TSTP Solution File: LCL154-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL154-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 04:55:06 EDT 2022
% Result : Unsatisfiable 1.27s 1.06s
% Output : Proof 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 79
% Syntax : Number of formulae : 288 ( 219 unt; 8 typ; 0 def)
% Number of atoms : 359 ( 349 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 118 ( 48 ~; 41 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 243 ( 225 !; 0 ?; 243 :)
% Comments :
%------------------------------------------------------------------------------
tff(x_type,type,
x: $i ).
tff(xor_type,type,
xor: ( $i * $i ) > $i ).
tff(not_type,type,
not: $i > $i ).
tff(truth_type,type,
truth: $i ).
tff(implies_type,type,
implies: ( $i * $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(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/sandbox/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(
( ( or(X,Y) = or(Y,X) )
<=> ( or(X,Y) = or(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',or_commutativity) ).
tff(14,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(truth),not(not(truth))) = or(not(not(truth)),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
or(not(truth),not(not(truth))) = or(not(not(truth)),not(truth)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,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(20,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)],[19]) ).
tff(21,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(22,axiom,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
tff(23,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(or(not(not(x)),not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
implies(implies(or(not(not(x)),not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,not(not(truth))) = not(not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(unit_resolution,[status(thm)],[28,7]) ).
tff(30,plain,
not(not(truth)) = implies(truth,not(not(truth))),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
implies(implies(or(not(not(x)),not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(or(not(not(x)),not(not(truth))),not(not(truth))),implies(truth,not(not(truth)))),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
implies(implies(or(not(not(x)),not(not(truth))),not(not(truth))),implies(truth,not(not(truth)))) = implies(implies(or(not(not(x)),not(not(truth))),not(not(truth))),not(not(truth))),
inference(symmetry,[status(thm)],[31]) ).
tff(33,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(34,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)],[33]) ).
tff(35,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(36,axiom,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).
tff(37,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(not(not(not(x)))),not(truth)),implies(truth,not(not(not(x))))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
implies(implies(not(not(not(not(x)))),not(truth)),implies(truth,not(not(not(x))))) = truth,
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,not(not(not(x)))) = not(not(not(x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
implies(truth,not(not(not(x)))) = not(not(not(x))),
inference(unit_resolution,[status(thm)],[42,7]) ).
tff(44,plain,
not(not(not(x))) = implies(truth,not(not(not(x)))),
inference(symmetry,[status(thm)],[43]) ).
tff(45,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(46,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)],[45]) ).
tff(47,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(48,axiom,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',or_definition) ).
tff(49,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(not(not(x))),not(truth)) = implies(not(not(not(not(x)))),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
or(not(not(not(x))),not(truth)) = implies(not(not(not(not(x)))),not(truth)),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(truth),not(not(not(x)))) = or(not(not(not(x))),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
or(not(truth),not(not(not(x)))) = or(not(not(not(x))),not(truth)),
inference(unit_resolution,[status(thm)],[54,16]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(truth),not(not(not(x)))) = implies(not(not(truth)),not(not(not(x)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
or(not(truth),not(not(not(x)))) = implies(not(not(truth)),not(not(not(x)))),
inference(unit_resolution,[status(thm)],[56,51]) ).
tff(58,plain,
implies(not(not(truth)),not(not(not(x)))) = or(not(truth),not(not(not(x)))),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
implies(not(not(truth)),not(not(not(x)))) = implies(not(not(not(not(x)))),not(truth)),
inference(transitivity,[status(thm)],[58,55,53]) ).
tff(60,plain,
implies(implies(not(not(truth)),not(not(not(x)))),not(not(not(x)))) = implies(implies(not(not(not(not(x)))),not(truth)),implies(truth,not(not(not(x))))),
inference(monotonicity,[status(thm)],[59,44]) ).
tff(61,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(not(not(truth)),not(not(not(x)))),not(not(not(x)))) = implies(implies(not(not(not(x))),not(not(truth))),not(not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
implies(implies(not(not(truth)),not(not(not(x)))),not(not(not(x)))) = implies(implies(not(not(not(x))),not(not(truth))),not(not(truth))),
inference(unit_resolution,[status(thm)],[61,25]) ).
