%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV001-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 1.37s 1.56s
% Output : Proof 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 188
% Syntax : Number of formulae : 595 ( 445 unt; 0 typ; 0 def)
% Number of atoms : 789 ( 751 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 262 ( 90 ~; 83 |; 0 &)
% ( 89 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 22 ( 22 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; 0-2 aty)
% Number of functors : 24 ( 24 usr; 19 con; 0-2 aty)
% Number of variables : 561 ( 518 !; 0 ?; 561 :)
% Comments :
%------------------------------------------------------------------------------
tff(circuit_type,type,
circuit: ( $i * $i ) > $o ).
tff(output_type,type,
output: ( $i * $i ) > $i ).
tff(a2_type,type,
a2: $i ).
tff(a1_type,type,
a1: $i ).
tff(input_type,type,
input: ( $i * $i ) > $i ).
tff(i2_type,type,
i2: $i ).
tff(i1_type,type,
i1: $i ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(and_type,type,
and: ( $i * $i ) > $i ).
tff(not_type,type,
not: $i > $i ).
tff(f3_type,type,
f3: $i ).
tff(e1_type,type,
e1: $i ).
tff(n0_type,type,
n0: $i ).
tff(f1_type,type,
f1: $i ).
tff(d3_type,type,
d3: $i ).
tff(d1_type,type,
d1: $i ).
tff(f2_type,type,
f2: $i ).
tff(n1_type,type,
n1: $i ).
tff(d2_type,type,
d2: $i ).
tff(e2_type,type,
e2: $i ).
tff(c2_type,type,
c2: $i ).
tff(c1_type,type,
c1: $i ).
tff(b3_type,type,
b3: $i ).
tff(b2_type,type,
b2: $i ).
tff(b1_type,type,
b1: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( or(and(X,Y),and(Y,not(X))) = Y )
<=> ( or(and(X,Y),and(Y,not(X))) = Y ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( or(and(X,Y),and(Y,not(X))) = Y )
<=> ! [Y: $i,X: $i] : ( or(and(X,Y),and(Y,not(X))) = Y ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( or(and(X,Y),and(Y,not(X))) = Y )
<=> ! [Y: $i,X: $i] : ( or(and(X,Y),and(Y,not(X))) = Y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( or(and(X,Y),and(Y,not(X))) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_not_simplification2) ).
tff(5,plain,
! [Y: $i,X: $i] : ( or(and(X,Y),and(Y,not(X))) = Y ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( or(and(X,Y),and(Y,not(X))) = Y ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( or(and(X,Y),and(Y,not(X))) = Y ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,Y),and(Y,not(X))) = Y )
| ( or(and(f3,i1),and(i1,not(f3))) = i1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
or(and(f3,i1),and(i1,not(f3))) = i1,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ! [X: $i] : ( not(not(X)) = X )
<=> ! [X: $i] : ( not(not(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
( ! [X: $i] : ( not(not(X)) = X )
<=> ! [X: $i] : ( not(not(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
! [X: $i] : ( not(not(X)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_simplification) ).
tff(13,plain,
! [X: $i] : ( not(not(X)) = X ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i] : ( not(not(X)) = X ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [X: $i] : ( not(not(X)) = X ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
( ~ ! [X: $i] : ( not(not(X)) = X )
| ( not(not(i1)) = i1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
not(not(i1)) = i1,
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
i1 = not(not(i1)),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
and(i1,not(f3)) = and(not(not(i1)),not(f3)),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
and(not(not(i1)),not(f3)) = and(i1,not(f3)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [Y: $i,X: $i] :
refl(( ( not(or(X,Y)) = and(not(X),not(Y)) )
<=> ( not(or(X,Y)) = and(not(X),not(Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Y: $i,X: $i] : ( not(or(X,Y)) = and(not(X),not(Y)) )
<=> ! [Y: $i,X: $i] : ( not(or(X,Y)) = and(not(X),not(Y)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Y: $i,X: $i] : ( not(or(X,Y)) = and(not(X),not(Y)) )
<=> ! [Y: $i,X: $i] : ( not(or(X,Y)) = and(not(X),not(Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [Y: $i,X: $i] : ( not(or(X,Y)) = and(not(X),not(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_canonicalization2) ).
tff(25,plain,
! [Y: $i,X: $i] : ( not(or(X,Y)) = and(not(X),not(Y)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( not(or(X,Y)) = and(not(X),not(Y)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] : ( not(or(X,Y)) = and(not(X),not(Y)) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] : ( not(or(X,Y)) = and(not(X),not(Y)) )
| ( not(or(not(i1),f3)) = and(not(not(i1)),not(f3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
not(or(not(i1),f3)) = and(not(not(i1)),not(f3)),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ( e1 = or(f1,f3) )
<=> ( e1 = or(f1,f3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
e1 = or(f1,f3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor11) ).
tff(32,plain,
e1 = or(f1,f3),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
or(f1,f3) = e1,
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ( f1 = not(i1) )
<=> ( f1 = not(i1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
f1 = not(i1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor13) ).
tff(36,plain,
f1 = not(i1),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
not(i1) = f1,
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
or(not(i1),f3) = or(f1,f3),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
or(not(i1),f3) = e1,
inference(transitivity,[status(thm)],[38,33]) ).
tff(40,plain,
not(or(not(i1),f3)) = not(e1),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
not(e1) = not(or(not(i1),f3)),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
^ [X: $i] :
refl(( ( or(X,n0) = X )
<=> ( or(X,n0) = X ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [X: $i] : ( or(X,n0) = X )
<=> ! [X: $i] : ( or(X,n0) = X ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [X: $i] : ( or(X,n0) = X )
<=> ! [X: $i] : ( or(X,n0) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
! [X: $i] : ( or(X,n0) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',or_definition1) ).
tff(46,plain,
! [X: $i] : ( or(X,n0) = X ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [X: $i] : ( or(X,n0) = X ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [X: $i] : ( or(X,n0) = X ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ~ ! [X: $i] : ( or(X,n0) = X )
| ( or(not(e1),n0) = not(e1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
or(not(e1),n0) = not(e1),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
^ [Y: $i,X: $i] :
refl(( ( or(X,Y) = or(Y,X) )
<=> ( or(X,Y) = or(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(52,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)],[51]) ).
tff(53,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(54,axiom,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_commutativity) ).
tff(55,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(e1),n0) = or(n0,not(e1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
or(not(e1),n0) = or(n0,not(e1)),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
or(n0,not(e1)) = or(not(e1),n0),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
or(n0,not(e1)) = and(i1,not(f3)),
inference(transitivity,[status(thm)],[60,50,41,29,20]) ).
tff(62,plain,
or(and(f3,i1),or(n0,not(e1))) = or(and(f3,i1),and(i1,not(f3))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( or(X,or(Y,Z)) = or(or(X,Y),Z) )
<=> ( or(X,or(Y,Z)) = or(or(X,Y),Z) ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_associativity) ).
tff(67,plain,
! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) )
| ( or(and(f3,i1),or(n0,not(e1))) = or(or(and(f3,i1),n0),not(e1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
or(and(f3,i1),or(n0,not(e1))) = or(or(and(f3,i1),n0),not(e1)),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
or(or(and(f3,i1),n0),not(e1)) = or(and(f3,i1),or(n0,not(e1))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [X: $i] : ( or(X,n0) = X )
| ( or(and(f3,i1),n0) = and(f3,i1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
or(and(f3,i1),n0) = and(f3,i1),
inference(unit_resolution,[status(thm)],[73,48]) ).
tff(75,plain,
and(f3,i1) = or(and(f3,i1),n0),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
^ [Y: $i,X: $i] :
refl(( ( and(X,Y) = and(Y,X) )
<=> ( and(X,Y) = and(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(77,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)],[76]) ).
tff(78,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(79,axiom,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_commutativity) ).
tff(80,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(i1,f3) = and(f3,i1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
and(i1,f3) = and(f3,i1),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
( ~ ! [X: $i] : ( or(X,n0) = X )
| ( or(and(i1,f3),n0) = and(i1,f3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
or(and(i1,f3),n0) = and(i1,f3),
inference(unit_resolution,[status(thm)],[85,48]) ).
tff(87,plain,
( ( f3 = and(i1,i2) )
<=> ( f3 = and(i1,i2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,axiom,
f3 = and(i1,i2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor15) ).
tff(89,plain,
f3 = and(i1,i2),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
and(f3,not(i1)) = and(and(i1,i2),not(i1)),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
and(and(i1,i2),not(i1)) = and(f3,not(i1)),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
^ [Y: $i,X: $i] :
refl(( ( and(and(X,Y),not(X)) = n0 )
<=> ( and(and(X,Y),not(X)) = n0 ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [Y: $i,X: $i] : ( and(and(X,Y),not(X)) = n0 )
<=> ! [Y: $i,X: $i] : ( and(and(X,Y),not(X)) = n0 ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [Y: $i,X: $i] : ( and(and(X,Y),not(X)) = n0 )
<=> ! [Y: $i,X: $i] : ( and(and(X,Y),not(X)) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,axiom,
! [Y: $i,X: $i] : ( and(and(X,Y),not(X)) = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_not_simplification3) ).
tff(96,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),not(X)) = n0 ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),not(X)) = n0 ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),not(X)) = n0 ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
( ~ ! [Y: $i,X: $i] : ( and(and(X,Y),not(X)) = n0 )
| ( and(and(i1,i2),not(i1)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
and(and(i1,i2),not(i1)) = n0,
inference(unit_resolution,[status(thm)],[99,98]) ).
