TSTP Solution File: HWV001-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV001-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 02:10:26 EDT 2022
% Result : Unsatisfiable 1.10s 0.98s
% Output : Proof 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 100
% Syntax : Number of formulae : 302 ( 216 unt; 12 typ; 0 def)
% Number of atoms : 394 ( 360 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 133 ( 44 ~; 37 |; 0 &)
% ( 52 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 367 ( 335 !; 0 ?; 367 :)
% Comments :
%------------------------------------------------------------------------------
tff(circuit_type,type,
circuit: ( $i * $i ) > $o ).
tff(output_type,type,
output: ( $i * $i ) > $i ).
tff(and_type,type,
and: ( $i * $i ) > $i ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(i2_type,type,
i2: $i ).
tff(i1_type,type,
i1: $i ).
tff(not_type,type,
not: $i > $i ).
tff(input_type,type,
input: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(n0_type,type,
n0: $i ).
tff(a2_type,type,
a2: $i ).
tff(a1_type,type,
a1: $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,plain,
! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X )
| ( or(and(i1,and(i1,i2)),and(i1,not(and(i1,i2)))) = i1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
or(and(i1,and(i1,i2)),and(i1,not(and(i1,i2)))) = 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(and(i1,i2))) = and(not(not(i1)),not(and(i1,i2))),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
and(not(not(i1)),not(and(i1,i2))) = and(i1,not(and(i1,i2))),
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),and(i1,i2))) = and(not(not(i1)),not(and(i1,i2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
not(or(not(i1),and(i1,i2))) = and(not(not(i1)),not(and(i1,i2))),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
not(or(not(i1),and(i1,i2))) = and(i1,not(and(i1,i2))),
inference(transitivity,[status(thm)],[29,20]) ).
tff(31,plain,
^ [Y: $i,X: $i] :
refl(
( ( and(X,Y) = and(Y,X) )
<=> ( and(X,Y) = and(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(32,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)],[31]) ).
tff(33,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(34,axiom,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_commutativity) ).
tff(35,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(and(i1,i2),i1) = and(i1,and(i1,i2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
and(and(i1,i2),i1) = and(i1,and(i1,i2)),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
^ [Y: $i,X: $i] :
refl(
( ( and(and(X,Y),X) = and(X,Y) )
<=> ( and(and(X,Y),X) = and(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [Y: $i,X: $i] : ( and(and(X,Y),X) = and(X,Y) )
<=> ! [Y: $i,X: $i] : ( and(and(X,Y),X) = and(X,Y) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [Y: $i,X: $i] : ( and(and(X,Y),X) = and(X,Y) )
<=> ! [Y: $i,X: $i] : ( and(and(X,Y),X) = and(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
! [Y: $i,X: $i] : ( and(and(X,Y),X) = and(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_simplification3) ).
tff(44,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),X) = and(X,Y) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),X) = and(X,Y) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),X) = and(X,Y) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [Y: $i,X: $i] : ( and(and(X,Y),X) = and(X,Y) )
| ( and(and(i1,i2),i1) = and(i1,i2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
and(and(i1,i2),i1) = and(i1,i2),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
and(i1,i2) = and(and(i1,i2),i1),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
and(i1,i2) = and(i1,and(i1,i2)),
inference(transitivity,[status(thm)],[49,39]) ).
tff(51,plain,
or(and(i1,i2),not(or(not(i1),and(i1,i2)))) = or(and(i1,and(i1,i2)),and(i1,not(and(i1,i2)))),
inference(monotonicity,[status(thm)],[50,30]) ).
tff(52,plain,
^ [Y: $i,X: $i] :
refl(
( ( or(X,Y) = or(Y,X) )
<=> ( or(X,Y) = or(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(53,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)],[52]) ).
tff(54,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(55,axiom,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_commutativity) ).
tff(56,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(i1,i2),not(or(not(i1),and(i1,i2)))) = or(not(or(not(i1),and(i1,i2))),and(i1,i2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
or(and(i1,i2),not(or(not(i1),and(i1,i2)))) = or(not(or(not(i1),and(i1,i2))),and(i1,i2)),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
or(not(or(not(i1),and(i1,i2))),and(i1,i2)) = or(and(i1,i2),not(or(not(i1),and(i1,i2)))),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X )
| ( or(and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))),and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),not(and(not(not(i2)),not(and(i1,i2)))))) = or(not(or(not(i1),and(i1,i2))),and(i1,i2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
or(and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))),and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),not(and(not(not(i2)),not(and(i1,i2)))))) = or(not(or(not(i1),and(i1,i2))),and(i1,i2)),
inference(unit_resolution,[status(thm)],[62,7]) ).
tff(64,plain,
( ~ ! [X: $i] : ( not(not(X)) = X )
| ( not(not(or(not(i2),and(i1,i2)))) = or(not(i2),and(i1,i2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
not(not(or(not(i2),and(i1,i2)))) = or(not(i2),and(i1,i2)),
inference(unit_resolution,[status(thm)],[64,15]) ).
