%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL153-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 02:59:23 PM UTC 2026
% Result : Unsatisfiable 101.56s 101.87s
% Output : Proof 101.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 122
% Syntax : Number of formulae : 516 ( 407 unt; 0 typ; 0 def)
% Number of atoms : 647 ( 635 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 209 ( 89 ~; 85 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 373 ( 350 !; 0 ?; 373 :)
% 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(falsehood_type,type,
falsehood: $i ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( xor(X,Y) = xor(Y,X) )
<=> ( xor(X,Y) = xor(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
<=> ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
<=> ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',xor_commutativity) ).
tff(5,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(truth,x) = xor(x,truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
xor(truth,x) = xor(x,truth),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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(14,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) )
| ( xor(truth,x) = or(and(truth,not(x)),and(not(truth),x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
xor(truth,x) = or(and(truth,not(x)),and(not(truth),x)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
or(and(truth,not(x)),and(not(truth),x)) = xor(truth,x),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [Y: $i,X: $i] :
refl(( ( and(X,Y) = and(Y,X) )
<=> ( and(X,Y) = and(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(21,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)],[20]) ).
tff(22,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(23,axiom,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',and_commutativity) ).
tff(24,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(falsehood,x) = and(x,falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
and(falsehood,x) = and(x,falsehood),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( ( not(truth) = falsehood )
<=> ( not(truth) = falsehood ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',false_definition) ).
tff(31,plain,
not(truth) = falsehood,
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
and(not(truth),x) = and(falsehood,x),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
and(not(truth),x) = and(x,falsehood),
inference(transitivity,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(truth,not(x)) = and(not(x),truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
and(truth,not(x)) = and(not(x),truth),
inference(unit_resolution,[status(thm)],[34,26]) ).
tff(36,plain,
or(and(truth,not(x)),and(not(truth),x)) = or(and(not(x),truth),and(x,falsehood)),
inference(monotonicity,[status(thm)],[35,33]) ).
tff(37,plain,
or(and(not(x),truth),and(x,falsehood)) = or(and(truth,not(x)),and(not(truth),x)),
inference(symmetry,[status(thm)],[36]) ).
tff(38,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(39,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)],[38]) ).
tff(40,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(41,axiom,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_definition) ).
tff(42,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(and(not(x),truth),and(x,falsehood)) = implies(not(and(not(x),truth)),and(x,falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
or(and(not(x),truth),and(x,falsehood)) = implies(not(and(not(x),truth)),and(x,falsehood)),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
implies(not(and(not(x),truth)),and(x,falsehood)) = or(and(not(x),truth),and(x,falsehood)),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
^ [X: $i] :
refl(( ( implies(truth,X) = X )
<=> ( implies(truth,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [X: $i] : ( implies(truth,X) = X )
<=> ! [X: $i] : ( implies(truth,X) = X ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X: $i] : ( implies(truth,X) = X )
<=> ! [X: $i] : ( implies(truth,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
! [X: $i] : ( implies(truth,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
tff(52,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,falsehood) = falsehood ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
implies(truth,falsehood) = falsehood,
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
falsehood = implies(truth,falsehood),
inference(symmetry,[status(thm)],[56]) ).
tff(58,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(59,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)],[58]) ).
tff(60,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(61,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(62,plain,
! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) )
| ( and(x,falsehood) = not(or(not(x),not(falsehood))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
and(x,falsehood) = not(or(not(x),not(falsehood))),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
implies(and(x,falsehood),falsehood) = implies(not(or(not(x),not(falsehood))),falsehood),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
implies(not(or(not(x),not(falsehood))),falsehood) = implies(and(x,falsehood),falsehood),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(or(not(x),not(falsehood)),falsehood) = implies(not(or(not(x),not(falsehood))),falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
or(or(not(x),not(falsehood)),falsehood) = implies(not(or(not(x),not(falsehood))),falsehood),
inference(unit_resolution,[status(thm)],[69,44]) ).
tff(71,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( or(or(X,Y),Z) = or(X,or(Y,Z)) )
<=> ( or(or(X,Y),Z) = or(X,or(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,axiom,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_associativity) ).
tff(75,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) )
| ( or(or(not(x),not(falsehood)),falsehood) = or(not(x),or(not(falsehood),falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
or(or(not(x),not(falsehood)),falsehood) = or(not(x),or(not(falsehood),falsehood)),
inference(unit_resolution,[status(thm)],[78,77]) ).
tff(80,plain,
or(not(x),or(not(falsehood),falsehood)) = or(or(not(x),not(falsehood)),falsehood),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,truth) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
implies(truth,truth) = truth,
inference(unit_resolution,[status(thm)],[81,54]) ).
tff(83,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(84,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)],[83]) ).
tff(85,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(86,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(87,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,truth),implies(implies(truth,falsehood),implies(truth,falsehood))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
implies(implies(truth,truth),implies(implies(truth,falsehood),implies(truth,falsehood))) = truth,
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[31]) ).
tff(93,plain,
implies(truth,falsehood) = not(truth),
inference(transitivity,[status(thm)],[56,92]) ).
tff(94,plain,
implies(implies(truth,falsehood),implies(truth,falsehood)) = implies(not(truth),not(truth)),
inference(monotonicity,[status(thm)],[93,93]) ).
tff(95,plain,
implies(not(truth),not(truth)) = implies(implies(truth,falsehood),implies(truth,falsehood)),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
implies(not(truth),not(truth)) = implies(not(truth),falsehood),
inference(monotonicity,[status(thm)],[31]) ).
tff(97,plain,
implies(not(truth),falsehood) = implies(not(truth),not(truth)),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
implies(not(truth),falsehood) = implies(implies(truth,falsehood),implies(truth,falsehood)),
inference(transitivity,[status(thm)],[97,95]) ).
tff(99,plain,
truth = implies(truth,truth),
inference(symmetry,[status(thm)],[82]) ).
tff(100,plain,
implies(truth,implies(not(truth),falsehood)) = implies(implies(truth,truth),implies(implies(truth,falsehood),implies(truth,falsehood))),
inference(monotonicity,[status(thm)],[99,98]) ).
tff(101,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(not(truth),falsehood)) = implies(not(truth),falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
implies(truth,implies(not(truth),falsehood)) = implies(not(truth),falsehood),
inference(unit_resolution,[status(thm)],[101,54]) ).
tff(103,plain,
implies(not(truth),falsehood) = implies(truth,implies(not(truth),falsehood)),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(truth,falsehood) = implies(not(truth),falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
or(truth,falsehood) = implies(not(truth),falsehood),
inference(unit_resolution,[status(thm)],[104,44]) ).
tff(106,plain,
^ [Y: $i,X: $i] :
refl(( ( or(X,Y) = or(Y,X) )
<=> ( or(X,Y) = or(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(107,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)],[106]) ).
tff(108,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(109,axiom,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_commutativity) ).
tff(110,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(falsehood,truth) = or(truth,falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
or(falsehood,truth) = or(truth,falsehood),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(falsehood,truth) = implies(not(falsehood),truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
or(falsehood,truth) = implies(not(falsehood),truth),
inference(unit_resolution,[status(thm)],[115,44]) ).
tff(117,plain,
implies(not(falsehood),truth) = or(falsehood,truth),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
implies(not(falsehood),truth) = truth,
inference(transitivity,[status(thm)],[117,114,105,103,100,91]) ).
tff(119,plain,
implies(implies(not(falsehood),truth),truth) = implies(truth,truth),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,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(121,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)],[120]) ).
tff(122,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(123,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(124,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(not(falsehood),truth),truth) = implies(implies(truth,not(falsehood)),not(falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
implies(implies(not(falsehood),truth),truth) = implies(implies(truth,not(falsehood)),not(falsehood)),
inference(unit_resolution,[status(thm)],[127,126]) ).
tff(129,plain,
implies(implies(truth,not(falsehood)),not(falsehood)) = implies(implies(not(falsehood),truth),truth),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,not(falsehood)) = not(falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
implies(truth,not(falsehood)) = not(falsehood),
inference(unit_resolution,[status(thm)],[130,54]) ).
tff(132,plain,
not(falsehood) = implies(truth,not(falsehood)),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
implies(not(falsehood),not(falsehood)) = implies(implies(truth,not(falsehood)),not(falsehood)),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(falsehood,not(falsehood)) = implies(not(falsehood),not(falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(135,plain,
or(falsehood,not(falsehood)) = implies(not(falsehood),not(falsehood)),
inference(unit_resolution,[status(thm)],[134,44]) ).
tff(136,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(falsehood),falsehood) = or(falsehood,not(falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
or(not(falsehood),falsehood) = or(falsehood,not(falsehood)),
inference(unit_resolution,[status(thm)],[136,112]) ).