tff(101,plain,
n0 = and(and(i1,i2),not(i1)),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
n0 = and(f3,not(i1)),
inference(transitivity,[status(thm)],[101,91]) ).
tff(103,plain,
or(and(i1,f3),n0) = or(and(i1,f3),and(f3,not(i1))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
or(and(i1,f3),and(f3,not(i1))) = or(and(i1,f3),n0),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,Y),and(Y,not(X))) = Y )
| ( or(and(i1,f3),and(f3,not(i1))) = f3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
or(and(i1,f3),and(f3,not(i1))) = f3,
inference(unit_resolution,[status(thm)],[105,7]) ).
tff(107,plain,
f3 = or(and(i1,f3),and(f3,not(i1))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
f3 = or(and(f3,i1),n0),
inference(transitivity,[status(thm)],[107,104,86,84,75]) ).
tff(109,plain,
or(f3,not(e1)) = or(or(and(f3,i1),n0),not(e1)),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(f3,not(e1)) = or(not(e1),f3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
or(f3,not(e1)) = or(not(e1),f3),
inference(unit_resolution,[status(thm)],[110,57]) ).
tff(112,plain,
or(not(e1),f3) = or(f3,not(e1)),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
( ( d3 = f3 )
<=> ( d3 = f3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,axiom,
d3 = f3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor8) ).
tff(115,plain,
d3 = f3,
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
( ( d1 = not(e1) )
<=> ( d1 = not(e1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,axiom,
d1 = not(e1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor9) ).
tff(118,plain,
d1 = not(e1),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
or(d1,d3) = or(not(e1),f3),
inference(monotonicity,[status(thm)],[118,115]) ).
tff(120,plain,
f3 = d3,
inference(symmetry,[status(thm)],[115]) ).
tff(121,plain,
^ [Y: $i,X: $i] :
refl(( ( or(and(X,Y),and(X,not(Y))) = X )
<=> ( or(and(X,Y),and(X,not(Y))) = X ) )),
inference(bind,[status(th)],[]) ).
tff(122,plain,
( ! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X )
<=> ! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X )
<=> ! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,axiom,
! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_not_simplification1) ).
tff(125,plain,
! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X ),
inference(skolemize,[status(sab)],[125]) ).
tff(127,plain,
! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X ),
inference(modus_ponens,[status(thm)],[126,122]) ).
tff(128,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X )
| ( or(and(f3,f3),and(f3,not(f3))) = f3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
or(and(f3,f3),and(f3,not(f3))) = f3,
inference(unit_resolution,[status(thm)],[128,127]) ).
tff(130,plain,
^ [X: $i] :
refl(( ( and(X,not(X)) = n0 )
<=> ( and(X,not(X)) = n0 ) )),
inference(bind,[status(th)],[]) ).
tff(131,plain,
( ! [X: $i] : ( and(X,not(X)) = n0 )
<=> ! [X: $i] : ( and(X,not(X)) = n0 ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
( ! [X: $i] : ( and(X,not(X)) = n0 )
<=> ! [X: $i] : ( and(X,not(X)) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,axiom,
! [X: $i] : ( and(X,not(X)) = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_not_simplification1) ).
tff(134,plain,
! [X: $i] : ( and(X,not(X)) = n0 ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [X: $i] : ( and(X,not(X)) = n0 ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [X: $i] : ( and(X,not(X)) = n0 ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
( ~ ! [X: $i] : ( and(X,not(X)) = n0 )
| ( and(f3,not(f3)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
and(f3,not(f3)) = n0,
inference(unit_resolution,[status(thm)],[137,136]) ).
tff(139,plain,
n0 = and(f3,not(f3)),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(not(i1),f3) = and(f3,not(i1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
and(not(i1),f3) = and(f3,not(i1)),
inference(unit_resolution,[status(thm)],[140,82]) ).
tff(142,plain,
and(not(i1),f3) = and(f3,not(f3)),
inference(transitivity,[status(thm)],[141,90,100,139]) ).
tff(143,plain,
or(and(f3,f3),and(not(i1),f3)) = or(and(f3,f3),and(f3,not(f3))),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,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(145,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)],[144]) ).
tff(146,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(147,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_canonicalization) ).
tff(148,plain,
! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) ),
inference(skolemize,[status(sab)],[148]) ).
tff(150,plain,
! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) ),
inference(modus_ponens,[status(thm)],[149,145]) ).
tff(151,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(f3,not(i1)),f3) = or(and(f3,f3),and(not(i1),f3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(152,plain,
and(or(f3,not(i1)),f3) = or(and(f3,f3),and(not(i1),f3)),
inference(unit_resolution,[status(thm)],[151,150]) ).
tff(153,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(f3,not(i1)) = or(not(i1),f3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
or(f3,not(i1)) = or(not(i1),f3),
inference(unit_resolution,[status(thm)],[153,57]) ).
tff(155,plain,
or(not(i1),f3) = or(f3,not(i1)),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
or(f1,f3) = or(not(i1),f3),
inference(symmetry,[status(thm)],[38]) ).
tff(157,plain,
or(f1,f3) = or(f3,not(i1)),
inference(transitivity,[status(thm)],[156,155]) ).
tff(158,plain,
and(or(f1,f3),f3) = and(or(f3,not(i1)),f3),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
and(or(not(i1),f3),f3) = and(or(f1,f3),f3),
inference(monotonicity,[status(thm)],[38]) ).
tff(160,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(not(i1),f3),f3) = or(and(not(i1),f3),and(f3,f3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(161,plain,
and(or(not(i1),f3),f3) = or(and(not(i1),f3),and(f3,f3)),
inference(unit_resolution,[status(thm)],[160,150]) ).
tff(162,plain,
or(and(not(i1),f3),and(f3,f3)) = and(or(not(i1),f3),f3),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
and(f3,not(i1)) = and(not(i1),f3),
inference(symmetry,[status(thm)],[141]) ).
tff(164,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(165,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)],[164]) ).
tff(166,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(167,axiom,
! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_not_simplification2) ).
tff(168,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 ),
inference(skolemize,[status(sab)],[168]) ).
tff(170,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 ),
inference(modus_ponens,[status(thm)],[169,165]) ).
tff(171,plain,
( ~ ! [Y: $i,X: $i] : ( and(and(X,Y),not(Y)) = n0 )
| ( and(and(i1,i2),not(i2)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
and(and(i1,i2),not(i2)) = n0,
inference(unit_resolution,[status(thm)],[171,170]) ).
tff(173,plain,
and(f3,not(i2)) = and(and(i1,i2),not(i2)),
inference(monotonicity,[status(thm)],[89]) ).
tff(174,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(not(i2),f3) = and(f3,not(i2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
and(not(i2),f3) = and(f3,not(i2)),
inference(unit_resolution,[status(thm)],[174,82]) ).
tff(176,plain,
and(not(i2),f3) = and(not(i1),f3),
inference(transitivity,[status(thm)],[175,173,172,101,91,163]) ).
tff(177,plain,
or(and(not(i2),f3),and(f3,f3)) = or(and(not(i1),f3),and(f3,f3)),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(not(i2),f3),f3) = or(and(not(i2),f3),and(f3,f3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
and(or(not(i2),f3),f3) = or(and(not(i2),f3),and(f3,f3)),
inference(unit_resolution,[status(thm)],[178,150]) ).
tff(180,plain,
( ( f2 = not(i2) )
<=> ( f2 = not(i2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(181,axiom,
f2 = not(i2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor14) ).
tff(182,plain,
f2 = not(i2),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
not(i2) = f2,
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
or(not(i2),f3) = or(f2,f3),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
or(f2,f3) = or(not(i2),f3),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
and(or(f2,f3),f3) = and(or(not(i2),f3),f3),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(or(f2,f3),f3) = and(f3,or(f2,f3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(188,plain,
and(or(f2,f3),f3) = and(f3,or(f2,f3)),
inference(unit_resolution,[status(thm)],[187,82]) ).
tff(189,plain,
and(f3,or(f2,f3)) = and(or(f2,f3),f3),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
and(f3,or(f2,f3)) = d3,
inference(transitivity,[status(thm)],[189,186,179,177,162,159,158,152,143,129,120]) ).
tff(191,plain,
not(e1) = d1,
inference(symmetry,[status(thm)],[118]) ).
tff(192,plain,
^ [X: $i] :
refl(( ( and(X,n1) = X )
<=> ( and(X,n1) = X ) )),
inference(bind,[status(th)],[]) ).
tff(193,plain,
( ! [X: $i] : ( and(X,n1) = X )
<=> ! [X: $i] : ( and(X,n1) = X ) ),
inference(quant_intro,[status(thm)],[192]) ).
tff(194,plain,
( ! [X: $i] : ( and(X,n1) = X )
<=> ! [X: $i] : ( and(X,n1) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(195,axiom,
! [X: $i] : ( and(X,n1) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',and_definition2) ).
tff(196,plain,
! [X: $i] : ( and(X,n1) = X ),
inference(modus_ponens,[status(thm)],[195,194]) ).
tff(197,plain,
! [X: $i] : ( and(X,n1) = X ),
inference(skolemize,[status(sab)],[196]) ).
tff(198,plain,
! [X: $i] : ( and(X,n1) = X ),
inference(modus_ponens,[status(thm)],[197,193]) ).
tff(199,plain,
( ~ ! [X: $i] : ( and(X,n1) = X )
| ( and(not(e1),n1) = not(e1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(200,plain,
and(not(e1),n1) = not(e1),
inference(unit_resolution,[status(thm)],[199,198]) ).