tff(66,plain,
( ~ ! [Y: $i,X: $i] : ( not(or(X,Y)) = and(not(X),not(Y)) )
| ( not(or(not(i2),and(i1,i2))) = and(not(not(i2)),not(and(i1,i2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
not(or(not(i2),and(i1,i2))) = and(not(not(i2)),not(and(i1,i2))),
inference(unit_resolution,[status(thm)],[66,27]) ).
tff(68,plain,
and(not(not(i2)),not(and(i1,i2))) = not(or(not(i2),and(i1,i2))),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
not(and(not(not(i2)),not(and(i1,i2)))) = not(not(or(not(i2),and(i1,i2)))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
not(and(not(not(i2)),not(and(i1,i2)))) = or(not(i2),and(i1,i2)),
inference(transitivity,[status(thm)],[69,65]) ).
tff(71,plain,
and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),not(and(not(not(i2)),not(and(i1,i2))))) = and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(i2),and(i1,i2))),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(i2),and(i1,i2))) = and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),not(and(not(not(i2)),not(and(i1,i2))))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,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(74,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)],[73]) ).
tff(75,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(76,axiom,
! [Y: $i,X: $i] : ( not(and(X,Y)) = or(not(X),not(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_canonicalization1) ).
tff(77,plain,
! [Y: $i,X: $i] : ( not(and(X,Y)) = or(not(X),not(Y)) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [Y: $i,X: $i] : ( not(and(X,Y)) = or(not(X),not(Y)) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [Y: $i,X: $i] : ( not(and(X,Y)) = or(not(X),not(Y)) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,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(81,plain,
not(and(i1,i2)) = or(not(i1),not(i2)),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
or(not(i1),not(i2)) = not(and(i1,i2)),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
( ~ ! [X: $i] : ( not(not(X)) = X )
| ( not(not(i2)) = i2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
not(not(i2)) = i2,
inference(unit_resolution,[status(thm)],[83,15]) ).
tff(85,plain,
i2 = not(not(i2)),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
and(i2,or(not(i1),not(i2))) = and(not(not(i2)),not(and(i1,i2))),
inference(monotonicity,[status(thm)],[85,82]) ).
tff(87,plain,
and(not(not(i2)),not(and(i1,i2))) = and(i2,or(not(i1),not(i2))),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
or(not(or(not(i1),and(i1,i2))),and(i1,i2)) = i1,
inference(transitivity,[status(thm)],[61,51,9]) ).
tff(89,plain,
and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))) = and(i1,and(i2,or(not(i1),not(i2)))),
inference(monotonicity,[status(thm)],[88,87]) ).
tff(90,plain,
and(i1,and(i2,or(not(i1),not(i2)))) = and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,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(92,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)],[91]) ).
tff(93,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(94,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(95,plain,
! [Z: $i,Y: $i,X: $i] : ( and(X,and(Y,Z)) = and(and(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [Z: $i,Y: $i,X: $i] : ( and(X,and(Y,Z)) = and(and(X,Y),Z) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [Z: $i,Y: $i,X: $i] : ( and(X,and(Y,Z)) = and(and(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(X,and(Y,Z)) = and(and(X,Y),Z) )
| ( and(i1,and(i2,or(not(i1),not(i2)))) = and(and(i1,i2),or(not(i1),not(i2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
and(i1,and(i2,or(not(i1),not(i2)))) = and(and(i1,i2),or(not(i1),not(i2))),
inference(unit_resolution,[status(thm)],[98,97]) ).
tff(100,plain,
and(and(i1,i2),or(not(i1),not(i2))) = and(i1,and(i2,or(not(i1),not(i2)))),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
and(and(i1,i2),or(not(i1),not(i2))) = and(and(i1,i2),not(and(i1,i2))),
inference(monotonicity,[status(thm)],[82]) ).
tff(102,plain,
and(and(i1,i2),not(and(i1,i2))) = and(and(i1,i2),or(not(i1),not(i2))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
^ [X: $i] :
refl(
( ( and(X,not(X)) = not(n1) )
<=> ( and(X,not(X)) = not(n1) ) )),
inference(bind,[status(th)],]) ).
tff(104,plain,
( ! [X: $i] : ( and(X,not(X)) = not(n1) )
<=> ! [X: $i] : ( and(X,not(X)) = not(n1) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
^ [X: $i] :
rewrite(
( ( and(X,not(X)) = n0 )
<=> ( and(X,not(X)) = not(n1) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [X: $i] : ( and(X,not(X)) = n0 )
<=> ! [X: $i] : ( and(X,not(X)) = not(n1) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [X: $i] : ( and(X,not(X)) = n0 )
<=> ! [X: $i] : ( and(X,not(X)) = n0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,axiom,
! [X: $i] : ( and(X,not(X)) = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_not_simplification1) ).
tff(109,plain,
! [X: $i] : ( and(X,not(X)) = n0 ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
! [X: $i] : ( and(X,not(X)) = not(n1) ),
inference(modus_ponens,[status(thm)],[109,106]) ).
tff(111,plain,
! [X: $i] : ( and(X,not(X)) = not(n1) ),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [X: $i] : ( and(X,not(X)) = not(n1) ),
inference(modus_ponens,[status(thm)],[111,104]) ).
