,217]) ).
tff(222,plain,
( ~ ! [X: $i] : ( and(X,n0) = n0 )
| ( and(and(a1,or(b1,carryout(a0,b0,n0))),n0) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(223,plain,
and(and(a1,or(b1,carryout(a0,b0,n0))),n0) = n0,
inference(unit_resolution,[status(thm)],[222,76]) ).
tff(224,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( and(and(X,Y),Z) = and(and(X,Z),Y) )
<=> ( and(and(X,Y),Z) = and(and(X,Z),Y) ) )),
inference(bind,[status(th)],[]) ).
tff(225,plain,
( ! [Z: $i,Y: $i,X: $i] : ( and(and(X,Y),Z) = and(and(X,Z),Y) )
<=> ! [Z: $i,Y: $i,X: $i] : ( and(and(X,Y),Z) = and(and(X,Z),Y) ) ),
inference(quant_intro,[status(thm)],[224]) ).
tff(226,plain,
( ! [Z: $i,Y: $i,X: $i] : ( and(and(X,Y),Z) = and(and(X,Z),Y) )
<=> ! [Z: $i,Y: $i,X: $i] : ( and(and(X,Y),Z) = and(and(X,Z),Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(227,axiom,
! [Z: $i,Y: $i,X: $i] : ( and(and(X,Y),Z) = and(and(X,Z),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_commutativity) ).
tff(228,plain,
! [Z: $i,Y: $i,X: $i] : ( and(and(X,Y),Z) = and(and(X,Z),Y) ),
inference(modus_ponens,[status(thm)],[227,226]) ).
tff(229,plain,
! [Z: $i,Y: $i,X: $i] : ( and(and(X,Y),Z) = and(and(X,Z),Y) ),
inference(skolemize,[status(sab)],[228]) ).
tff(230,plain,
! [Z: $i,Y: $i,X: $i] : ( and(and(X,Y),Z) = and(and(X,Z),Y) ),
inference(modus_ponens,[status(thm)],[229,225]) ).
tff(231,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(and(X,Y),Z) = and(and(X,Z),Y) )
| ( and(and(a1,or(b1,carryout(a0,b0,n0))),n0) = and(and(a1,n0),or(b1,carryout(a0,b0,n0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(232,plain,
and(and(a1,or(b1,carryout(a0,b0,n0))),n0) = and(and(a1,n0),or(b1,carryout(a0,b0,n0))),
inference(unit_resolution,[status(thm)],[231,230]) ).
tff(233,plain,
and(and(a1,n0),or(b1,carryout(a0,b0,n0))) = and(and(a1,or(b1,carryout(a0,b0,n0))),n0),
inference(symmetry,[status(thm)],[232]) ).
tff(234,plain,
( ~ ! [X: $i] : ( and(X,n0) = n0 )
| ( and(a1,n0) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(235,plain,
and(a1,n0) = n0,
inference(unit_resolution,[status(thm)],[234,76]) ).
tff(236,plain,
n0 = and(a1,n0),
inference(symmetry,[status(thm)],[235]) ).
tff(237,plain,
and(n0,or(b1,carryout(a0,b0,n0))) = and(and(a1,n0),or(b1,carryout(a0,b0,n0))),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
and(n0,or(b1,carryout(a0,b0,n0))) = n0,
inference(transitivity,[status(thm)],[237,233,223]) ).
tff(239,plain,
or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(n0,or(b1,carryout(a0,b0,n0)))) = or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),n0),
inference(monotonicity,[status(thm)],[238]) ).
tff(240,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(and(a1,b1),n0),or(b1,carryout(a0,b0,n0))) = or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(n0,or(b1,carryout(a0,b0,n0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(241,plain,
and(or(and(a1,b1),n0),or(b1,carryout(a0,b0,n0))) = or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(n0,or(b1,carryout(a0,b0,n0)))),
inference(unit_resolution,[status(thm)],[240,25]) ).