tff(138,plain,
or(not(falsehood),falsehood) = truth,
inference(transitivity,[status(thm)],[137,135,133,129,119,82]) ).
tff(139,plain,
or(not(x),or(not(falsehood),falsehood)) = or(not(x),truth),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
or(not(x),truth) = or(not(x),or(not(falsehood),falsehood)),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(x),truth) = or(truth,not(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
or(not(x),truth) = or(truth,not(x)),
inference(unit_resolution,[status(thm)],[141,112]) ).
tff(143,plain,
or(truth,not(x)) = or(not(x),truth),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(truth,not(x)) = implies(not(truth),not(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
or(truth,not(x)) = implies(not(truth),not(x)),
inference(unit_resolution,[status(thm)],[144,44]) ).
tff(146,plain,
implies(not(truth),not(x)) = or(truth,not(x)),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(not(truth),not(x))) = implies(not(truth),not(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
implies(truth,implies(not(truth),not(x))) = implies(not(truth),not(x)),
inference(unit_resolution,[status(thm)],[147,54]) ).
tff(149,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(x),truth) = implies(not(not(x)),truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
or(not(x),truth) = implies(not(not(x)),truth),
inference(unit_resolution,[status(thm)],[149,44]) ).
tff(151,plain,
implies(not(not(x)),truth) = or(not(x),truth),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
implies(not(not(x)),truth) = implies(not(truth),not(x)),
inference(transitivity,[status(thm)],[151,142,145]) ).
tff(153,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))) = truth,
inference(unit_resolution,[status(thm)],[153,89]) ).
tff(155,plain,
implies(implies(x,truth),implies(truth,truth)) = implies(implies(x,truth),truth),
inference(monotonicity,[status(thm)],[82]) ).
tff(156,plain,
implies(implies(x,truth),truth) = implies(implies(x,truth),implies(truth,truth)),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(x,truth),truth) = implies(implies(truth,x),x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(158,plain,
implies(implies(x,truth),truth) = implies(implies(truth,x),x),
inference(unit_resolution,[status(thm)],[157,126]) ).
tff(159,plain,
implies(implies(truth,x),x) = implies(implies(x,truth),truth),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,x) = x ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(161,plain,
implies(truth,x) = x,
inference(unit_resolution,[status(thm)],[160,54]) ).
tff(162,plain,
implies(implies(truth,x),x) = implies(x,x),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
implies(x,x) = implies(implies(truth,x),x),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
implies(x,x) = implies(implies(x,truth),implies(truth,truth)),
inference(transitivity,[status(thm)],[163,159,156]) ).
tff(165,plain,
implies(implies(truth,x),implies(x,x)) = implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(x,x)) = implies(x,x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
implies(truth,implies(x,x)) = implies(x,x),
inference(unit_resolution,[status(thm)],[166,54]) ).
tff(168,plain,
implies(implies(truth,x),implies(truth,x)) = implies(x,x),
inference(monotonicity,[status(thm)],[161,161]) ).
tff(169,plain,
implies(x,x) = implies(implies(truth,x),implies(truth,x)),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
implies(truth,implies(x,x)) = implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x))),
inference(monotonicity,[status(thm)],[99,169]) ).
tff(171,plain,
implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x))) = implies(truth,implies(x,x)),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x))) = truth,
inference(unit_resolution,[status(thm)],[172,89]) ).
tff(174,plain,
truth = implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x))),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
truth = implies(x,x),
inference(transitivity,[status(thm)],[174,171,167]) ).
tff(176,plain,
x = implies(truth,x),
inference(symmetry,[status(thm)],[161]) ).
tff(177,plain,
implies(x,truth) = implies(implies(truth,x),implies(x,x)),
inference(monotonicity,[status(thm)],[176,175]) ).
tff(178,plain,
implies(x,truth) = truth,
inference(transitivity,[status(thm)],[177,165,154]) ).
tff(179,plain,
implies(implies(x,truth),implies(not(not(x)),truth)) = implies(truth,implies(not(truth),not(x))),
inference(monotonicity,[status(thm)],[178,152]) ).
tff(180,plain,
implies(truth,implies(not(truth),not(x))) = implies(implies(x,truth),implies(not(not(x)),truth)),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
implies(not(truth),not(x)) = implies(truth,implies(not(truth),not(x))),
inference(symmetry,[status(thm)],[148]) ).
tff(182,plain,
implies(not(truth),not(x)) = implies(implies(x,truth),implies(not(not(x)),truth)),
inference(transitivity,[status(thm)],[181,180]) ).
tff(183,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(x),x) = implies(not(not(x)),x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
or(not(x),x) = implies(not(not(x)),x),
inference(unit_resolution,[status(thm)],[183,44]) ).
tff(185,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(x),x) = or(x,not(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(186,plain,
or(not(x),x) = or(x,not(x)),
inference(unit_resolution,[status(thm)],[185,112]) ).
tff(187,plain,
or(x,not(x)) = or(not(x),x),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(x,not(x)) = implies(not(x),not(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
or(x,not(x)) = implies(not(x),not(x)),
inference(unit_resolution,[status(thm)],[188,44]) ).
tff(190,plain,
implies(not(x),not(x)) = or(x,not(x)),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(not(x),not(x))) = implies(not(x),not(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
implies(truth,implies(not(x),not(x))) = implies(not(x),not(x)),
inference(unit_resolution,[status(thm)],[191,54]) ).
tff(193,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,not(x)) = not(x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(194,plain,
implies(truth,not(x)) = not(x),
inference(unit_resolution,[status(thm)],[193,54]) ).
tff(195,plain,
implies(implies(truth,not(x)),implies(truth,not(x))) = implies(not(x),not(x)),
inference(monotonicity,[status(thm)],[194,194]) ).
tff(196,plain,
implies(not(x),not(x)) = implies(implies(truth,not(x)),implies(truth,not(x))),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
implies(truth,implies(not(x),not(x))) = implies(implies(truth,truth),implies(implies(truth,not(x)),implies(truth,not(x)))),
inference(monotonicity,[status(thm)],[99,196]) ).
tff(198,plain,
implies(implies(truth,truth),implies(implies(truth,not(x)),implies(truth,not(x)))) = implies(truth,implies(not(x),not(x))),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,truth),implies(implies(truth,not(x)),implies(truth,not(x)))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(200,plain,
implies(implies(truth,truth),implies(implies(truth,not(x)),implies(truth,not(x)))) = truth,
inference(unit_resolution,[status(thm)],[199,89]) ).
tff(201,plain,
truth = implies(implies(truth,truth),implies(implies(truth,not(x)),implies(truth,not(x)))),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
truth = implies(not(not(x)),x),
inference(transitivity,[status(thm)],[201,198,192,190,187,184]) ).
tff(203,plain,
implies(truth,implies(not(truth),not(x))) = implies(implies(not(not(x)),x),implies(implies(x,truth),implies(not(not(x)),truth))),
inference(monotonicity,[status(thm)],[202,182]) ).
tff(204,plain,
implies(implies(not(not(x)),x),implies(implies(x,truth),implies(not(not(x)),truth))) = implies(truth,implies(not(truth),not(x))),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(not(not(x)),x),implies(implies(x,truth),implies(not(not(x)),truth))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(206,plain,
implies(implies(not(not(x)),x),implies(implies(x,truth),implies(not(not(x)),truth))) = truth,
inference(unit_resolution,[status(thm)],[205,89]) ).
tff(207,plain,
truth = implies(implies(not(not(x)),x),implies(implies(x,truth),implies(not(not(x)),truth))),
inference(symmetry,[status(thm)],[206]) ).
tff(208,plain,
truth = implies(and(x,falsehood),falsehood),
inference(transitivity,[status(thm)],[207,204,148,146,143,140,80,70,68]) ).
tff(209,plain,
implies(truth,falsehood) = implies(implies(and(x,falsehood),falsehood),implies(truth,falsehood)),
inference(monotonicity,[status(thm)],[208,57]) ).
tff(210,plain,
implies(implies(and(x,falsehood),falsehood),implies(truth,falsehood)) = implies(truth,falsehood),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
implies(implies(and(x,falsehood),falsehood),implies(truth,falsehood)) = implies(implies(and(x,falsehood),falsehood),falsehood),
inference(monotonicity,[status(thm)],[56]) ).
tff(212,plain,
implies(implies(and(x,falsehood),falsehood),falsehood) = implies(implies(and(x,falsehood),falsehood),implies(truth,falsehood)),
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(falsehood,and(x,falsehood)),and(x,falsehood)) = implies(implies(and(x,falsehood),falsehood),falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(214,plain,
implies(implies(falsehood,and(x,falsehood)),and(x,falsehood)) = implies(implies(and(x,falsehood),falsehood),falsehood),
inference(unit_resolution,[status(thm)],[213,126]) ).
