%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL154-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n010.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 02:59:24 PM UTC 2026
% Result : Unsatisfiable 4.07s 4.38s
% Output : Proof 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 80
% Syntax : Number of formulae : 333 ( 264 unt; 0 typ; 0 def)
% Number of atoms : 420 ( 410 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 131 ( 53 ~; 49 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 9 ( 9 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 : 268 ( 249 !; 0 ?; 268 :)
% Comments :
%------------------------------------------------------------------------------
tff(x_type,type,
x: $i ).
tff(xor_type,type,
xor: ( $i * $i ) > $i ).
tff(falsehood_type,type,
falsehood: $i ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(truth_type,type,
truth: $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(1,plain,
^ [X: $i] :
refl(( ( implies(truth,X) = X )
<=> ( implies(truth,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( implies(truth,X) = X )
<=> ! [X: $i] : ( implies(truth,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( implies(truth,X) = X )
<=> ! [X: $i] : ( implies(truth,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( implies(truth,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
tff(5,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,x) = x ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
implies(truth,x) = x,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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(14,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(not(falsehood)),not(truth)),implies(truth,not(falsehood))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
implies(implies(not(not(falsehood)),not(truth)),implies(truth,not(falsehood))) = truth,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ( not(truth) = falsehood )
<=> ( not(truth) = falsehood ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',false_definition) ).
tff(21,plain,
not(truth) = falsehood,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
implies(not(not(falsehood)),not(truth)) = implies(not(not(falsehood)),falsehood),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
implies(not(not(falsehood)),falsehood) = implies(not(not(falsehood)),not(truth)),
inference(symmetry,[status(thm)],[22]) ).
tff(24,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(25,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)],[24]) ).
tff(26,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(27,axiom,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_definition) ).
tff(28,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(falsehood),falsehood) = implies(not(not(falsehood)),falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
or(not(falsehood),falsehood) = implies(not(not(falsehood)),falsehood),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
^ [Y: $i,X: $i] :
refl(( ( or(X,Y) = or(Y,X) )
<=> ( or(X,Y) = or(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(34,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)],[33]) ).
tff(35,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(36,axiom,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_commutativity) ).
tff(37,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,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(41,plain,
or(not(falsehood),falsehood) = or(falsehood,not(falsehood)),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
or(falsehood,not(falsehood)) = or(not(falsehood),falsehood),
inference(symmetry,[status(thm)],[41]) ).
tff(43,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(44,plain,
or(falsehood,not(falsehood)) = implies(not(falsehood),not(falsehood)),
inference(unit_resolution,[status(thm)],[43,30]) ).
tff(45,plain,
implies(not(falsehood),not(falsehood)) = or(falsehood,not(falsehood)),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
implies(not(falsehood),not(falsehood)) = implies(not(not(falsehood)),not(truth)),
inference(transitivity,[status(thm)],[45,42,32,23]) ).
tff(47,plain,
implies(implies(not(falsehood),not(falsehood)),implies(truth,not(falsehood))) = implies(implies(not(not(falsehood)),not(truth)),implies(truth,not(falsehood))),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,not(falsehood)) = not(falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
implies(truth,not(falsehood)) = not(falsehood),
inference(unit_resolution,[status(thm)],[48,7]) ).
tff(50,plain,
not(falsehood) = implies(truth,not(falsehood)),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
implies(truth,implies(truth,not(falsehood))) = implies(truth,not(falsehood)),
inference(monotonicity,[status(thm)],[49]) ).
tff(52,plain,
implies(truth,not(falsehood)) = implies(truth,implies(truth,not(falsehood))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
not(falsehood) = implies(truth,implies(truth,not(falsehood))),
inference(transitivity,[status(thm)],[50,52]) ).
tff(54,plain,
implies(not(falsehood),not(falsehood)) = implies(implies(truth,implies(truth,not(falsehood))),implies(truth,not(falsehood))),
inference(monotonicity,[status(thm)],[53,50]) ).
tff(55,plain,
implies(implies(truth,implies(truth,not(falsehood))),implies(truth,not(falsehood))) = implies(not(falsehood),not(falsehood)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,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(57,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)],[56]) ).
tff(58,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(59,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(60,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(implies(truth,not(falsehood)),truth),truth) = implies(implies(truth,implies(truth,not(falsehood))),implies(truth,not(falsehood))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
implies(implies(implies(truth,not(falsehood)),truth),truth) = implies(implies(truth,implies(truth,not(falsehood))),implies(truth,not(falsehood))),
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,truth) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
implies(truth,truth) = truth,
inference(unit_resolution,[status(thm)],[65,7]) ).
tff(67,plain,
truth = implies(truth,truth),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
implies(implies(implies(truth,not(falsehood)),truth),truth) = implies(implies(implies(truth,not(falsehood)),truth),implies(truth,truth)),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
implies(implies(implies(truth,not(falsehood)),truth),implies(truth,truth)) = implies(implies(implies(truth,not(falsehood)),truth),truth),
inference(symmetry,[status(thm)],[68]) ).
tff(70,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(71,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)],[70]) ).
tff(72,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(73,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(74,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,not(falsehood)),implies(implies(not(falsehood),falsehood),implies(truth,falsehood))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
implies(implies(truth,not(falsehood)),implies(implies(not(falsehood),falsehood),implies(truth,falsehood))) = truth,
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[21]) ).