tff(242,plain,
^ [Y: $i,X: $i] :
refl(( ( or(and(X,not(Y)),Y) = or(X,Y) )
<=> ( or(and(X,not(Y)),Y) = or(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(243,plain,
( ! [Y: $i,X: $i] : ( or(and(X,not(Y)),Y) = or(X,Y) )
<=> ! [Y: $i,X: $i] : ( or(and(X,not(Y)),Y) = or(X,Y) ) ),
inference(quant_intro,[status(thm)],[242]) ).
tff(244,plain,
( ! [Y: $i,X: $i] : ( or(and(X,not(Y)),Y) = or(X,Y) )
<=> ! [Y: $i,X: $i] : ( or(and(X,not(Y)),Y) = or(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(245,axiom,
! [Y: $i,X: $i] : ( or(and(X,not(Y)),Y) = or(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',karnaugh1) ).
tff(246,plain,
! [Y: $i,X: $i] : ( or(and(X,not(Y)),Y) = or(X,Y) ),
inference(modus_ponens,[status(thm)],[245,244]) ).
tff(247,plain,
! [Y: $i,X: $i] : ( or(and(X,not(Y)),Y) = or(X,Y) ),
inference(skolemize,[status(sab)],[246]) ).
tff(248,plain,
! [Y: $i,X: $i] : ( or(and(X,not(Y)),Y) = or(X,Y) ),
inference(modus_ponens,[status(thm)],[247,243]) ).
tff(249,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,not(Y)),Y) = or(X,Y) )
| ( or(and(and(a1,b1),not(n0)),n0) = or(and(a1,b1),n0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(250,plain,
or(and(and(a1,b1),not(n0)),n0) = or(and(a1,b1),n0),
inference(unit_resolution,[status(thm)],[249,248]) ).
tff(251,plain,
or(and(and(a1,b1),not(n0)),n0) = or(and(and(a1,b1),not(n0)),and(a1,n0)),
inference(monotonicity,[status(thm)],[236]) ).
tff(252,plain,
or(and(and(a1,b1),not(n0)),and(a1,n0)) = or(and(and(a1,b1),not(n0)),n0),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) )
| ( or(and(and(a1,b1),not(n0)),and(a1,n0)) = or(and(a1,b1),and(a1,n0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(254,plain,
or(and(and(a1,b1),not(n0)),and(a1,n0)) = or(and(a1,b1),and(a1,n0)),
inference(unit_resolution,[status(thm)],[253,66]) ).
tff(255,plain,
or(and(a1,b1),and(a1,n0)) = or(and(and(a1,b1),not(n0)),and(a1,n0)),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(a1,n0),and(a1,b1)) = or(and(a1,b1),and(a1,n0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(257,plain,
or(and(a1,n0),and(a1,b1)) = or(and(a1,b1),and(a1,n0)),
inference(unit_resolution,[status(thm)],[256,7]) ).
tff(258,plain,
and(a1,b1) = and(and(a1,b1),n1),
inference(symmetry,[status(thm)],[191]) ).
tff(259,plain,
( ~ ! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 )
| ( and(and(and(a1,b1),n1),not(n1)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(260,plain,
and(and(and(a1,b1),n1),not(n1)) = n0,
inference(unit_resolution,[status(thm)],[259,102]) ).
tff(261,plain,
n0 = and(and(and(a1,b1),n1),not(n1)),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
and(a1,n0) = and(and(and(a1,b1),n1),not(n1)),
inference(transitivity,[status(thm)],[235,261]) ).
tff(263,plain,
or(and(a1,n0),and(a1,b1)) = or(and(and(and(a1,b1),n1),not(n1)),and(and(a1,b1),n1)),
inference(monotonicity,[status(thm)],[262,258]) ).
tff(264,plain,
or(and(and(and(a1,b1),n1),not(n1)),and(and(a1,b1),n1)) = or(and(a1,n0),and(a1,b1)),
inference(symmetry,[status(thm)],[263]) ).
