TSTP Solution File: LCL153-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL153-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 : Sun Sep 18 04:55:06 EDT 2022
% Result : Unsatisfiable 10.53s 7.08s
% Output : Proof 10.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 77
% Syntax : Number of formulae : 329 ( 261 unt; 7 typ; 0 def)
% Number of atoms : 399 ( 390 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 117 ( 48 ~; 44 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 228 ( 212 !; 0 ?; 228 :)
% Comments :
%------------------------------------------------------------------------------
tff(xor_type,type,
xor: ( $i * $i ) > $i ).
tff(truth_type,type,
truth: $i ).
tff(x_type,type,
x: $i ).
tff(not_type,type,
not: $i > $i ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(and_type,type,
and: ( $i * $i ) > $i ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) )
<=> ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) )
<=> ! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) )
<=> ! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',xor_definition) ).
tff(5,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) )
| ( xor(x,truth) = or(and(x,not(truth)),and(not(x),truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
xor(x,truth) = or(and(x,not(truth)),and(not(x),truth)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
or(and(x,not(truth)),and(not(x),truth)) = xor(x,truth),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [Y: $i,X: $i] :
refl(
( ( or(X,Y) = implies(not(X),Y) )
<=> ( or(X,Y) = implies(not(X),Y) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
<=> ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
<=> ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_definition) ).
tff(15,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(and(x,not(truth)),and(not(x),truth)) = implies(not(and(x,not(truth))),and(not(x),truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
or(and(x,not(truth)),and(not(x),truth)) = implies(not(and(x,not(truth))),and(not(x),truth)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
implies(not(and(x,not(truth))),and(not(x),truth)) = or(and(x,not(truth)),and(not(x),truth)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [X: $i] :
refl(
( ( implies(truth,X) = X )
<=> ( implies(truth,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X: $i] : ( implies(truth,X) = X )
<=> ! [X: $i] : ( implies(truth,X) = X ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] : ( implies(truth,X) = X )
<=> ! [X: $i] : ( implies(truth,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [X: $i] : ( implies(truth,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
tff(25,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,or(not(x),not(not(truth)))) = or(not(x),not(not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
implies(truth,or(not(x),not(not(truth)))) = or(not(x),not(not(truth))),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,not(not(truth))) = not(not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(unit_resolution,[status(thm)],[30,27]) ).
tff(32,plain,
not(not(truth)) = implies(truth,not(not(truth))),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(x),not(not(truth))) = implies(not(not(x)),not(not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
or(not(x),not(not(truth))) = implies(not(not(x)),not(not(truth))),
inference(unit_resolution,[status(thm)],[33,17]) ).
tff(35,plain,
implies(or(not(x),not(not(truth))),not(not(truth))) = implies(implies(not(not(x)),not(not(truth))),not(not(truth))),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
implies(implies(not(not(x)),not(not(truth))),not(not(truth))) = implies(or(not(x),not(not(truth))),not(not(truth))),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
^ [Y: $i,X: $i] :
refl(
( ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
<=> ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
<=> ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
<=> ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
tff(41,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(not(not(truth)),not(not(x))),not(not(x))) = implies(implies(not(not(x)),not(not(truth))),not(not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
implies(implies(not(not(truth)),not(not(x))),not(not(x))) = implies(implies(not(not(x)),not(not(truth))),not(not(truth))),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,not(not(x))) = not(not(x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
implies(truth,not(not(x))) = not(not(x)),
inference(unit_resolution,[status(thm)],[46,27]) ).
tff(48,plain,
not(not(x)) = implies(truth,not(not(x))),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(not(x)),not(truth)) = implies(not(not(not(x))),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
or(not(not(x)),not(truth)) = implies(not(not(not(x))),not(truth)),
inference(unit_resolution,[status(thm)],[49,17]) ).
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/Axioms/LCL001-2.ax',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(truth),not(not(x))) = or(not(not(x)),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
or(not(truth),not(not(x))) = or(not(not(x)),not(truth)),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(truth),not(not(x))) = implies(not(not(truth)),not(not(x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
or(not(truth),not(not(x))) = implies(not(not(truth)),not(not(x))),
inference(unit_resolution,[status(thm)],[60,17]) ).
tff(62,plain,
implies(not(not(truth)),not(not(x))) = or(not(truth),not(not(x))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
implies(not(not(truth)),not(not(x))) = implies(not(not(not(x))),not(truth)),
inference(transitivity,[status(thm)],[62,59,50]) ).
tff(64,plain,
implies(implies(not(not(truth)),not(not(x))),not(not(x))) = implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))),
inference(monotonicity,[status(thm)],[63,48]) ).
tff(65,plain,
implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))) = implies(implies(not(not(truth)),not(not(x))),not(not(x))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
^ [Y: $i,X: $i] :
refl(
( ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
<=> ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
<=> ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
<=> ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,axiom,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).
tff(70,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))) = truth,
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
truth = implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
truth = implies(or(not(x),not(not(truth))),not(not(truth))),
inference(transitivity,[status(thm)],[75,65,45,36]) ).