tff(113,plain,
( ~ ! [X: $i] : ( and(X,not(X)) = not(n1) )
| ( and(and(i1,i2),not(and(i1,i2))) = not(n1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
and(and(i1,i2),not(and(i1,i2))) = not(n1),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
not(n1) = and(and(i1,i2),not(and(i1,i2))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [X: $i] : ( and(X,not(X)) = not(n1) )
| ( and(not(or(not(i2),and(i1,i2))),not(not(or(not(i2),and(i1,i2))))) = not(n1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
and(not(or(not(i2),and(i1,i2))),not(not(or(not(i2),and(i1,i2))))) = not(n1),
inference(unit_resolution,[status(thm)],[116,112]) ).
tff(118,plain,
or(not(i2),and(i1,i2)) = not(not(or(not(i2),and(i1,i2)))),
inference(symmetry,[status(thm)],[65]) ).
tff(119,plain,
and(and(not(not(i2)),not(and(i1,i2))),or(not(i2),and(i1,i2))) = and(not(or(not(i2),and(i1,i2))),not(not(or(not(i2),and(i1,i2))))),
inference(monotonicity,[status(thm)],[68,118]) ).
tff(120,plain,
and(and(not(not(i2)),not(and(i1,i2))),or(not(i2),and(i1,i2))) = and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))),
inference(transitivity,[status(thm)],[119,117,115,102,100,90]) ).
tff(121,plain,
or(and(and(not(not(i2)),not(and(i1,i2))),or(not(i2),and(i1,i2))),and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(i2),and(i1,i2)))) = or(and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))),and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),not(and(not(not(i2)),not(and(i1,i2)))))),
inference(monotonicity,[status(thm)],[120,72]) ).
tff(122,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(123,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)],[122]) ).
tff(124,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(125,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(126,plain,
! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(and(not(not(i2)),not(and(i1,i2))),or(not(or(not(i1),and(i1,i2))),and(i1,i2))),or(not(i2),and(i1,i2))) = or(and(and(not(not(i2)),not(and(i1,i2))),or(not(i2),and(i1,i2))),and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(i2),and(i1,i2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
and(or(and(not(not(i2)),not(and(i1,i2))),or(not(or(not(i1),and(i1,i2))),and(i1,i2))),or(not(i2),and(i1,i2))) = or(and(and(not(not(i2)),not(and(i1,i2))),or(not(i2),and(i1,i2))),and(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(i2),and(i1,i2)))),
inference(unit_resolution,[status(thm)],[129,128]) ).
tff(131,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(not(not(i2)),not(and(i1,i2))),or(not(or(not(i1),and(i1,i2))),and(i1,i2))) = or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(132,plain,
or(and(not(not(i2)),not(and(i1,i2))),or(not(or(not(i1),and(i1,i2))),and(i1,i2))) = or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))),
inference(unit_resolution,[status(thm)],[131,58]) ).
tff(133,plain,
or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))) = or(and(not(not(i2)),not(and(i1,i2))),or(not(or(not(i1),and(i1,i2))),and(i1,i2))),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))) = or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),not(or(not(i2),and(i1,i2)))),
inference(monotonicity,[status(thm)],[68]) ).
tff(135,plain,
or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),not(or(not(i2),and(i1,i2)))) = or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
and(not(not(i1)),not(and(i1,i2))) = not(or(not(i1),and(i1,i2))),
inference(symmetry,[status(thm)],[29]) ).
tff(137,plain,
or(and(i1,i2),and(not(not(i1)),not(and(i1,i2)))) = or(and(i1,i2),not(or(not(i1),and(i1,i2)))),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
or(and(i1,i2),not(or(not(i1),and(i1,i2)))) = or(and(i1,i2),and(not(not(i1)),not(and(i1,i2)))),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
or(not(or(not(i1),and(i1,i2))),and(i1,i2)) = or(and(i1,i2),and(not(not(i1)),not(and(i1,i2)))),
inference(transitivity,[status(thm)],[61,138]) ).
tff(140,plain,
or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),not(or(not(i2),and(i1,i2)))) = or(or(and(i1,i2),and(not(not(i1)),not(and(i1,i2)))),and(not(not(i2)),not(and(i1,i2)))),
inference(monotonicity,[status(thm)],[139,67]) ).
tff(141,plain,
or(or(and(i1,i2),and(not(not(i1)),not(and(i1,i2)))),and(not(not(i2)),not(and(i1,i2)))) = or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),not(or(not(i2),and(i1,i2)))),
inference(symmetry,[status(thm)],[140]) ).
tff(142,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(143,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)],[142]) ).
tff(144,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(145,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(146,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) ),
inference(skolemize,[status(sab)],[146]) ).
tff(148,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) ),
inference(modus_ponens,[status(thm)],[147,143]) ).
tff(149,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) )
| ( or(or(and(i1,i2),and(not(not(i2)),not(and(i1,i2)))),and(not(not(i1)),not(and(i1,i2)))) = or(or(and(i1,i2),and(not(not(i1)),not(and(i1,i2)))),and(not(not(i2)),not(and(i1,i2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(150,plain,
or(or(and(i1,i2),and(not(not(i2)),not(and(i1,i2)))),and(not(not(i1)),not(and(i1,i2)))) = or(or(and(i1,i2),and(not(not(i1)),not(and(i1,i2)))),and(not(not(i2)),not(and(i1,i2)))),
inference(unit_resolution,[status(thm)],[149,148]) ).