tff(265,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) )
| ( or(and(and(and(a1,b1),n1),not(n1)),and(and(a1,b1),n1)) = or(and(and(a1,b1),n1),and(and(a1,b1),n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(266,plain,
or(and(and(and(a1,b1),n1),not(n1)),and(and(a1,b1),n1)) = or(and(and(a1,b1),n1),and(and(a1,b1),n1)),
inference(unit_resolution,[status(thm)],[265,66]) ).
tff(267,plain,
or(and(and(a1,b1),n1),and(and(a1,b1),n1)) = or(and(and(and(a1,b1),n1),not(n1)),and(and(a1,b1),n1)),
inference(symmetry,[status(thm)],[266]) ).
tff(268,plain,
and(and(a1,b1),n1) = and(b1,a1),
inference(transitivity,[status(thm)],[191,164]) ).
tff(269,plain,
or(and(and(a1,b1),n1),and(and(a1,b1),n1)) = or(and(b1,a1),and(b1,a1)),
inference(monotonicity,[status(thm)],[268,268]) ).
tff(270,plain,
or(and(b1,a1),and(b1,a1)) = or(and(and(a1,b1),n1),and(and(a1,b1),n1)),
inference(symmetry,[status(thm)],[269]) ).
tff(271,plain,
and(b1,a1) = and(and(a1,b1),n1),
inference(transitivity,[status(thm)],[163,258]) ).
tff(272,plain,
or(and(b1,a1),and(b1,a1)) = or(and(and(a1,b1),n1),and(a1,b1)),
inference(monotonicity,[status(thm)],[271,163]) ).
tff(273,plain,
or(and(and(a1,b1),n1),and(a1,b1)) = or(and(b1,a1),and(b1,a1)),
inference(symmetry,[status(thm)],[272]) ).
tff(274,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,Y),X) = X )
| ( or(and(and(a1,b1),n1),and(a1,b1)) = and(a1,b1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(275,plain,
or(and(and(a1,b1),n1),and(a1,b1)) = and(a1,b1),
inference(unit_resolution,[status(thm)],[274,136]) ).
tff(276,plain,
and(a1,b1) = or(and(and(a1,b1),n1),and(a1,b1)),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
and(a1,b1) = or(and(a1,b1),n0),
inference(transitivity,[status(thm)],[276,273,270,267,264,257,255,252,250]) ).
tff(278,plain,
and(and(a1,b1),or(b1,carryout(a0,b0,n0))) = and(or(and(a1,b1),n0),or(b1,carryout(a0,b0,n0))),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
and(and(a1,b1),or(b1,carryout(a0,b0,n0))) = and(b1,a1),
inference(transitivity,[status(thm)],[278,241,239,221,210,207,193,191,164]) ).
tff(280,plain,
or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(b1,carryout(a0,b0,n0))) = or(and(b1,a1),and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0))))),
inference(monotonicity,[status(thm)],[279,189]) ).
tff(281,plain,
or(and(b1,a1),and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0))))) = or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(b1,carryout(a0,b0,n0))),
inference(symmetry,[status(thm)],[280]) ).
tff(282,plain,
or(and(a1,b1),and(b1,carryout(a0,b0,n0))) = or(and(b1,a1),and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0))))),
inference(monotonicity,[status(thm)],[164,189]) ).
tff(283,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(b1,carryout(a0,b0,n0)),and(a1,b1)) = or(and(a1,b1),and(b1,carryout(a0,b0,n0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(284,plain,
or(and(b1,carryout(a0,b0,n0)),and(a1,b1)) = or(and(a1,b1),and(b1,carryout(a0,b0,n0))),
inference(unit_resolution,[status(thm)],[283,7]) ).
tff(285,plain,
or(and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))),and(b1,a1)) = or(and(b1,carryout(a0,b0,n0)),and(a1,b1)),
inference(monotonicity,[status(thm)],[188,163]) ).