tff(63,plain,
implies(implies(not(not(not(x))),not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),not(not(not(x)))),not(not(not(x)))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(not(x)),not(not(truth))) = implies(not(not(not(x))),not(not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
or(not(not(x)),not(not(truth))) = implies(not(not(not(x))),not(not(truth))),
inference(unit_resolution,[status(thm)],[64,51]) ).
tff(66,plain,
implies(or(not(not(x)),not(not(truth))),not(not(truth))) = implies(implies(not(not(not(x))),not(not(truth))),not(not(truth))),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
implies(or(not(not(x)),not(not(truth))),not(not(truth))) = truth,
inference(transitivity,[status(thm)],[66,63,60,41]) ).
tff(68,plain,
implies(implies(or(not(not(x)),not(not(truth))),not(not(truth))),implies(truth,not(not(truth)))) = implies(truth,not(not(truth))),
inference(monotonicity,[status(thm)],[67,29]) ).
tff(69,plain,
implies(truth,not(not(truth))) = implies(implies(or(not(not(x)),not(not(truth))),not(not(truth))),implies(truth,not(not(truth)))),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
not(not(truth)) = implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))),
inference(transitivity,[status(thm)],[30,69,32,27]) ).
tff(71,plain,
or(not(truth),not(not(truth))) = or(not(truth),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
or(not(truth),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))) = or(not(truth),not(not(truth))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(truth),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))) = implies(not(not(truth)),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
or(not(truth),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))) = implies(not(not(truth)),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))),
inference(unit_resolution,[status(thm)],[73,51]) ).
tff(75,plain,
implies(not(not(truth)),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))) = or(not(truth),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
implies(not(not(truth)),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))) = implies(implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))),
inference(monotonicity,[status(thm)],[70]) ).
tff(77,plain,
implies(implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))) = implies(not(not(truth)),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))) = implies(implies(or(not(not(x)),not(not(truth))),not(not(truth))),not(not(truth))),
inference(symmetry,[status(thm)],[27]) ).
tff(79,plain,
implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))) = not(not(truth)),
inference(transitivity,[status(thm)],[78,31,68,29]) ).
tff(80,plain,
implies(truth,implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))) = implies(truth,not(not(truth))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
implies(truth,not(not(truth))) = implies(truth,implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))) = implies(truth,implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))),
inference(transitivity,[status(thm)],[78,31,68,81]) ).
tff(83,plain,
implies(implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))) = implies(implies(truth,implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
implies(implies(truth,implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))) = implies(implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))),truth),truth) = implies(implies(truth,implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
implies(implies(implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))),truth),truth) = implies(implies(truth,implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))),implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth))))),
inference(unit_resolution,[status(thm)],[85,25]) ).
tff(87,plain,
implies(implies(truth,not(not(truth))),implies(or(not(not(x)),not(not(truth))),not(not(truth)))) = implies(not(not(truth)),truth),
inference(monotonicity,[status(thm)],[29,67]) ).
tff(88,plain,
implies(not(not(truth)),truth) = implies(implies(truth,not(not(truth))),implies(or(not(not(x)),not(not(truth))),not(not(truth)))),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
implies(implies(not(not(truth)),not(not(not(x)))),implies(truth,not(not(not(x))))) = implies(implies(not(not(not(not(x)))),not(truth)),implies(truth,not(not(not(x))))),
inference(monotonicity,[status(thm)],[59]) ).
tff(90,plain,
implies(implies(not(not(not(not(x)))),not(truth)),implies(truth,not(not(not(x))))) = implies(implies(not(not(truth)),not(not(not(x)))),implies(truth,not(not(not(x))))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
truth = implies(implies(not(not(not(not(x)))),not(truth)),implies(truth,not(not(not(x))))),
inference(symmetry,[status(thm)],[41]) ).
tff(92,plain,
truth = implies(implies(not(not(truth)),not(not(not(x)))),implies(truth,not(not(not(x))))),
inference(transitivity,[status(thm)],[91,90]) ).
tff(93,plain,
implies(not(not(truth)),truth) = implies(implies(truth,not(not(truth))),implies(implies(not(not(truth)),not(not(not(x)))),implies(truth,not(not(not(x)))))),
inference(monotonicity,[status(thm)],[30,92]) ).
tff(94,plain,
implies(implies(truth,not(not(truth))),implies(implies(not(not(truth)),not(not(not(x)))),implies(truth,not(not(not(x)))))) = implies(not(not(truth)),truth),
inference(symmetry,[status(thm)],[93]) ).