tff(201,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(n1,not(e1)) = and(not(e1),n1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,plain,
and(n1,not(e1)) = and(not(e1),n1),
inference(unit_resolution,[status(thm)],[201,82]) ).
tff(203,plain,
^ [Y: $i,X: $i] :
refl(( ( or(or(X,Y),not(Y)) = n1 )
<=> ( or(or(X,Y),not(Y)) = n1 ) )),
inference(bind,[status(th)],[]) ).
tff(204,plain,
( ! [Y: $i,X: $i] : ( or(or(X,Y),not(Y)) = n1 )
<=> ! [Y: $i,X: $i] : ( or(or(X,Y),not(Y)) = n1 ) ),
inference(quant_intro,[status(thm)],[203]) ).
tff(205,plain,
( ! [Y: $i,X: $i] : ( or(or(X,Y),not(Y)) = n1 )
<=> ! [Y: $i,X: $i] : ( or(or(X,Y),not(Y)) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(206,axiom,
! [Y: $i,X: $i] : ( or(or(X,Y),not(Y)) = n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_not_simplification2) ).
tff(207,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),not(Y)) = n1 ),
inference(modus_ponens,[status(thm)],[206,205]) ).
tff(208,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),not(Y)) = n1 ),
inference(skolemize,[status(sab)],[207]) ).
tff(209,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),not(Y)) = n1 ),
inference(modus_ponens,[status(thm)],[208,204]) ).
tff(210,plain,
( ~ ! [Y: $i,X: $i] : ( or(or(X,Y),not(Y)) = n1 )
| ( or(or(f3,not(i2)),not(not(i2))) = n1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(211,plain,
or(or(f3,not(i2)),not(not(i2))) = n1,
inference(unit_resolution,[status(thm)],[210,209]) ).
tff(212,plain,
( ~ ! [X: $i] : ( not(not(X)) = X )
| ( not(not(i2)) = i2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
not(not(i2)) = i2,
inference(unit_resolution,[status(thm)],[212,15]) ).
tff(214,plain,
i2 = not(not(i2)),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(f3,not(i2)) = or(not(i2),f3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
or(f3,not(i2)) = or(not(i2),f3),
inference(unit_resolution,[status(thm)],[215,57]) ).
tff(217,plain,
or(not(i2),f3) = or(f3,not(i2)),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
or(f2,f3) = or(f3,not(i2)),
inference(transitivity,[status(thm)],[185,217]) ).
tff(219,plain,
or(or(f2,f3),i2) = or(or(f3,not(i2)),not(not(i2))),
inference(monotonicity,[status(thm)],[218,214]) ).
tff(220,plain,
or(or(f2,f3),i2) = n1,
inference(transitivity,[status(thm)],[219,211]) ).
tff(221,plain,
and(or(or(f2,f3),i2),not(e1)) = and(n1,not(e1)),
inference(monotonicity,[status(thm)],[220]) ).
tff(222,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(or(f2,f3),i2),not(e1)) = or(and(or(f2,f3),not(e1)),and(i2,not(e1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(223,plain,
and(or(or(f2,f3),i2),not(e1)) = or(and(or(f2,f3),not(e1)),and(i2,not(e1))),
inference(unit_resolution,[status(thm)],[222,150]) ).
tff(224,plain,
or(and(or(f2,f3),not(e1)),and(i2,not(e1))) = and(or(or(f2,f3),i2),not(e1)),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
not(f3) = not(and(i1,i2)),
inference(monotonicity,[status(thm)],[89]) ).
tff(226,plain,
not(and(i1,i2)) = not(f3),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
^ [Y: $i,X: $i] :
refl(( ( not(and(X,Y)) = or(not(X),not(Y)) )
<=> ( not(and(X,Y)) = or(not(X),not(Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(228,plain,
( ! [Y: $i,X: $i] : ( not(and(X,Y)) = or(not(X),not(Y)) )
<=> ! [Y: $i,X: $i] : ( not(and(X,Y)) = or(not(X),not(Y)) ) ),
inference(quant_intro,[status(thm)],[227]) ).
tff(229,plain,
( ! [Y: $i,X: $i] : ( not(and(X,Y)) = or(not(X),not(Y)) )
<=> ! [Y: $i,X: $i] : ( not(and(X,Y)) = or(not(X),not(Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(230,axiom,
! [Y: $i,X: $i] : ( not(and(X,Y)) = or(not(X),not(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_canonicalization1) ).
tff(231,plain,
! [Y: $i,X: $i] : ( not(and(X,Y)) = or(not(X),not(Y)) ),
inference(modus_ponens,[status(thm)],[230,229]) ).
tff(232,plain,
! [Y: $i,X: $i] : ( not(and(X,Y)) = or(not(X),not(Y)) ),
inference(skolemize,[status(sab)],[231]) ).
tff(233,plain,
! [Y: $i,X: $i] : ( not(and(X,Y)) = or(not(X),not(Y)) ),
inference(modus_ponens,[status(thm)],[232,228]) ).
tff(234,plain,
( ~ ! [Y: $i,X: $i] : ( not(and(X,Y)) = or(not(X),not(Y)) )
| ( not(and(i1,i2)) = or(not(i1),not(i2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(235,plain,
not(and(i1,i2)) = or(not(i1),not(i2)),
inference(unit_resolution,[status(thm)],[234,233]) ).
tff(236,plain,
or(not(i1),not(i2)) = not(and(i1,i2)),
inference(symmetry,[status(thm)],[235]) ).
tff(237,plain,
or(not(i1),not(i2)) = not(f3),
inference(transitivity,[status(thm)],[236,226]) ).
tff(238,plain,
and(i1,or(not(i1),not(i2))) = and(not(not(i1)),not(f3)),
inference(monotonicity,[status(thm)],[18,237]) ).
tff(239,plain,
and(not(not(i1)),not(f3)) = and(i1,or(not(i1),not(i2))),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
not(e1) = and(i1,or(not(i1),not(i2))),
inference(transitivity,[status(thm)],[41,29,239]) ).
tff(241,plain,
and(i2,not(e1)) = and(i2,and(i1,or(not(i1),not(i2)))),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
and(i2,and(i1,or(not(i1),not(i2)))) = and(i2,not(e1)),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( and(X,and(Y,Z)) = and(and(X,Y),Z) )
<=> ( and(X,and(Y,Z)) = and(and(X,Y),Z) ) )),
inference(bind,[status(th)],[]) ).
tff(244,plain,
( ! [Z: $i,Y: $i,X: $i] : ( and(X,and(Y,Z)) = and(and(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( and(X,and(Y,Z)) = and(and(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[243]) ).
tff(245,plain,
( ! [Z: $i,Y: $i,X: $i] : ( and(X,and(Y,Z)) = and(and(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( and(X,and(Y,Z)) = and(and(X,Y),Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(246,axiom,
! [Z: $i,Y: $i,X: $i] : ( and(X,and(Y,Z)) = and(and(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_associativity) ).
tff(247,plain,
! [Z: $i,Y: $i,X: $i] : ( and(X,and(Y,Z)) = and(and(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[246,245]) ).
tff(248,plain,
! [Z: $i,Y: $i,X: $i] : ( and(X,and(Y,Z)) = and(and(X,Y),Z) ),
inference(skolemize,[status(sab)],[247]) ).
tff(249,plain,
! [Z: $i,Y: $i,X: $i] : ( and(X,and(Y,Z)) = and(and(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[248,244]) ).
tff(250,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(X,and(Y,Z)) = and(and(X,Y),Z) )
| ( and(i2,and(i1,or(not(i1),not(i2)))) = and(and(i2,i1),or(not(i1),not(i2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(251,plain,
and(i2,and(i1,or(not(i1),not(i2)))) = and(and(i2,i1),or(not(i1),not(i2))),
inference(unit_resolution,[status(thm)],[250,249]) ).
tff(252,plain,
and(and(i2,i1),or(not(i1),not(i2))) = and(i2,and(i1,or(not(i1),not(i2)))),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
and(i1,i2) = f3,
inference(symmetry,[status(thm)],[89]) ).
tff(254,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(i2,i1) = and(i1,i2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(255,plain,
and(i2,i1) = and(i1,i2),
inference(unit_resolution,[status(thm)],[254,82]) ).
tff(256,plain,
and(i2,i1) = f3,
inference(transitivity,[status(thm)],[255,253]) ).
tff(257,plain,
and(and(i2,i1),or(not(i1),not(i2))) = and(f3,not(f3)),
inference(monotonicity,[status(thm)],[256,237]) ).
tff(258,plain,
and(f3,not(f3)) = and(and(i2,i1),or(not(i1),not(i2))),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
^ [X: $i] :
refl(( ( and(X,n0) = n0 )
<=> ( and(X,n0) = n0 ) )),
inference(bind,[status(th)],[]) ).
tff(260,plain,
( ! [X: $i] : ( and(X,n0) = n0 )
<=> ! [X: $i] : ( and(X,n0) = n0 ) ),
inference(quant_intro,[status(thm)],[259]) ).
tff(261,plain,
( ! [X: $i] : ( and(X,n0) = n0 )
<=> ! [X: $i] : ( and(X,n0) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(262,axiom,
! [X: $i] : ( and(X,n0) = n0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',and_definition1) ).
tff(263,plain,
! [X: $i] : ( and(X,n0) = n0 ),
inference(modus_ponens,[status(thm)],[262,261]) ).