tff(80,plain,
implies(not(falsehood),falsehood) = implies(not(falsehood),not(truth)),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
implies(implies(not(falsehood),falsehood),implies(truth,falsehood)) = implies(implies(not(falsehood),not(truth)),implies(truth,falsehood)),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
implies(implies(not(falsehood),not(truth)),implies(truth,falsehood)) = implies(implies(not(falsehood),falsehood),implies(truth,falsehood)),
inference(symmetry,[status(thm)],[81]) ).
tff(83,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(84,plain,
implies(implies(not(falsehood),not(truth)),implies(truth,falsehood)) = truth,
inference(unit_resolution,[status(thm)],[83,16]) ).
tff(85,plain,
truth = implies(implies(not(falsehood),not(truth)),implies(truth,falsehood)),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
truth = implies(implies(not(falsehood),falsehood),implies(truth,falsehood)),
inference(transitivity,[status(thm)],[85,82]) ).
tff(87,plain,
implies(implies(truth,not(falsehood)),truth) = implies(implies(truth,not(falsehood)),implies(implies(not(falsehood),falsehood),implies(truth,falsehood))),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
implies(implies(truth,not(falsehood)),truth) = truth,
inference(transitivity,[status(thm)],[87,78]) ).
tff(89,plain,
implies(implies(implies(truth,not(falsehood)),truth),implies(truth,truth)) = implies(truth,truth),
inference(monotonicity,[status(thm)],[88,66]) ).
tff(90,plain,
implies(truth,truth) = implies(implies(implies(truth,not(falsehood)),truth),implies(truth,truth)),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
truth = implies(not(falsehood),not(falsehood)),
inference(transitivity,[status(thm)],[67,90,69,64,55]) ).
tff(92,plain,
implies(truth,not(falsehood)) = implies(implies(not(falsehood),not(falsehood)),implies(truth,not(falsehood))),
inference(monotonicity,[status(thm)],[91,50]) ).
tff(93,plain,
not(falsehood) = truth,
inference(transitivity,[status(thm)],[50,92,47,18]) ).
tff(94,plain,
implies(not(falsehood),x) = implies(truth,x),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(falsehood,x) = implies(not(falsehood),x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
or(falsehood,x) = implies(not(falsehood),x),
inference(unit_resolution,[status(thm)],[95,30]) ).
tff(97,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(falsehood,x) = or(x,falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
or(falsehood,x) = or(x,falsehood),
inference(unit_resolution,[status(thm)],[97,39]) ).
tff(99,plain,
or(x,falsehood) = or(falsehood,x),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(x,falsehood) = implies(not(x),falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
or(x,falsehood) = implies(not(x),falsehood),
inference(unit_resolution,[status(thm)],[100,30]) ).
tff(102,plain,
implies(not(x),falsehood) = or(x,falsehood),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
implies(not(x),not(truth)) = implies(not(x),falsehood),
inference(monotonicity,[status(thm)],[21]) ).
tff(104,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,not(x)) = not(x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
implies(truth,not(x)) = not(x),
inference(unit_resolution,[status(thm)],[104,7]) ).
tff(106,plain,
implies(not(falsehood),not(x)) = implies(truth,not(x)),
inference(monotonicity,[status(thm)],[93]) ).
tff(107,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(falsehood,not(x)) = implies(not(falsehood),not(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
or(falsehood,not(x)) = implies(not(falsehood),not(x)),
inference(unit_resolution,[status(thm)],[107,30]) ).
tff(109,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(x),falsehood) = or(falsehood,not(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
or(not(x),falsehood) = or(falsehood,not(x)),
inference(unit_resolution,[status(thm)],[109,39]) ).
tff(111,plain,
not(not(falsehood)) = not(truth),
inference(monotonicity,[status(thm)],[93]) ).
tff(112,plain,
not(not(falsehood)) = falsehood,
inference(transitivity,[status(thm)],[111,21]) ).
tff(113,plain,
or(not(x),not(not(falsehood))) = or(not(x),falsehood),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
or(not(x),not(not(falsehood))) = not(x),
inference(transitivity,[status(thm)],[113,110,108,106,105]) ).
tff(115,plain,
or(or(not(x),not(not(falsehood))),falsehood) = or(not(x),falsehood),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(or(not(x),not(not(falsehood))),falsehood) = implies(not(or(not(x),not(not(falsehood)))),falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
or(or(not(x),not(not(falsehood))),falsehood) = implies(not(or(not(x),not(not(falsehood)))),falsehood),
inference(unit_resolution,[status(thm)],[116,30]) ).
tff(118,plain,
implies(not(or(not(x),not(not(falsehood)))),falsehood) = or(or(not(x),not(not(falsehood))),falsehood),
inference(symmetry,[status(thm)],[117]) ).
tff(119,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(120,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)],[119]) ).
tff(121,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(122,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(123,plain,
! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ),
inference(modus_ponens,[status(thm)],[124,120]) ).
tff(126,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) )
| ( and(x,not(falsehood)) = not(or(not(x),not(not(falsehood)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
and(x,not(falsehood)) = not(or(not(x),not(not(falsehood)))),
inference(unit_resolution,[status(thm)],[126,125]) ).