tff(95,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(96,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)],[95]) ).
tff(97,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(98,axiom,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
tff(99,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,not(not(truth))),implies(implies(not(not(truth)),not(not(not(x)))),implies(truth,not(not(not(x)))))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
implies(implies(truth,not(not(truth))),implies(implies(not(not(truth)),not(not(not(x)))),implies(truth,not(not(not(x)))))) = truth,
inference(unit_resolution,[status(thm)],[102,101]) ).
tff(104,plain,
truth = implies(implies(truth,not(not(truth))),implies(implies(not(not(truth)),not(not(not(x)))),implies(truth,not(not(not(x)))))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
truth = implies(implies(truth,not(not(truth))),implies(or(not(not(x)),not(not(truth))),not(not(truth)))),
inference(transitivity,[status(thm)],[104,94,88]) ).
tff(106,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(107,plain,
or(truth,not(not(x))) = implies(not(truth),not(not(x))),
inference(unit_resolution,[status(thm)],[106,51]) ).
tff(108,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(not(x)),truth) = or(truth,not(not(x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
or(not(not(x)),truth) = or(truth,not(not(x))),
inference(unit_resolution,[status(thm)],[108,16]) ).
tff(110,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(not(x)),truth) = implies(not(not(not(x))),truth) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
or(not(not(x)),truth) = implies(not(not(not(x))),truth),
inference(unit_resolution,[status(thm)],[110,51]) ).
tff(112,plain,
implies(not(not(not(x))),truth) = or(not(not(x)),truth),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
implies(or(not(not(not(x))),not(truth)),not(not(not(x)))) = implies(implies(not(not(not(not(x)))),not(truth)),implies(truth,not(not(not(x))))),
inference(monotonicity,[status(thm)],[53,44]) ).
tff(114,plain,
implies(implies(not(not(not(not(x)))),not(truth)),implies(truth,not(not(not(x))))) = implies(or(not(not(not(x))),not(truth)),not(not(not(x)))),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
truth = implies(or(not(not(not(x))),not(truth)),not(not(not(x)))),
inference(transitivity,[status(thm)],[91,114]) ).
tff(116,plain,
implies(truth,not(not(not(x)))) = implies(implies(or(not(not(not(x))),not(truth)),not(not(not(x)))),implies(truth,not(not(not(x))))),
inference(monotonicity,[status(thm)],[115,44]) ).
tff(117,plain,
implies(implies(or(not(not(not(x))),not(truth)),not(not(not(x)))),implies(truth,not(not(not(x))))) = implies(truth,not(not(not(x)))),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
implies(implies(or(not(not(not(x))),not(truth)),not(not(not(x)))),implies(truth,not(not(not(x))))) = implies(implies(or(not(not(not(x))),not(truth)),not(not(not(x)))),not(not(not(x)))),
inference(monotonicity,[status(thm)],[43]) ).
tff(119,plain,
implies(implies(or(not(not(not(x))),not(truth)),not(not(not(x)))),not(not(not(x)))) = implies(implies(or(not(not(not(x))),not(truth)),not(not(not(x)))),implies(truth,not(not(not(x))))),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(or(not(not(not(x))),not(truth)),not(not(not(x)))),not(not(not(x)))) = implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
implies(implies(or(not(not(not(x))),not(truth)),not(not(not(x)))),not(not(not(x)))) = implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth))),
inference(unit_resolution,[status(thm)],[120,25]) ).
tff(122,plain,
implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth))) = implies(implies(or(not(not(not(x))),not(truth)),not(not(not(x)))),not(not(not(x)))),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth))) = not(not(not(x))),
inference(transitivity,[status(thm)],[122,119,117,43]) ).
tff(124,plain,
implies(implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth))),not(not(truth))) = implies(not(not(not(x))),not(not(truth))),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
implies(implies(implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth))),not(not(truth))),implies(truth,not(not(truth)))) = implies(implies(not(not(not(x))),not(not(truth))),not(not(truth))),
inference(monotonicity,[status(thm)],[124,29]) ).
tff(126,plain,
implies(implies(not(not(not(x))),not(not(truth))),not(not(truth))) = implies(implies(implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth))),not(not(truth))),implies(truth,not(not(truth)))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
implies(implies(not(not(not(not(x)))),not(truth)),implies(truth,not(not(not(x))))) = implies(implies(not(not(truth)),not(not(not(x)))),not(not(not(x)))),
inference(symmetry,[status(thm)],[60]) ).