tff(264,plain,
! [X: $i] : ( and(X,n0) = n0 ),
inference(skolemize,[status(sab)],[263]) ).
tff(265,plain,
! [X: $i] : ( and(X,n0) = n0 ),
inference(modus_ponens,[status(thm)],[264,260]) ).
tff(266,plain,
( ~ ! [X: $i] : ( and(X,n0) = n0 )
| ( and(or(f2,f3),n0) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(267,plain,
and(or(f2,f3),n0) = n0,
inference(unit_resolution,[status(thm)],[266,265]) ).
tff(268,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(n0,or(f2,f3)) = and(or(f2,f3),n0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(269,plain,
and(n0,or(f2,f3)) = and(or(f2,f3),n0),
inference(unit_resolution,[status(thm)],[268,82]) ).
tff(270,plain,
and(n0,or(f2,f3)) = and(i2,not(e1)),
inference(transitivity,[status(thm)],[269,267,139,258,252,242]) ).
tff(271,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(or(f2,f3),not(e1)) = and(not(e1),or(f2,f3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(272,plain,
and(or(f2,f3),not(e1)) = and(not(e1),or(f2,f3)),
inference(unit_resolution,[status(thm)],[271,82]) ).
tff(273,plain,
and(not(e1),or(f2,f3)) = and(or(f2,f3),not(e1)),
inference(symmetry,[status(thm)],[272]) ).
tff(274,plain,
( ~ ! [X: $i] : ( or(X,n0) = X )
| ( or(and(not(e1),not(e1)),n0) = and(not(e1),not(e1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(275,plain,
or(and(not(e1),not(e1)),n0) = and(not(e1),not(e1)),
inference(unit_resolution,[status(thm)],[274,48]) ).
tff(276,plain,
and(not(e1),not(e1)) = or(and(not(e1),not(e1)),n0),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
^ [X: $i] :
refl(( ( and(X,X) = X )
<=> ( and(X,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(278,plain,
( ! [X: $i] : ( and(X,X) = X )
<=> ! [X: $i] : ( and(X,X) = X ) ),
inference(quant_intro,[status(thm)],[277]) ).
tff(279,plain,
( ! [X: $i] : ( and(X,X) = X )
<=> ! [X: $i] : ( and(X,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(280,axiom,
! [X: $i] : ( and(X,X) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_simplification1) ).
tff(281,plain,
! [X: $i] : ( and(X,X) = X ),
inference(modus_ponens,[status(thm)],[280,279]) ).
tff(282,plain,
! [X: $i] : ( and(X,X) = X ),
inference(skolemize,[status(sab)],[281]) ).
tff(283,plain,
! [X: $i] : ( and(X,X) = X ),
inference(modus_ponens,[status(thm)],[282,278]) ).
tff(284,plain,
( ~ ! [X: $i] : ( and(X,X) = X )
| ( and(not(e1),not(e1)) = not(e1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(285,plain,
and(not(e1),not(e1)) = not(e1),
inference(unit_resolution,[status(thm)],[284,283]) ).
tff(286,plain,
not(e1) = and(not(e1),not(e1)),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
not(e1) = or(and(not(e1),not(e1)),n0),
inference(transitivity,[status(thm)],[286,276]) ).
tff(288,plain,
and(not(e1),or(f2,f3)) = and(or(and(not(e1),not(e1)),n0),or(f2,f3)),
inference(monotonicity,[status(thm)],[287]) ).
tff(289,plain,
and(or(and(not(e1),not(e1)),n0),or(f2,f3)) = and(not(e1),or(f2,f3)),
inference(symmetry,[status(thm)],[288]) ).
tff(290,plain,
and(and(not(e1),not(e1)),or(f2,f3)) = and(or(and(not(e1),not(e1)),n0),or(f2,f3)),
inference(monotonicity,[status(thm)],[276]) ).
tff(291,plain,
and(and(not(e1),not(e1)),or(f2,f3)) = and(or(f2,f3),not(e1)),
inference(transitivity,[status(thm)],[290,289,273]) ).
tff(292,plain,
or(and(and(not(e1),not(e1)),or(f2,f3)),and(n0,or(f2,f3))) = or(and(or(f2,f3),not(e1)),and(i2,not(e1))),
inference(monotonicity,[status(thm)],[291,270]) ).
tff(293,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(and(not(e1),not(e1)),n0),or(f2,f3)) = or(and(and(not(e1),not(e1)),or(f2,f3)),and(n0,or(f2,f3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(294,plain,
and(or(and(not(e1),not(e1)),n0),or(f2,f3)) = or(and(and(not(e1),not(e1)),or(f2,f3)),and(n0,or(f2,f3))),
inference(unit_resolution,[status(thm)],[293,150]) ).
tff(295,plain,
and(not(e1),or(f2,f3)) = d1,
inference(transitivity,[status(thm)],[288,294,292,224,221,202,200,191]) ).
tff(296,plain,
or(and(not(e1),or(f2,f3)),and(f3,or(f2,f3))) = or(d1,d3),
inference(monotonicity,[status(thm)],[295,190]) ).
tff(297,plain,
and(or(not(i2),f3),f3) = and(or(f2,f3),f3),
inference(symmetry,[status(thm)],[186]) ).
tff(298,plain,
or(and(not(i2),f3),and(f3,f3)) = and(or(not(i2),f3),f3),
inference(symmetry,[status(thm)],[179]) ).
tff(299,plain,
or(and(not(i1),f3),and(f3,f3)) = or(and(not(i2),f3),and(f3,f3)),
inference(symmetry,[status(thm)],[177]) ).
tff(300,plain,
and(or(f1,f3),f3) = and(or(not(i1),f3),f3),
inference(symmetry,[status(thm)],[159]) ).
tff(301,plain,
and(or(f3,not(i1)),f3) = and(or(f1,f3),f3),
inference(symmetry,[status(thm)],[158]) ).
tff(302,plain,
or(and(f3,f3),and(not(i1),f3)) = and(or(f3,not(i1)),f3),
inference(symmetry,[status(thm)],[152]) ).
tff(303,plain,
or(and(f3,f3),and(f3,not(f3))) = or(and(f3,f3),and(not(i1),f3)),
inference(symmetry,[status(thm)],[143]) ).
tff(304,plain,
f3 = or(and(f3,f3),and(f3,not(f3))),
inference(symmetry,[status(thm)],[129]) ).
tff(305,plain,
( ~ ! [X: $i] : ( and(X,n1) = X )
| ( and(f3,n1) = f3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(306,plain,
and(f3,n1) = f3,
inference(unit_resolution,[status(thm)],[305,198]) ).
tff(307,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(n1,f3) = and(f3,n1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(308,plain,
and(n1,f3) = and(f3,n1),
inference(unit_resolution,[status(thm)],[307,82]) ).
tff(309,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(310,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)],[309]) ).
tff(311,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(312,axiom,
! [Y: $i,X: $i] : ( or(or(X,Y),not(X)) = n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_not_simplification3) ).
tff(313,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),not(X)) = n1 ),
inference(modus_ponens,[status(thm)],[312,311]) ).
tff(314,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),not(X)) = n1 ),
inference(skolemize,[status(sab)],[313]) ).
tff(315,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),not(X)) = n1 ),
inference(modus_ponens,[status(thm)],[314,310]) ).
tff(316,plain,
( ~ ! [Y: $i,X: $i] : ( or(or(X,Y),not(X)) = n1 )
| ( or(or(f3,not(i2)),not(f3)) = n1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(317,plain,
or(or(f3,not(i2)),not(f3)) = n1,
inference(unit_resolution,[status(thm)],[316,315]) ).
tff(318,plain,
or(or(f2,f3),or(not(i1),not(i2))) = or(or(f3,not(i2)),not(f3)),
inference(monotonicity,[status(thm)],[218,237]) ).
tff(319,plain,
or(or(f2,f3),or(not(i1),not(i2))) = n1,
inference(transitivity,[status(thm)],[318,317]) ).
tff(320,plain,
and(or(or(f2,f3),or(not(i1),not(i2))),f3) = and(n1,f3),
inference(monotonicity,[status(thm)],[319]) ).
tff(321,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(or(f2,f3),or(not(i1),not(i2))),f3) = or(and(or(f2,f3),f3),and(or(not(i1),not(i2)),f3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(322,plain,
and(or(or(f2,f3),or(not(i1),not(i2))),f3) = or(and(or(f2,f3),f3),and(or(not(i1),not(i2)),f3)),
inference(unit_resolution,[status(thm)],[321,150]) ).
tff(323,plain,
or(and(or(f2,f3),f3),and(or(not(i1),not(i2)),f3)) = and(or(or(f2,f3),or(not(i1),not(i2))),f3),
inference(symmetry,[status(thm)],[322]) ).
tff(324,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(or(not(i1),not(i2)),f3) = and(f3,or(not(i1),not(i2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(325,plain,
and(or(not(i1),not(i2)),f3) = and(f3,or(not(i1),not(i2))),
inference(unit_resolution,[status(thm)],[324,82]) ).
tff(326,plain,
and(f3,or(not(i1),not(i2))) = and(or(not(i1),not(i2)),f3),
inference(symmetry,[status(thm)],[325]) ).
tff(327,plain,
and(f3,or(not(i1),not(i2))) = and(f3,not(f3)),
inference(monotonicity,[status(thm)],[237]) ).
tff(328,plain,
and(f3,not(f3)) = and(f3,or(not(i1),not(i2))),
inference(symmetry,[status(thm)],[327]) ).
