TSTP Solution File: LCL157-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL157-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 04:55:07 EDT 2022
% Result : Unsatisfiable 3.91s 2.75s
% Output : Proof 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 55
% Syntax : Number of formulae : 184 ( 137 unt; 7 typ; 0 def)
% Number of atoms : 231 ( 223 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 78 ( 31 ~; 24 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 173 ( 159 !; 0 ?; 173 :)
% Comments :
%------------------------------------------------------------------------------
tff(not_type,type,
not: $i > $i ).
tff(truth_type,type,
truth: $i ).
tff(and_star_type,type,
and_star: ( $i * $i ) > $i ).
tff(x_type,type,
x: $i ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(falsehood_type,type,
falsehood: $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,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(x)),implies(not(not(not(truth))),not(x)))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(truth),not(x)),implies(not(not(not(truth))),not(x)))) = truth,
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/sandbox2/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(not(truth)),not(x)) = or(not(x),not(not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
or(not(not(truth)),not(x)) = or(not(x),not(not(truth))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,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(20,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)],[19]) ).
tff(21,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(22,axiom,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_definition) ).
tff(23,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(not(truth)),not(x)) = implies(not(not(not(truth))),not(x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
or(not(not(truth)),not(x)) = implies(not(not(not(truth))),not(x)),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
implies(not(not(not(truth))),not(x)) = or(not(not(truth)),not(x)),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
implies(not(not(not(truth))),not(x)) = or(not(x),not(not(truth))),
inference(transitivity,[status(thm)],[28,18]) ).
tff(30,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth))))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth))))) = truth,
inference(unit_resolution,[status(thm)],[30,7]) ).
tff(32,plain,
^ [X: $i] :
refl(
( ( implies(truth,X) = X )
<=> ( implies(truth,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X: $i] : ( implies(truth,X) = X )
<=> ! [X: $i] : ( implies(truth,X) = X ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] : ( implies(truth,X) = X )
<=> ! [X: $i] : ( implies(truth,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [X: $i] : ( implies(truth,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
tff(36,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,not(not(truth))) = not(not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,not(not(x))) = not(not(x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
implies(truth,not(not(x))) = not(not(x)),
inference(unit_resolution,[status(thm)],[41,38]) ).
tff(43,plain,
not(not(x)) = implies(truth,not(not(x))),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(not(x)),not(truth)) = implies(not(not(not(x))),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
or(not(not(x)),not(truth)) = implies(not(not(not(x))),not(truth)),
inference(unit_resolution,[status(thm)],[44,25]) ).
tff(46,plain,
implies(or(not(not(x)),not(truth)),not(not(x))) = implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))),
inference(monotonicity,[status(thm)],[45,43]) ).
tff(47,plain,
implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))) = implies(or(not(not(x)),not(truth)),not(not(x))),
inference(symmetry,[status(thm)],[46]) ).
tff(48,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(49,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)],[48]) ).
tff(50,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(51,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(52,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth )
| ( implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))) = truth,
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
truth = implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
truth = implies(or(not(not(x)),not(truth)),not(not(x))),
inference(transitivity,[status(thm)],[57,47]) ).
tff(59,plain,
implies(truth,not(not(x))) = implies(implies(or(not(not(x)),not(truth)),not(not(x))),implies(truth,not(not(x)))),
inference(monotonicity,[status(thm)],[58,43]) ).
tff(60,plain,
implies(implies(or(not(not(x)),not(truth)),not(not(x))),implies(truth,not(not(x)))) = implies(truth,not(not(x))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
implies(implies(or(not(not(x)),not(truth)),not(not(x))),implies(truth,not(not(x)))) = implies(implies(or(not(not(x)),not(truth)),not(not(x))),not(not(x))),
inference(monotonicity,[status(thm)],[42]) ).
tff(62,plain,
implies(implies(or(not(not(x)),not(truth)),not(not(x))),not(not(x))) = implies(implies(or(not(not(x)),not(truth)),not(not(x))),implies(truth,not(not(x)))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,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(64,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)],[63]) ).
tff(65,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(66,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(67,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(or(not(not(x)),not(truth)),not(not(x))),not(not(x))) = implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
implies(implies(or(not(not(x)),not(truth)),not(not(x))),not(not(x))) = implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))) = implies(implies(or(not(not(x)),not(truth)),not(not(x))),not(not(x))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))) = not(not(x)),
inference(transitivity,[status(thm)],[72,62,60,42]) ).
tff(74,plain,
implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))) = implies(not(not(x)),not(not(truth))),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth)))) = implies(implies(not(not(x)),not(not(truth))),not(not(truth))),
inference(monotonicity,[status(thm)],[74,40]) ).
tff(76,plain,
implies(implies(not(not(x)),not(not(truth))),not(not(truth))) = implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth)))),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(not(not(truth)),not(not(x))),not(not(x))) = implies(implies(not(not(x)),not(not(truth))),not(not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
implies(implies(not(not(truth)),not(not(x))),not(not(x))) = implies(implies(not(not(x)),not(not(truth))),not(not(truth))),
inference(unit_resolution,[status(thm)],[77,69]) ).