tff(286,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) )
| ( or(and(and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))),not(a1)),and(b1,a1)) = or(and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))),and(b1,a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(287,plain,
or(and(and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))),not(a1)),and(b1,a1)) = or(and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))),and(b1,a1)),
inference(unit_resolution,[status(thm)],[286,66]) ).
tff(288,plain,
and(and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))),not(a1)) = and(and(b1,carryout(a0,b0,n0)),not(a1)),
inference(monotonicity,[status(thm)],[188]) ).
tff(289,plain,
and(and(b1,carryout(a0,b0,n0)),not(a1)) = and(and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))),not(a1)),
inference(symmetry,[status(thm)],[288]) ).
tff(290,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(and(b1,carryout(a0,b0,n0)),not(a1)) = and(not(a1),and(b1,carryout(a0,b0,n0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(291,plain,
and(and(b1,carryout(a0,b0,n0)),not(a1)) = and(not(a1),and(b1,carryout(a0,b0,n0))),
inference(unit_resolution,[status(thm)],[290,16]) ).
tff(292,plain,
and(not(a1),and(b1,carryout(a0,b0,n0))) = and(and(b1,carryout(a0,b0,n0)),not(a1)),
inference(symmetry,[status(thm)],[291]) ).
tff(293,plain,
and(not(a1),and(b1,carryout(a0,b0,n0))) = and(and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))),not(a1)),
inference(transitivity,[status(thm)],[292,289]) ).
tff(294,plain,
or(and(not(a1),and(b1,carryout(a0,b0,n0))),and(a1,b1)) = or(and(and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))),not(a1)),and(b1,a1)),
inference(monotonicity,[status(thm)],[293,164]) ).
tff(295,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(a1,b1),and(not(a1),and(b1,carryout(a0,b0,n0)))) = or(and(not(a1),and(b1,carryout(a0,b0,n0))),and(a1,b1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(296,plain,
or(and(a1,b1),and(not(a1),and(b1,carryout(a0,b0,n0)))) = or(and(not(a1),and(b1,carryout(a0,b0,n0))),and(a1,b1)),
inference(unit_resolution,[status(thm)],[295,7]) ).
tff(297,plain,
and(and(a1,b1),or(b1,carryout(a0,b0,n0))) = and(a1,b1),
inference(transitivity,[status(thm)],[278,241,239,221,210,207,193,191]) ).
tff(298,plain,
or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(not(a1),and(b1,carryout(a0,b0,n0)))) = or(and(a1,b1),and(not(a1),and(b1,carryout(a0,b0,n0)))),
inference(monotonicity,[status(thm)],[297]) ).
tff(299,plain,
or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(not(a1),and(b1,carryout(a0,b0,n0)))) = or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(b1,carryout(a0,b0,n0))),
inference(transitivity,[status(thm)],[298,296,294,287,285,284,282,281]) ).
tff(300,plain,
or(or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(not(a1),and(b1,carryout(a0,b0,n0)))),and(a1,or(b1,carryout(a0,b0,n0)))) = or(or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))),
inference(monotonicity,[status(thm)],[299]) ).
tff(301,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) )
| ( or(or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))),and(not(a1),and(b1,carryout(a0,b0,n0)))) = or(or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(not(a1),and(b1,carryout(a0,b0,n0)))),and(a1,or(b1,carryout(a0,b0,n0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(302,plain,
or(or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))),and(not(a1),and(b1,carryout(a0,b0,n0)))) = or(or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(not(a1),and(b1,carryout(a0,b0,n0)))),and(a1,or(b1,carryout(a0,b0,n0)))),
inference(unit_resolution,[status(thm)],[301,152]) ).
tff(303,plain,
and(a1,or(b1,carryout(a0,b0,n0))) = and(or(and(a1,b1),a1),or(b1,carryout(a0,b0,n0))),
inference(symmetry,[status(thm)],[179]) ).
tff(304,plain,
and(a1,or(b1,carryout(a0,b0,n0))) = or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))),
inference(transitivity,[status(thm)],[303,181]) ).