tff(128,plain,
truth = implies(implies(implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth))),not(not(truth))),implies(truth,not(not(truth)))),
inference(transitivity,[status(thm)],[91,127,62,126]) ).
tff(129,plain,
implies(truth,implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth)))) = implies(truth,not(not(not(x)))),
inference(monotonicity,[status(thm)],[123]) ).
tff(130,plain,
implies(truth,not(not(not(x)))) = implies(truth,implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth)))),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
not(not(not(x))) = implies(truth,implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth)))),
inference(transitivity,[status(thm)],[44,130]) ).
tff(132,plain,
implies(not(not(not(x))),truth) = implies(implies(truth,implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth)))),implies(implies(implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth))),not(not(truth))),implies(truth,not(not(truth))))),
inference(monotonicity,[status(thm)],[131,128]) ).
tff(133,plain,
implies(implies(truth,implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth)))),implies(implies(implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth))),not(not(truth))),implies(truth,not(not(truth))))) = implies(not(not(not(x))),truth),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth)))),implies(implies(implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth))),not(not(truth))),implies(truth,not(not(truth))))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
implies(implies(truth,implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth)))),implies(implies(implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth))),not(not(truth))),implies(truth,not(not(truth))))) = truth,
inference(unit_resolution,[status(thm)],[134,101]) ).
tff(136,plain,
truth = implies(implies(truth,implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth)))),implies(implies(implies(implies(not(not(not(x))),or(not(not(not(x))),not(truth))),or(not(not(not(x))),not(truth))),not(not(truth))),implies(truth,not(not(truth))))),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
truth = implies(not(truth),not(not(x))),
inference(transitivity,[status(thm)],[136,133,112,109,107]) ).
tff(138,plain,
implies(or(not(not(x)),not(not(truth))),truth) = implies(implies(not(not(not(x))),not(not(truth))),implies(not(truth),not(not(x)))),
inference(monotonicity,[status(thm)],[65,137]) ).
tff(139,plain,
implies(implies(not(not(not(x))),not(not(truth))),implies(not(truth),not(not(x)))) = implies(or(not(not(x)),not(not(truth))),truth),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(not(not(x))),not(not(truth))),implies(not(truth),not(not(x)))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
implies(implies(not(not(not(x))),not(not(truth))),implies(not(truth),not(not(x)))) = truth,
inference(unit_resolution,[status(thm)],[140,39]) ).
tff(142,plain,
truth = implies(implies(not(not(not(x))),not(not(truth))),implies(not(truth),not(not(x)))),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
implies(implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))),truth) = implies(not(not(truth)),truth),
inference(monotonicity,[status(thm)],[79]) ).
tff(144,plain,
implies(implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))),truth) = implies(or(not(not(x)),not(not(truth))),truth),
inference(transitivity,[status(thm)],[143,93,103,142,139]) ).
tff(145,plain,
implies(implies(implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))),truth),truth) = implies(implies(or(not(not(x)),not(not(truth))),truth),implies(implies(truth,not(not(truth))),implies(or(not(not(x)),not(not(truth))),not(not(truth))))),
inference(monotonicity,[status(thm)],[144,105]) ).
tff(146,plain,
implies(implies(or(not(not(x)),not(not(truth))),truth),implies(implies(truth,not(not(truth))),implies(or(not(not(x)),not(not(truth))),not(not(truth))))) = implies(implies(implies(implies(not(not(truth)),or(not(not(x)),not(not(truth)))),or(not(not(x)),not(not(truth)))),truth),truth),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(or(not(not(x)),not(not(truth))),truth),implies(implies(truth,not(not(truth))),implies(or(not(not(x)),not(not(truth))),not(not(truth))))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(148,plain,
implies(implies(or(not(not(x)),not(not(truth))),truth),implies(implies(truth,not(not(truth))),implies(or(not(not(x)),not(not(truth))),not(not(truth))))) = truth,
inference(unit_resolution,[status(thm)],[147,101]) ).
tff(149,plain,
truth = implies(implies(or(not(not(x)),not(not(truth))),truth),implies(implies(truth,not(not(truth))),implies(or(not(not(x)),not(not(truth))),not(not(truth))))),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
truth = or(not(not(truth)),not(truth)),
inference(transitivity,[status(thm)],[149,146,86,84,77,75,72,18]) ).