tff(128,plain,
implies(and(x,not(falsehood)),falsehood) = implies(not(or(not(x),not(not(falsehood)))),falsehood),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
implies(and(x,not(falsehood)),falsehood) = not(x),
inference(transitivity,[status(thm)],[128,118,115,110,108,106,105]) ).
tff(130,plain,
implies(implies(and(x,not(falsehood)),falsehood),falsehood) = implies(not(x),not(truth)),
inference(monotonicity,[status(thm)],[129,79]) ).
tff(131,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(and(x,not(falsehood)),falsehood),falsehood) = implies(implies(falsehood,and(x,not(falsehood))),and(x,not(falsehood))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(132,plain,
implies(implies(and(x,not(falsehood)),falsehood),falsehood) = implies(implies(falsehood,and(x,not(falsehood))),and(x,not(falsehood))),
inference(unit_resolution,[status(thm)],[131,62]) ).
tff(133,plain,
implies(implies(falsehood,and(x,not(falsehood))),and(x,not(falsehood))) = implies(implies(and(x,not(falsehood)),falsehood),falsehood),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
not(or(not(x),not(not(falsehood)))) = and(x,not(falsehood)),
inference(symmetry,[status(thm)],[127]) ).
tff(135,plain,
or(not(x),falsehood) = or(not(x),not(not(falsehood))),
inference(symmetry,[status(thm)],[113]) ).
tff(136,plain,
or(falsehood,not(x)) = or(not(x),falsehood),
inference(symmetry,[status(thm)],[110]) ).
tff(137,plain,
implies(not(falsehood),not(x)) = or(falsehood,not(x)),
inference(symmetry,[status(thm)],[108]) ).
tff(138,plain,
implies(truth,not(x)) = implies(not(falsehood),not(x)),
inference(symmetry,[status(thm)],[106]) ).
tff(139,plain,
not(x) = implies(truth,not(x)),
inference(symmetry,[status(thm)],[105]) ).
tff(140,plain,
not(x) = or(not(x),not(not(falsehood))),
inference(transitivity,[status(thm)],[139,138,137,136,135]) ).
tff(141,plain,
not(not(x)) = not(or(not(x),not(not(falsehood)))),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
not(not(x)) = and(x,not(falsehood)),
inference(transitivity,[status(thm)],[141,134]) ).
tff(143,plain,
implies(not(truth),not(not(x))) = implies(falsehood,and(x,not(falsehood))),
inference(monotonicity,[status(thm)],[21,142]) ).
tff(144,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(truth,not(not(x))) = implies(not(truth),not(not(x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
or(truth,not(not(x))) = implies(not(truth),not(not(x))),
inference(unit_resolution,[status(thm)],[144,30]) ).
tff(146,plain,
or(not(falsehood),not(not(x))) = or(truth,not(not(x))),
inference(monotonicity,[status(thm)],[93]) ).
tff(147,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(falsehood),not(not(x))) = or(not(not(x)),not(falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
or(not(falsehood),not(not(x))) = or(not(not(x)),not(falsehood)),
inference(unit_resolution,[status(thm)],[147,39]) ).
tff(149,plain,
or(not(not(x)),not(falsehood)) = or(not(falsehood),not(not(x))),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
or(not(not(x)),not(falsehood)) = implies(falsehood,and(x,not(falsehood))),
inference(transitivity,[status(thm)],[149,146,145,143]) ).
tff(151,plain,
implies(or(not(not(x)),not(falsehood)),and(x,not(falsehood))) = implies(implies(falsehood,and(x,not(falsehood))),and(x,not(falsehood))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
or(truth,not(not(x))) = or(not(falsehood),not(not(x))),
inference(symmetry,[status(thm)],[146]) ).
tff(153,plain,
implies(not(truth),not(not(x))) = or(truth,not(not(x))),
inference(symmetry,[status(thm)],[145]) ).
tff(154,plain,
implies(falsehood,and(x,not(falsehood))) = implies(not(truth),not(not(x))),
inference(symmetry,[status(thm)],[143]) ).
tff(155,plain,
implies(falsehood,and(x,not(falsehood))) = implies(not(truth),and(x,not(falsehood))),
inference(monotonicity,[status(thm)],[79]) ).
tff(156,plain,
implies(not(truth),and(x,not(falsehood))) = implies(falsehood,and(x,not(falsehood))),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(truth,and(x,not(falsehood))) = implies(not(truth),and(x,not(falsehood))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(158,plain,
or(truth,and(x,not(falsehood))) = implies(not(truth),and(x,not(falsehood))),
inference(unit_resolution,[status(thm)],[157,30]) ).
tff(159,plain,
or(not(x),truth) = or(or(not(x),not(not(falsehood))),truth),
inference(monotonicity,[status(thm)],[140]) ).
tff(160,plain,
or(or(not(x),not(not(falsehood))),truth) = or(not(x),truth),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(or(not(x),not(not(falsehood))),truth) = implies(not(or(not(x),not(not(falsehood)))),truth) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,plain,
or(or(not(x),not(not(falsehood))),truth) = implies(not(or(not(x),not(not(falsehood)))),truth),
inference(unit_resolution,[status(thm)],[161,30]) ).
tff(163,plain,
implies(not(or(not(x),not(not(falsehood)))),truth) = or(or(not(x),not(not(falsehood))),truth),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
implies(not(or(not(x),not(not(falsehood)))),truth) = implies(and(x,not(falsehood)),truth),
inference(monotonicity,[status(thm)],[134]) ).