tff(151,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(i1,i2),not(or(not(i2),and(i1,i2)))) = or(not(or(not(i2),and(i1,i2))),and(i1,i2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,plain,
or(and(i1,i2),not(or(not(i2),and(i1,i2)))) = or(not(or(not(i2),and(i1,i2))),and(i1,i2)),
inference(unit_resolution,[status(thm)],[151,58]) ).
tff(153,plain,
or(and(i1,i2),and(not(not(i2)),not(and(i1,i2)))) = or(and(i1,i2),not(or(not(i2),and(i1,i2)))),
inference(monotonicity,[status(thm)],[68]) ).
tff(154,plain,
or(and(i1,i2),and(not(not(i2)),not(and(i1,i2)))) = or(not(or(not(i2),and(i1,i2))),and(i1,i2)),
inference(transitivity,[status(thm)],[153,152]) ).
tff(155,plain,
or(or(and(i1,i2),and(not(not(i2)),not(and(i1,i2)))),and(not(not(i1)),not(and(i1,i2)))) = or(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(not(not(i1)),not(and(i1,i2)))),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
or(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(not(not(i1)),not(and(i1,i2)))) = or(or(and(i1,i2),and(not(not(i2)),not(and(i1,i2)))),and(not(not(i1)),not(and(i1,i2)))),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(not(not(i1)),not(and(i1,i2)))) = or(and(not(not(i1)),not(and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
or(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(not(not(i1)),not(and(i1,i2)))) = or(and(not(not(i1)),not(and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),
inference(unit_resolution,[status(thm)],[157,58]) ).
tff(159,plain,
or(and(not(not(i1)),not(and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))) = or(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(not(not(i1)),not(and(i1,i2)))),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
or(and(not(not(i1)),not(and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))) = or(not(or(not(i1),and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),
inference(monotonicity,[status(thm)],[136]) ).
tff(161,plain,
or(not(or(not(i1),and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))) = or(and(not(not(i1)),not(and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
or(not(or(not(i1),and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))) = or(and(not(not(i2)),not(and(i1,i2))),or(not(or(not(i1),and(i1,i2))),and(i1,i2))),
inference(transitivity,[status(thm)],[161,159,156,150,141,135,133]) ).
tff(163,plain,
and(or(not(or(not(i1),and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),or(not(i2),and(i1,i2))) = and(or(and(not(not(i2)),not(and(i1,i2))),or(not(or(not(i1),and(i1,i2))),and(i1,i2))),or(not(i2),and(i1,i2))),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
or(and(i1,i2),not(or(not(i2),and(i1,i2)))) = or(and(i1,i2),and(not(not(i2)),not(and(i1,i2)))),
inference(symmetry,[status(thm)],[153]) ).
tff(165,plain,
or(not(or(not(i2),and(i1,i2))),and(i1,i2)) = or(and(i1,i2),not(or(not(i2),and(i1,i2)))),
inference(symmetry,[status(thm)],[152]) ).
tff(166,plain,
or(not(or(not(i2),and(i1,i2))),and(i1,i2)) = or(and(i1,i2),and(not(not(i2)),not(and(i1,i2)))),
inference(transitivity,[status(thm)],[165,164]) ).
tff(167,plain,
or(not(or(not(i1),and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))) = or(and(not(not(i1)),not(and(i1,i2))),or(and(i1,i2),and(not(not(i2)),not(and(i1,i2))))),
inference(monotonicity,[status(thm)],[29,166]) ).
tff(168,plain,
or(and(not(not(i1)),not(and(i1,i2))),or(and(i1,i2),and(not(not(i2)),not(and(i1,i2))))) = or(not(or(not(i1),and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),
inference(symmetry,[status(thm)],[167]) ).
tff(169,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(170,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)],[169]) ).
tff(171,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(172,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(173,plain,
! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) ),
inference(skolemize,[status(sab)],[173]) ).
tff(175,plain,
! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[174,170]) ).
tff(176,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) )
| ( or(and(not(not(i1)),not(and(i1,i2))),or(and(i1,i2),and(not(not(i2)),not(and(i1,i2))))) = or(or(and(not(not(i1)),not(and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(177,plain,
or(and(not(not(i1)),not(and(i1,i2))),or(and(i1,i2),and(not(not(i2)),not(and(i1,i2))))) = or(or(and(not(not(i1)),not(and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))),
inference(unit_resolution,[status(thm)],[176,175]) ).
tff(178,plain,
or(or(and(not(not(i1)),not(and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))) = or(and(not(not(i1)),not(and(i1,i2))),or(and(i1,i2),and(not(not(i2)),not(and(i1,i2))))),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(or(X,Z),Y) )
| ( or(or(and(not(not(i1)),not(and(i1,i2))),and(not(not(i2)),not(and(i1,i2)))),and(i1,i2)) = or(or(and(not(not(i1)),not(and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(180,plain,
or(or(and(not(not(i1)),not(and(i1,i2))),and(not(not(i2)),not(and(i1,i2)))),and(i1,i2)) = or(or(and(not(not(i1)),not(and(i1,i2))),and(i1,i2)),and(not(not(i2)),not(and(i1,i2)))),
inference(unit_resolution,[status(thm)],[179,148]) ).