tff(329,plain,
n0 = and(or(not(i1),not(i2)),f3),
inference(transitivity,[status(thm)],[139,328,326]) ).
tff(330,plain,
or(and(or(f2,f3),f3),n0) = or(and(or(f2,f3),f3),and(or(not(i1),not(i2)),f3)),
inference(monotonicity,[status(thm)],[329]) ).
tff(331,plain,
or(and(f3,or(f2,f3)),n0) = or(and(or(f2,f3),f3),n0),
inference(monotonicity,[status(thm)],[189]) ).
tff(332,plain,
( ~ ! [X: $i] : ( and(X,not(X)) = n0 )
| ( and(not(e2),not(not(e2))) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
and(not(e2),not(not(e2))) = n0,
inference(unit_resolution,[status(thm)],[332,136]) ).
tff(334,plain,
( ( d2 = not(e2) )
<=> ( d2 = not(e2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(335,axiom,
d2 = not(e2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor10) ).
tff(336,plain,
d2 = not(e2),
inference(modus_ponens,[status(thm)],[335,334]) ).
tff(337,plain,
not(e2) = d2,
inference(symmetry,[status(thm)],[336]) ).
tff(338,plain,
not(not(e2)) = not(d2),
inference(monotonicity,[status(thm)],[337]) ).
tff(339,plain,
not(d2) = not(not(e2)),
inference(symmetry,[status(thm)],[338]) ).
tff(340,plain,
( ( e2 = or(f2,f3) )
<=> ( e2 = or(f2,f3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(341,axiom,
e2 = or(f2,f3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor12) ).
tff(342,plain,
e2 = or(f2,f3),
inference(modus_ponens,[status(thm)],[341,340]) ).
tff(343,plain,
or(f2,f3) = e2,
inference(symmetry,[status(thm)],[342]) ).
tff(344,plain,
not(or(f2,f3)) = not(e2),
inference(monotonicity,[status(thm)],[343]) ).
tff(345,plain,
not(e2) = not(or(f2,f3)),
inference(symmetry,[status(thm)],[344]) ).
tff(346,plain,
d2 = not(or(f2,f3)),
inference(transitivity,[status(thm)],[336,345]) ).
tff(347,plain,
not(d2) = not(not(or(f2,f3))),
inference(monotonicity,[status(thm)],[346]) ).
tff(348,plain,
not(not(or(f2,f3))) = not(d2),
inference(symmetry,[status(thm)],[347]) ).
tff(349,plain,
( ~ ! [X: $i] : ( not(not(X)) = X )
| ( not(not(or(f2,f3))) = or(f2,f3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(350,plain,
not(not(or(f2,f3))) = or(f2,f3),
inference(unit_resolution,[status(thm)],[349,15]) ).
tff(351,plain,
or(f2,f3) = not(not(or(f2,f3))),
inference(symmetry,[status(thm)],[350]) ).
tff(352,plain,
or(f2,f3) = not(not(e2)),
inference(transitivity,[status(thm)],[351,348,339]) ).
tff(353,plain,
and(not(e2),or(f2,f3)) = and(not(e2),not(not(e2))),
inference(monotonicity,[status(thm)],[352]) ).
tff(354,plain,
and(not(e2),or(f2,f3)) = n0,
inference(transitivity,[status(thm)],[353,333]) ).
tff(355,plain,
or(and(f3,or(f2,f3)),and(not(e2),or(f2,f3))) = or(and(f3,or(f2,f3)),n0),
inference(monotonicity,[status(thm)],[354]) ).
tff(356,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(f3,not(e2)),or(f2,f3)) = or(and(f3,or(f2,f3)),and(not(e2),or(f2,f3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(357,plain,
and(or(f3,not(e2)),or(f2,f3)) = or(and(f3,or(f2,f3)),and(not(e2),or(f2,f3))),
inference(unit_resolution,[status(thm)],[356,150]) ).
tff(358,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(f3,not(e2)) = or(not(e2),f3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(359,plain,
or(f3,not(e2)) = or(not(e2),f3),
inference(unit_resolution,[status(thm)],[358,57]) ).
tff(360,plain,
or(not(e2),f3) = or(f3,not(e2)),
inference(symmetry,[status(thm)],[359]) ).
tff(361,plain,
or(d2,d3) = or(not(e2),f3),
inference(monotonicity,[status(thm)],[336,115]) ).
tff(362,plain,
or(d2,d3) = or(f3,not(e2)),
inference(transitivity,[status(thm)],[361,360]) ).
tff(363,plain,
and(or(d2,d3),or(f2,f3)) = and(or(f3,not(e2)),or(f2,f3)),
inference(monotonicity,[status(thm)],[362]) ).
tff(364,plain,
and(or(d2,d3),or(f2,f3)) = and(f3,or(f2,f3)),
inference(transitivity,[status(thm)],[363,357,355,331,330,323,320,308,306,304,303,302,301,300,161,299,298,297,188]) ).
tff(365,plain,
or(and(not(e1),or(f2,f3)),and(or(d2,d3),or(f2,f3))) = or(and(not(e1),or(f2,f3)),and(f3,or(f2,f3))),
inference(monotonicity,[status(thm)],[364]) ).
tff(366,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(not(e1),or(d2,d3)),or(f2,f3)) = or(and(not(e1),or(f2,f3)),and(or(d2,d3),or(f2,f3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(367,plain,
and(or(not(e1),or(d2,d3)),or(f2,f3)) = or(and(not(e1),or(f2,f3)),and(or(d2,d3),or(f2,f3))),
inference(unit_resolution,[status(thm)],[366,150]) ).
tff(368,plain,
not(d2) = or(f2,f3),
inference(transitivity,[status(thm)],[347,350]) ).
tff(369,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(or(d2,d3),not(e1)) = or(not(e1),or(d2,d3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(370,plain,
or(or(d2,d3),not(e1)) = or(not(e1),or(d2,d3)),
inference(unit_resolution,[status(thm)],[369,57]) ).
tff(371,plain,
or(or(d2,d3),not(e1)) = or(or(f3,not(e2)),not(e1)),
inference(monotonicity,[status(thm)],[362]) ).
tff(372,plain,
or(or(f3,not(e2)),not(e1)) = or(or(d2,d3),not(e1)),
inference(symmetry,[status(thm)],[371]) ).
tff(373,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(374,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)],[373]) ).
tff(375,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(376,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_sorting) ).
tff(377,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) ),
inference(modus_ponens,[status(thm)],[376,375]) ).
tff(378,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) ),
inference(skolemize,[status(sab)],[377]) ).
tff(379,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) ),
inference(modus_ponens,[status(thm)],[378,374]) ).
tff(380,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) )
| ( or(or(f3,not(e2)),not(e1)) = or(or(f3,not(e1)),not(e2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(381,plain,
or(or(f3,not(e2)),not(e1)) = or(or(f3,not(e1)),not(e2)),
inference(unit_resolution,[status(thm)],[380,379]) ).
tff(382,plain,
or(or(f3,not(e1)),not(e2)) = or(or(f3,not(e2)),not(e1)),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) )
| ( or(f3,or(not(e1),not(e2))) = or(or(f3,not(e1)),not(e2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(384,plain,
or(f3,or(not(e1),not(e2))) = or(or(f3,not(e1)),not(e2)),
inference(unit_resolution,[status(thm)],[383,69]) ).
tff(385,plain,
^ [Y: $i,X: $i] :
refl(( ( or(or(X,Y),X) = or(X,Y) )
<=> ( or(or(X,Y),X) = or(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(386,plain,
( ! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) )
<=> ! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) ) ),
inference(quant_intro,[status(thm)],[385]) ).
tff(387,plain,
( ! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) )
<=> ! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(388,axiom,
! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_simplification3) ).
tff(389,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) ),
inference(modus_ponens,[status(thm)],[388,387]) ).
tff(390,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) ),
inference(skolemize,[status(sab)],[389]) ).
tff(391,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) ),
inference(modus_ponens,[status(thm)],[390,386]) ).
tff(392,plain,
( ~ ! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) )
| ( or(or(f3,or(not(e1),not(e2))),f3) = or(f3,or(not(e1),not(e2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(393,plain,
or(or(f3,or(not(e1),not(e2))),f3) = or(f3,or(not(e1),not(e2))),
inference(unit_resolution,[status(thm)],[392,391]) ).
tff(394,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) )
| ( or(or(f3,f3),or(not(e1),not(e2))) = or(or(f3,or(not(e1),not(e2))),f3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(395,plain,
or(or(f3,f3),or(not(e1),not(e2))) = or(or(f3,or(not(e1),not(e2))),f3),
inference(unit_resolution,[status(thm)],[394,379]) ).
tff(396,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) )
| ( or(f3,or(f3,or(not(e1),not(e2)))) = or(or(f3,f3),or(not(e1),not(e2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(397,plain,
or(f3,or(f3,or(not(e1),not(e2)))) = or(or(f3,f3),or(not(e1),not(e2))),
inference(unit_resolution,[status(thm)],[396,69]) ).
tff(398,plain,
or(f3,or(not(e1),not(e2))) = or(not(e1),or(d2,d3)),
inference(transitivity,[status(thm)],[384,382,372,370]) ).
tff(399,plain,
or(f3,or(f3,or(not(e1),not(e2)))) = or(f3,or(not(e1),or(d2,d3))),
inference(monotonicity,[status(thm)],[398]) ).
tff(400,plain,
or(f3,or(not(e1),or(d2,d3))) = or(f3,or(f3,or(not(e1),not(e2)))),
inference(symmetry,[status(thm)],[399]) ).