tff(165,plain,
implies(and(x,not(falsehood)),truth) = implies(not(or(not(x),not(not(falsehood)))),truth),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(not(truth),falsehood)) = implies(not(truth),falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
implies(truth,implies(not(truth),falsehood)) = implies(not(truth),falsehood),
inference(unit_resolution,[status(thm)],[166,7]) ).
tff(168,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,falsehood) = falsehood ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(169,plain,
implies(truth,falsehood) = falsehood,
inference(unit_resolution,[status(thm)],[168,7]) ).
tff(170,plain,
implies(truth,falsehood) = not(truth),
inference(transitivity,[status(thm)],[169,79]) ).
tff(171,plain,
implies(implies(truth,falsehood),implies(truth,falsehood)) = implies(not(truth),not(truth)),
inference(monotonicity,[status(thm)],[170,170]) ).
tff(172,plain,
implies(not(truth),not(truth)) = implies(implies(truth,falsehood),implies(truth,falsehood)),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
implies(not(truth),not(truth)) = implies(not(truth),falsehood),
inference(monotonicity,[status(thm)],[21]) ).
tff(174,plain,
implies(not(truth),falsehood) = implies(not(truth),not(truth)),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
implies(not(truth),falsehood) = implies(implies(truth,falsehood),implies(truth,falsehood)),
inference(transitivity,[status(thm)],[174,172]) ).
tff(176,plain,
implies(truth,implies(not(truth),falsehood)) = implies(implies(truth,truth),implies(implies(truth,falsehood),implies(truth,falsehood))),
inference(monotonicity,[status(thm)],[67,175]) ).
tff(177,plain,
implies(implies(truth,truth),implies(implies(truth,falsehood),implies(truth,falsehood))) = implies(truth,implies(not(truth),falsehood)),
inference(symmetry,[status(thm)],[176]) ).
tff(178,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(179,plain,
implies(implies(truth,truth),implies(implies(truth,falsehood),implies(truth,falsehood))) = truth,
inference(unit_resolution,[status(thm)],[178,76]) ).
tff(180,plain,
truth = implies(implies(truth,truth),implies(implies(truth,falsehood),implies(truth,falsehood))),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
truth = implies(not(truth),falsehood),
inference(transitivity,[status(thm)],[180,177,167]) ).
tff(182,plain,
implies(not(falsehood),not(not(x))) = implies(truth,not(not(x))),
inference(monotonicity,[status(thm)],[93]) ).
tff(183,plain,
implies(truth,not(not(x))) = implies(not(falsehood),not(not(x))),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
implies(truth,not(not(x))) = implies(truth,and(x,not(falsehood))),
inference(monotonicity,[status(thm)],[142]) ).
tff(185,plain,
implies(truth,and(x,not(falsehood))) = implies(truth,not(not(x))),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,and(x,not(falsehood))) = and(x,not(falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(187,plain,
implies(truth,and(x,not(falsehood))) = and(x,not(falsehood)),
inference(unit_resolution,[status(thm)],[186,7]) ).
tff(188,plain,
and(x,not(falsehood)) = implies(truth,and(x,not(falsehood))),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
and(x,not(falsehood)) = implies(not(falsehood),not(not(x))),
inference(transitivity,[status(thm)],[188,185,183]) ).
tff(190,plain,
implies(and(x,not(falsehood)),truth) = implies(implies(not(falsehood),not(not(x))),implies(not(truth),falsehood)),
inference(monotonicity,[status(thm)],[189,181]) ).
tff(191,plain,
implies(implies(not(falsehood),not(not(x))),implies(not(truth),falsehood)) = implies(and(x,not(falsehood)),truth),
inference(symmetry,[status(thm)],[190]) ).
tff(192,plain,
implies(implies(truth,implies(truth,not(falsehood))),implies(truth,not(falsehood))) = implies(implies(implies(truth,not(falsehood)),truth),truth),
inference(symmetry,[status(thm)],[64]) ).
tff(193,plain,
implies(not(falsehood),not(falsehood)) = truth,
inference(transitivity,[status(thm)],[54,192,68,89,66]) ).
tff(194,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(195,plain,
or(truth,not(x)) = implies(not(truth),not(x)),
inference(unit_resolution,[status(thm)],[194,30]) ).
tff(196,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(197,plain,
or(not(x),truth) = or(truth,not(x)),
inference(unit_resolution,[status(thm)],[196,39]) ).
tff(198,plain,
or(not(x),not(falsehood)) = or(not(x),truth),
inference(monotonicity,[status(thm)],[93]) ).
tff(199,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(200,plain,
or(not(x),not(falsehood)) = implies(not(not(x)),not(falsehood)),
inference(unit_resolution,[status(thm)],[199,30]) ).
tff(201,plain,
implies(not(not(x)),not(falsehood)) = or(not(x),not(falsehood)),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
implies(not(not(x)),not(falsehood)) = implies(not(truth),not(x)),
inference(transitivity,[status(thm)],[201,198,197,195]) ).
tff(203,plain,
implies(implies(not(not(x)),not(falsehood)),implies(not(falsehood),not(falsehood))) = implies(implies(not(truth),not(x)),truth),
inference(monotonicity,[status(thm)],[202,193]) ).