tff(77,plain,
implies(truth,not(not(truth))) = implies(implies(or(not(x),not(not(truth))),not(not(truth))),implies(truth,not(not(truth)))),
inference(monotonicity,[status(thm)],[76,32]) ).
tff(78,plain,
implies(implies(or(not(x),not(not(truth))),not(not(truth))),implies(truth,not(not(truth)))) = implies(truth,not(not(truth))),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
implies(implies(or(not(x),not(not(truth))),not(not(truth))),implies(truth,not(not(truth)))) = implies(implies(or(not(x),not(not(truth))),not(not(truth))),not(not(truth))),
inference(monotonicity,[status(thm)],[31]) ).
tff(80,plain,
implies(implies(or(not(x),not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(or(not(x),not(not(truth))),not(not(truth))),implies(truth,not(not(truth)))),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(or(not(x),not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
implies(implies(or(not(x),not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))),
inference(unit_resolution,[status(thm)],[81,43]) ).
tff(83,plain,
implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))) = implies(implies(or(not(x),not(not(truth))),not(not(truth))),not(not(truth))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))) = not(not(truth)),
inference(transitivity,[status(thm)],[83,80,78,31]) ).
tff(85,plain,
implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))) = implies(truth,not(not(truth))),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
implies(truth,not(not(truth))) = implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
<=> ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
<=> ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
<=> ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,axiom,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
tff(91,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth),implies(implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth),implies(implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))))) = truth,
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
implies(not(not(x)),not(not(truth))) = or(not(x),not(not(truth))),
inference(symmetry,[status(thm)],[34]) ).
tff(97,plain,
implies(or(not(not(x)),not(truth)),not(not(x))) = implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))),
inference(monotonicity,[status(thm)],[50,48]) ).
tff(98,plain,
implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))) = implies(or(not(not(x)),not(truth)),not(not(x))),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
truth = implies(or(not(not(x)),not(truth)),not(not(x))),
inference(transitivity,[status(thm)],[75,98]) ).
tff(100,plain,
implies(truth,not(not(x))) = implies(implies(or(not(not(x)),not(truth)),not(not(x))),implies(truth,not(not(x)))),
inference(monotonicity,[status(thm)],[99,48]) ).
tff(101,plain,
implies(implies(or(not(not(x)),not(truth)),not(not(x))),implies(truth,not(not(x)))) = implies(truth,not(not(x))),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
implies(implies(or(not(not(x)),not(truth)),not(not(x))),implies(truth,not(not(x)))) = implies(implies(or(not(not(x)),not(truth)),not(not(x))),not(not(x))),
inference(monotonicity,[status(thm)],[47]) ).
tff(103,plain,
implies(implies(or(not(not(x)),not(truth)),not(not(x))),not(not(x))) = implies(implies(or(not(not(x)),not(truth)),not(not(x))),implies(truth,not(not(x)))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(or(not(not(x)),not(truth)),not(not(x))),not(not(x))) = implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
implies(implies(or(not(not(x)),not(truth)),not(not(x))),not(not(x))) = implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),
inference(unit_resolution,[status(thm)],[104,43]) ).
tff(106,plain,
implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))) = implies(implies(or(not(not(x)),not(truth)),not(not(x))),not(not(x))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))) = not(not(x)),
inference(transitivity,[status(thm)],[106,103,101,47]) ).
tff(108,plain,
implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))) = implies(not(not(x)),not(not(truth))),
inference(monotonicity,[status(thm)],[107,84]) ).
tff(109,plain,
implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))) = or(not(x),not(not(truth))),
inference(transitivity,[status(thm)],[108,96]) ).
tff(110,plain,
implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))) = not(not(truth)),
inference(transitivity,[status(thm)],[85,31]) ).
tff(111,plain,
implies(implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))))) = implies(not(not(truth)),or(not(x),not(not(truth)))),
inference(monotonicity,[status(thm)],[110,109]) ).
tff(112,plain,
implies(not(not(truth)),or(not(x),not(not(truth)))) = implies(implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))))),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth) = implies(not(not(x)),truth),
inference(monotonicity,[status(thm)],[107]) ).
tff(114,plain,
implies(not(not(x)),truth) = implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))) = implies(not(not(x)),not(not(truth))),
inference(monotonicity,[status(thm)],[107]) ).
tff(116,plain,
implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth)))) = implies(implies(not(not(x)),not(not(truth))),not(not(truth))),
inference(monotonicity,[status(thm)],[115,31]) ).
tff(117,plain,
implies(implies(not(not(x)),not(not(truth))),not(not(truth))) = implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth)))),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
truth = implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth)))),
inference(transitivity,[status(thm)],[75,65,45,117]) ).
tff(119,plain,
implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))) = implies(truth,not(not(x))),
inference(monotonicity,[status(thm)],[107]) ).