tff(215,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,and(x,falsehood)) = and(x,falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
implies(truth,and(x,falsehood)) = and(x,falsehood),
inference(unit_resolution,[status(thm)],[215,54]) ).
tff(217,plain,
and(x,falsehood) = implies(truth,and(x,falsehood)),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
implies(implies(falsehood,and(x,falsehood)),and(x,falsehood)) = implies(implies(falsehood,and(x,falsehood)),implies(truth,and(x,falsehood))),
inference(monotonicity,[status(thm)],[217]) ).
tff(219,plain,
implies(implies(falsehood,and(x,falsehood)),implies(truth,and(x,falsehood))) = implies(implies(falsehood,and(x,falsehood)),and(x,falsehood)),
inference(symmetry,[status(thm)],[218]) ).
tff(220,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,not(and(x,not(truth)))),implies(implies(not(and(x,not(truth))),truth),implies(truth,truth))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(221,plain,
implies(implies(truth,not(and(x,not(truth)))),implies(implies(not(and(x,not(truth))),truth),implies(truth,truth))) = truth,
inference(unit_resolution,[status(thm)],[220,89]) ).
tff(222,plain,
truth = implies(not(x),not(x)),
inference(transitivity,[status(thm)],[201,198,192]) ).
tff(223,plain,
implies(implies(not(not(x)),not(not(x))),truth) = implies(implies(not(not(x)),not(not(x))),implies(not(x),not(x))),
inference(monotonicity,[status(thm)],[222]) ).
tff(224,plain,
implies(implies(not(not(x)),not(not(x))),implies(not(x),not(x))) = implies(implies(not(not(x)),not(not(x))),truth),
inference(symmetry,[status(thm)],[223]) ).
tff(225,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(226,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)],[225]) ).
tff(227,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(228,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(229,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(modus_ponens,[status(thm)],[228,227]) ).
tff(230,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(skolemize,[status(sab)],[229]) ).
tff(231,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(modus_ponens,[status(thm)],[230,226]) ).
tff(232,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(not(x)),not(not(x))),implies(not(x),not(x))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(233,plain,
implies(implies(not(not(x)),not(not(x))),implies(not(x),not(x))) = truth,
inference(unit_resolution,[status(thm)],[232,231]) ).
tff(234,plain,
truth = implies(implies(not(not(x)),not(not(x))),implies(not(x),not(x))),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
implies(truth,truth) = implies(implies(not(not(x)),not(not(x))),truth),
inference(transitivity,[status(thm)],[82,234,224]) ).
tff(236,plain,
implies(implies(not(and(x,not(truth))),truth),implies(truth,truth)) = implies(implies(not(and(x,not(truth))),truth),implies(implies(not(not(x)),not(not(x))),truth)),
inference(monotonicity,[status(thm)],[235]) ).
tff(237,plain,
implies(implies(not(and(x,not(truth))),truth),implies(implies(not(not(x)),not(not(x))),truth)) = implies(implies(not(and(x,not(truth))),truth),implies(truth,truth)),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
implies(implies(truth,x),implies(x,x)) = implies(x,truth),
inference(symmetry,[status(thm)],[177]) ).
tff(239,plain,
implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))) = implies(implies(truth,x),implies(x,x)),
inference(symmetry,[status(thm)],[165]) ).
tff(240,plain,
truth = implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))),
inference(symmetry,[status(thm)],[154]) ).
tff(241,plain,
truth = implies(x,truth),
inference(transitivity,[status(thm)],[240,239,238]) ).
tff(242,plain,
implies(implies(not(truth),not(x)),truth) = implies(implies(not(truth),not(x)),implies(x,truth)),
inference(monotonicity,[status(thm)],[241]) ).
tff(243,plain,
implies(implies(not(truth),not(x)),implies(x,truth)) = implies(implies(not(truth),not(x)),truth),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(truth),not(x)),implies(x,truth)) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(245,plain,
implies(implies(not(truth),not(x)),implies(x,truth)) = truth,
inference(unit_resolution,[status(thm)],[244,231]) ).
tff(246,plain,
truth = implies(implies(not(truth),not(x)),implies(x,truth)),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
implies(truth,truth) = implies(implies(not(truth),not(x)),truth),
inference(transitivity,[status(thm)],[82,246,243]) ).
tff(248,plain,
implies(implies(or(not(x),not(falsehood)),truth),implies(truth,truth)) = implies(implies(or(not(x),not(falsehood)),truth),implies(implies(not(truth),not(x)),truth)),
inference(monotonicity,[status(thm)],[247]) ).
tff(249,plain,
implies(implies(or(not(x),not(falsehood)),truth),implies(implies(not(truth),not(x)),truth)) = implies(implies(or(not(x),not(falsehood)),truth),implies(truth,truth)),
inference(symmetry,[status(thm)],[248]) ).
tff(250,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(not(x)),not(falsehood)),implies(falsehood,not(x))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(251,plain,
implies(implies(not(not(x)),not(falsehood)),implies(falsehood,not(x))) = truth,
inference(unit_resolution,[status(thm)],[250,231]) ).
tff(252,plain,
implies(falsehood,not(x)) = implies(not(truth),not(x)),
inference(monotonicity,[status(thm)],[92]) ).
tff(253,plain,
implies(not(truth),not(x)) = implies(falsehood,not(x)),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(x),not(falsehood)) = implies(not(not(x)),not(falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(255,plain,
or(not(x),not(falsehood)) = implies(not(not(x)),not(falsehood)),
inference(unit_resolution,[status(thm)],[254,44]) ).
tff(256,plain,
implies(or(not(x),not(falsehood)),implies(not(truth),not(x))) = implies(implies(not(not(x)),not(falsehood)),implies(falsehood,not(x))),
inference(monotonicity,[status(thm)],[255,253]) ).
tff(257,plain,
implies(or(not(x),not(falsehood)),implies(not(truth),not(x))) = truth,
inference(transitivity,[status(thm)],[256,251]) ).
tff(258,plain,
implies(implies(truth,implies(not(truth),not(x))),implies(or(not(x),not(falsehood)),implies(not(truth),not(x)))) = implies(implies(not(truth),not(x)),truth),
inference(monotonicity,[status(thm)],[148,257]) ).
tff(259,plain,
implies(implies(not(truth),not(x)),truth) = implies(implies(truth,implies(not(truth),not(x))),implies(or(not(x),not(falsehood)),implies(not(truth),not(x)))),
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
implies(implies(or(not(x),not(falsehood)),truth),implies(implies(not(truth),not(x)),truth)) = implies(implies(or(not(x),not(falsehood)),truth),implies(implies(truth,implies(not(truth),not(x))),implies(or(not(x),not(falsehood)),implies(not(truth),not(x))))),
inference(monotonicity,[status(thm)],[259]) ).
tff(261,plain,
implies(implies(or(not(x),not(falsehood)),truth),implies(implies(truth,implies(not(truth),not(x))),implies(or(not(x),not(falsehood)),implies(not(truth),not(x))))) = implies(implies(or(not(x),not(falsehood)),truth),implies(implies(not(truth),not(x)),truth)),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(or(not(x),not(falsehood)),truth),implies(implies(truth,implies(not(truth),not(x))),implies(or(not(x),not(falsehood)),implies(not(truth),not(x))))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(263,plain,
implies(implies(or(not(x),not(falsehood)),truth),implies(implies(truth,implies(not(truth),not(x))),implies(or(not(x),not(falsehood)),implies(not(truth),not(x))))) = truth,
inference(unit_resolution,[status(thm)],[262,89]) ).
tff(264,plain,
truth = implies(implies(or(not(x),not(falsehood)),truth),implies(implies(truth,implies(not(truth),not(x))),implies(or(not(x),not(falsehood)),implies(not(truth),not(x))))),
inference(symmetry,[status(thm)],[263]) ).
tff(265,plain,
truth = implies(implies(or(not(x),not(falsehood)),truth),implies(truth,truth)),
inference(transitivity,[status(thm)],[264,261,249]) ).
tff(266,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,or(not(x),not(falsehood))) = or(not(x),not(falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(267,plain,
implies(truth,or(not(x),not(falsehood))) = or(not(x),not(falsehood)),
inference(unit_resolution,[status(thm)],[266,54]) ).
tff(268,plain,
or(not(x),not(falsehood)) = implies(truth,or(not(x),not(falsehood))),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
implies(or(not(x),not(falsehood)),truth) = implies(implies(truth,or(not(x),not(falsehood))),implies(implies(or(not(x),not(falsehood)),truth),implies(truth,truth))),
inference(monotonicity,[status(thm)],[268,265]) ).