tff(204,plain,
implies(implies(not(truth),not(x)),truth) = implies(implies(not(not(x)),not(falsehood)),implies(not(falsehood),not(falsehood))),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
implies(implies(x,truth),implies(truth,truth)) = implies(implies(x,truth),truth),
inference(monotonicity,[status(thm)],[66]) ).
tff(206,plain,
implies(implies(x,truth),truth) = implies(implies(x,truth),implies(truth,truth)),
inference(symmetry,[status(thm)],[205]) ).
tff(207,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(208,plain,
implies(implies(x,truth),truth) = implies(implies(truth,x),x),
inference(unit_resolution,[status(thm)],[207,62]) ).
tff(209,plain,
implies(implies(truth,x),x) = implies(implies(x,truth),truth),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
implies(implies(truth,x),x) = implies(x,x),
inference(monotonicity,[status(thm)],[9]) ).
tff(211,plain,
implies(x,x) = implies(implies(truth,x),x),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(x,x)) = implies(x,x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
implies(truth,implies(x,x)) = implies(x,x),
inference(unit_resolution,[status(thm)],[212,7]) ).
tff(214,plain,
implies(implies(truth,x),implies(truth,x)) = implies(x,x),
inference(monotonicity,[status(thm)],[9,9]) ).
tff(215,plain,
implies(x,x) = implies(implies(truth,x),implies(truth,x)),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
implies(truth,implies(x,x)) = implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x))),
inference(monotonicity,[status(thm)],[67,215]) ).
tff(217,plain,
implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x))) = implies(truth,implies(x,x)),
inference(symmetry,[status(thm)],[216]) ).
tff(218,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(219,plain,
implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x))) = truth,
inference(unit_resolution,[status(thm)],[218,76]) ).
tff(220,plain,
truth = implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x))),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
truth = implies(implies(x,truth),implies(truth,truth)),
inference(transitivity,[status(thm)],[220,217,213,211,209,206]) ).
tff(222,plain,
x = implies(truth,x),
inference(symmetry,[status(thm)],[9]) ).
tff(223,plain,
implies(x,truth) = implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))),
inference(monotonicity,[status(thm)],[222,221]) ).
tff(224,plain,
implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))) = implies(x,truth),
inference(symmetry,[status(thm)],[223]) ).
tff(225,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(226,plain,
implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))) = truth,
inference(unit_resolution,[status(thm)],[225,76]) ).
tff(227,plain,
truth = implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))),
inference(symmetry,[status(thm)],[226]) ).
tff(228,plain,
truth = implies(x,truth),
inference(transitivity,[status(thm)],[227,224]) ).
tff(229,plain,
implies(implies(not(truth),not(x)),truth) = implies(implies(not(truth),not(x)),implies(x,truth)),
inference(monotonicity,[status(thm)],[228]) ).
tff(230,plain,
implies(implies(not(truth),not(x)),implies(x,truth)) = implies(implies(not(truth),not(x)),truth),
inference(symmetry,[status(thm)],[229]) ).
tff(231,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(232,plain,
implies(implies(not(truth),not(x)),implies(x,truth)) = truth,
inference(unit_resolution,[status(thm)],[231,16]) ).
tff(233,plain,
truth = implies(implies(not(truth),not(x)),implies(x,truth)),
inference(symmetry,[status(thm)],[232]) ).
tff(234,plain,
implies(not(truth),falsehood) = implies(truth,implies(not(truth),falsehood)),
inference(symmetry,[status(thm)],[167]) ).
tff(235,plain,
implies(not(truth),falsehood) = implies(implies(not(not(x)),not(falsehood)),implies(not(falsehood),not(falsehood))),
inference(transitivity,[status(thm)],[234,176,179,233,230,204]) ).
tff(236,plain,
implies(implies(not(falsehood),not(not(x))),implies(not(truth),falsehood)) = implies(implies(not(falsehood),not(not(x))),implies(implies(not(not(x)),not(falsehood)),implies(not(falsehood),not(falsehood)))),
inference(monotonicity,[status(thm)],[235]) ).
tff(237,plain,
implies(implies(not(falsehood),not(not(x))),implies(implies(not(not(x)),not(falsehood)),implies(not(falsehood),not(falsehood)))) = implies(implies(not(falsehood),not(not(x))),implies(not(truth),falsehood)),
inference(symmetry,[status(thm)],[236]) ).
tff(238,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(not(falsehood),not(not(x))),implies(implies(not(not(x)),not(falsehood)),implies(not(falsehood),not(falsehood)))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(239,plain,
implies(implies(not(falsehood),not(not(x))),implies(implies(not(not(x)),not(falsehood)),implies(not(falsehood),not(falsehood)))) = truth,
inference(unit_resolution,[status(thm)],[238,76]) ).
tff(240,plain,
truth = implies(implies(not(falsehood),not(not(x))),implies(implies(not(not(x)),not(falsehood)),implies(not(falsehood),not(falsehood)))),
inference(symmetry,[status(thm)],[239]) ).
tff(241,plain,
truth = or(not(x),truth),
inference(transitivity,[status(thm)],[240,237,191,165,163,160]) ).
tff(242,plain,
or(truth,and(x,not(falsehood))) = or(or(not(x),truth),and(x,not(falsehood))),
inference(monotonicity,[status(thm)],[241]) ).