tff(120,plain,
implies(truth,not(not(x))) = implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
not(not(x)) = implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),
inference(transitivity,[status(thm)],[48,120]) ).
tff(122,plain,
implies(not(not(x)),truth) = implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth))))),
inference(monotonicity,[status(thm)],[121,118]) ).
tff(123,plain,
implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth))))) = implies(not(not(x)),truth),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth))))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth))))) = truth,
inference(unit_resolution,[status(thm)],[124,93]) ).
tff(126,plain,
truth = implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth))))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
truth = implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth),
inference(transitivity,[status(thm)],[126,123,114]) ).
tff(128,plain,
implies(truth,implies(not(not(truth)),or(not(x),not(not(truth))))) = implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth),implies(implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))))),
inference(monotonicity,[status(thm)],[127,112]) ).
tff(129,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(not(not(truth)),or(not(x),not(not(truth))))) = implies(not(not(truth)),or(not(x),not(not(truth)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
implies(truth,implies(not(not(truth)),or(not(x),not(not(truth))))) = implies(not(not(truth)),or(not(x),not(not(truth)))),
inference(unit_resolution,[status(thm)],[129,27]) ).
tff(131,plain,
implies(not(not(truth)),or(not(x),not(not(truth)))) = implies(truth,implies(not(not(truth)),or(not(x),not(not(truth))))),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
implies(not(not(truth)),or(not(x),not(not(truth)))) = truth,
inference(transitivity,[status(thm)],[131,128,95]) ).
tff(133,plain,
implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))) = implies(truth,or(not(x),not(not(truth)))),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
implies(truth,or(not(x),not(not(truth)))) = implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
or(not(x),not(not(truth))) = implies(truth,or(not(x),not(not(truth)))),
inference(symmetry,[status(thm)],[29]) ).
tff(136,plain,
or(not(x),not(not(truth))) = implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),
inference(transitivity,[status(thm)],[135,134,83,80,78,86]) ).
tff(137,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))),not(truth)) = implies(not(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
or(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))),not(truth)) = implies(not(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),not(truth)),
inference(unit_resolution,[status(thm)],[137,17]) ).
tff(139,plain,
implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))) = or(not(x),not(not(truth))),
inference(transitivity,[status(thm)],[133,29]) ).
tff(140,plain,
or(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))),not(truth)) = or(or(not(x),not(not(truth))),not(truth)),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
or(or(not(x),not(not(truth))),not(truth)) = or(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))),not(truth)),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(or(not(x),not(not(truth))),not(truth)) = or(not(truth),or(not(x),not(not(truth)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
or(or(not(x),not(not(truth))),not(truth)) = or(not(truth),or(not(x),not(not(truth)))),
inference(unit_resolution,[status(thm)],[142,57]) ).
tff(144,plain,
or(not(truth),or(not(x),not(not(truth)))) = or(or(not(x),not(not(truth))),not(truth)),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(truth),or(not(x),not(not(truth)))) = implies(not(not(truth)),or(not(x),not(not(truth)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(146,plain,
or(not(truth),or(not(x),not(not(truth)))) = implies(not(not(truth)),or(not(x),not(not(truth)))),
inference(unit_resolution,[status(thm)],[145,17]) ).
tff(147,plain,
implies(not(not(truth)),or(not(x),not(not(truth)))) = or(not(truth),or(not(x),not(not(truth)))),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth),implies(implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))))) = implies(truth,implies(not(not(truth)),or(not(x),not(not(truth))))),
inference(symmetry,[status(thm)],[128]) ).
tff(149,plain,
truth = implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth),implies(implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))))),
inference(symmetry,[status(thm)],[95]) ).
tff(150,plain,
truth = implies(not(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),not(truth)),
inference(transitivity,[status(thm)],[149,148,130,147,144,141,138]) ).
tff(151,plain,
implies(truth,or(not(x),not(not(truth)))) = implies(implies(not(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),not(truth)),implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))))),
inference(monotonicity,[status(thm)],[150,136]) ).
tff(152,plain,
implies(implies(not(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),not(truth)),implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))))) = implies(truth,or(not(x),not(not(truth)))),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),not(truth)),implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
implies(implies(not(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),not(truth)),implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))))) = truth,
inference(unit_resolution,[status(thm)],[153,72]) ).
tff(155,plain,
truth = implies(implies(not(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),not(truth)),implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))))),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
truth = or(not(x),not(not(truth))),
inference(transitivity,[status(thm)],[155,152,29]) ).
tff(157,plain,
not(truth) = not(or(not(x),not(not(truth)))),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
not(or(not(x),not(not(truth)))) = not(truth),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
^ [Y: $i,X: $i] :
refl(
( ( and(X,Y) = not(or(not(X),not(Y))) )
<=> ( and(X,Y) = not(or(not(X),not(Y))) ) )),
inference(bind,[status(th)],]) ).
tff(160,plain,
( ! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) )
<=> ! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,plain,
( ! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) )
<=> ! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(162,axiom,
! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',and_definition) ).