tff(181,plain,
^ [Y: $i,X: $i] :
refl(
( ( or(or(X,Y),Y) = or(X,Y) )
<=> ( or(or(X,Y),Y) = or(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(182,plain,
( ! [Y: $i,X: $i] : ( or(or(X,Y),Y) = or(X,Y) )
<=> ! [Y: $i,X: $i] : ( or(or(X,Y),Y) = or(X,Y) ) ),
inference(quant_intro,[status(thm)],[181]) ).
tff(183,plain,
( ! [Y: $i,X: $i] : ( or(or(X,Y),Y) = or(X,Y) )
<=> ! [Y: $i,X: $i] : ( or(or(X,Y),Y) = or(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(184,axiom,
! [Y: $i,X: $i] : ( or(or(X,Y),Y) = or(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_simplification2) ).
tff(185,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),Y) = or(X,Y) ),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),Y) = or(X,Y) ),
inference(skolemize,[status(sab)],[185]) ).
tff(187,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),Y) = or(X,Y) ),
inference(modus_ponens,[status(thm)],[186,182]) ).
tff(188,plain,
( ~ ! [Y: $i,X: $i] : ( or(or(X,Y),Y) = or(X,Y) )
| ( or(or(or(and(not(not(i1)),not(and(i1,i2))),and(not(not(i2)),not(and(i1,i2)))),and(i1,i2)),and(i1,i2)) = or(or(and(not(not(i1)),not(and(i1,i2))),and(not(not(i2)),not(and(i1,i2)))),and(i1,i2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(189,plain,
or(or(or(and(not(not(i1)),not(and(i1,i2))),and(not(not(i2)),not(and(i1,i2)))),and(i1,i2)),and(i1,i2)) = or(or(and(not(not(i1)),not(and(i1,i2))),and(not(not(i2)),not(and(i1,i2)))),and(i1,i2)),
inference(unit_resolution,[status(thm)],[188,187]) ).
tff(190,plain,
or(or(and(not(not(i1)),not(and(i1,i2))),and(not(not(i2)),not(and(i1,i2)))),and(i1,i2)) = or(and(not(not(i1)),not(and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),
inference(transitivity,[status(thm)],[180,178,168,161]) ).
tff(191,plain,
or(or(or(and(not(not(i1)),not(and(i1,i2))),and(not(not(i2)),not(and(i1,i2)))),and(i1,i2)),and(i1,i2)) = or(or(and(not(not(i1)),not(and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),and(i1,i2)),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
or(or(and(not(not(i1)),not(and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),and(i1,i2)) = or(or(or(and(not(not(i1)),not(and(i1,i2))),and(not(not(i2)),not(and(i1,i2)))),and(i1,i2)),and(i1,i2)),
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) )
| ( or(and(not(not(i1)),not(and(i1,i2))),or(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(i1,i2))) = or(or(and(not(not(i1)),not(and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),and(i1,i2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(194,plain,
or(and(not(not(i1)),not(and(i1,i2))),or(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(i1,i2))) = or(or(and(not(not(i1)),not(and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),and(i1,i2)),
inference(unit_resolution,[status(thm)],[193,175]) ).
tff(195,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(i1,i2)) = or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(196,plain,
or(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(i1,i2)) = or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),
inference(unit_resolution,[status(thm)],[195,58]) ).
tff(197,plain,
or(and(not(not(i1)),not(and(i1,i2))),or(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(i1,i2))) = or(not(or(not(i1),and(i1,i2))),or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),
inference(monotonicity,[status(thm)],[136,196]) ).
tff(198,plain,
or(not(or(not(i1),and(i1,i2))),or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))) = or(and(not(not(i1)),not(and(i1,i2))),or(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(i1,i2))),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(X,or(Y,Z)) = or(or(X,Y),Z) )
| ( or(not(or(not(i1),and(i1,i2))),or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))) = or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(200,plain,
or(not(or(not(i1),and(i1,i2))),or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))) = or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),
inference(unit_resolution,[status(thm)],[199,175]) ).
tff(201,plain,
or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))) = or(not(or(not(i1),and(i1,i2))),or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))) = or(not(or(not(i1),and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),
inference(transitivity,[status(thm)],[201,198,194,192,189,180,178,168]) ).
tff(203,plain,
and(or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),not(not(or(not(i2),and(i1,i2))))) = and(or(not(or(not(i1),and(i1,i2))),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),or(not(i2),and(i1,i2))),
inference(monotonicity,[status(thm)],[202,65]) ).
tff(204,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),not(not(or(not(i2),and(i1,i2))))) = and(not(not(or(not(i2),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(205,plain,
and(or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),not(not(or(not(i2),and(i1,i2))))) = and(not(not(or(not(i2),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),
inference(unit_resolution,[status(thm)],[204,37]) ).