tff(270,plain,
implies(implies(truth,or(not(x),not(falsehood))),implies(implies(or(not(x),not(falsehood)),truth),implies(truth,truth))) = implies(or(not(x),not(falsehood)),truth),
inference(symmetry,[status(thm)],[269]) ).
tff(271,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,or(not(x),not(falsehood))),implies(implies(or(not(x),not(falsehood)),truth),implies(truth,truth))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(272,plain,
implies(implies(truth,or(not(x),not(falsehood))),implies(implies(or(not(x),not(falsehood)),truth),implies(truth,truth))) = truth,
inference(unit_resolution,[status(thm)],[271,89]) ).
tff(273,plain,
truth = implies(implies(truth,or(not(x),not(falsehood))),implies(implies(or(not(x),not(falsehood)),truth),implies(truth,truth))),
inference(symmetry,[status(thm)],[272]) ).
tff(274,plain,
implies(implies(not(not(x)),not(not(x))),truth) = implies(or(not(x),not(falsehood)),truth),
inference(transitivity,[status(thm)],[223,233,273,270]) ).
tff(275,plain,
not(or(not(x),not(falsehood))) = and(x,falsehood),
inference(symmetry,[status(thm)],[66]) ).
tff(276,plain,
implies(not(truth),not(or(not(x),not(falsehood)))) = implies(falsehood,and(x,falsehood)),
inference(monotonicity,[status(thm)],[31,275]) ).
tff(277,plain,
implies(falsehood,and(x,falsehood)) = implies(not(truth),not(or(not(x),not(falsehood)))),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
implies(falsehood,and(x,falsehood)) = implies(not(truth),and(x,falsehood)),
inference(monotonicity,[status(thm)],[92]) ).
tff(279,plain,
implies(not(truth),and(x,falsehood)) = implies(falsehood,and(x,falsehood)),
inference(symmetry,[status(thm)],[278]) ).
tff(280,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(truth,and(x,falsehood)) = implies(not(truth),and(x,falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(281,plain,
or(truth,and(x,falsehood)) = implies(not(truth),and(x,falsehood)),
inference(unit_resolution,[status(thm)],[280,44]) ).
tff(282,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(x,falsehood),truth) = or(truth,and(x,falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(283,plain,
or(and(x,falsehood),truth) = or(truth,and(x,falsehood)),
inference(unit_resolution,[status(thm)],[282,112]) ).
tff(284,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(and(x,falsehood),truth) = implies(not(and(x,falsehood)),truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(285,plain,
or(and(x,falsehood),truth) = implies(not(and(x,falsehood)),truth),
inference(unit_resolution,[status(thm)],[284,44]) ).
tff(286,plain,
implies(not(and(x,falsehood)),truth) = or(and(x,falsehood),truth),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
and(x,not(truth)) = and(x,falsehood),
inference(monotonicity,[status(thm)],[31]) ).
tff(288,plain,
and(x,falsehood) = and(x,not(truth)),
inference(symmetry,[status(thm)],[287]) ).
tff(289,plain,
not(and(x,falsehood)) = not(and(x,not(truth))),
inference(monotonicity,[status(thm)],[288]) ).
tff(290,plain,
implies(not(and(x,falsehood)),truth) = implies(not(and(x,not(truth))),truth),
inference(monotonicity,[status(thm)],[289]) ).
tff(291,plain,
implies(not(and(x,not(truth))),truth) = implies(not(and(x,falsehood)),truth),
inference(symmetry,[status(thm)],[290]) ).
tff(292,plain,
implies(not(and(x,not(truth))),truth) = implies(not(truth),not(or(not(x),not(falsehood)))),
inference(transitivity,[status(thm)],[291,286,283,281,279,277]) ).
tff(293,plain,
implies(implies(not(and(x,not(truth))),truth),implies(implies(not(not(x)),not(not(x))),truth)) = implies(implies(not(truth),not(or(not(x),not(falsehood)))),implies(or(not(x),not(falsehood)),truth)),
inference(monotonicity,[status(thm)],[292,274]) ).
tff(294,plain,
implies(implies(not(truth),not(or(not(x),not(falsehood)))),implies(or(not(x),not(falsehood)),truth)) = implies(implies(not(and(x,not(truth))),truth),implies(implies(not(not(x)),not(not(x))),truth)),
inference(symmetry,[status(thm)],[293]) ).
tff(295,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(truth),not(or(not(x),not(falsehood)))),implies(or(not(x),not(falsehood)),truth)) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(296,plain,
implies(implies(not(truth),not(or(not(x),not(falsehood)))),implies(or(not(x),not(falsehood)),truth)) = truth,
inference(unit_resolution,[status(thm)],[295,231]) ).
tff(297,plain,
truth = implies(implies(not(truth),not(or(not(x),not(falsehood)))),implies(or(not(x),not(falsehood)),truth)),
inference(symmetry,[status(thm)],[296]) ).
tff(298,plain,
truth = implies(implies(not(and(x,not(truth))),truth),implies(truth,truth)),
inference(transitivity,[status(thm)],[297,294,237]) ).
tff(299,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,not(and(x,not(truth)))) = not(and(x,not(truth))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(300,plain,
implies(truth,not(and(x,not(truth)))) = not(and(x,not(truth))),
inference(unit_resolution,[status(thm)],[299,54]) ).
tff(301,plain,
not(and(x,not(truth))) = implies(truth,not(and(x,not(truth)))),
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
implies(not(and(x,not(truth))),truth) = implies(implies(truth,not(and(x,not(truth)))),implies(implies(not(and(x,not(truth))),truth),implies(truth,truth))),
inference(monotonicity,[status(thm)],[301,298]) ).
tff(303,plain,
or(truth,and(x,falsehood)) = or(and(x,falsehood),truth),
inference(symmetry,[status(thm)],[283]) ).
tff(304,plain,
implies(not(truth),and(x,falsehood)) = or(truth,and(x,falsehood)),
inference(symmetry,[status(thm)],[281]) ).
tff(305,plain,
implies(falsehood,and(x,falsehood)) = truth,
inference(transitivity,[status(thm)],[278,304,303,285,290,302,221]) ).
tff(306,plain,
implies(implies(falsehood,and(x,falsehood)),implies(truth,and(x,falsehood))) = implies(truth,and(x,falsehood)),
inference(monotonicity,[status(thm)],[305,216]) ).
tff(307,plain,
implies(truth,and(x,falsehood)) = implies(implies(falsehood,and(x,falsehood)),implies(truth,and(x,falsehood))),
inference(symmetry,[status(thm)],[306]) ).
tff(308,plain,
and(x,falsehood) = falsehood,
inference(transitivity,[status(thm)],[217,307,219,214,212,210,56]) ).
tff(309,plain,
implies(not(and(not(x),truth)),and(x,falsehood)) = implies(not(and(not(x),truth)),falsehood),
inference(monotonicity,[status(thm)],[308]) ).
tff(310,plain,
implies(not(and(not(x),truth)),falsehood) = implies(not(and(not(x),truth)),and(x,falsehood)),
inference(symmetry,[status(thm)],[309]) ).
tff(311,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(and(not(x),truth),falsehood) = implies(not(and(not(x),truth)),falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(312,plain,
or(and(not(x),truth),falsehood) = implies(not(and(not(x),truth)),falsehood),
inference(unit_resolution,[status(thm)],[311,44]) ).
tff(313,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(not(x),truth),falsehood) = or(falsehood,and(not(x),truth)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(314,plain,
or(and(not(x),truth),falsehood) = or(falsehood,and(not(x),truth)),
inference(unit_resolution,[status(thm)],[313,112]) ).
tff(315,plain,
or(falsehood,and(not(x),truth)) = or(and(not(x),truth),falsehood),
inference(symmetry,[status(thm)],[314]) ).
tff(316,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(falsehood,and(not(x),truth)) = implies(not(falsehood),and(not(x),truth)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(317,plain,
or(falsehood,and(not(x),truth)) = implies(not(falsehood),and(not(x),truth)),
inference(unit_resolution,[status(thm)],[316,44]) ).
tff(318,plain,
implies(not(falsehood),and(not(x),truth)) = or(falsehood,and(not(x),truth)),
inference(symmetry,[status(thm)],[317]) ).
tff(319,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(320,plain,
and(not(x),truth) = not(or(not(not(x)),not(truth))),
inference(unit_resolution,[status(thm)],[319,64]) ).
tff(321,plain,
implies(not(falsehood),and(not(x),truth)) = implies(not(falsehood),not(or(not(not(x)),not(truth)))),
inference(monotonicity,[status(thm)],[320]) ).