tff(305,plain,
or(and(a1,or(b1,carryout(a0,b0,n0))),and(not(a1),and(b1,carryout(a0,b0,n0)))) = or(or(and(and(a1,b1),or(b1,carryout(a0,b0,n0))),and(a1,or(b1,carryout(a0,b0,n0)))),and(not(a1),and(b1,carryout(a0,b0,n0)))),
inference(monotonicity,[status(thm)],[304]) ).
tff(306,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( carryout(X,Y,Z) = or(and(X,or(Y,Z)),and(not(X),and(Y,Z))) )
| ( carryout(a1,b1,carryout(a0,b0,n0)) = or(and(a1,or(b1,carryout(a0,b0,n0))),and(not(a1),and(b1,carryout(a0,b0,n0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(307,plain,
carryout(a1,b1,carryout(a0,b0,n0)) = or(and(a1,or(b1,carryout(a0,b0,n0))),and(not(a1),and(b1,carryout(a0,b0,n0)))),
inference(unit_resolution,[status(thm)],[306,35]) ).
tff(308,plain,
( ( overflow = carryout(a1,b1,carryout(a0,b0,n0)) )
<=> ( overflow = carryout(a1,b1,carryout(a0,b0,n0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(309,axiom,
overflow = carryout(a1,b1,carryout(a0,b0,n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',overflow_definition) ).
tff(310,plain,
overflow = carryout(a1,b1,carryout(a0,b0,n0)),
inference(modus_ponens,[status(thm)],[309,308]) ).
tff(311,plain,
overflow = or(and(a1,b1),and(and(a0,b0),or(a1,b1))),
inference(transitivity,[status(thm)],[310,307,305,302,300,187,184,176,155,145,9]) ).
tff(312,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( sum(X,Y,Z) = xor(xor(X,Y),Z) )
<=> ( sum(X,Y,Z) = xor(xor(X,Y),Z) ) )),
inference(bind,[status(th)],[]) ).
tff(313,plain,
( ! [Z: $i,Y: $i,X: $i] : ( sum(X,Y,Z) = xor(xor(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( sum(X,Y,Z) = xor(xor(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[312]) ).
tff(314,plain,
( ! [Z: $i,Y: $i,X: $i] : ( sum(X,Y,Z) = xor(xor(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( sum(X,Y,Z) = xor(xor(X,Y),Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(315,axiom,
! [Z: $i,Y: $i,X: $i] : ( sum(X,Y,Z) = xor(xor(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_definition) ).
tff(316,plain,
! [Z: $i,Y: $i,X: $i] : ( sum(X,Y,Z) = xor(xor(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[315,314]) ).
tff(317,plain,
! [Z: $i,Y: $i,X: $i] : ( sum(X,Y,Z) = xor(xor(X,Y),Z) ),
inference(skolemize,[status(sab)],[316]) ).
tff(318,plain,
! [Z: $i,Y: $i,X: $i] : ( sum(X,Y,Z) = xor(xor(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[317,313]) ).
tff(319,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( sum(X,Y,Z) = xor(xor(X,Y),Z) )
| ( sum(a1,b1,carryout(a0,b0,n0)) = xor(xor(a1,b1),carryout(a0,b0,n0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(320,plain,
sum(a1,b1,carryout(a0,b0,n0)) = xor(xor(a1,b1),carryout(a0,b0,n0)),
inference(unit_resolution,[status(thm)],[319,318]) ).
tff(321,plain,
( ( s1 = sum(a1,b1,carryout(a0,b0,n0)) )
<=> ( s1 = sum(a1,b1,carryout(a0,b0,n0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(322,axiom,
s1 = sum(a1,b1,carryout(a0,b0,n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_definition) ).
tff(323,plain,
s1 = sum(a1,b1,carryout(a0,b0,n0)),
inference(modus_ponens,[status(thm)],[322,321]) ).
tff(324,plain,
s1 = xor(xor(a1,b1),carryout(a0,b0,n0)),
inference(transitivity,[status(thm)],[323,320]) ).