tff(151,plain,
not(truth) = not(or(not(not(truth)),not(truth))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
not(or(not(not(truth)),not(truth))) = not(truth),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
not(not(or(not(not(truth)),not(truth)))) = not(not(truth)),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
not(not(truth)) = not(not(or(not(not(truth)),not(truth)))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(not(truth)),not(truth)) = implies(not(not(not(truth))),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
or(not(not(truth)),not(truth)) = implies(not(not(not(truth))),not(truth)),
inference(unit_resolution,[status(thm)],[155,51]) ).
tff(157,plain,
truth = implies(not(not(not(truth))),not(truth)),
inference(transitivity,[status(thm)],[149,146,86,84,77,75,72,18,156]) ).
tff(158,plain,
implies(truth,not(not(truth))) = implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))),
inference(monotonicity,[status(thm)],[157,30]) ).
tff(159,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))) = implies(truth,not(not(truth))),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))) = truth,
inference(unit_resolution,[status(thm)],[160,39]) ).
tff(162,plain,
truth = implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))),
inference(symmetry,[status(thm)],[161]) ).
tff(163,plain,
truth = not(not(or(not(not(truth)),not(truth)))),
inference(transitivity,[status(thm)],[162,159,29,154]) ).
tff(164,plain,
implies(truth,x) = implies(not(not(or(not(not(truth)),not(truth)))),x),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
implies(not(not(or(not(not(truth)),not(truth)))),x) = implies(truth,x),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(or(not(not(truth)),not(truth))),x) = implies(not(not(or(not(not(truth)),not(truth)))),x) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(167,plain,
or(not(or(not(not(truth)),not(truth))),x) = implies(not(not(or(not(not(truth)),not(truth)))),x),
inference(unit_resolution,[status(thm)],[166,51]) ).
tff(168,plain,
or(not(or(not(not(truth)),not(truth))),x) = or(not(truth),x),
inference(monotonicity,[status(thm)],[152]) ).
tff(169,plain,
or(not(truth),x) = or(not(or(not(not(truth)),not(truth))),x),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(truth),x) = or(x,not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
or(not(truth),x) = or(x,not(truth)),
inference(unit_resolution,[status(thm)],[170,16]) ).
tff(172,plain,
or(x,not(truth)) = or(not(truth),x),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(x,not(truth)) = implies(not(x),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
or(x,not(truth)) = implies(not(x),not(truth)),
inference(unit_resolution,[status(thm)],[173,51]) ).
tff(175,plain,
implies(not(x),not(truth)) = or(x,not(truth)),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(truth),not(x)) = implies(not(not(truth)),not(x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(177,plain,
or(not(truth),not(x)) = implies(not(not(truth)),not(x)),
inference(unit_resolution,[status(thm)],[176,51]) ).
tff(178,plain,
implies(not(not(truth)),not(x)) = or(not(truth),not(x)),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
truth = not(not(truth)),
inference(transitivity,[status(thm)],[162,159,29]) ).
tff(180,plain,
implies(truth,not(x)) = implies(not(not(truth)),not(x)),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,not(x)) = not(x) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,plain,
implies(truth,not(x)) = not(x),
inference(unit_resolution,[status(thm)],[181,7]) ).
tff(183,plain,
not(x) = implies(truth,not(x)),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
not(x) = or(not(truth),not(x)),
inference(transitivity,[status(thm)],[183,180,178]) ).
tff(185,plain,
not(not(x)) = not(or(not(truth),not(x))),
inference(monotonicity,[status(thm)],[184]) ).
tff(186,plain,
not(or(not(truth),not(x))) = not(not(x)),
inference(symmetry,[status(thm)],[185]) ).
tff(187,plain,
implies(not(or(not(truth),not(x))),not(or(not(not(truth)),not(truth)))) = implies(not(not(x)),not(truth)),
inference(monotonicity,[status(thm)],[186,152]) ).
tff(188,plain,
implies(not(not(x)),not(truth)) = implies(not(or(not(truth),not(x))),not(or(not(not(truth)),not(truth)))),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(x),not(truth)) = implies(not(not(x)),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(190,plain,
or(not(x),not(truth)) = implies(not(not(x)),not(truth)),
inference(unit_resolution,[status(thm)],[189,51]) ).