tff(401,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(f3,or(not(e1),or(d2,d3))) = or(or(not(e1),or(d2,d3)),f3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(402,plain,
or(f3,or(not(e1),or(d2,d3))) = or(or(not(e1),or(d2,d3)),f3),
inference(unit_resolution,[status(thm)],[401,57]) ).
tff(403,plain,
or(or(not(e1),or(d2,d3)),f3) = or(f3,or(not(e1),or(d2,d3))),
inference(symmetry,[status(thm)],[402]) ).
tff(404,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) )
| ( or(or(not(e1),or(d2,d3)),f3) = or(or(not(e1),f3),or(d2,d3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(405,plain,
or(or(not(e1),or(d2,d3)),f3) = or(or(not(e1),f3),or(d2,d3)),
inference(unit_resolution,[status(thm)],[404,379]) ).
tff(406,plain,
or(or(not(e1),f3),or(d2,d3)) = or(or(not(e1),or(d2,d3)),f3),
inference(symmetry,[status(thm)],[405]) ).
tff(407,plain,
( ( c2 = or(d2,d3) )
<=> ( c2 = or(d2,d3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(408,axiom,
c2 = or(d2,d3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor7) ).
tff(409,plain,
c2 = or(d2,d3),
inference(modus_ponens,[status(thm)],[408,407]) ).
tff(410,plain,
or(d2,d3) = c2,
inference(symmetry,[status(thm)],[409]) ).
tff(411,plain,
( ( c1 = or(d1,d3) )
<=> ( c1 = or(d1,d3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(412,axiom,
c1 = or(d1,d3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor6) ).
tff(413,plain,
c1 = or(d1,d3),
inference(modus_ponens,[status(thm)],[412,411]) ).
tff(414,plain,
or(d1,d3) = c1,
inference(symmetry,[status(thm)],[413]) ).
tff(415,plain,
or(not(e1),f3) = or(d1,d3),
inference(symmetry,[status(thm)],[119]) ).
tff(416,plain,
or(not(e1),f3) = c1,
inference(transitivity,[status(thm)],[415,414]) ).
tff(417,plain,
or(or(not(e1),f3),or(d2,d3)) = or(c1,c2),
inference(monotonicity,[status(thm)],[416,410]) ).
tff(418,plain,
or(c1,c2) = or(or(not(e1),f3),or(d2,d3)),
inference(symmetry,[status(thm)],[417]) ).
tff(419,plain,
or(c1,c2) = or(not(e1),or(d2,d3)),
inference(transitivity,[status(thm)],[418,406,403,400,397,395,393,384,382,372,370]) ).
tff(420,plain,
and(or(c1,c2),not(d2)) = and(or(not(e1),or(d2,d3)),or(f2,f3)),
inference(monotonicity,[status(thm)],[419,368]) ).
tff(421,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(or(c1,c2),not(d2)) = and(not(d2),or(c1,c2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(422,plain,
and(or(c1,c2),not(d2)) = and(not(d2),or(c1,c2)),
inference(unit_resolution,[status(thm)],[421,82]) ).
tff(423,plain,
and(not(d2),or(c1,c2)) = and(or(c1,c2),not(d2)),
inference(symmetry,[status(thm)],[422]) ).
tff(424,plain,
( ( b3 = or(c1,c2) )
<=> ( b3 = or(c1,c2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(425,axiom,
b3 = or(c1,c2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor5) ).
tff(426,plain,
b3 = or(c1,c2),
inference(modus_ponens,[status(thm)],[425,424]) ).
tff(427,plain,
( ( b2 = not(d2) )
<=> ( b2 = not(d2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(428,axiom,
b2 = not(d2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor4) ).
tff(429,plain,
b2 = not(d2),
inference(modus_ponens,[status(thm)],[428,427]) ).
tff(430,plain,
and(b2,b3) = and(not(d2),or(c1,c2)),
inference(monotonicity,[status(thm)],[429,426]) ).
tff(431,plain,
( ( a2 = and(b2,b3) )
<=> ( a2 = and(b2,b3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(432,axiom,
a2 = and(b2,b3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor2) ).
tff(433,plain,
a2 = and(b2,b3),
inference(modus_ponens,[status(thm)],[432,431]) ).
tff(434,plain,
a2 = i1,
inference(transitivity,[status(thm)],[433,430,423,420,367,365,296,119,112,109,72,62,9]) ).
tff(435,plain,
( ~ ! [X: $i] : ( and(X,n1) = X )
| ( and(i2,n1) = i2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(436,plain,
and(i2,n1) = i2,
inference(unit_resolution,[status(thm)],[435,198]) ).
tff(437,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(n1,i2) = and(i2,n1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(438,plain,
and(n1,i2) = and(i2,n1),
inference(unit_resolution,[status(thm)],[437,82]) ).
tff(439,plain,
^ [X: $i] :
refl(( ( or(X,not(X)) = n1 )
<=> ( or(X,not(X)) = n1 ) )),
inference(bind,[status(th)],[]) ).
tff(440,plain,
( ! [X: $i] : ( or(X,not(X)) = n1 )
<=> ! [X: $i] : ( or(X,not(X)) = n1 ) ),
inference(quant_intro,[status(thm)],[439]) ).
tff(441,plain,
( ! [X: $i] : ( or(X,not(X)) = n1 )
<=> ! [X: $i] : ( or(X,not(X)) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(442,axiom,
! [X: $i] : ( or(X,not(X)) = n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_not_simplification1) ).
tff(443,plain,
! [X: $i] : ( or(X,not(X)) = n1 ),
inference(modus_ponens,[status(thm)],[442,441]) ).
tff(444,plain,
! [X: $i] : ( or(X,not(X)) = n1 ),
inference(skolemize,[status(sab)],[443]) ).
tff(445,plain,
! [X: $i] : ( or(X,not(X)) = n1 ),
inference(modus_ponens,[status(thm)],[444,440]) ).
tff(446,plain,
( ~ ! [X: $i] : ( or(X,not(X)) = n1 )
| ( or(n0,not(n0)) = n1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(447,plain,
or(n0,not(n0)) = n1,
inference(unit_resolution,[status(thm)],[446,445]) ).
tff(448,plain,
( ( not(n0) = n1 )
<=> ( not(n0) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(449,axiom,
not(n0) = n1,
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',not_definition1) ).
tff(450,plain,
not(n0) = n1,
inference(modus_ponens,[status(thm)],[449,448]) ).
tff(451,plain,
n1 = not(n0),
inference(symmetry,[status(thm)],[450]) ).
tff(452,plain,
( ~ ! [X: $i] : ( or(X,not(X)) = n1 )
| ( or(or(f1,f3),not(or(f1,f3))) = n1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(453,plain,
or(or(f1,f3),not(or(f1,f3))) = n1,
inference(unit_resolution,[status(thm)],[452,445]) ).
tff(454,plain,
not(or(f1,f3)) = not(e1),
inference(monotonicity,[status(thm)],[33]) ).
tff(455,plain,
not(e1) = not(or(f1,f3)),
inference(symmetry,[status(thm)],[454]) ).
tff(456,plain,
or(or(f1,f3),not(e1)) = or(or(f1,f3),not(or(f1,f3))),
inference(monotonicity,[status(thm)],[455]) ).
tff(457,plain,
or(or(f1,f3),not(e1)) = not(n0),
inference(transitivity,[status(thm)],[456,453,451]) ).
tff(458,plain,
or(n0,or(or(f1,f3),not(e1))) = or(n0,not(n0)),
inference(monotonicity,[status(thm)],[457]) ).
tff(459,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) )
| ( or(n0,or(or(f1,f3),not(e1))) = or(or(n0,or(f1,f3)),not(e1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(460,plain,
or(n0,or(or(f1,f3),not(e1))) = or(or(n0,or(f1,f3)),not(e1)),
inference(unit_resolution,[status(thm)],[459,69]) ).
tff(461,plain,
or(or(n0,or(f1,f3)),not(e1)) = or(n0,or(or(f1,f3),not(e1))),
inference(symmetry,[status(thm)],[460]) ).
tff(462,plain,
or(or(n0,or(f1,f3)),not(e1)) = n1,
inference(transitivity,[status(thm)],[461,458,447]) ).
tff(463,plain,
and(or(or(n0,or(f1,f3)),not(e1)),i2) = and(n1,i2),
inference(monotonicity,[status(thm)],[462]) ).
tff(464,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(or(n0,or(f1,f3)),not(e1)),i2) = or(and(or(n0,or(f1,f3)),i2),and(not(e1),i2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(465,plain,
and(or(or(n0,or(f1,f3)),not(e1)),i2) = or(and(or(n0,or(f1,f3)),i2),and(not(e1),i2)),
inference(unit_resolution,[status(thm)],[464,150]) ).
tff(466,plain,
or(and(or(n0,or(f1,f3)),i2),and(not(e1),i2)) = and(or(or(n0,or(f1,f3)),not(e1)),i2),
inference(symmetry,[status(thm)],[465]) ).
tff(467,plain,
and(not(e1),i2) = and(and(i1,or(not(i1),not(i2))),i2),
inference(monotonicity,[status(thm)],[240]) ).
tff(468,plain,
and(and(i1,or(not(i1),not(i2))),i2) = and(not(e1),i2),
inference(symmetry,[status(thm)],[467]) ).
tff(469,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(470,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)],[469]) ).
tff(471,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(472,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_sorting) ).