tff(325,plain,
^ [Y: $i,X: $i] :
refl(( ( xor(X,Y) = or(and(X,not(Y)),and(Y,not(X))) )
<=> ( xor(X,Y) = or(and(X,not(Y)),and(Y,not(X))) ) )),
inference(bind,[status(th)],[]) ).
tff(326,plain,
( ! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(Y,not(X))) )
<=> ! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(Y,not(X))) ) ),
inference(quant_intro,[status(thm)],[325]) ).
tff(327,plain,
( ! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(Y,not(X))) )
<=> ! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(Y,not(X))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(328,axiom,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(Y,not(X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_definition) ).
tff(329,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(Y,not(X))) ),
inference(modus_ponens,[status(thm)],[328,327]) ).
tff(330,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(Y,not(X))) ),
inference(skolemize,[status(sab)],[329]) ).
tff(331,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(Y,not(X))) ),
inference(modus_ponens,[status(thm)],[330,326]) ).
tff(332,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(Y,not(X))) )
| ( xor(a0,b0) = or(and(a0,not(b0)),and(b0,not(a0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
xor(a0,b0) = or(and(a0,not(b0)),and(b0,not(a0))),
inference(unit_resolution,[status(thm)],[332,331]) ).
tff(334,plain,
or(and(a0,not(b0)),and(b0,not(a0))) = xor(a0,b0),
inference(symmetry,[status(thm)],[333]) ).
tff(335,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,Y),X) = X )
| ( or(and(or(and(a0,not(b0)),and(b0,not(a0))),n1),or(and(a0,not(b0)),and(b0,not(a0)))) = or(and(a0,not(b0)),and(b0,not(a0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(336,plain,
or(and(or(and(a0,not(b0)),and(b0,not(a0))),n1),or(and(a0,not(b0)),and(b0,not(a0)))) = or(and(a0,not(b0)),and(b0,not(a0))),
inference(unit_resolution,[status(thm)],[335,136]) ).
tff(337,plain,
( ~ ! [X: $i] : ( and(X,n1) = X )
| ( and(or(and(a0,not(b0)),and(b0,not(a0))),n1) = or(and(a0,not(b0)),and(b0,not(a0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(338,plain,
and(or(and(a0,not(b0)),and(b0,not(a0))),n1) = or(and(a0,not(b0)),and(b0,not(a0))),
inference(unit_resolution,[status(thm)],[337,118]) ).
tff(339,plain,
or(and(or(and(a0,not(b0)),and(b0,not(a0))),n1),and(or(and(a0,not(b0)),and(b0,not(a0))),n1)) = or(and(or(and(a0,not(b0)),and(b0,not(a0))),n1),or(and(a0,not(b0)),and(b0,not(a0)))),
inference(monotonicity,[status(thm)],[338]) ).
tff(340,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(and(and(X,Y),not(Z)),and(X,Z)) = or(and(X,Y),and(X,Z)) )
| ( or(and(and(or(and(a0,not(b0)),and(b0,not(a0))),n1),not(n1)),and(or(and(a0,not(b0)),and(b0,not(a0))),n1)) = or(and(or(and(a0,not(b0)),and(b0,not(a0))),n1),and(or(and(a0,not(b0)),and(b0,not(a0))),n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(341,plain,
or(and(and(or(and(a0,not(b0)),and(b0,not(a0))),n1),not(n1)),and(or(and(a0,not(b0)),and(b0,not(a0))),n1)) = or(and(or(and(a0,not(b0)),and(b0,not(a0))),n1),and(or(and(a0,not(b0)),and(b0,not(a0))),n1)),
inference(unit_resolution,[status(thm)],[340,66]) ).
tff(342,plain,
or(and(a0,not(b0)),and(b0,not(a0))) = and(or(and(a0,not(b0)),and(b0,not(a0))),n1),
inference(symmetry,[status(thm)],[338]) ).