tff(322,plain,
implies(not(falsehood),not(or(not(not(x)),not(truth)))) = implies(not(falsehood),and(not(x),truth)),
inference(symmetry,[status(thm)],[321]) ).
tff(323,plain,
not(or(not(not(x)),not(truth))) = and(not(x),truth),
inference(symmetry,[status(thm)],[320]) ).
tff(324,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(falsehood),not(truth)),implies(truth,falsehood)) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(325,plain,
implies(implies(not(falsehood),not(truth)),implies(truth,falsehood)) = truth,
inference(unit_resolution,[status(thm)],[324,231]) ).
tff(326,plain,
implies(not(falsehood),not(truth)) = implies(not(falsehood),falsehood),
inference(monotonicity,[status(thm)],[31]) ).
tff(327,plain,
implies(not(falsehood),falsehood) = implies(not(falsehood),not(truth)),
inference(symmetry,[status(thm)],[326]) ).
tff(328,plain,
implies(implies(not(falsehood),falsehood),implies(truth,falsehood)) = implies(implies(not(falsehood),not(truth)),implies(truth,falsehood)),
inference(monotonicity,[status(thm)],[327]) ).
tff(329,plain,
implies(implies(not(falsehood),falsehood),falsehood) = implies(implies(not(falsehood),falsehood),implies(truth,falsehood)),
inference(monotonicity,[status(thm)],[57]) ).
tff(330,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(not(falsehood),falsehood),falsehood) = implies(implies(falsehood,not(falsehood)),not(falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(331,plain,
implies(implies(not(falsehood),falsehood),falsehood) = implies(implies(falsehood,not(falsehood)),not(falsehood)),
inference(unit_resolution,[status(thm)],[330,126]) ).
tff(332,plain,
implies(implies(falsehood,not(falsehood)),not(falsehood)) = implies(implies(not(falsehood),falsehood),falsehood),
inference(symmetry,[status(thm)],[331]) ).
tff(333,plain,
implies(falsehood,not(falsehood)) = implies(not(truth),not(falsehood)),
inference(monotonicity,[status(thm)],[92]) ).
tff(334,plain,
implies(not(truth),not(falsehood)) = implies(falsehood,not(falsehood)),
inference(symmetry,[status(thm)],[333]) ).
tff(335,plain,
implies(implies(not(truth),not(falsehood)),not(falsehood)) = implies(implies(falsehood,not(falsehood)),not(falsehood)),
inference(monotonicity,[status(thm)],[334]) ).
tff(336,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(truth,not(falsehood)) = implies(not(truth),not(falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(337,plain,
or(truth,not(falsehood)) = implies(not(truth),not(falsehood)),
inference(unit_resolution,[status(thm)],[336,44]) ).
tff(338,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(falsehood),truth) = or(truth,not(falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(339,plain,
or(not(falsehood),truth) = or(truth,not(falsehood)),
inference(unit_resolution,[status(thm)],[338,112]) ).
tff(340,plain,
implies(not(x),not(x)) = implies(truth,implies(not(x),not(x))),
inference(symmetry,[status(thm)],[192]) ).
tff(341,plain,
or(not(x),x) = truth,
inference(transitivity,[status(thm)],[186,189,340,197,200]) ).
tff(342,plain,
or(not(falsehood),or(not(x),x)) = or(not(falsehood),truth),
inference(monotonicity,[status(thm)],[341]) ).
tff(343,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) )
| ( or(or(not(falsehood),not(x)),x) = or(not(falsehood),or(not(x),x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(344,plain,
or(or(not(falsehood),not(x)),x) = or(not(falsehood),or(not(x),x)),
inference(unit_resolution,[status(thm)],[343,77]) ).
tff(345,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(falsehood),not(x)) = or(not(x),not(falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(346,plain,
or(not(falsehood),not(x)) = or(not(x),not(falsehood)),
inference(unit_resolution,[status(thm)],[345,112]) ).
tff(347,plain,
or(not(x),not(falsehood)) = or(not(falsehood),not(x)),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
or(or(not(x),not(falsehood)),x) = or(or(not(falsehood),not(x)),x),
inference(monotonicity,[status(thm)],[347]) ).
tff(349,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(or(not(x),not(falsehood)),x) = implies(not(or(not(x),not(falsehood))),x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(350,plain,
or(or(not(x),not(falsehood)),x) = implies(not(or(not(x),not(falsehood))),x),
inference(unit_resolution,[status(thm)],[349,44]) ).
tff(351,plain,
implies(not(or(not(x),not(falsehood))),x) = or(or(not(x),not(falsehood)),x),
inference(symmetry,[status(thm)],[350]) ).
tff(352,plain,
implies(not(or(not(x),not(falsehood))),x) = implies(not(truth),not(falsehood)),
inference(transitivity,[status(thm)],[351,348,344,342,339,337]) ).
tff(353,plain,
implies(implies(not(or(not(x),not(falsehood))),x),not(falsehood)) = implies(implies(not(truth),not(falsehood)),not(falsehood)),
inference(monotonicity,[status(thm)],[352]) ).
tff(354,plain,
or(or(not(falsehood),not(x)),x) = or(or(not(x),not(falsehood)),x),
inference(symmetry,[status(thm)],[348]) ).
tff(355,plain,
or(not(falsehood),or(not(x),x)) = or(or(not(falsehood),not(x)),x),
inference(symmetry,[status(thm)],[344]) ).
tff(356,plain,
or(not(falsehood),truth) = or(not(falsehood),or(not(x),x)),
inference(symmetry,[status(thm)],[342]) ).
tff(357,plain,
or(truth,not(falsehood)) = or(not(falsehood),truth),
inference(symmetry,[status(thm)],[339]) ).
tff(358,plain,
implies(not(truth),falsehood) = or(truth,falsehood),
inference(symmetry,[status(thm)],[105]) ).
tff(359,plain,
implies(implies(truth,truth),implies(implies(truth,falsehood),implies(truth,falsehood))) = implies(truth,implies(not(truth),falsehood)),
inference(symmetry,[status(thm)],[100]) ).
tff(360,plain,
truth = implies(implies(truth,truth),implies(implies(truth,falsehood),implies(truth,falsehood))),
inference(symmetry,[status(thm)],[91]) ).
tff(361,plain,
truth = or(truth,falsehood),
inference(transitivity,[status(thm)],[360,359,102,358]) ).
tff(362,plain,
or(truth,not(falsehood)) = or(or(truth,falsehood),not(falsehood)),
inference(monotonicity,[status(thm)],[361]) ).
tff(363,plain,
or(or(truth,falsehood),not(falsehood)) = or(truth,not(falsehood)),
inference(symmetry,[status(thm)],[362]) ).
tff(364,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) )
| ( or(or(truth,falsehood),not(falsehood)) = or(truth,or(falsehood,not(falsehood))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(365,plain,
or(or(truth,falsehood),not(falsehood)) = or(truth,or(falsehood,not(falsehood))),
inference(unit_resolution,[status(thm)],[364,77]) ).
tff(366,plain,
or(truth,or(falsehood,not(falsehood))) = or(or(truth,falsehood),not(falsehood)),
inference(symmetry,[status(thm)],[365]) ).
tff(367,plain,
or(falsehood,not(falsehood)) = truth,
inference(transitivity,[status(thm)],[135,133,129,119,82]) ).
tff(368,plain,
or(truth,or(falsehood,not(falsehood))) = or(truth,truth),
inference(monotonicity,[status(thm)],[367]) ).
tff(369,plain,
or(truth,truth) = or(truth,or(falsehood,not(falsehood))),
inference(symmetry,[status(thm)],[368]) ).
tff(370,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(truth,truth) = implies(not(truth),truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(371,plain,
or(truth,truth) = implies(not(truth),truth),
inference(unit_resolution,[status(thm)],[370,44]) ).
tff(372,plain,
implies(not(truth),truth) = or(truth,truth),
inference(symmetry,[status(thm)],[371]) ).
tff(373,plain,
implies(not(truth),truth) = implies(falsehood,truth),
inference(monotonicity,[status(thm)],[31]) ).
tff(374,plain,
implies(falsehood,truth) = implies(not(truth),truth),
inference(symmetry,[status(thm)],[373]) ).
tff(375,plain,
implies(implies(falsehood,truth),implies(truth,truth)) = implies(implies(falsehood,truth),implies(implies(not(truth),not(x)),truth)),
inference(monotonicity,[status(thm)],[247]) ).
tff(376,plain,
implies(implies(falsehood,truth),implies(implies(not(truth),not(x)),truth)) = implies(implies(falsehood,truth),implies(truth,truth)),
inference(symmetry,[status(thm)],[375]) ).