tff(163,plain,
! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ),
inference(skolemize,[status(sab)],[163]) ).
tff(165,plain,
! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ),
inference(modus_ponens,[status(thm)],[164,160]) ).
tff(166,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) )
| ( and(x,not(truth)) = not(or(not(x),not(not(truth)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(167,plain,
and(x,not(truth)) = not(or(not(x),not(not(truth)))),
inference(unit_resolution,[status(thm)],[166,165]) ).
tff(168,plain,
and(x,not(truth)) = not(truth),
inference(transitivity,[status(thm)],[167,158]) ).
tff(169,plain,
not(and(x,not(truth))) = not(not(truth)),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
not(not(truth)) = not(and(x,not(truth))),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
or(not(x),not(not(truth))) = not(and(x,not(truth))),
inference(transitivity,[status(thm)],[135,134,83,80,78,31,170]) ).
tff(172,plain,
implies(or(not(x),not(not(truth))),and(not(x),truth)) = implies(not(and(x,not(truth))),and(not(x),truth)),
inference(monotonicity,[status(thm)],[171]) ).
tff(173,plain,
implies(truth,and(not(x),truth)) = implies(or(not(x),not(not(truth))),and(not(x),truth)),
inference(monotonicity,[status(thm)],[156]) ).
tff(174,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,and(not(x),truth)) = and(not(x),truth) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(175,plain,
implies(truth,and(not(x),truth)) = and(not(x),truth),
inference(unit_resolution,[status(thm)],[174,27]) ).
tff(176,plain,
and(not(x),truth) = implies(truth,and(not(x),truth)),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) )
| ( and(not(x),truth) = not(or(not(not(x)),not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(178,plain,
and(not(x),truth) = not(or(not(not(x)),not(truth))),
inference(unit_resolution,[status(thm)],[177,165]) ).
tff(179,plain,
not(or(not(not(x)),not(truth))) = and(not(x),truth),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,or(not(not(x)),not(truth))) = or(not(not(x)),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(181,plain,
implies(truth,or(not(not(x)),not(truth))) = or(not(not(x)),not(truth)),
inference(unit_resolution,[status(thm)],[180,27]) ).
tff(182,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(not(not(truth)),truth),implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(not(not(truth)),implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(183,plain,
implies(implies(not(not(truth)),truth),implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(not(not(truth)),implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))))) = truth,
inference(unit_resolution,[status(thm)],[182,93]) ).
tff(184,plain,
implies(not(not(truth)),implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))) = implies(not(not(truth)),not(not(x))),
inference(monotonicity,[status(thm)],[107]) ).
tff(185,plain,
implies(not(not(truth)),implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))) = or(not(not(x)),not(truth)),
inference(transitivity,[status(thm)],[184,62,59]) ).
tff(186,plain,
implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))) = not(not(x)),
inference(transitivity,[status(thm)],[119,47]) ).
tff(187,plain,
implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(not(not(truth)),implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))))) = implies(not(not(x)),or(not(not(x)),not(truth))),
inference(monotonicity,[status(thm)],[186,185]) ).
tff(188,plain,
implies(not(not(x)),or(not(not(x)),not(truth))) = implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(not(not(truth)),implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))))),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
implies(implies(not(not(truth)),not(not(x))),implies(truth,not(not(x)))) = implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))),
inference(monotonicity,[status(thm)],[63]) ).
tff(190,plain,
implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))) = implies(implies(not(not(truth)),not(not(x))),implies(truth,not(not(x)))),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
truth = implies(implies(not(not(truth)),not(not(x))),implies(truth,not(not(x)))),
inference(transitivity,[status(thm)],[75,190]) ).
tff(192,plain,
implies(not(not(truth)),truth) = implies(implies(truth,not(not(truth))),implies(implies(not(not(truth)),not(not(x))),implies(truth,not(not(x))))),
inference(monotonicity,[status(thm)],[32,191]) ).
tff(193,plain,
implies(implies(truth,not(not(truth))),implies(implies(not(not(truth)),not(not(x))),implies(truth,not(not(x))))) = implies(not(not(truth)),truth),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,not(not(truth))),implies(implies(not(not(truth)),not(not(x))),implies(truth,not(not(x))))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(195,plain,
implies(implies(truth,not(not(truth))),implies(implies(not(not(truth)),not(not(x))),implies(truth,not(not(x))))) = truth,
inference(unit_resolution,[status(thm)],[194,93]) ).
tff(196,plain,
truth = implies(implies(truth,not(not(truth))),implies(implies(not(not(truth)),not(not(x))),implies(truth,not(not(x))))),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
truth = implies(not(not(truth)),truth),
inference(transitivity,[status(thm)],[196,193]) ).
tff(198,plain,
implies(truth,implies(not(not(x)),or(not(not(x)),not(truth)))) = implies(implies(not(not(truth)),truth),implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(not(not(truth)),implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))))),
inference(monotonicity,[status(thm)],[197,188]) ).