tff(343,plain,
( ~ ! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 )
| ( and(and(or(and(a0,not(b0)),and(b0,not(a0))),n1),not(n1)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(344,plain,
and(and(or(and(a0,not(b0)),and(b0,not(a0))),n1),not(n1)) = n0,
inference(unit_resolution,[status(thm)],[343,102]) ).
tff(345,plain,
n0 = and(and(or(and(a0,not(b0)),and(b0,not(a0))),n1),not(n1)),
inference(symmetry,[status(thm)],[344]) ).
tff(346,plain,
or(n0,or(and(a0,not(b0)),and(b0,not(a0)))) = or(and(and(or(and(a0,not(b0)),and(b0,not(a0))),n1),not(n1)),and(or(and(a0,not(b0)),and(b0,not(a0))),n1)),
inference(monotonicity,[status(thm)],[345,342]) ).
tff(347,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,not(Y)),Y) = or(X,Y) )
| ( or(and(n0,not(or(and(a0,not(b0)),and(b0,not(a0))))),or(and(a0,not(b0)),and(b0,not(a0)))) = or(n0,or(and(a0,not(b0)),and(b0,not(a0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(348,plain,
or(and(n0,not(or(and(a0,not(b0)),and(b0,not(a0))))),or(and(a0,not(b0)),and(b0,not(a0)))) = or(n0,or(and(a0,not(b0)),and(b0,not(a0)))),
inference(unit_resolution,[status(thm)],[347,248]) ).
tff(349,plain,
and(or(and(a0,not(b0)),and(b0,not(a0))),not(n0)) = and(or(and(a0,not(b0)),and(b0,not(a0))),n1),
inference(monotonicity,[status(thm)],[94]) ).
tff(350,plain,
and(or(and(a0,not(b0)),and(b0,not(a0))),not(n0)) = or(and(a0,not(b0)),and(b0,not(a0))),
inference(transitivity,[status(thm)],[349,338]) ).
tff(351,plain,
or(and(n0,not(or(and(a0,not(b0)),and(b0,not(a0))))),and(or(and(a0,not(b0)),and(b0,not(a0))),not(n0))) = or(and(n0,not(or(and(a0,not(b0)),and(b0,not(a0))))),or(and(a0,not(b0)),and(b0,not(a0)))),
inference(monotonicity,[status(thm)],[350]) ).
tff(352,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(n0,not(or(and(a0,not(b0)),and(b0,not(a0))))),and(or(and(a0,not(b0)),and(b0,not(a0))),not(n0))) = or(and(or(and(a0,not(b0)),and(b0,not(a0))),not(n0)),and(n0,not(or(and(a0,not(b0)),and(b0,not(a0)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(353,plain,
or(and(n0,not(or(and(a0,not(b0)),and(b0,not(a0))))),and(or(and(a0,not(b0)),and(b0,not(a0))),not(n0))) = or(and(or(and(a0,not(b0)),and(b0,not(a0))),not(n0)),and(n0,not(or(and(a0,not(b0)),and(b0,not(a0)))))),
inference(unit_resolution,[status(thm)],[352,7]) ).
tff(354,plain,
or(and(or(and(a0,not(b0)),and(b0,not(a0))),not(n0)),and(n0,not(or(and(a0,not(b0)),and(b0,not(a0)))))) = or(and(n0,not(or(and(a0,not(b0)),and(b0,not(a0))))),and(or(and(a0,not(b0)),and(b0,not(a0))),not(n0))),
inference(symmetry,[status(thm)],[353]) ).
tff(355,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(Y,not(X))) )
| ( xor(or(and(a0,not(b0)),and(b0,not(a0))),n0) = or(and(or(and(a0,not(b0)),and(b0,not(a0))),not(n0)),and(n0,not(or(and(a0,not(b0)),and(b0,not(a0)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(356,plain,
xor(or(and(a0,not(b0)),and(b0,not(a0))),n0) = or(and(or(and(a0,not(b0)),and(b0,not(a0))),not(n0)),and(n0,not(or(and(a0,not(b0)),and(b0,not(a0)))))),
inference(unit_resolution,[status(thm)],[355,331]) ).