tff(377,plain,
implies(implies(not(truth),not(x)),truth) = truth,
inference(transitivity,[status(thm)],[242,245]) ).
tff(378,plain,
implies(implies(falsehood,truth),implies(implies(not(truth),not(x)),truth)) = implies(implies(falsehood,truth),truth),
inference(monotonicity,[status(thm)],[377]) ).
tff(379,plain,
implies(implies(falsehood,truth),truth) = implies(implies(falsehood,truth),implies(implies(not(truth),not(x)),truth)),
inference(symmetry,[status(thm)],[378]) ).
tff(380,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(falsehood,truth),truth) = implies(implies(truth,falsehood),falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(381,plain,
implies(implies(falsehood,truth),truth) = implies(implies(truth,falsehood),falsehood),
inference(unit_resolution,[status(thm)],[380,126]) ).
tff(382,plain,
implies(implies(truth,falsehood),falsehood) = implies(implies(falsehood,truth),truth),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
implies(implies(truth,falsehood),falsehood) = implies(not(truth),not(truth)),
inference(monotonicity,[status(thm)],[93,92]) ).
tff(384,plain,
implies(not(truth),not(truth)) = implies(implies(truth,falsehood),falsehood),
inference(symmetry,[status(thm)],[383]) ).
tff(385,plain,
truth = implies(implies(falsehood,truth),implies(truth,truth)),
inference(transitivity,[status(thm)],[360,359,102,97,384,382,379,376]) ).
tff(386,plain,
implies(falsehood,truth) = implies(implies(truth,falsehood),implies(implies(falsehood,truth),implies(truth,truth))),
inference(monotonicity,[status(thm)],[57,385]) ).
tff(387,plain,
implies(implies(truth,falsehood),implies(implies(falsehood,truth),implies(truth,truth))) = implies(falsehood,truth),
inference(symmetry,[status(thm)],[386]) ).
tff(388,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,falsehood),implies(implies(falsehood,truth),implies(truth,truth))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(389,plain,
implies(implies(truth,falsehood),implies(implies(falsehood,truth),implies(truth,truth))) = truth,
inference(unit_resolution,[status(thm)],[388,89]) ).
tff(390,plain,
truth = implies(implies(truth,falsehood),implies(implies(falsehood,truth),implies(truth,truth))),
inference(symmetry,[status(thm)],[389]) ).
tff(391,plain,
truth = implies(not(or(not(x),not(falsehood))),x),
inference(transitivity,[status(thm)],[390,387,374,372,369,366,363,357,356,355,354,350]) ).
tff(392,plain,
implies(truth,not(falsehood)) = implies(implies(not(or(not(x),not(falsehood))),x),not(falsehood)),
inference(monotonicity,[status(thm)],[391]) ).
tff(393,plain,
not(falsehood) = truth,
inference(transitivity,[status(thm)],[132,392,353,335,332,329,328,325]) ).
tff(394,plain,
implies(not(falsehood),not(or(not(not(x)),not(truth)))) = implies(truth,and(not(x),truth)),
inference(monotonicity,[status(thm)],[393,323]) ).
tff(395,plain,
implies(truth,and(not(x),truth)) = implies(not(falsehood),not(or(not(not(x)),not(truth)))),
inference(symmetry,[status(thm)],[394]) ).
tff(396,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,and(not(x),truth)) = and(not(x),truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(397,plain,
implies(truth,and(not(x),truth)) = and(not(x),truth),
inference(unit_resolution,[status(thm)],[396,54]) ).
tff(398,plain,
and(not(x),truth) = implies(truth,and(not(x),truth)),
inference(symmetry,[status(thm)],[397]) ).
tff(399,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)),falsehood),implies(not(x),falsehood)),implies(implies(implies(not(x),falsehood),x),implies(or(not(not(x)),falsehood),x))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(400,plain,
implies(implies(or(not(not(x)),falsehood),implies(not(x),falsehood)),implies(implies(implies(not(x),falsehood),x),implies(or(not(not(x)),falsehood),x))) = truth,
inference(unit_resolution,[status(thm)],[399,89]) ).
tff(401,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(402,plain,
implies(implies(not(x),not(truth)),implies(truth,x)) = truth,
inference(unit_resolution,[status(thm)],[401,231]) ).
tff(403,plain,
implies(not(x),not(truth)) = implies(not(x),falsehood),
inference(monotonicity,[status(thm)],[31]) ).
tff(404,plain,
implies(not(x),falsehood) = implies(not(x),not(truth)),
inference(symmetry,[status(thm)],[403]) ).
tff(405,plain,
implies(implies(not(x),falsehood),x) = implies(implies(not(x),not(truth)),implies(truth,x)),
inference(monotonicity,[status(thm)],[404,176]) ).
tff(406,plain,
implies(implies(not(x),falsehood),x) = implies(x,x),
inference(transitivity,[status(thm)],[405,402,174,171,167]) ).
tff(407,plain,
implies(implies(implies(not(x),falsehood),x),implies(or(not(not(x)),falsehood),x)) = implies(implies(x,x),implies(or(not(not(x)),falsehood),x)),
inference(monotonicity,[status(thm)],[406]) ).
tff(408,plain,
implies(implies(x,x),implies(or(not(not(x)),falsehood),x)) = implies(implies(implies(not(x),falsehood),x),implies(or(not(not(x)),falsehood),x)),
inference(symmetry,[status(thm)],[407]) ).
tff(409,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(not(x)),falsehood) = implies(not(not(not(x))),falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(410,plain,
or(not(not(x)),falsehood) = implies(not(not(not(x))),falsehood),
inference(unit_resolution,[status(thm)],[409,44]) ).
tff(411,plain,
implies(or(not(not(x)),falsehood),implies(not(x),falsehood)) = implies(implies(not(not(not(x))),falsehood),implies(not(x),falsehood)),
inference(monotonicity,[status(thm)],[410]) ).
tff(412,plain,
implies(implies(not(not(not(x))),falsehood),implies(not(x),falsehood)) = implies(or(not(not(x)),falsehood),implies(not(x),falsehood)),
inference(symmetry,[status(thm)],[411]) ).
tff(413,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(falsehood,not(not(x))) = implies(not(falsehood),not(not(x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(414,plain,
or(falsehood,not(not(x))) = implies(not(falsehood),not(not(x))),
inference(unit_resolution,[status(thm)],[413,44]) ).
tff(415,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(falsehood,not(not(x))) = or(not(not(x)),falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(416,plain,
or(falsehood,not(not(x))) = or(not(not(x)),falsehood),
inference(unit_resolution,[status(thm)],[415,112]) ).
tff(417,plain,
or(not(not(x)),falsehood) = or(falsehood,not(not(x))),
inference(symmetry,[status(thm)],[416]) ).
tff(418,plain,
implies(not(not(not(x))),falsehood) = or(not(not(x)),falsehood),
inference(symmetry,[status(thm)],[410]) ).
tff(419,plain,
implies(not(not(not(x))),falsehood) = implies(not(falsehood),not(not(x))),
inference(transitivity,[status(thm)],[418,417,414]) ).
tff(420,plain,
implies(implies(not(not(not(x))),falsehood),implies(not(x),falsehood)) = implies(implies(not(falsehood),not(not(x))),implies(not(x),falsehood)),
inference(monotonicity,[status(thm)],[419]) ).
tff(421,plain,
implies(implies(not(falsehood),not(not(x))),implies(not(x),falsehood)) = implies(implies(not(not(not(x))),falsehood),implies(not(x),falsehood)),
inference(symmetry,[status(thm)],[420]) ).
tff(422,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(falsehood),not(not(x))),implies(not(x),falsehood)) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(423,plain,
implies(implies(not(falsehood),not(not(x))),implies(not(x),falsehood)) = truth,
inference(unit_resolution,[status(thm)],[422,231]) ).
tff(424,plain,
truth = implies(implies(not(falsehood),not(not(x))),implies(not(x),falsehood)),
inference(symmetry,[status(thm)],[423]) ).
tff(425,plain,
truth = implies(or(not(not(x)),falsehood),implies(not(x),falsehood)),
inference(transitivity,[status(thm)],[424,421,412]) ).
tff(426,plain,
implies(truth,implies(implies(x,x),implies(or(not(not(x)),falsehood),x))) = implies(implies(or(not(not(x)),falsehood),implies(not(x),falsehood)),implies(implies(implies(not(x),falsehood),x),implies(or(not(not(x)),falsehood),x))),
inference(monotonicity,[status(thm)],[425,408]) ).