tff(243,plain,
or(or(not(x),truth),and(x,not(falsehood))) = or(truth,and(x,not(falsehood))),
inference(symmetry,[status(thm)],[242]) ).
tff(244,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(245,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)],[244]) ).
tff(246,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(247,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(248,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) ),
inference(modus_ponens,[status(thm)],[247,246]) ).
tff(249,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) ),
inference(skolemize,[status(sab)],[248]) ).
tff(250,plain,
! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) ),
inference(modus_ponens,[status(thm)],[249,245]) ).
tff(251,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( or(or(X,Y),Z) = or(X,or(Y,Z)) )
| ( or(or(not(x),truth),and(x,not(falsehood))) = or(not(x),or(truth,and(x,not(falsehood)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(252,plain,
or(or(not(x),truth),and(x,not(falsehood))) = or(not(x),or(truth,and(x,not(falsehood)))),
inference(unit_resolution,[status(thm)],[251,250]) ).
tff(253,plain,
or(not(x),or(truth,and(x,not(falsehood)))) = or(or(not(x),truth),and(x,not(falsehood))),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
or(truth,and(x,not(falsehood))) = or(not(not(x)),not(falsehood)),
inference(transitivity,[status(thm)],[158,156,154,153,152,148]) ).
tff(255,plain,
or(not(x),or(truth,and(x,not(falsehood)))) = or(or(not(x),not(not(falsehood))),or(not(not(x)),not(falsehood))),
inference(monotonicity,[status(thm)],[140,254]) ).
tff(256,plain,
or(or(not(x),not(not(falsehood))),or(not(not(x)),not(falsehood))) = or(not(x),or(truth,and(x,not(falsehood)))),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(or(not(x),not(not(falsehood))),or(not(not(x)),not(falsehood))) = implies(not(or(not(x),not(not(falsehood)))),or(not(not(x)),not(falsehood))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(258,plain,
or(or(not(x),not(not(falsehood))),or(not(not(x)),not(falsehood))) = implies(not(or(not(x),not(not(falsehood)))),or(not(not(x)),not(falsehood))),
inference(unit_resolution,[status(thm)],[257,30]) ).
tff(259,plain,
implies(not(or(not(x),not(not(falsehood)))),or(not(not(x)),not(falsehood))) = or(or(not(x),not(not(falsehood))),or(not(not(x)),not(falsehood))),
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(not(or(not(x),not(not(falsehood)))),or(not(not(x)),not(falsehood)))) = implies(not(or(not(x),not(not(falsehood)))),or(not(not(x)),not(falsehood))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(261,plain,
implies(truth,implies(not(or(not(x),not(not(falsehood)))),or(not(not(x)),not(falsehood)))) = implies(not(or(not(x),not(not(falsehood)))),or(not(not(x)),not(falsehood))),
inference(unit_resolution,[status(thm)],[260,7]) ).
tff(262,plain,
implies(and(x,not(falsehood)),or(not(not(x)),not(falsehood))) = implies(not(or(not(x),not(not(falsehood)))),or(not(not(x)),not(falsehood))),
inference(monotonicity,[status(thm)],[127]) ).
tff(263,plain,
implies(not(or(not(x),not(not(falsehood)))),or(not(not(x)),not(falsehood))) = implies(and(x,not(falsehood)),or(not(not(x)),not(falsehood))),
inference(symmetry,[status(thm)],[262]) ).
tff(264,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(not(x)),not(falsehood)) = implies(not(not(not(x))),not(falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(265,plain,
or(not(not(x)),not(falsehood)) = implies(not(not(not(x))),not(falsehood)),
inference(unit_resolution,[status(thm)],[264,30]) ).
tff(266,plain,
implies(not(not(not(x))),not(falsehood)) = or(not(not(x)),not(falsehood)),
inference(symmetry,[status(thm)],[265]) ).
tff(267,plain,
implies(implies(not(falsehood),not(falsehood)),implies(not(not(not(x))),not(falsehood))) = implies(truth,or(not(not(x)),not(falsehood))),
inference(monotonicity,[status(thm)],[193,266]) ).
tff(268,plain,
implies(truth,or(not(not(x)),not(falsehood))) = implies(implies(not(falsehood),not(falsehood)),implies(not(not(not(x))),not(falsehood))),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,or(not(not(x)),not(falsehood))) = or(not(not(x)),not(falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(270,plain,
implies(truth,or(not(not(x)),not(falsehood))) = or(not(not(x)),not(falsehood)),
inference(unit_resolution,[status(thm)],[269,7]) ).
tff(271,plain,
or(not(not(x)),not(falsehood)) = implies(truth,or(not(not(x)),not(falsehood))),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
or(not(not(x)),not(falsehood)) = implies(implies(not(falsehood),not(falsehood)),implies(not(not(not(x))),not(falsehood))),
inference(transitivity,[status(thm)],[271,268]) ).
tff(273,plain,
implies(or(not(not(x)),not(falsehood)),or(not(not(x)),not(falsehood))) = implies(implies(not(not(not(x))),not(falsehood)),implies(implies(not(falsehood),not(falsehood)),implies(not(not(not(x))),not(falsehood)))),
inference(monotonicity,[status(thm)],[265,272]) ).