tff(191,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(x),not(truth)) = or(not(truth),not(x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(192,plain,
or(not(x),not(truth)) = or(not(truth),not(x)),
inference(unit_resolution,[status(thm)],[191,16]) ).
tff(193,plain,
or(not(truth),not(x)) = or(not(x),not(truth)),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
not(x) = implies(not(or(not(truth),not(x))),not(or(not(not(truth)),not(truth)))),
inference(transitivity,[status(thm)],[183,180,178,193,190,188]) ).
tff(195,plain,
implies(not(x),not(truth)) = implies(implies(not(or(not(truth),not(x))),not(or(not(not(truth)),not(truth)))),not(or(not(not(truth)),not(truth)))),
inference(monotonicity,[status(thm)],[194,151]) ).
tff(196,plain,
implies(implies(not(or(not(truth),not(x))),not(or(not(not(truth)),not(truth)))),not(or(not(not(truth)),not(truth)))) = implies(not(x),not(truth)),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(not(or(not(truth),not(x))),not(or(not(not(truth)),not(truth)))),not(or(not(not(truth)),not(truth)))) = implies(implies(not(or(not(not(truth)),not(truth))),not(or(not(truth),not(x)))),not(or(not(truth),not(x)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(198,plain,
implies(implies(not(or(not(truth),not(x))),not(or(not(not(truth)),not(truth)))),not(or(not(not(truth)),not(truth)))) = implies(implies(not(or(not(not(truth)),not(truth))),not(or(not(truth),not(x)))),not(or(not(truth),not(x)))),
inference(unit_resolution,[status(thm)],[197,25]) ).
tff(199,plain,
implies(implies(not(or(not(not(truth)),not(truth))),not(or(not(truth),not(x)))),not(or(not(truth),not(x)))) = implies(implies(not(or(not(truth),not(x))),not(or(not(not(truth)),not(truth)))),not(or(not(not(truth)),not(truth)))),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
not(not(truth)) = truth,
inference(transitivity,[status(thm)],[30,158,161]) ).
tff(201,plain,
and(x,not(not(truth))) = and(x,truth),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,plain,
and(x,truth) = and(x,not(not(truth))),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
^ [Y: $i,X: $i] :
refl(
( ( and(X,Y) = and(Y,X) )
<=> ( and(X,Y) = and(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(204,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)],[203]) ).
tff(205,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(206,axiom,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',and_commutativity) ).
tff(207,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(modus_ponens,[status(thm)],[206,205]) ).
tff(208,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(skolemize,[status(sab)],[207]) ).
tff(209,plain,
! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) ),
inference(modus_ponens,[status(thm)],[208,204]) ).
tff(210,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = and(Y,X) )
| ( and(x,truth) = and(truth,x) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(211,plain,
and(x,truth) = and(truth,x),
inference(unit_resolution,[status(thm)],[210,209]) ).
tff(212,plain,
and(truth,x) = and(x,truth),
inference(symmetry,[status(thm)],[211]) ).
tff(213,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(214,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)],[213]) ).
tff(215,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(216,axiom,
! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',and_definition) ).
tff(217,plain,
! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ),
inference(skolemize,[status(sab)],[217]) ).
tff(219,plain,
! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) ),
inference(modus_ponens,[status(thm)],[218,214]) ).
tff(220,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) )
| ( and(truth,x) = not(or(not(truth),not(x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(221,plain,
and(truth,x) = not(or(not(truth),not(x))),
inference(unit_resolution,[status(thm)],[220,219]) ).
tff(222,plain,
not(or(not(truth),not(x))) = and(truth,x),
inference(symmetry,[status(thm)],[221]) ).
tff(223,plain,
not(or(not(truth),not(x))) = and(x,not(not(truth))),
inference(transitivity,[status(thm)],[222,212,202]) ).
tff(224,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,or(not(not(x)),not(not(truth)))) = or(not(not(x)),not(not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(225,plain,
implies(truth,or(not(not(x)),not(not(truth)))) = or(not(not(x)),not(not(truth))),
inference(unit_resolution,[status(thm)],[224,7]) ).
tff(226,plain,
implies(truth,or(not(not(x)),not(not(truth)))) = implies(implies(not(not(not(truth))),not(truth)),or(not(not(x)),not(not(truth)))),
inference(monotonicity,[status(thm)],[157]) ).