tff(427,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(implies(x,x),implies(or(not(not(x)),falsehood),x))) = implies(implies(x,x),implies(or(not(not(x)),falsehood),x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(428,plain,
implies(truth,implies(implies(x,x),implies(or(not(not(x)),falsehood),x))) = implies(implies(x,x),implies(or(not(not(x)),falsehood),x)),
inference(unit_resolution,[status(thm)],[427,54]) ).
tff(429,plain,
implies(implies(x,x),implies(or(not(not(x)),falsehood),x)) = implies(truth,implies(implies(x,x),implies(or(not(not(x)),falsehood),x))),
inference(symmetry,[status(thm)],[428]) ).
tff(430,plain,
or(not(not(x)),not(truth)) = or(not(not(x)),falsehood),
inference(monotonicity,[status(thm)],[31]) ).
tff(431,plain,
or(not(not(x)),falsehood) = or(not(not(x)),not(truth)),
inference(symmetry,[status(thm)],[430]) ).
tff(432,plain,
implies(or(not(not(x)),falsehood),x) = implies(or(not(not(x)),not(truth)),x),
inference(monotonicity,[status(thm)],[431]) ).
tff(433,plain,
implies(or(not(not(x)),not(truth)),x) = implies(or(not(not(x)),falsehood),x),
inference(symmetry,[status(thm)],[432]) ).
tff(434,plain,
implies(truth,implies(or(not(not(x)),not(truth)),x)) = implies(implies(x,x),implies(or(not(not(x)),falsehood),x)),
inference(monotonicity,[status(thm)],[175,433]) ).
tff(435,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(or(not(not(x)),not(truth)),x)) = implies(or(not(not(x)),not(truth)),x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(436,plain,
implies(truth,implies(or(not(not(x)),not(truth)),x)) = implies(or(not(not(x)),not(truth)),x),
inference(unit_resolution,[status(thm)],[435,54]) ).
tff(437,plain,
implies(or(not(not(x)),not(truth)),x) = implies(truth,implies(or(not(not(x)),not(truth)),x)),
inference(symmetry,[status(thm)],[436]) ).
tff(438,plain,
implies(or(not(not(x)),falsehood),x) = truth,
inference(transitivity,[status(thm)],[432,437,434,429,426,400]) ).
tff(439,plain,
implies(implies(or(not(not(x)),falsehood),x),implies(truth,x)) = implies(truth,x),
inference(monotonicity,[status(thm)],[438,161]) ).
tff(440,plain,
implies(implies(or(not(not(x)),falsehood),x),x) = implies(implies(or(not(not(x)),falsehood),x),implies(truth,x)),
inference(monotonicity,[status(thm)],[176]) ).
tff(441,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(x,or(not(not(x)),falsehood)),or(not(not(x)),falsehood)) = implies(implies(or(not(not(x)),falsehood),x),x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(442,plain,
implies(implies(x,or(not(not(x)),falsehood)),or(not(not(x)),falsehood)) = implies(implies(or(not(not(x)),falsehood),x),x),
inference(unit_resolution,[status(thm)],[441,126]) ).
tff(443,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,or(not(not(x)),falsehood)) = or(not(not(x)),falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(444,plain,
implies(truth,or(not(not(x)),falsehood)) = or(not(not(x)),falsehood),
inference(unit_resolution,[status(thm)],[443,54]) ).
tff(445,plain,
implies(implies(x,or(not(not(x)),falsehood)),implies(truth,or(not(not(x)),falsehood))) = implies(implies(x,or(not(not(x)),falsehood)),or(not(not(x)),falsehood)),
inference(monotonicity,[status(thm)],[444]) ).
tff(446,plain,
or(not(not(x)),falsehood) = implies(truth,or(not(not(x)),falsehood)),
inference(symmetry,[status(thm)],[444]) ).
tff(447,plain,
or(not(not(x)),not(truth)) = implies(truth,or(not(not(x)),falsehood)),
inference(transitivity,[status(thm)],[430,446]) ).
tff(448,plain,
implies(x,or(not(not(x)),falsehood)) = implies(x,or(not(not(x)),not(truth))),
inference(monotonicity,[status(thm)],[431]) ).
tff(449,plain,
implies(x,or(not(not(x)),not(truth))) = implies(x,or(not(not(x)),falsehood)),
inference(symmetry,[status(thm)],[448]) ).
tff(450,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(x,or(not(not(x)),not(truth)))) = implies(x,or(not(not(x)),not(truth))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(451,plain,
implies(truth,implies(x,or(not(not(x)),not(truth)))) = implies(x,or(not(not(x)),not(truth))),
inference(unit_resolution,[status(thm)],[450,54]) ).
tff(452,plain,
implies(or(not(not(x)),falsehood),or(not(not(x)),falsehood)) = implies(or(not(not(x)),not(truth)),or(not(not(x)),not(truth))),
inference(monotonicity,[status(thm)],[431,431]) ).
tff(453,plain,
implies(or(not(not(x)),not(truth)),or(not(not(x)),not(truth))) = implies(or(not(not(x)),falsehood),or(not(not(x)),falsehood)),
inference(symmetry,[status(thm)],[452]) ).
tff(454,plain,
implies(not(not(not(x))),falsehood) = or(not(not(x)),not(truth)),
inference(transitivity,[status(thm)],[418,431]) ).
tff(455,plain,
implies(falsehood,falsehood) = implies(not(truth),not(truth)),
inference(monotonicity,[status(thm)],[92,92]) ).
tff(456,plain,
implies(falsehood,falsehood) = truth,
inference(transitivity,[status(thm)],[455,96,103,100,91]) ).
tff(457,plain,
implies(implies(falsehood,falsehood),implies(not(not(not(x))),falsehood)) = implies(truth,or(not(not(x)),not(truth))),
inference(monotonicity,[status(thm)],[456,454]) ).
tff(458,plain,
implies(truth,or(not(not(x)),not(truth))) = implies(implies(falsehood,falsehood),implies(not(not(not(x))),falsehood)),
inference(symmetry,[status(thm)],[457]) ).
tff(459,plain,
implies(truth,or(not(not(x)),falsehood)) = implies(truth,or(not(not(x)),not(truth))),
inference(monotonicity,[status(thm)],[431]) ).
tff(460,plain,
or(not(not(x)),not(truth)) = implies(implies(falsehood,falsehood),implies(not(not(not(x))),falsehood)),
inference(transitivity,[status(thm)],[430,446,459,458]) ).
tff(461,plain,
or(not(not(x)),not(truth)) = implies(not(not(not(x))),falsehood),
inference(transitivity,[status(thm)],[430,410]) ).
tff(462,plain,
implies(or(not(not(x)),not(truth)),or(not(not(x)),not(truth))) = implies(implies(not(not(not(x))),falsehood),implies(implies(falsehood,falsehood),implies(not(not(not(x))),falsehood))),
inference(monotonicity,[status(thm)],[461,460]) ).
tff(463,plain,
implies(implies(not(not(not(x))),falsehood),implies(implies(falsehood,falsehood),implies(not(not(not(x))),falsehood))) = implies(or(not(not(x)),not(truth)),or(not(not(x)),not(truth))),
inference(symmetry,[status(thm)],[462]) ).
tff(464,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(not(not(not(x))),falsehood),implies(implies(falsehood,falsehood),implies(not(not(not(x))),falsehood))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(465,plain,
implies(implies(not(not(not(x))),falsehood),implies(implies(falsehood,falsehood),implies(not(not(not(x))),falsehood))) = truth,
inference(unit_resolution,[status(thm)],[464,89]) ).
tff(466,plain,
truth = implies(implies(not(not(not(x))),falsehood),implies(implies(falsehood,falsehood),implies(not(not(not(x))),falsehood))),
inference(symmetry,[status(thm)],[465]) ).
tff(467,plain,
truth = implies(or(not(not(x)),falsehood),or(not(not(x)),falsehood)),
inference(transitivity,[status(thm)],[466,463,453]) ).
tff(468,plain,
implies(truth,implies(x,or(not(not(x)),not(truth)))) = implies(implies(or(not(not(x)),falsehood),or(not(not(x)),falsehood)),implies(x,or(not(not(x)),falsehood))),
inference(monotonicity,[status(thm)],[467,449]) ).
tff(469,plain,
implies(implies(or(not(not(x)),falsehood),or(not(not(x)),falsehood)),implies(x,or(not(not(x)),falsehood))) = implies(truth,implies(x,or(not(not(x)),not(truth)))),
inference(symmetry,[status(thm)],[468]) ).
tff(470,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(not(or(not(not(x)),not(truth))),not(x))) = implies(not(or(not(not(x)),not(truth))),not(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(471,plain,
implies(truth,implies(not(or(not(not(x)),not(truth))),not(x))) = implies(not(or(not(not(x)),not(truth))),not(x)),
inference(unit_resolution,[status(thm)],[470,54]) ).