tff(274,plain,
implies(implies(not(not(not(x))),not(falsehood)),implies(implies(not(falsehood),not(falsehood)),implies(not(not(not(x))),not(falsehood)))) = implies(or(not(not(x)),not(falsehood)),or(not(not(x)),not(falsehood))),
inference(symmetry,[status(thm)],[273]) ).
tff(275,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))),not(falsehood)),implies(implies(not(falsehood),not(falsehood)),implies(not(not(not(x))),not(falsehood)))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(276,plain,
implies(implies(not(not(not(x))),not(falsehood)),implies(implies(not(falsehood),not(falsehood)),implies(not(not(not(x))),not(falsehood)))) = truth,
inference(unit_resolution,[status(thm)],[275,76]) ).
tff(277,plain,
truth = implies(implies(not(not(not(x))),not(falsehood)),implies(implies(not(falsehood),not(falsehood)),implies(not(not(not(x))),not(falsehood)))),
inference(symmetry,[status(thm)],[276]) ).
tff(278,plain,
truth = implies(or(not(not(x)),not(falsehood)),or(not(not(x)),not(falsehood))),
inference(transitivity,[status(thm)],[277,274]) ).
tff(279,plain,
implies(truth,implies(not(or(not(x),not(not(falsehood)))),or(not(not(x)),not(falsehood)))) = implies(implies(or(not(not(x)),not(falsehood)),or(not(not(x)),not(falsehood))),implies(and(x,not(falsehood)),or(not(not(x)),not(falsehood)))),
inference(monotonicity,[status(thm)],[278,263]) ).
tff(280,plain,
implies(implies(or(not(not(x)),not(falsehood)),or(not(not(x)),not(falsehood))),implies(and(x,not(falsehood)),or(not(not(x)),not(falsehood)))) = implies(truth,implies(not(or(not(x),not(not(falsehood)))),or(not(not(x)),not(falsehood)))),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
implies(falsehood,and(x,not(falsehood))) = or(not(not(x)),not(falsehood)),
inference(transitivity,[status(thm)],[154,153,152,148]) ).
tff(282,plain,
implies(implies(truth,and(x,not(falsehood))),implies(falsehood,and(x,not(falsehood)))) = implies(and(x,not(falsehood)),or(not(not(x)),not(falsehood))),
inference(monotonicity,[status(thm)],[187,281]) ).
tff(283,plain,
implies(and(x,not(falsehood)),or(not(not(x)),not(falsehood))) = implies(implies(truth,and(x,not(falsehood))),implies(falsehood,and(x,not(falsehood)))),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
implies(implies(falsehood,truth),implies(truth,truth)) = implies(implies(falsehood,truth),truth),
inference(monotonicity,[status(thm)],[66]) ).
tff(285,plain,
implies(implies(falsehood,truth),truth) = implies(implies(falsehood,truth),implies(truth,truth)),
inference(symmetry,[status(thm)],[284]) ).
tff(286,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(287,plain,
implies(implies(falsehood,truth),truth) = implies(implies(truth,falsehood),falsehood),
inference(unit_resolution,[status(thm)],[286,62]) ).
tff(288,plain,
implies(implies(truth,falsehood),falsehood) = implies(implies(falsehood,truth),truth),
inference(symmetry,[status(thm)],[287]) ).
tff(289,plain,
implies(implies(truth,falsehood),falsehood) = implies(not(truth),not(truth)),
inference(monotonicity,[status(thm)],[170,79]) ).
tff(290,plain,
implies(not(truth),not(truth)) = implies(implies(truth,falsehood),falsehood),
inference(symmetry,[status(thm)],[289]) ).
tff(291,plain,
truth = implies(implies(falsehood,truth),implies(truth,truth)),
inference(transitivity,[status(thm)],[180,177,167,174,290,288,285]) ).
tff(292,plain,
falsehood = implies(truth,falsehood),
inference(symmetry,[status(thm)],[169]) ).
tff(293,plain,
implies(falsehood,truth) = implies(implies(truth,falsehood),implies(implies(falsehood,truth),implies(truth,truth))),
inference(monotonicity,[status(thm)],[292,291]) ).
tff(294,plain,
implies(implies(truth,falsehood),implies(implies(falsehood,truth),implies(truth,truth))) = implies(falsehood,truth),
inference(symmetry,[status(thm)],[293]) ).
tff(295,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(296,plain,
implies(implies(truth,falsehood),implies(implies(falsehood,truth),implies(truth,truth))) = truth,
inference(unit_resolution,[status(thm)],[295,76]) ).
tff(297,plain,
truth = implies(implies(truth,falsehood),implies(implies(falsehood,truth),implies(truth,truth))),
inference(symmetry,[status(thm)],[296]) ).
tff(298,plain,
implies(or(not(not(x)),not(falsehood)),or(not(not(x)),not(falsehood))) = implies(falsehood,truth),
inference(transitivity,[status(thm)],[273,276,297,294]) ).
tff(299,plain,
implies(implies(or(not(not(x)),not(falsehood)),or(not(not(x)),not(falsehood))),implies(and(x,not(falsehood)),or(not(not(x)),not(falsehood)))) = implies(implies(falsehood,truth),implies(implies(truth,and(x,not(falsehood))),implies(falsehood,and(x,not(falsehood))))),
inference(monotonicity,[status(thm)],[298,283]) ).