tff(357,plain,
xor(xor(a0,b0),n0) = xor(or(and(a0,not(b0)),and(b0,not(a0))),n0),
inference(monotonicity,[status(thm)],[333]) ).
tff(358,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( sum(X,Y,Z) = xor(xor(X,Y),Z) )
| ( sum(a0,b0,n0) = xor(xor(a0,b0),n0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(359,plain,
sum(a0,b0,n0) = xor(xor(a0,b0),n0),
inference(unit_resolution,[status(thm)],[358,318]) ).
tff(360,plain,
( ( s0 = sum(a0,b0,n0) )
<=> ( s0 = sum(a0,b0,n0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(361,axiom,
s0 = sum(a0,b0,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s0_definition) ).
tff(362,plain,
s0 = sum(a0,b0,n0),
inference(modus_ponens,[status(thm)],[361,360]) ).
tff(363,plain,
s0 = xor(a0,b0),
inference(transitivity,[status(thm)],[362,359,357,356,354,351,348,346,341,339,336,334]) ).
tff(364,plain,
( circuit(s0,s1,overflow)
<=> circuit(xor(a0,b0),xor(xor(a1,b1),carryout(a0,b0,n0)),or(and(a1,b1),and(and(a0,b0),or(a1,b1)))) ),
inference(monotonicity,[status(thm)],[363,324,311]) ).
tff(365,plain,
( circuit(xor(a0,b0),xor(xor(a1,b1),carryout(a0,b0,n0)),or(and(a1,b1),and(and(a0,b0),or(a1,b1))))
<=> circuit(s0,s1,overflow) ),
inference(symmetry,[status(thm)],[364]) ).
tff(366,plain,
( ~ circuit(xor(a0,b0),xor(xor(a1,b1),carryout(a0,b0,n0)),or(and(a1,b1),and(and(a0,b0),or(a1,b1))))
<=> ~ circuit(s0,s1,overflow) ),
inference(monotonicity,[status(thm)],[365]) ).
tff(367,plain,
( ~ circuit(xor(a0,b0),xor(xor(a1,b1),carryout(a0,b0,n0)),or(and(a1,b1),and(and(a0,b0),or(a1,b1))))
<=> ~ circuit(xor(a0,b0),xor(xor(a1,b1),carryout(a0,b0,n0)),or(and(a1,b1),and(and(a0,b0),or(a1,b1)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(368,axiom,
~ circuit(xor(a0,b0),xor(xor(a1,b1),carryout(a0,b0,n0)),or(and(a1,b1),and(and(a0,b0),or(a1,b1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_circuit) ).
tff(369,plain,
~ circuit(xor(a0,b0),xor(xor(a1,b1),carryout(a0,b0,n0)),or(and(a1,b1),and(and(a0,b0),or(a1,b1)))),
inference(modus_ponens,[status(thm)],[368,367]) ).
tff(370,plain,
~ circuit(s0,s1,overflow),
inference(modus_ponens,[status(thm)],[369,366]) ).
tff(371,plain,
( circuit(s0,s1,overflow)
<=> circuit(s0,s1,overflow) ),
inference(rewrite,[status(thm)],[]) ).
tff(372,axiom,
circuit(s0,s1,overflow),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_output_circuit) ).
tff(373,plain,
circuit(s0,s1,overflow),
inference(modus_ponens,[status(thm)],[372,371]) ).
tff(374,plain,
$false,
inference(unit_resolution,[status(thm)],[373,370]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : HWV004-1 : TPTP v9.0.0. Released v1.1.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 17:20:16 EDT 2025
% 0.14/0.36 % CPUTime :
% 16.22/16.41 % SZS status Unsatisfiable
% 16.22/16.41 % SZS output start Proof
% See solution above
% 16.22/16.45 % E exiting
%------------------------------------------------------------------------------