tff(206,plain,
and(not(not(or(not(i2),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))) = and(or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),not(not(or(not(i2),and(i1,i2))))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
and(not(not(or(not(i2),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))) = i1,
inference(transitivity,[status(thm)],[206,203,163,130,121,63,61,51,9]) ).
tff(208,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X )
| ( or(and(i2,and(i1,i2)),and(i2,not(and(i1,i2)))) = i2 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(209,plain,
or(and(i2,and(i1,i2)),and(i2,not(and(i1,i2)))) = i2,
inference(unit_resolution,[status(thm)],[208,7]) ).
tff(210,plain,
and(i2,not(and(i1,i2))) = and(not(not(i2)),not(and(i1,i2))),
inference(monotonicity,[status(thm)],[85]) ).
tff(211,plain,
and(not(not(i2)),not(and(i1,i2))) = and(i2,not(and(i1,i2))),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
not(or(not(i2),and(i1,i2))) = and(i2,not(and(i1,i2))),
inference(transitivity,[status(thm)],[67,211]) ).
tff(213,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(and(i1,i2),i2) = and(i2,and(i1,i2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(214,plain,
and(and(i1,i2),i2) = and(i2,and(i1,i2)),
inference(unit_resolution,[status(thm)],[213,37]) ).
tff(215,plain,
^ [Y: $i,X: $i] :
refl(
( ( and(and(X,Y),Y) = and(X,Y) )
<=> ( and(and(X,Y),Y) = and(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(216,plain,
( ! [Y: $i,X: $i] : ( and(and(X,Y),Y) = and(X,Y) )
<=> ! [Y: $i,X: $i] : ( and(and(X,Y),Y) = and(X,Y) ) ),
inference(quant_intro,[status(thm)],[215]) ).
tff(217,plain,
( ! [Y: $i,X: $i] : ( and(and(X,Y),Y) = and(X,Y) )
<=> ! [Y: $i,X: $i] : ( and(and(X,Y),Y) = and(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(218,axiom,
! [Y: $i,X: $i] : ( and(and(X,Y),Y) = and(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_simplification2) ).
tff(219,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),Y) = and(X,Y) ),
inference(modus_ponens,[status(thm)],[218,217]) ).
tff(220,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),Y) = and(X,Y) ),
inference(skolemize,[status(sab)],[219]) ).
tff(221,plain,
! [Y: $i,X: $i] : ( and(and(X,Y),Y) = and(X,Y) ),
inference(modus_ponens,[status(thm)],[220,216]) ).
tff(222,plain,
( ~ ! [Y: $i,X: $i] : ( and(and(X,Y),Y) = and(X,Y) )
| ( and(and(i1,i2),i2) = and(i1,i2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(223,plain,
and(and(i1,i2),i2) = and(i1,i2),
inference(unit_resolution,[status(thm)],[222,221]) ).
tff(224,plain,
and(i1,i2) = and(and(i1,i2),i2),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
and(i1,i2) = and(i2,and(i1,i2)),
inference(transitivity,[status(thm)],[224,214]) ).
tff(226,plain,
or(and(i1,i2),not(or(not(i2),and(i1,i2)))) = or(and(i2,and(i1,i2)),and(i2,not(and(i1,i2)))),
inference(monotonicity,[status(thm)],[225,212]) ).
tff(227,plain,
( ~ ! [Y: $i,X: $i] : ( or(and(X,Y),and(X,not(Y))) = X )
| ( or(and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(not(not(i1)),not(and(i1,i2)))),and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),not(and(not(not(i1)),not(and(i1,i2)))))) = or(not(or(not(i2),and(i1,i2))),and(i1,i2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(228,plain,
or(and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(not(not(i1)),not(and(i1,i2)))),and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),not(and(not(not(i1)),not(and(i1,i2)))))) = or(not(or(not(i2),and(i1,i2))),and(i1,i2)),
inference(unit_resolution,[status(thm)],[227,7]) ).
tff(229,plain,
( ~ ! [X: $i] : ( not(not(X)) = X )
| ( not(not(or(not(i1),and(i1,i2)))) = or(not(i1),and(i1,i2)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(230,plain,
not(not(or(not(i1),and(i1,i2)))) = or(not(i1),and(i1,i2)),
inference(unit_resolution,[status(thm)],[229,15]) ).
tff(231,plain,
not(and(not(not(i1)),not(and(i1,i2)))) = not(not(or(not(i1),and(i1,i2)))),
inference(monotonicity,[status(thm)],[136]) ).
tff(232,plain,
not(and(not(not(i1)),not(and(i1,i2)))) = or(not(i1),and(i1,i2)),
inference(transitivity,[status(thm)],[231,230]) ).
tff(233,plain,
and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),not(and(not(not(i1)),not(and(i1,i2))))) = and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),or(not(i1),and(i1,i2))),
inference(monotonicity,[status(thm)],[232]) ).
tff(234,plain,
and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),or(not(i1),and(i1,i2))) = and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),not(and(not(not(i1)),not(and(i1,i2))))),
inference(symmetry,[status(thm)],[233]) ).
tff(235,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(236,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)],[235]) ).