tff(227,plain,
implies(implies(not(not(not(truth))),not(truth)),or(not(not(x)),not(not(truth)))) = implies(truth,or(not(not(x)),not(not(truth)))),
inference(symmetry,[status(thm)],[226]) ).
tff(228,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(not(truth)),not(not(x))) = or(not(not(x)),not(not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(229,plain,
or(not(not(truth)),not(not(x))) = or(not(not(x)),not(not(truth))),
inference(unit_resolution,[status(thm)],[228,16]) ).
tff(230,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(not(truth)),not(not(x))) = implies(not(not(not(truth))),not(not(x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(231,plain,
or(not(not(truth)),not(not(x))) = implies(not(not(not(truth))),not(not(x))),
inference(unit_resolution,[status(thm)],[230,51]) ).
tff(232,plain,
implies(not(not(not(truth))),not(not(x))) = or(not(not(truth)),not(not(x))),
inference(symmetry,[status(thm)],[231]) ).
tff(233,plain,
implies(not(not(not(truth))),not(not(x))) = or(not(not(x)),not(not(truth))),
inference(transitivity,[status(thm)],[232,229]) ).
tff(234,plain,
or(truth,not(not(x))) = or(not(not(x)),truth),
inference(symmetry,[status(thm)],[109]) ).
tff(235,plain,
implies(not(truth),not(not(x))) = or(truth,not(not(x))),
inference(symmetry,[status(thm)],[107]) ).
tff(236,plain,
implies(not(truth),not(not(x))) = truth,
inference(transitivity,[status(thm)],[235,234,111,132,135]) ).
tff(237,plain,
implies(implies(not(truth),not(not(x))),implies(not(not(not(truth))),not(not(x)))) = implies(truth,or(not(not(x)),not(not(truth)))),
inference(monotonicity,[status(thm)],[236,233]) ).
tff(238,plain,
implies(truth,or(not(not(x)),not(not(truth)))) = implies(implies(not(truth),not(not(x))),implies(not(not(not(truth))),not(not(x)))),
inference(symmetry,[status(thm)],[237]) ).
tff(239,plain,
or(not(not(x)),not(not(truth))) = implies(truth,or(not(not(x)),not(not(truth)))),
inference(symmetry,[status(thm)],[225]) ).
tff(240,plain,
or(not(not(x)),not(not(truth))) = implies(implies(not(truth),not(not(x))),implies(not(not(not(truth))),not(not(x)))),
inference(transitivity,[status(thm)],[239,238]) ).
tff(241,plain,
implies(implies(not(not(not(truth))),not(truth)),or(not(not(x)),not(not(truth)))) = implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(truth),not(not(x))),implies(not(not(not(truth))),not(not(x))))),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(truth),not(not(x))),implies(not(not(not(truth))),not(not(x))))) = implies(implies(not(not(not(truth))),not(truth)),or(not(not(x)),not(not(truth)))),
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(truth),not(not(x))),implies(not(not(not(truth))),not(not(x))))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(244,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(truth),not(not(x))),implies(not(not(not(truth))),not(not(x))))) = truth,
inference(unit_resolution,[status(thm)],[243,101]) ).
tff(245,plain,
truth = implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(truth),not(not(x))),implies(not(not(not(truth))),not(not(x))))),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
implies(not(or(not(not(truth)),not(truth))),not(or(not(truth),not(x)))) = implies(not(truth),not(not(x))),
inference(monotonicity,[status(thm)],[152,186]) ).
tff(247,plain,
implies(not(or(not(not(truth)),not(truth))),not(or(not(truth),not(x)))) = or(not(not(x)),not(not(truth))),
inference(transitivity,[status(thm)],[246,235,234,111,132,135,245,242,227,225]) ).
tff(248,plain,
implies(implies(not(or(not(not(truth)),not(truth))),not(or(not(truth),not(x)))),not(or(not(truth),not(x)))) = implies(or(not(not(x)),not(not(truth))),and(x,not(not(truth)))),
inference(monotonicity,[status(thm)],[247,223]) ).
tff(249,plain,
implies(or(not(not(x)),not(not(truth))),and(x,not(not(truth)))) = implies(implies(not(or(not(not(truth)),not(truth))),not(or(not(truth),not(x)))),not(or(not(truth),not(x)))),
inference(symmetry,[status(thm)],[248]) ).