tff(473,plain,
! [Z: $i,Y: $i,X: $i] : ( and(and(X,Y),Z) = and(and(X,Z),Y) ),
inference(modus_ponens,[status(thm)],[472,471]) ).
tff(474,plain,
! [Z: $i,Y: $i,X: $i] : ( and(and(X,Y),Z) = and(and(X,Z),Y) ),
inference(skolemize,[status(sab)],[473]) ).
tff(475,plain,
! [Z: $i,Y: $i,X: $i] : ( and(and(X,Y),Z) = and(and(X,Z),Y) ),
inference(modus_ponens,[status(thm)],[474,470]) ).
tff(476,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(and(X,Y),Z) = and(and(X,Z),Y) )
| ( and(and(i1,or(not(i1),not(i2))),i2) = and(and(i1,i2),or(not(i1),not(i2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(477,plain,
and(and(i1,or(not(i1),not(i2))),i2) = and(and(i1,i2),or(not(i1),not(i2))),
inference(unit_resolution,[status(thm)],[476,475]) ).
tff(478,plain,
and(and(i1,i2),or(not(i1),not(i2))) = and(and(i1,or(not(i1),not(i2))),i2),
inference(symmetry,[status(thm)],[477]) ).
tff(479,plain,
and(and(i1,i2),or(not(i1),not(i2))) = and(f3,not(f3)),
inference(monotonicity,[status(thm)],[253,237]) ).
tff(480,plain,
and(f3,not(f3)) = and(and(i1,i2),or(not(i1),not(i2))),
inference(symmetry,[status(thm)],[479]) ).
tff(481,plain,
n0 = and(not(e1),i2),
inference(transitivity,[status(thm)],[139,480,478,468]) ).
tff(482,plain,
( ~ ! [X: $i] : ( or(X,n0) = X )
| ( or(or(f1,f3),n0) = or(f1,f3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(483,plain,
or(or(f1,f3),n0) = or(f1,f3),
inference(unit_resolution,[status(thm)],[482,48]) ).
tff(484,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(or(f1,f3),n0) = or(n0,or(f1,f3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(485,plain,
or(or(f1,f3),n0) = or(n0,or(f1,f3)),
inference(unit_resolution,[status(thm)],[484,57]) ).
tff(486,plain,
or(n0,or(f1,f3)) = or(or(f1,f3),n0),
inference(symmetry,[status(thm)],[485]) ).
tff(487,plain,
or(n0,or(f1,f3)) = or(f1,f3),
inference(transitivity,[status(thm)],[486,483]) ).
tff(488,plain,
and(or(n0,or(f1,f3)),i2) = and(or(f1,f3),i2),
inference(monotonicity,[status(thm)],[487]) ).
tff(489,plain,
and(or(f1,f3),i2) = and(or(n0,or(f1,f3)),i2),
inference(symmetry,[status(thm)],[488]) ).
tff(490,plain,
or(not(e2),f3) = or(d2,d3),
inference(symmetry,[status(thm)],[361]) ).
tff(491,plain,
( ~ ! [X: $i] : ( or(X,n0) = X )
| ( or(and(f3,i2),n0) = and(f3,i2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(492,plain,
or(and(f3,i2),n0) = and(f3,i2),
inference(unit_resolution,[status(thm)],[491,48]) ).
tff(493,plain,
and(f3,i2) = or(and(f3,i2),n0),
inference(symmetry,[status(thm)],[492]) ).
tff(494,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(i2,f3) = and(f3,i2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(495,plain,
and(i2,f3) = and(f3,i2),
inference(unit_resolution,[status(thm)],[494,82]) ).
tff(496,plain,
( ~ ! [X: $i] : ( or(X,n0) = X )
| ( or(and(i2,f3),n0) = and(i2,f3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(497,plain,
or(and(i2,f3),n0) = and(i2,f3),
inference(unit_resolution,[status(thm)],[496,48]) ).
tff(498,plain,
and(and(i1,i2),not(i2)) = and(f3,not(i2)),
inference(symmetry,[status(thm)],[173]) ).
tff(499,plain,
n0 = and(and(i1,i2),not(i2)),
inference(symmetry,[status(thm)],[172]) ).
tff(500,plain,
n0 = and(f3,not(i2)),
inference(transitivity,[status(thm)],[499,498]) ).
tff(501,plain,
or(and(i2,f3),n0) = or(and(i2,f3),and(f3,not(i2))),
inference(monotonicity,[status(thm)],[500]) ).
tff(502,plain,
or(and(i2,f3),and(f3,not(i2))) = or(and(i2,f3),n0),
inference(symmetry,[status(thm)],[501]) ).
tff(503,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,Y),and(Y,not(X))) = Y )
| ( or(and(i2,f3),and(f3,not(i2))) = f3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(504,plain,
or(and(i2,f3),and(f3,not(i2))) = f3,
inference(unit_resolution,[status(thm)],[503,7]) ).
tff(505,plain,
f3 = or(and(i2,f3),and(f3,not(i2))),
inference(symmetry,[status(thm)],[504]) ).
tff(506,plain,
f3 = or(and(f3,i2),n0),
inference(transitivity,[status(thm)],[505,502,497,495,493]) ).
tff(507,plain,
or(f3,not(e2)) = or(or(and(f3,i2),n0),not(e2)),
inference(monotonicity,[status(thm)],[506]) ).
tff(508,plain,
or(or(and(f3,i2),n0),not(e2)) = or(f3,not(e2)),
inference(symmetry,[status(thm)],[507]) ).
tff(509,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) )
| ( or(and(f3,i2),or(n0,not(e2))) = or(or(and(f3,i2),n0),not(e2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(510,plain,
or(and(f3,i2),or(n0,not(e2))) = or(or(and(f3,i2),n0),not(e2)),
inference(unit_resolution,[status(thm)],[509,69]) ).
tff(511,plain,
and(i2,not(f3)) = and(not(not(i2)),not(f3)),
inference(monotonicity,[status(thm)],[214]) ).
tff(512,plain,
and(not(not(i2)),not(f3)) = and(i2,not(f3)),
inference(symmetry,[status(thm)],[511]) ).
tff(513,plain,
( ~ ! [Y: $i,X: $i] : ( not(or(X,Y)) = and(not(X),not(Y)) )
| ( not(or(not(i2),f3)) = and(not(not(i2)),not(f3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(514,plain,
not(or(not(i2),f3)) = and(not(not(i2)),not(f3)),
inference(unit_resolution,[status(thm)],[513,27]) ).
tff(515,plain,
or(not(i2),f3) = e2,
inference(transitivity,[status(thm)],[184,343]) ).
tff(516,plain,
not(or(not(i2),f3)) = not(e2),
inference(monotonicity,[status(thm)],[515]) ).
tff(517,plain,
not(e2) = not(or(not(i2),f3)),
inference(symmetry,[status(thm)],[516]) ).
tff(518,plain,
( ~ ! [X: $i] : ( or(X,n0) = X )
| ( or(not(e2),n0) = not(e2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(519,plain,
or(not(e2),n0) = not(e2),
inference(unit_resolution,[status(thm)],[518,48]) ).
tff(520,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(e2),n0) = or(n0,not(e2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(521,plain,
or(not(e2),n0) = or(n0,not(e2)),
inference(unit_resolution,[status(thm)],[520,57]) ).
tff(522,plain,
or(n0,not(e2)) = or(not(e2),n0),
inference(symmetry,[status(thm)],[521]) ).
tff(523,plain,
or(n0,not(e2)) = and(i2,not(f3)),
inference(transitivity,[status(thm)],[522,519,517,514,512]) ).
tff(524,plain,
or(and(f3,i2),or(n0,not(e2))) = or(and(f3,i2),and(i2,not(f3))),
inference(monotonicity,[status(thm)],[523]) ).
tff(525,plain,
or(and(f3,i2),and(i2,not(f3))) = or(and(f3,i2),or(n0,not(e2))),
inference(symmetry,[status(thm)],[524]) ).
tff(526,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,Y),and(Y,not(X))) = Y )
| ( or(and(f3,i2),and(i2,not(f3))) = i2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(527,plain,
or(and(f3,i2),and(i2,not(f3))) = i2,
inference(unit_resolution,[status(thm)],[526,7]) ).
tff(528,plain,
i2 = or(and(f3,i2),and(i2,not(f3))),
inference(symmetry,[status(thm)],[527]) ).
tff(529,plain,
i2 = or(d2,d3),
inference(transitivity,[status(thm)],[528,525,510,508,359,490]) ).
tff(530,plain,
and(or(f1,f3),i2) = and(or(f1,f3),or(d2,d3)),
inference(monotonicity,[status(thm)],[529]) ).
tff(531,plain,
and(or(f1,f3),or(d2,d3)) = and(or(f1,f3),i2),
inference(symmetry,[status(thm)],[530]) ).
tff(532,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(or(f1,f3),or(d2,d3)) = and(or(d2,d3),or(f1,f3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(533,plain,
and(or(f1,f3),or(d2,d3)) = and(or(d2,d3),or(f1,f3)),
inference(unit_resolution,[status(thm)],[532,82]) ).
tff(534,plain,
and(or(d2,d3),or(f1,f3)) = and(or(f1,f3),or(d2,d3)),
inference(symmetry,[status(thm)],[533]) ).
tff(535,plain,
or(f3,or(d2,d3)) = or(f3,or(not(e2),f3)),
inference(monotonicity,[status(thm)],[361]) ).
tff(536,plain,
or(f3,or(not(e2),f3)) = or(f3,or(d2,d3)),
inference(symmetry,[status(thm)],[535]) ).