tff(79,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(not(truth),not(not(x))) = or(not(not(x)),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
or(not(truth),not(not(x))) = or(not(not(x)),not(truth)),
inference(unit_resolution,[status(thm)],[79,16]) ).
tff(81,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(truth),not(not(x))) = implies(not(not(truth)),not(not(x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
or(not(truth),not(not(x))) = implies(not(not(truth)),not(not(x))),
inference(unit_resolution,[status(thm)],[81,25]) ).
tff(83,plain,
implies(not(not(truth)),not(not(x))) = or(not(truth),not(not(x))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
implies(not(not(truth)),not(not(x))) = implies(not(not(not(x))),not(truth)),
inference(transitivity,[status(thm)],[83,80,45]) ).
tff(85,plain,
implies(implies(not(not(truth)),not(not(x))),not(not(x))) = implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))),
inference(monotonicity,[status(thm)],[84,43]) ).
tff(86,plain,
implies(implies(not(not(not(x))),not(truth)),implies(truth,not(not(x)))) = implies(implies(not(not(truth)),not(not(x))),not(not(x))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
truth = implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth)))),
inference(transitivity,[status(thm)],[57,86,78,76]) ).
tff(88,plain,
implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))) = implies(truth,not(not(x))),
inference(monotonicity,[status(thm)],[73]) ).
tff(89,plain,
implies(truth,not(not(x))) = implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
not(not(x)) = implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),
inference(transitivity,[status(thm)],[43,89]) ).
tff(91,plain,
implies(not(not(x)),truth) = implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth))))),
inference(monotonicity,[status(thm)],[90,87]) ).
tff(92,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(x),truth) = implies(not(not(x)),truth) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
or(not(x),truth) = implies(not(not(x)),truth),
inference(unit_resolution,[status(thm)],[92,25]) ).
tff(94,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(95,plain,
or(not(x),truth) = or(truth,not(x)),
inference(unit_resolution,[status(thm)],[94,16]) ).
tff(96,plain,
or(truth,not(x)) = or(not(x),truth),
inference(symmetry,[status(thm)],[95]) ).
tff(97,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(98,plain,
or(truth,not(x)) = implies(not(truth),not(x)),
inference(unit_resolution,[status(thm)],[97,25]) ).
tff(99,plain,
implies(not(truth),not(x)) = or(truth,not(x)),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
implies(not(truth),not(x)) = truth,
inference(transitivity,[status(thm)],[99,96,93,91,31]) ).
tff(101,plain,
implies(implies(not(truth),not(x)),implies(not(not(not(truth))),not(x))) = implies(truth,or(not(x),not(not(truth)))),
inference(monotonicity,[status(thm)],[100,29]) ).
tff(102,plain,
implies(truth,or(not(x),not(not(truth)))) = implies(implies(not(truth),not(x)),implies(not(not(not(truth))),not(x))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,or(not(x),not(not(truth)))) = or(not(x),not(not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
implies(truth,or(not(x),not(not(truth)))) = or(not(x),not(not(truth))),
inference(unit_resolution,[status(thm)],[103,38]) ).
tff(105,plain,
or(not(x),not(not(truth))) = implies(truth,or(not(x),not(not(truth)))),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
or(not(x),not(not(truth))) = implies(implies(not(truth),not(x)),implies(not(not(not(truth))),not(x))),
inference(transitivity,[status(thm)],[105,102]) ).
tff(107,plain,
not(not(truth)) = implies(truth,not(not(truth))),
inference(symmetry,[status(thm)],[40]) ).
tff(108,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(x),not(not(truth))) = implies(not(not(x)),not(not(truth))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
or(not(x),not(not(truth))) = implies(not(not(x)),not(not(truth))),
inference(unit_resolution,[status(thm)],[108,25]) ).
tff(110,plain,
implies(or(not(x),not(not(truth))),not(not(truth))) = implies(implies(not(not(x)),not(not(truth))),not(not(truth))),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
implies(implies(not(not(x)),not(not(truth))),not(not(truth))) = implies(or(not(x),not(not(truth))),not(not(truth))),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
truth = implies(or(not(x),not(not(truth))),not(not(truth))),
inference(transitivity,[status(thm)],[57,86,78,111]) ).
tff(113,plain,
implies(truth,not(not(truth))) = implies(implies(or(not(x),not(not(truth))),not(not(truth))),implies(truth,not(not(truth)))),
inference(monotonicity,[status(thm)],[112,107]) ).
tff(114,plain,
implies(implies(or(not(x),not(not(truth))),not(not(truth))),implies(truth,not(not(truth)))) = implies(truth,not(not(truth))),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
implies(implies(or(not(x),not(not(truth))),not(not(truth))),implies(truth,not(not(truth)))) = implies(implies(or(not(x),not(not(truth))),not(not(truth))),not(not(truth))),
inference(monotonicity,[status(thm)],[40]) ).