tff(199,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(not(not(x)),or(not(not(x)),not(truth)))) = implies(not(not(x)),or(not(not(x)),not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(200,plain,
implies(truth,implies(not(not(x)),or(not(not(x)),not(truth)))) = implies(not(not(x)),or(not(not(x)),not(truth))),
inference(unit_resolution,[status(thm)],[199,27]) ).
tff(201,plain,
implies(not(not(x)),or(not(not(x)),not(truth))) = implies(truth,implies(not(not(x)),or(not(not(x)),not(truth)))),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
implies(not(not(x)),or(not(not(x)),not(truth))) = truth,
inference(transitivity,[status(thm)],[201,198,183]) ).
tff(203,plain,
implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))) = implies(truth,or(not(not(x)),not(truth))),
inference(monotonicity,[status(thm)],[202]) ).
tff(204,plain,
implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))) = or(not(not(x)),not(truth)),
inference(transitivity,[status(thm)],[203,181]) ).
tff(205,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(and(not(x),truth),not(x)),implies(implies(not(x),not(truth)),implies(and(not(x),truth),not(truth)))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(206,plain,
implies(implies(and(not(x),truth),not(x)),implies(implies(not(x),not(truth)),implies(and(not(x),truth),not(truth)))) = truth,
inference(unit_resolution,[status(thm)],[205,93]) ).
tff(207,plain,
implies(not(not(not(x))),not(truth)) = or(not(not(x)),not(truth)),
inference(symmetry,[status(thm)],[50]) ).
tff(208,plain,
not(not(x)) = or(not(not(x)),not(truth)),
inference(transitivity,[status(thm)],[48,100,102,105,203,181]) ).
tff(209,plain,
not(not(not(x))) = not(or(not(not(x)),not(truth))),
inference(monotonicity,[status(thm)],[208]) ).
tff(210,plain,
not(or(not(not(x)),not(truth))) = not(not(not(x))),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
and(not(x),truth) = not(not(not(x))),
inference(transitivity,[status(thm)],[178,210]) ).
tff(212,plain,
implies(and(not(x),truth),not(truth)) = implies(not(not(not(x))),not(truth)),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
implies(and(not(x),truth),not(truth)) = or(not(not(x)),not(truth)),
inference(transitivity,[status(thm)],[212,207]) ).
tff(214,plain,
implies(implies(not(x),not(truth)),implies(and(not(x),truth),not(truth))) = implies(implies(not(x),not(truth)),or(not(not(x)),not(truth))),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,plain,
implies(implies(not(x),not(truth)),or(not(not(x)),not(truth))) = implies(implies(not(x),not(truth)),implies(and(not(x),truth),not(truth))),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
implies(and(not(x),truth),not(x)) = implies(not(or(not(not(x)),not(truth))),not(x)),
inference(monotonicity,[status(thm)],[178]) ).
tff(217,plain,
implies(not(or(not(not(x)),not(truth))),not(x)) = implies(and(not(x),truth),not(x)),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(or(not(not(x)),not(truth)),not(x)) = implies(not(or(not(not(x)),not(truth))),not(x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(219,plain,
or(or(not(not(x)),not(truth)),not(x)) = implies(not(or(not(not(x)),not(truth))),not(x)),
inference(unit_resolution,[status(thm)],[218,17]) ).
tff(220,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(or(not(not(x)),not(truth)),not(x)) = or(not(x),or(not(not(x)),not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(221,plain,
or(or(not(not(x)),not(truth)),not(x)) = or(not(x),or(not(not(x)),not(truth))),
inference(unit_resolution,[status(thm)],[220,57]) ).
tff(222,plain,
or(not(x),or(not(not(x)),not(truth))) = or(or(not(not(x)),not(truth)),not(x)),
inference(symmetry,[status(thm)],[221]) ).
tff(223,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(x),or(not(not(x)),not(truth))) = implies(not(not(x)),or(not(not(x)),not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(224,plain,
or(not(x),or(not(not(x)),not(truth))) = implies(not(not(x)),or(not(not(x)),not(truth))),
inference(unit_resolution,[status(thm)],[223,17]) ).
tff(225,plain,
implies(not(not(x)),or(not(not(x)),not(truth))) = or(not(x),or(not(not(x)),not(truth))),
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
implies(implies(not(not(truth)),truth),implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(not(not(truth)),implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))))) = implies(truth,implies(not(not(x)),or(not(not(x)),not(truth)))),
inference(symmetry,[status(thm)],[198]) ).
tff(227,plain,
truth = implies(implies(not(not(truth)),truth),implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(not(not(truth)),implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))))),
inference(symmetry,[status(thm)],[183]) ).
tff(228,plain,
truth = implies(and(not(x),truth),not(x)),
inference(transitivity,[status(thm)],[227,226,200,225,222,219,217]) ).