tff(472,plain,
implies(and(not(x),truth),not(x)) = implies(not(or(not(not(x)),not(truth))),not(x)),
inference(monotonicity,[status(thm)],[320]) ).
tff(473,plain,
implies(not(or(not(not(x)),not(truth))),not(x)) = implies(and(not(x),truth),not(x)),
inference(symmetry,[status(thm)],[472]) ).
tff(474,plain,
implies(truth,implies(not(or(not(not(x)),not(truth))),not(x))) = implies(implies(not(x),not(x)),implies(and(not(x),truth),not(x))),
inference(monotonicity,[status(thm)],[222,473]) ).
tff(475,plain,
implies(implies(not(x),not(x)),implies(and(not(x),truth),not(x))) = implies(truth,implies(not(or(not(not(x)),not(truth))),not(x))),
inference(symmetry,[status(thm)],[474]) ).
tff(476,plain,
implies(not(falsehood),not(not(x))) = or(falsehood,not(not(x))),
inference(symmetry,[status(thm)],[414]) ).
tff(477,plain,
implies(not(falsehood),not(not(x))) = or(not(not(x)),falsehood),
inference(transitivity,[status(thm)],[476,416]) ).
tff(478,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,not(not(x))) = not(not(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(479,plain,
implies(truth,not(not(x))) = not(not(x)),
inference(unit_resolution,[status(thm)],[478,54]) ).
tff(480,plain,
implies(implies(truth,not(not(x))),implies(not(falsehood),not(not(x)))) = implies(not(not(x)),or(not(not(x)),falsehood)),
inference(monotonicity,[status(thm)],[479,477]) ).
tff(481,plain,
implies(not(not(x)),or(not(not(x)),falsehood)) = implies(implies(truth,not(not(x))),implies(not(falsehood),not(not(x)))),
inference(symmetry,[status(thm)],[480]) ).
tff(482,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(x),or(not(not(x)),falsehood)) = implies(not(not(x)),or(not(not(x)),falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(483,plain,
or(not(x),or(not(not(x)),falsehood)) = implies(not(not(x)),or(not(not(x)),falsehood)),
inference(unit_resolution,[status(thm)],[482,44]) ).
tff(484,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(x),or(not(not(x)),falsehood)) = or(or(not(not(x)),falsehood),not(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(485,plain,
or(not(x),or(not(not(x)),falsehood)) = or(or(not(not(x)),falsehood),not(x)),
inference(unit_resolution,[status(thm)],[484,112]) ).
tff(486,plain,
or(or(not(not(x)),falsehood),not(x)) = or(not(x),or(not(not(x)),falsehood)),
inference(symmetry,[status(thm)],[485]) ).
tff(487,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(or(not(not(x)),falsehood),not(x)) = implies(not(or(not(not(x)),falsehood)),not(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(488,plain,
or(or(not(not(x)),falsehood),not(x)) = implies(not(or(not(not(x)),falsehood)),not(x)),
inference(unit_resolution,[status(thm)],[487,44]) ).
tff(489,plain,
implies(not(or(not(not(x)),falsehood)),not(x)) = or(or(not(not(x)),falsehood),not(x)),
inference(symmetry,[status(thm)],[488]) ).
tff(490,plain,
not(or(not(not(x)),falsehood)) = not(or(not(not(x)),not(truth))),
inference(monotonicity,[status(thm)],[431]) ).
tff(491,plain,
implies(not(or(not(not(x)),falsehood)),not(x)) = implies(not(or(not(not(x)),not(truth))),not(x)),
inference(monotonicity,[status(thm)],[490]) ).
tff(492,plain,
implies(not(or(not(not(x)),not(truth))),not(x)) = implies(not(or(not(not(x)),falsehood)),not(x)),
inference(symmetry,[status(thm)],[491]) ).
tff(493,plain,
implies(and(not(x),truth),not(x)) = implies(implies(truth,not(not(x))),implies(not(falsehood),not(not(x)))),
inference(transitivity,[status(thm)],[472,492,489,486,483,481]) ).
tff(494,plain,
or(truth,falsehood) = or(falsehood,truth),
inference(symmetry,[status(thm)],[114]) ).
tff(495,plain,
implies(not(x),not(x)) = implies(not(falsehood),truth),
inference(transitivity,[status(thm)],[340,197,200,360,359,102,358,494,116]) ).
tff(496,plain,
implies(implies(not(x),not(x)),implies(and(not(x),truth),not(x))) = implies(implies(not(falsehood),truth),implies(implies(truth,not(not(x))),implies(not(falsehood),not(not(x))))),
inference(monotonicity,[status(thm)],[495,493]) ).
tff(497,plain,
implies(implies(not(falsehood),truth),implies(implies(truth,not(not(x))),implies(not(falsehood),not(not(x))))) = implies(implies(not(x),not(x)),implies(and(not(x),truth),not(x))),
inference(symmetry,[status(thm)],[496]) ).
tff(498,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(not(falsehood),truth),implies(implies(truth,not(not(x))),implies(not(falsehood),not(not(x))))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(499,plain,
implies(implies(not(falsehood),truth),implies(implies(truth,not(not(x))),implies(not(falsehood),not(not(x))))) = truth,
inference(unit_resolution,[status(thm)],[498,89]) ).
tff(500,plain,
truth = implies(implies(not(falsehood),truth),implies(implies(truth,not(not(x))),implies(not(falsehood),not(not(x))))),
inference(symmetry,[status(thm)],[499]) ).
tff(501,plain,
implies(or(not(not(x)),falsehood),or(not(not(x)),falsehood)) = implies(not(or(not(not(x)),not(truth))),not(x)),
inference(transitivity,[status(thm)],[452,462,465,500,497,475,471]) ).
tff(502,plain,
implies(implies(or(not(not(x)),falsehood),or(not(not(x)),falsehood)),implies(x,or(not(not(x)),falsehood))) = implies(implies(not(or(not(not(x)),not(truth))),not(x)),implies(x,or(not(not(x)),not(truth)))),
inference(monotonicity,[status(thm)],[501,448]) ).
tff(503,plain,
implies(implies(not(or(not(not(x)),not(truth))),not(x)),implies(x,or(not(not(x)),not(truth)))) = implies(implies(or(not(not(x)),falsehood),or(not(not(x)),falsehood)),implies(x,or(not(not(x)),falsehood))),
inference(symmetry,[status(thm)],[502]) ).
tff(504,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(or(not(not(x)),not(truth))),not(x)),implies(x,or(not(not(x)),not(truth)))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(505,plain,
implies(implies(not(or(not(not(x)),not(truth))),not(x)),implies(x,or(not(not(x)),not(truth)))) = truth,
inference(unit_resolution,[status(thm)],[504,231]) ).
tff(506,plain,
truth = implies(implies(not(or(not(not(x)),not(truth))),not(x)),implies(x,or(not(not(x)),not(truth)))),
inference(symmetry,[status(thm)],[505]) ).
tff(507,plain,
truth = implies(x,or(not(not(x)),falsehood)),
inference(transitivity,[status(thm)],[506,503,469,451,449]) ).
tff(508,plain,
implies(truth,or(not(not(x)),not(truth))) = implies(implies(x,or(not(not(x)),falsehood)),implies(truth,or(not(not(x)),falsehood))),
inference(monotonicity,[status(thm)],[507,447]) ).
tff(509,plain,
or(not(not(x)),not(truth)) = x,
inference(transitivity,[status(thm)],[430,446,459,508,445,442,440,439,161]) ).
tff(510,plain,
not(or(not(not(x)),not(truth))) = not(x),
inference(monotonicity,[status(thm)],[509]) ).
tff(511,plain,
not(x) = not(or(not(not(x)),not(truth))),
inference(symmetry,[status(thm)],[510]) ).
tff(512,plain,
not(x) = xor(x,truth),
inference(transitivity,[status(thm)],[511,323,398,395,322,318,315,312,310,47,37,19,9]) ).
tff(513,plain,
( ( not(x) != xor(x,truth) )
<=> ( not(x) != xor(x,truth) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(514,axiom,
not(x) != xor(x,truth),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
tff(515,plain,
not(x) != xor(x,truth),
inference(modus_ponens,[status(thm)],[514,513]) ).
tff(516,plain,
$false,
inference(unit_resolution,[status(thm)],[515,512]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL153-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n027.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 11:50:15 UTC 2026
% 0.08/0.34 % CPUTime :
% 101.56/101.87 % SZS status Unsatisfiable
% 101.56/101.87 % SZS output start Proof
% See solution above
% 101.65/101.95 % E exiting
%------------------------------------------------------------------------------