tff(537,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) )
| ( or(f3,or(not(e2),f3)) = or(or(f3,not(e2)),f3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(538,plain,
or(f3,or(not(e2),f3)) = or(or(f3,not(e2)),f3),
inference(unit_resolution,[status(thm)],[537,69]) ).
tff(539,plain,
or(or(f3,not(e2)),f3) = or(f3,or(not(e2),f3)),
inference(symmetry,[status(thm)],[538]) ).
tff(540,plain,
( ~ ! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) )
| ( or(or(f3,not(e2)),f3) = or(f3,not(e2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(541,plain,
or(or(f3,not(e2)),f3) = or(f3,not(e2)),
inference(unit_resolution,[status(thm)],[540,391]) ).
tff(542,plain,
or(f3,not(e2)) = or(or(f3,not(e2)),f3),
inference(symmetry,[status(thm)],[541]) ).
tff(543,plain,
or(d2,d3) = or(f3,or(d2,d3)),
inference(transitivity,[status(thm)],[361,360,542,539,536]) ).
tff(544,plain,
and(or(d2,d3),or(f1,f3)) = and(or(f3,or(d2,d3)),or(f1,f3)),
inference(monotonicity,[status(thm)],[543]) ).
tff(545,plain,
and(or(f3,or(d2,d3)),or(f1,f3)) = and(or(d2,d3),or(f1,f3)),
inference(symmetry,[status(thm)],[544]) ).
tff(546,plain,
and(or(f3,or(d2,d3)),or(f1,f3)) = and(or(n0,or(f1,f3)),i2),
inference(transitivity,[status(thm)],[545,534,531,489]) ).
tff(547,plain,
or(and(or(f3,or(d2,d3)),or(f1,f3)),n0) = or(and(or(n0,or(f1,f3)),i2),and(not(e1),i2)),
inference(monotonicity,[status(thm)],[546,481]) ).
tff(548,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(or(f3,or(d2,d3)),or(f1,f3)),n0) = or(n0,and(or(f3,or(d2,d3)),or(f1,f3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(549,plain,
or(and(or(f3,or(d2,d3)),or(f1,f3)),n0) = or(n0,and(or(f3,or(d2,d3)),or(f1,f3))),
inference(unit_resolution,[status(thm)],[548,57]) ).
tff(550,plain,
or(n0,and(or(f3,or(d2,d3)),or(f1,f3))) = or(and(or(f3,or(d2,d3)),or(f1,f3)),n0),
inference(symmetry,[status(thm)],[549]) ).
tff(551,plain,
( ~ ! [X: $i] : ( and(X,not(X)) = n0 )
| ( and(not(e1),not(not(e1))) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(552,plain,
and(not(e1),not(not(e1))) = n0,
inference(unit_resolution,[status(thm)],[551,136]) ).
tff(553,plain,
not(not(e1)) = not(d1),
inference(monotonicity,[status(thm)],[191]) ).
tff(554,plain,
not(d1) = not(not(e1)),
inference(symmetry,[status(thm)],[553]) ).
tff(555,plain,
d1 = not(or(f1,f3)),
inference(transitivity,[status(thm)],[118,455]) ).
tff(556,plain,
not(d1) = not(not(or(f1,f3))),
inference(monotonicity,[status(thm)],[555]) ).
tff(557,plain,
not(not(or(f1,f3))) = not(d1),
inference(symmetry,[status(thm)],[556]) ).
tff(558,plain,
( ~ ! [X: $i] : ( not(not(X)) = X )
| ( not(not(or(f1,f3))) = or(f1,f3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(559,plain,
not(not(or(f1,f3))) = or(f1,f3),
inference(unit_resolution,[status(thm)],[558,15]) ).
tff(560,plain,
or(f1,f3) = not(not(or(f1,f3))),
inference(symmetry,[status(thm)],[559]) ).
tff(561,plain,
or(f1,f3) = not(not(e1)),
inference(transitivity,[status(thm)],[560,557,554]) ).
tff(562,plain,
and(not(e1),or(f1,f3)) = and(not(e1),not(not(e1))),
inference(monotonicity,[status(thm)],[561]) ).
tff(563,plain,
and(not(e1),or(f1,f3)) = n0,
inference(transitivity,[status(thm)],[562,552]) ).
tff(564,plain,
or(and(not(e1),or(f1,f3)),and(or(f3,or(d2,d3)),or(f1,f3))) = or(n0,and(or(f3,or(d2,d3)),or(f1,f3))),
inference(monotonicity,[status(thm)],[563]) ).
tff(565,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(not(e1),or(f3,or(d2,d3))),or(f1,f3)) = or(and(not(e1),or(f1,f3)),and(or(f3,or(d2,d3)),or(f1,f3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(566,plain,
and(or(not(e1),or(f3,or(d2,d3))),or(f1,f3)) = or(and(not(e1),or(f1,f3)),and(or(f3,or(d2,d3)),or(f1,f3))),
inference(unit_resolution,[status(thm)],[565,150]) ).
tff(567,plain,
not(d1) = or(f1,f3),
inference(transitivity,[status(thm)],[556,559]) ).
tff(568,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) )
| ( or(not(e1),or(f3,or(d2,d3))) = or(or(not(e1),f3),or(d2,d3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(569,plain,
or(not(e1),or(f3,or(d2,d3))) = or(or(not(e1),f3),or(d2,d3)),
inference(unit_resolution,[status(thm)],[568,69]) ).
tff(570,plain,
or(or(not(e1),f3),or(d2,d3)) = or(not(e1),or(f3,or(d2,d3))),
inference(symmetry,[status(thm)],[569]) ).
tff(571,plain,
or(c1,c2) = or(not(e1),or(f3,or(d2,d3))),
inference(transitivity,[status(thm)],[418,570]) ).
tff(572,plain,
and(or(c1,c2),not(d1)) = and(or(not(e1),or(f3,or(d2,d3))),or(f1,f3)),
inference(monotonicity,[status(thm)],[571,567]) ).
tff(573,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(or(c1,c2),not(d1)) = and(not(d1),or(c1,c2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(574,plain,
and(or(c1,c2),not(d1)) = and(not(d1),or(c1,c2)),
inference(unit_resolution,[status(thm)],[573,82]) ).
tff(575,plain,
and(not(d1),or(c1,c2)) = and(or(c1,c2),not(d1)),
inference(symmetry,[status(thm)],[574]) ).
tff(576,plain,
( ( b1 = not(d1) )
<=> ( b1 = not(d1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(577,axiom,
b1 = not(d1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor3) ).
tff(578,plain,
b1 = not(d1),
inference(modus_ponens,[status(thm)],[577,576]) ).
tff(579,plain,
and(b1,b3) = and(not(d1),or(c1,c2)),
inference(monotonicity,[status(thm)],[578,426]) ).
tff(580,plain,
( ( a1 = and(b1,b3) )
<=> ( a1 = and(b1,b3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(581,axiom,
a1 = and(b1,b3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor1) ).
tff(582,plain,
a1 = and(b1,b3),
inference(modus_ponens,[status(thm)],[581,580]) ).
tff(583,plain,
a1 = i2,
inference(transitivity,[status(thm)],[582,579,575,572,566,564,550,547,466,463,438,436]) ).
tff(584,plain,
output(a1,a2) = output(i2,i1),
inference(monotonicity,[status(thm)],[583,434]) ).
tff(585,plain,
( circuit(input(i1,i2),output(a1,a2))
<=> circuit(input(i1,i2),output(i2,i1)) ),
inference(monotonicity,[status(thm)],[584]) ).
tff(586,plain,
( circuit(input(i1,i2),output(i2,i1))
<=> circuit(input(i1,i2),output(a1,a2)) ),
inference(symmetry,[status(thm)],[585]) ).
tff(587,plain,
( ~ circuit(input(i1,i2),output(i2,i1))
<=> ~ circuit(input(i1,i2),output(a1,a2)) ),
inference(monotonicity,[status(thm)],[586]) ).
tff(588,plain,
( ~ circuit(input(i1,i2),output(i2,i1))
<=> ~ circuit(input(i1,i2),output(i2,i1)) ),
inference(rewrite,[status(thm)],[]) ).
tff(589,axiom,
~ circuit(input(i1,i2),output(i2,i1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_interchange) ).
tff(590,plain,
~ circuit(input(i1,i2),output(i2,i1)),
inference(modus_ponens,[status(thm)],[589,588]) ).
tff(591,plain,
~ circuit(input(i1,i2),output(a1,a2)),
inference(modus_ponens,[status(thm)],[590,587]) ).
tff(592,plain,
( circuit(input(i1,i2),output(a1,a2))
<=> circuit(input(i1,i2),output(a1,a2)) ),
inference(rewrite,[status(thm)],[]) ).
tff(593,axiom,
circuit(input(i1,i2),output(a1,a2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',circuit_description) ).
tff(594,plain,
circuit(input(i1,i2),output(a1,a2)),
inference(modus_ponens,[status(thm)],[593,592]) ).
tff(595,plain,
$false,
inference(unit_resolution,[status(thm)],[594,591]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : HWV001-1 : TPTP v9.0.0. Released v1.1.0.
% 0.13/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 17:22:18 EDT 2025
% 0.13/0.35 % CPUTime :
% 1.37/1.56 % SZS status Unsatisfiable
% 1.37/1.56 % SZS output start Proof
% See solution above
% 1.37/1.59 % E exiting
%------------------------------------------------------------------------------