tff(237,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(238,axiom,
! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_simplification3) ).
tff(239,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) ),
inference(modus_ponens,[status(thm)],[238,237]) ).
tff(240,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) ),
inference(skolemize,[status(sab)],[239]) ).
tff(241,plain,
! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) ),
inference(modus_ponens,[status(thm)],[240,236]) ).
tff(242,plain,
( ~ ! [Y: $i,X: $i] : ( or(or(X,Y),X) = or(X,Y) )
| ( or(or(and(i1,i2),and(not(not(i2)),not(and(i1,i2)))),and(i1,i2)) = or(and(i1,i2),and(not(not(i2)),not(and(i1,i2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(243,plain,
or(or(and(i1,i2),and(not(not(i2)),not(and(i1,i2)))),and(i1,i2)) = or(and(i1,i2),and(not(not(i2)),not(and(i1,i2)))),
inference(unit_resolution,[status(thm)],[242,241]) ).
tff(244,plain,
or(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(i1,i2)) = or(or(and(i1,i2),and(not(not(i2)),not(and(i1,i2)))),and(i1,i2)),
inference(monotonicity,[status(thm)],[166]) ).
tff(245,plain,
or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2))) = or(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(i1,i2)),
inference(symmetry,[status(thm)],[196]) ).
tff(246,plain,
or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2))) = or(not(or(not(i2),and(i1,i2))),and(i1,i2)),
inference(transitivity,[status(thm)],[245,244,243,153,152]) ).
tff(247,plain,
and(or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),or(not(i1),and(i1,i2))) = and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),or(not(i1),and(i1,i2))),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
and(or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),or(not(i1),and(i1,i2))) = and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),not(and(not(not(i1)),not(and(i1,i2))))),
inference(transitivity,[status(thm)],[247,234]) ).
tff(249,plain,
and(i1,or(not(i1),not(i2))) = and(not(not(i1)),not(and(i1,i2))),
inference(monotonicity,[status(thm)],[18,82]) ).
tff(250,plain,
and(not(not(i1)),not(and(i1,i2))) = and(i1,or(not(i1),not(i2))),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
or(not(or(not(i2),and(i1,i2))),and(i1,i2)) = i2,
inference(transitivity,[status(thm)],[165,226,209]) ).
tff(252,plain,
and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(not(not(i1)),not(and(i1,i2)))) = and(i2,and(i1,or(not(i1),not(i2)))),
inference(monotonicity,[status(thm)],[251,250]) ).
tff(253,plain,
and(i2,and(i1,or(not(i1),not(i2)))) = and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(not(not(i1)),not(and(i1,i2)))),
inference(symmetry,[status(thm)],[252]) ).
tff(254,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(255,plain,
and(i2,and(i1,or(not(i1),not(i2)))) = and(and(i2,i1),or(not(i1),not(i2))),
inference(unit_resolution,[status(thm)],[254,97]) ).
tff(256,plain,
and(and(i2,i1),or(not(i1),not(i2))) = and(i2,and(i1,or(not(i1),not(i2)))),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(i2,i1) = and(i1,i2) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(258,plain,
and(i2,i1) = and(i1,i2),
inference(unit_resolution,[status(thm)],[257,37]) ).
tff(259,plain,
and(and(i2,i1),or(not(i1),not(i2))) = and(and(i1,i2),not(and(i1,i2))),
inference(monotonicity,[status(thm)],[258,82]) ).
tff(260,plain,
and(and(i1,i2),not(and(i1,i2))) = and(and(i2,i1),or(not(i1),not(i2))),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
( ~ ! [X: $i] : ( and(X,not(X)) = not(n1) )
| ( and(not(or(not(i1),and(i1,i2))),not(not(or(not(i1),and(i1,i2))))) = not(n1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(262,plain,
and(not(or(not(i1),and(i1,i2))),not(not(or(not(i1),and(i1,i2))))) = not(n1),
inference(unit_resolution,[status(thm)],[261,112]) ).
tff(263,plain,
or(not(i1),and(i1,i2)) = not(not(or(not(i1),and(i1,i2)))),
inference(symmetry,[status(thm)],[230]) ).
tff(264,plain,
and(and(not(not(i1)),not(and(i1,i2))),or(not(i1),and(i1,i2))) = and(not(or(not(i1),and(i1,i2))),not(not(or(not(i1),and(i1,i2))))),
inference(monotonicity,[status(thm)],[136,263]) ).
tff(265,plain,
and(and(not(not(i1)),not(and(i1,i2))),or(not(i1),and(i1,i2))) = and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(not(not(i1)),not(and(i1,i2)))),
inference(transitivity,[status(thm)],[264,262,115,260,256,253]) ).
tff(266,plain,
or(and(and(not(not(i1)),not(and(i1,i2))),or(not(i1),and(i1,i2))),and(or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),or(not(i1),and(i1,i2)))) = or(and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),and(not(not(i1)),not(and(i1,i2)))),and(or(not(or(not(i2),and(i1,i2))),and(i1,i2)),not(and(not(not(i1)),not(and(i1,i2)))))),
inference(monotonicity,[status(thm)],[265,248]) ).