tff(229,plain,
implies(truth,implies(implies(not(x),not(truth)),or(not(not(x)),not(truth)))) = implies(implies(and(not(x),truth),not(x)),implies(implies(not(x),not(truth)),implies(and(not(x),truth),not(truth)))),
inference(monotonicity,[status(thm)],[228,215]) ).
tff(230,plain,
implies(truth,or(not(not(x)),not(truth))) = implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),
inference(symmetry,[status(thm)],[203]) ).
tff(231,plain,
or(not(not(x)),not(truth)) = implies(truth,or(not(not(x)),not(truth))),
inference(symmetry,[status(thm)],[181]) ).
tff(232,plain,
or(not(not(x)),not(truth)) = not(not(x)),
inference(transitivity,[status(thm)],[231,230,106,103,101,47]) ).
tff(233,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,x) = x ) ),
inference(quant_inst,[status(thm)],]) ).
tff(234,plain,
implies(truth,x) = x,
inference(unit_resolution,[status(thm)],[233,27]) ).
tff(235,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(x),not(truth)),implies(truth,x)) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(236,plain,
implies(implies(not(x),not(truth)),implies(truth,x)) = truth,
inference(unit_resolution,[status(thm)],[235,72]) ).
tff(237,plain,
x = implies(truth,x),
inference(symmetry,[status(thm)],[234]) ).
tff(238,plain,
implies(implies(not(x),not(truth)),x) = implies(implies(not(x),not(truth)),implies(truth,x)),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
implies(implies(not(x),not(truth)),x) = truth,
inference(transitivity,[status(thm)],[238,236]) ).
tff(240,plain,
implies(implies(implies(not(x),not(truth)),x),implies(truth,x)) = implies(truth,x),
inference(monotonicity,[status(thm)],[239,234]) ).
tff(241,plain,
implies(implies(implies(not(x),not(truth)),x),x) = implies(implies(implies(not(x),not(truth)),x),implies(truth,x)),
inference(monotonicity,[status(thm)],[237]) ).
tff(242,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(implies(not(x),not(truth)),x),x) = implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(243,plain,
implies(implies(implies(not(x),not(truth)),x),x) = implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))),
inference(unit_resolution,[status(thm)],[242,43]) ).
tff(244,plain,
implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))) = implies(implies(implies(not(x),not(truth)),x),x),
inference(symmetry,[status(thm)],[243]) ).
tff(245,plain,
implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))) = x,
inference(transitivity,[status(thm)],[244,241,240,234]) ).
tff(246,plain,
or(not(x),not(not(truth))) = truth,
inference(transitivity,[status(thm)],[135,151,154]) ).
tff(247,plain,
implies(or(not(x),not(not(truth))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))) = implies(truth,x),
inference(monotonicity,[status(thm)],[246,245]) ).
tff(248,plain,
implies(implies(implies(not(x),not(truth)),x),implies(truth,x)) = implies(implies(implies(not(x),not(truth)),x),x),
inference(symmetry,[status(thm)],[241]) ).
tff(249,plain,
implies(truth,x) = implies(implies(implies(not(x),not(truth)),x),implies(truth,x)),
inference(symmetry,[status(thm)],[240]) ).
tff(250,plain,
x = implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))),
inference(transitivity,[status(thm)],[237,249,248,243]) ).
tff(251,plain,
not(not(truth)) = or(not(x),not(not(truth))),
inference(transitivity,[status(thm)],[32,77,79,82,133,29]) ).
tff(252,plain,
implies(not(not(truth)),x) = implies(or(not(x),not(not(truth))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),
inference(monotonicity,[status(thm)],[251,250]) ).
tff(253,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(truth),x) = implies(not(not(truth)),x) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(254,plain,
or(not(truth),x) = implies(not(not(truth)),x),
inference(unit_resolution,[status(thm)],[253,17]) ).
tff(255,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(truth),x) = or(x,not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(256,plain,
or(not(truth),x) = or(x,not(truth)),
inference(unit_resolution,[status(thm)],[255,57]) ).
tff(257,plain,
or(x,not(truth)) = or(not(truth),x),
inference(symmetry,[status(thm)],[256]) ).
tff(258,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(x,not(truth)) = implies(not(x),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(259,plain,
or(x,not(truth)) = implies(not(x),not(truth)),
inference(unit_resolution,[status(thm)],[258,17]) ).
tff(260,plain,
implies(not(x),not(truth)) = or(x,not(truth)),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
implies(not(x),not(truth)) = x,
inference(transitivity,[status(thm)],[260,257,254,252,247,234]) ).
tff(262,plain,
implies(implies(not(x),not(truth)),or(not(not(x)),not(truth))) = implies(x,not(not(x))),
inference(monotonicity,[status(thm)],[261,232]) ).
tff(263,plain,
implies(x,not(not(x))) = implies(implies(not(x),not(truth)),or(not(not(x)),not(truth))),
inference(symmetry,[status(thm)],[262]) ).