tff(300,plain,
implies(implies(falsehood,truth),implies(implies(truth,and(x,not(falsehood))),implies(falsehood,and(x,not(falsehood))))) = implies(implies(or(not(not(x)),not(falsehood)),or(not(not(x)),not(falsehood))),implies(and(x,not(falsehood)),or(not(not(x)),not(falsehood)))),
inference(symmetry,[status(thm)],[299]) ).
tff(301,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(falsehood,truth),implies(implies(truth,and(x,not(falsehood))),implies(falsehood,and(x,not(falsehood))))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(302,plain,
implies(implies(falsehood,truth),implies(implies(truth,and(x,not(falsehood))),implies(falsehood,and(x,not(falsehood))))) = truth,
inference(unit_resolution,[status(thm)],[301,76]) ).
tff(303,plain,
truth = implies(implies(falsehood,truth),implies(implies(truth,and(x,not(falsehood))),implies(falsehood,and(x,not(falsehood))))),
inference(symmetry,[status(thm)],[302]) ).
tff(304,plain,
truth = or(not(not(x)),not(falsehood)),
inference(transitivity,[status(thm)],[303,300,280,261,259,256,253,243,158,156,154,153,152,148]) ).
tff(305,plain,
implies(truth,and(x,not(falsehood))) = implies(or(not(not(x)),not(falsehood)),and(x,not(falsehood))),
inference(monotonicity,[status(thm)],[304]) ).
tff(306,plain,
implies(not(falsehood),and(x,not(falsehood))) = implies(truth,and(x,not(falsehood))),
inference(monotonicity,[status(thm)],[93]) ).
tff(307,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(falsehood,and(x,not(falsehood))) = implies(not(falsehood),and(x,not(falsehood))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(308,plain,
or(falsehood,and(x,not(falsehood))) = implies(not(falsehood),and(x,not(falsehood))),
inference(unit_resolution,[status(thm)],[307,30]) ).
tff(309,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(falsehood,and(x,not(falsehood))) = or(and(x,not(falsehood)),falsehood) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(310,plain,
or(falsehood,and(x,not(falsehood))) = or(and(x,not(falsehood)),falsehood),
inference(unit_resolution,[status(thm)],[309,39]) ).
tff(311,plain,
or(and(x,not(falsehood)),falsehood) = or(falsehood,and(x,not(falsehood))),
inference(symmetry,[status(thm)],[310]) ).
tff(312,plain,
implies(not(or(not(x),not(not(falsehood)))),or(not(not(x)),not(falsehood))) = implies(truth,implies(not(or(not(x),not(not(falsehood)))),or(not(not(x)),not(falsehood)))),
inference(symmetry,[status(thm)],[261]) ).
tff(313,plain,
implies(not(truth),and(x,not(falsehood))) = or(truth,and(x,not(falsehood))),
inference(symmetry,[status(thm)],[158]) ).
tff(314,plain,
or(not(not(x)),not(falsehood)) = truth,
inference(transitivity,[status(thm)],[149,146,145,143,155,313,242,252,255,258,312,279,299,302]) ).
tff(315,plain,
not(or(not(not(x)),not(falsehood))) = not(truth),
inference(monotonicity,[status(thm)],[314]) ).
tff(316,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) )
| ( and(not(x),falsehood) = not(or(not(not(x)),not(falsehood))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(317,plain,
and(not(x),falsehood) = not(or(not(not(x)),not(falsehood))),
inference(unit_resolution,[status(thm)],[316,125]) ).
tff(318,plain,
and(not(x),falsehood) = falsehood,
inference(transitivity,[status(thm)],[317,315,21]) ).
tff(319,plain,
or(and(x,not(falsehood)),and(not(x),falsehood)) = or(and(x,not(falsehood)),falsehood),
inference(monotonicity,[status(thm)],[318]) ).
tff(320,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(321,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)],[320]) ).
tff(322,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(323,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(324,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
inference(modus_ponens,[status(thm)],[323,322]) ).
tff(325,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
inference(skolemize,[status(sab)],[324]) ).
tff(326,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
inference(modus_ponens,[status(thm)],[325,321]) ).
tff(327,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) )
| ( xor(x,falsehood) = or(and(x,not(falsehood)),and(not(x),falsehood)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(328,plain,
xor(x,falsehood) = or(and(x,not(falsehood)),and(not(x),falsehood)),
inference(unit_resolution,[status(thm)],[327,326]) ).
tff(329,plain,
xor(x,falsehood) = x,
inference(transitivity,[status(thm)],[328,319,311,308,306,305,151,133,130,103,102,99,96,94,9]) ).
tff(330,plain,
( ( xor(x,falsehood) != x )
<=> ( xor(x,falsehood) != x ) ),
inference(rewrite,[status(thm)],[]) ).
tff(331,axiom,
xor(x,falsehood) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
tff(332,plain,
xor(x,falsehood) != x,
inference(modus_ponens,[status(thm)],[331,330]) ).
tff(333,plain,
$false,
inference(unit_resolution,[status(thm)],[332,329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL154-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 00:25:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 4.07/4.38 % SZS status Unsatisfiable
% 4.07/4.38 % SZS output start Proof
% See solution above
% 4.07/4.40 % E exiting
%------------------------------------------------------------------------------