tff(267,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( and(or(X,Y),Z) = or(and(X,Z),and(Y,Z)) )
| ( and(or(and(not(not(i1)),not(and(i1,i2))),or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),or(not(i1),and(i1,i2))) = or(and(and(not(not(i1)),not(and(i1,i2))),or(not(i1),and(i1,i2))),and(or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),or(not(i1),and(i1,i2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(268,plain,
and(or(and(not(not(i1)),not(and(i1,i2))),or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),or(not(i1),and(i1,i2))) = or(and(and(not(not(i1)),not(and(i1,i2))),or(not(i1),and(i1,i2))),and(or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),or(not(i1),and(i1,i2)))),
inference(unit_resolution,[status(thm)],[267,128]) ).
tff(269,plain,
or(and(not(not(i1)),not(and(i1,i2))),or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))) = or(not(or(not(i1),and(i1,i2))),or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),
inference(monotonicity,[status(thm)],[136]) ).
tff(270,plain,
or(not(or(not(i1),and(i1,i2))),or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))) = or(and(not(not(i1)),not(and(i1,i2))),or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),
inference(symmetry,[status(thm)],[269]) ).
tff(271,plain,
or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))) = or(and(not(not(i1)),not(and(i1,i2))),or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),
inference(transitivity,[status(thm)],[201,270]) ).
tff(272,plain,
and(or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),not(not(or(not(i1),and(i1,i2))))) = and(or(and(not(not(i1)),not(and(i1,i2))),or(and(i1,i2),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),or(not(i1),and(i1,i2))),
inference(monotonicity,[status(thm)],[271,230]) ).
tff(273,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),not(not(or(not(i1),and(i1,i2))))) = and(not(not(or(not(i1),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(274,plain,
and(or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),not(not(or(not(i1),and(i1,i2))))) = and(not(not(or(not(i1),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),
inference(unit_resolution,[status(thm)],[273,37]) ).
tff(275,plain,
and(not(not(or(not(i1),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))) = and(or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))),not(not(or(not(i1),and(i1,i2))))),
inference(symmetry,[status(thm)],[274]) ).
tff(276,plain,
and(not(not(or(not(i1),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))) = i2,
inference(transitivity,[status(thm)],[275,272,268,266,228,165,226,209]) ).
tff(277,plain,
output(and(not(not(or(not(i1),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),and(not(not(or(not(i2),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))))) = output(i2,i1),
inference(monotonicity,[status(thm)],[276,207]) ).
tff(278,plain,
( circuit(input(i1,i2),output(and(not(not(or(not(i1),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),and(not(not(or(not(i2),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2))))))
<=> circuit(input(i1,i2),output(i2,i1)) ),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
( circuit(input(i1,i2),output(i2,i1))
<=> circuit(input(i1,i2),output(and(not(not(or(not(i1),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),and(not(not(or(not(i2),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))))) ),
inference(symmetry,[status(thm)],[278]) ).
tff(280,plain,
( ~ circuit(input(i1,i2),output(i2,i1))
<=> ~ circuit(input(i1,i2),output(and(not(not(or(not(i1),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),and(not(not(or(not(i2),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))))) ),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
( ~ circuit(input(i1,i2),output(i2,i1))
<=> ~ circuit(input(i1,i2),output(i2,i1)) ),
inference(rewrite,[status(thm)],]) ).
tff(282,axiom,
~ circuit(input(i1,i2),output(i2,i1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_interchange) ).
tff(283,plain,
~ circuit(input(i1,i2),output(i2,i1)),
inference(modus_ponens,[status(thm)],[282,281]) ).
tff(284,plain,
~ circuit(input(i1,i2),output(and(not(not(or(not(i1),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),and(not(not(or(not(i2),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))))),
inference(modus_ponens,[status(thm)],[283,280]) ).
tff(285,plain,
( circuit(input(i1,i2),output(a1,a2))
<=> circuit(input(i1,i2),output(and(not(not(or(not(i1),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),and(not(not(or(not(i2),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))))) ),
inference(rewrite,[status(thm)],]) ).
tff(286,plain,
( circuit(input(i1,i2),output(a1,a2))
<=> circuit(input(i1,i2),output(a1,a2)) ),
inference(rewrite,[status(thm)],]) ).
tff(287,axiom,
circuit(input(i1,i2),output(a1,a2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',circuit_description) ).
tff(288,plain,
circuit(input(i1,i2),output(a1,a2)),
inference(modus_ponens,[status(thm)],[287,286]) ).
tff(289,plain,
circuit(input(i1,i2),output(and(not(not(or(not(i1),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))),and(not(not(or(not(i2),and(i1,i2)))),or(or(not(or(not(i1),and(i1,i2))),and(i1,i2)),or(not(or(not(i2),and(i1,i2))),and(i1,i2)))))),
inference(modus_ponens,[status(thm)],[288,285]) ).
tff(290,plain,
$false,
inference(unit_resolution,[status(thm)],[289,284]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : HWV001-1 : TPTP v8.1.0. Released v1.1.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 22:07:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.10/0.98 % SZS status Unsatisfiable
% 1.10/0.98 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------