tff(264,plain,
implies(truth,implies(x,not(not(x)))) = implies(truth,implies(implies(not(x),not(truth)),or(not(not(x)),not(truth)))),
inference(monotonicity,[status(thm)],[263]) ).
tff(265,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(x,not(not(x)))) = implies(x,not(not(x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(266,plain,
implies(truth,implies(x,not(not(x)))) = implies(x,not(not(x))),
inference(unit_resolution,[status(thm)],[265,27]) ).
tff(267,plain,
implies(x,not(not(x))) = implies(truth,implies(x,not(not(x)))),
inference(symmetry,[status(thm)],[266]) ).
tff(268,plain,
implies(x,not(not(x))) = truth,
inference(transitivity,[status(thm)],[267,264,229,206]) ).
tff(269,plain,
implies(implies(x,not(not(x))),implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))) = implies(truth,or(not(not(x)),not(truth))),
inference(monotonicity,[status(thm)],[268,204]) ).
tff(270,plain,
implies(implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))),or(not(not(x)),not(truth))) = implies(x,not(not(x))),
inference(monotonicity,[status(thm)],[245,232]) ).
tff(271,plain,
implies(implies(implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))),or(not(not(x)),not(truth))),implies(truth,or(not(not(x)),not(truth)))) = implies(implies(x,not(not(x))),implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),
inference(monotonicity,[status(thm)],[270,230]) ).
tff(272,plain,
implies(implies(implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))) = implies(implies(implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))),or(not(not(x)),not(truth))),implies(truth,or(not(not(x)),not(truth)))),
inference(monotonicity,[status(thm)],[231]) ).
tff(273,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))) = implies(implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(274,plain,
implies(implies(implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))) = implies(implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),
inference(unit_resolution,[status(thm)],[273,43]) ).
tff(275,plain,
implies(implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))) = implies(implies(implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),
inference(symmetry,[status(thm)],[274]) ).
tff(276,plain,
implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))) = implies(or(not(not(x)),not(truth)),x),
inference(monotonicity,[status(thm)],[245]) ).
tff(277,plain,
implies(or(not(not(x)),not(truth)),x) = implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
or(not(not(x)),not(truth)) = implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),
inference(transitivity,[status(thm)],[231,230]) ).
tff(279,plain,
implies(or(not(not(x)),not(truth)),x) = implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),x),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),x) = implies(or(not(not(x)),not(truth)),x),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),x) = implies(not(not(x)),x),
inference(monotonicity,[status(thm)],[107]) ).
tff(282,plain,
implies(not(not(x)),x) = implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),x),
inference(symmetry,[status(thm)],[281]) ).
tff(283,plain,
implies(not(not(x)),x) = implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),
inference(transitivity,[status(thm)],[282,280,277]) ).
tff(284,plain,
implies(implies(not(not(x)),x),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))) = implies(implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),
inference(monotonicity,[status(thm)],[283]) ).
tff(285,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(not(not(x)),x)) = implies(not(not(x)),x) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(286,plain,
implies(truth,implies(not(not(x)),x)) = implies(not(not(x)),x),
inference(unit_resolution,[status(thm)],[285,27]) ).
tff(287,plain,
implies(not(not(x)),x) = implies(or(not(not(x)),not(truth)),x),
inference(transitivity,[status(thm)],[282,280]) ).
tff(288,plain,
implies(truth,implies(not(not(x)),x)) = implies(truth,implies(or(not(not(x)),not(truth)),x)),
inference(monotonicity,[status(thm)],[287]) ).
tff(289,plain,
implies(truth,implies(or(not(not(x)),not(truth)),x)) = implies(truth,implies(not(not(x)),x)),
inference(symmetry,[status(thm)],[288]) ).
tff(290,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,implies(not(x),not(truth))),implies(implies(implies(not(x),not(truth)),x),implies(truth,x))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(291,plain,
implies(implies(truth,implies(not(x),not(truth))),implies(implies(implies(not(x),not(truth)),x),implies(truth,x))) = truth,
inference(unit_resolution,[status(thm)],[290,93]) ).
tff(292,plain,
implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))) = implies(implies(implies(not(x),not(truth)),x),implies(truth,x)),
inference(transitivity,[status(thm)],[244,241]) ).
tff(293,plain,
implies(implies(truth,implies(not(x),not(truth))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))) = implies(implies(truth,implies(not(x),not(truth))),implies(implies(implies(not(x),not(truth)),x),implies(truth,x))),
inference(monotonicity,[status(thm)],[292]) ).
tff(294,plain,
implies(implies(truth,implies(not(x),not(truth))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))) = truth,
inference(transitivity,[status(thm)],[293,291]) ).
tff(295,plain,
implies(implies(implies(truth,implies(not(x),not(truth))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))))) = implies(truth,implies(or(not(not(x)),not(truth)),x)),
inference(monotonicity,[status(thm)],[294,276]) ).
tff(296,plain,
implies(truth,implies(or(not(not(x)),not(truth)),x)) = implies(implies(implies(truth,implies(not(x),not(truth))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))))),
inference(symmetry,[status(thm)],[295]) ).