tff(250,plain,
or(not(not(x)),not(not(truth))) = truth,
inference(transitivity,[status(thm)],[239,226,241,244]) ).
tff(251,plain,
not(or(not(not(x)),not(not(truth)))) = not(truth),
inference(monotonicity,[status(thm)],[250]) ).
tff(252,plain,
( ~ ! [Y: $i,X: $i] : ( and(X,Y) = not(or(not(X),not(Y))) )
| ( and(not(x),not(truth)) = not(or(not(not(x)),not(not(truth)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(253,plain,
and(not(x),not(truth)) = not(or(not(not(x)),not(not(truth)))),
inference(unit_resolution,[status(thm)],[252,219]) ).
tff(254,plain,
and(not(x),not(truth)) = not(truth),
inference(transitivity,[status(thm)],[253,251]) ).
tff(255,plain,
not(and(not(x),not(truth))) = not(not(truth)),
inference(monotonicity,[status(thm)],[254]) ).
tff(256,plain,
not(not(truth)) = not(and(not(x),not(truth))),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
or(not(not(x)),not(not(truth))) = not(and(not(x),not(truth))),
inference(transitivity,[status(thm)],[239,226,241,244,162,159,29,256]) ).
tff(258,plain,
implies(or(not(not(x)),not(not(truth))),and(x,not(not(truth)))) = implies(not(and(not(x),not(truth))),and(x,not(not(truth)))),
inference(monotonicity,[status(thm)],[257]) ).
tff(259,plain,
implies(not(and(not(x),not(truth))),and(x,not(not(truth)))) = implies(or(not(not(x)),not(not(truth))),and(x,not(not(truth)))),
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(and(not(x),not(truth)),and(x,not(not(truth)))) = implies(not(and(not(x),not(truth))),and(x,not(not(truth)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(261,plain,
or(and(not(x),not(truth)),and(x,not(not(truth)))) = implies(not(and(not(x),not(truth))),and(x,not(not(truth)))),
inference(unit_resolution,[status(thm)],[260,51]) ).
tff(262,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(and(not(x),not(truth)),and(x,not(not(truth)))) = or(and(x,not(not(truth))),and(not(x),not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(263,plain,
or(and(not(x),not(truth)),and(x,not(not(truth)))) = or(and(x,not(not(truth))),and(not(x),not(truth))),
inference(unit_resolution,[status(thm)],[262,16]) ).
tff(264,plain,
or(and(x,not(not(truth))),and(not(x),not(truth))) = or(and(not(x),not(truth)),and(x,not(not(truth)))),
inference(symmetry,[status(thm)],[263]) ).
tff(265,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(266,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)],[265]) ).
tff(267,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(268,axiom,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',xor_definition) ).
tff(269,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
inference(modus_ponens,[status(thm)],[268,267]) ).
tff(270,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
inference(skolemize,[status(sab)],[269]) ).
tff(271,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
inference(modus_ponens,[status(thm)],[270,266]) ).
tff(272,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) )
| ( xor(x,not(truth)) = or(and(x,not(not(truth))),and(not(x),not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(273,plain,
xor(x,not(truth)) = or(and(x,not(not(truth))),and(not(x),not(truth))),
inference(unit_resolution,[status(thm)],[272,271]) ).
tff(274,plain,
xor(x,not(truth)) = x,
inference(transitivity,[status(thm)],[273,264,261,259,249,199,196,175,172,169,167,165,9]) ).
tff(275,plain,
( ( xor(x,falsehood) != x )
<=> ( xor(x,not(truth)) != x ) ),
inference(rewrite,[status(thm)],]) ).
tff(276,plain,
( ( xor(x,falsehood) != x )
<=> ( xor(x,falsehood) != x ) ),
inference(rewrite,[status(thm)],]) ).
tff(277,axiom,
xor(x,falsehood) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
tff(278,plain,
xor(x,falsehood) != x,
inference(modus_ponens,[status(thm)],[277,276]) ).
tff(279,plain,
xor(x,not(truth)) != x,
inference(modus_ponens,[status(thm)],[278,275]) ).
tff(280,plain,
$false,
inference(unit_resolution,[status(thm)],[279,274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL154-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 18:30:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.27/1.06 % SZS status Unsatisfiable
% 1.27/1.06 % SZS output start Proof
% See solution above
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