tff(297,plain,
implies(not(not(x)),x) = implies(truth,implies(not(not(x)),x)),
inference(symmetry,[status(thm)],[286]) ).
tff(298,plain,
implies(or(not(not(x)),not(truth)),x) = implies(implies(implies(truth,implies(not(x),not(truth))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth))))),
inference(transitivity,[status(thm)],[279,281,297,288,296]) ).
tff(299,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(not(x),not(truth))) = implies(not(x),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(300,plain,
implies(truth,implies(not(x),not(truth))) = implies(not(x),not(truth)),
inference(unit_resolution,[status(thm)],[299,27]) ).
tff(301,plain,
or(not(not(x)),not(truth)) = or(not(truth),not(not(x))),
inference(symmetry,[status(thm)],[59]) ).
tff(302,plain,
or(not(not(x)),not(truth)) = implies(not(not(truth)),not(not(x))),
inference(transitivity,[status(thm)],[301,61]) ).
tff(303,plain,
implies(or(not(not(x)),not(truth)),implies(truth,implies(not(x),not(truth)))) = implies(implies(not(not(truth)),not(not(x))),implies(not(x),not(truth))),
inference(monotonicity,[status(thm)],[302,300]) ).
tff(304,plain,
implies(implies(not(not(truth)),not(not(x))),implies(not(x),not(truth))) = implies(or(not(not(x)),not(truth)),implies(truth,implies(not(x),not(truth)))),
inference(symmetry,[status(thm)],[303]) ).
tff(305,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(not(truth)),not(not(x))),implies(not(x),not(truth))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(306,plain,
implies(implies(not(not(truth)),not(not(x))),implies(not(x),not(truth))) = truth,
inference(unit_resolution,[status(thm)],[305,72]) ).
tff(307,plain,
truth = implies(implies(not(not(truth)),not(not(x))),implies(not(x),not(truth))),
inference(symmetry,[status(thm)],[306]) ).
tff(308,plain,
truth = implies(or(not(not(x)),not(truth)),implies(truth,implies(not(x),not(truth)))),
inference(transitivity,[status(thm)],[307,304]) ).
tff(309,plain,
implies(truth,implies(or(not(not(x)),not(truth)),x)) = implies(implies(or(not(not(x)),not(truth)),implies(truth,implies(not(x),not(truth)))),implies(implies(implies(truth,implies(not(x),not(truth))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))))),
inference(monotonicity,[status(thm)],[308,298]) ).
tff(310,plain,
implies(implies(or(not(not(x)),not(truth)),implies(truth,implies(not(x),not(truth)))),implies(implies(implies(truth,implies(not(x),not(truth))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))))) = implies(truth,implies(or(not(not(x)),not(truth)),x)),
inference(symmetry,[status(thm)],[309]) ).
tff(311,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(or(not(not(x)),not(truth)),implies(truth,implies(not(x),not(truth)))),implies(implies(implies(truth,implies(not(x),not(truth))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(312,plain,
implies(implies(or(not(not(x)),not(truth)),implies(truth,implies(not(x),not(truth)))),implies(implies(implies(truth,implies(not(x),not(truth))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))))) = truth,
inference(unit_resolution,[status(thm)],[311,93]) ).
tff(313,plain,
truth = implies(implies(or(not(not(x)),not(truth)),implies(truth,implies(not(x),not(truth)))),implies(implies(implies(truth,implies(not(x),not(truth))),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),implies(or(not(not(x)),not(truth)),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))))),
inference(symmetry,[status(thm)],[312]) ).
tff(314,plain,
truth = implies(not(not(x)),x),
inference(transitivity,[status(thm)],[313,310,289,286]) ).
tff(315,plain,
implies(truth,x) = implies(implies(not(not(x)),x),implies(implies(x,implies(not(x),not(truth))),implies(not(x),not(truth)))),
inference(monotonicity,[status(thm)],[314,250]) ).
tff(316,plain,
x = or(not(not(x)),not(truth)),
inference(transitivity,[status(thm)],[237,315,284,275,272,271,269,181]) ).
tff(317,plain,
not(x) = not(or(not(not(x)),not(truth))),
inference(monotonicity,[status(thm)],[316]) ).
tff(318,plain,
not(x) = xor(x,truth),
inference(transitivity,[status(thm)],[317,179,176,173,172,20,10]) ).
tff(319,plain,
( ( not(x) != xor(x,truth) )
<=> ( not(x) != xor(x,truth) ) ),
inference(rewrite,[status(thm)],]) ).
tff(320,axiom,
not(x) != xor(x,truth),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
tff(321,plain,
not(x) != xor(x,truth),
inference(modus_ponens,[status(thm)],[320,319]) ).
tff(322,plain,
$false,
inference(unit_resolution,[status(thm)],[321,318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : LCL153-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 18:18:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 10.53/7.08 % SZS status Unsatisfiable
% 10.53/7.08 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------