tff(116,plain,
implies(implies(or(not(x),not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(or(not(x),not(not(truth))),not(not(truth))),implies(truth,not(not(truth)))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(or(not(x),not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
implies(implies(or(not(x),not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))),
inference(unit_resolution,[status(thm)],[117,69]) ).
tff(119,plain,
implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))) = implies(implies(or(not(x),not(not(truth))),not(not(truth))),not(not(truth))),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))) = not(not(truth)),
inference(transitivity,[status(thm)],[119,116,114,40]) ).
tff(121,plain,
not(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))) = not(not(not(truth))),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
not(not(not(truth))) = not(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
implies(not(not(not(truth))),not(truth)) = implies(not(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),not(truth)),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
implies(not(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),not(truth)) = implies(not(not(not(truth))),not(truth)),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))),not(truth)) = implies(not(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(126,plain,
or(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))),not(truth)) = implies(not(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),not(truth)),
inference(unit_resolution,[status(thm)],[125,25]) ).
tff(127,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth),implies(implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))))) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth),implies(implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))))) = truth,
inference(unit_resolution,[status(thm)],[127,7]) ).
tff(129,plain,
implies(not(not(x)),not(not(truth))) = or(not(x),not(not(truth))),
inference(symmetry,[status(thm)],[109]) ).
tff(130,plain,
implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))) = implies(not(not(x)),not(not(truth))),
inference(monotonicity,[status(thm)],[73,120]) ).
tff(131,plain,
implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))) = or(not(x),not(not(truth))),
inference(transitivity,[status(thm)],[130,129]) ).
tff(132,plain,
implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))) = implies(truth,not(not(truth))),
inference(monotonicity,[status(thm)],[120]) ).
tff(133,plain,
implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))) = not(not(truth)),
inference(transitivity,[status(thm)],[132,40]) ).
tff(134,plain,
implies(implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))))) = implies(not(not(truth)),or(not(x),not(not(truth)))),
inference(monotonicity,[status(thm)],[133,131]) ).
tff(135,plain,
implies(not(not(truth)),or(not(x),not(not(truth)))) = implies(implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth) = implies(not(not(x)),truth),
inference(monotonicity,[status(thm)],[73]) ).
tff(137,plain,
implies(not(not(x)),truth) = implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth))))) = implies(not(not(x)),truth),
inference(symmetry,[status(thm)],[91]) ).
tff(139,plain,
truth = implies(implies(truth,implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth)))),implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),not(not(truth))),implies(truth,not(not(truth))))),
inference(symmetry,[status(thm)],[31]) ).
tff(140,plain,
truth = implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth),
inference(transitivity,[status(thm)],[139,138,137]) ).
tff(141,plain,
implies(truth,implies(not(not(truth)),or(not(x),not(not(truth))))) = implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth),implies(implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))))),
inference(monotonicity,[status(thm)],[140,135]) ).
tff(142,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,implies(not(not(truth)),or(not(x),not(not(truth))))) = implies(not(not(truth)),or(not(x),not(not(truth)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
implies(truth,implies(not(not(truth)),or(not(x),not(not(truth))))) = implies(not(not(truth)),or(not(x),not(not(truth)))),
inference(unit_resolution,[status(thm)],[142,38]) ).
tff(144,plain,
implies(not(not(truth)),or(not(x),not(not(truth)))) = implies(truth,implies(not(not(truth)),or(not(x),not(not(truth))))),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
implies(not(not(truth)),or(not(x),not(not(truth)))) = truth,
inference(transitivity,[status(thm)],[144,141,128]) ).
tff(146,plain,
implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))) = implies(truth,or(not(x),not(not(truth)))),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))) = or(not(x),not(not(truth))),
inference(transitivity,[status(thm)],[146,104]) ).
tff(148,plain,
or(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))),not(truth)) = or(or(not(x),not(not(truth))),not(truth)),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
or(or(not(x),not(not(truth))),not(truth)) = or(implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth)))),not(truth)),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = or(Y,X) )
| ( or(or(not(x),not(not(truth))),not(truth)) = or(not(truth),or(not(x),not(not(truth)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(151,plain,
or(or(not(x),not(not(truth))),not(truth)) = or(not(truth),or(not(x),not(not(truth)))),
inference(unit_resolution,[status(thm)],[150,16]) ).
tff(152,plain,
or(not(truth),or(not(x),not(not(truth)))) = or(or(not(x),not(not(truth))),not(truth)),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
( ~ ! [Y: $i,X: $i] : ( or(X,Y) = implies(not(X),Y) )
| ( or(not(truth),or(not(x),not(not(truth)))) = implies(not(not(truth)),or(not(x),not(not(truth)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
or(not(truth),or(not(x),not(not(truth)))) = implies(not(not(truth)),or(not(x),not(not(truth)))),
inference(unit_resolution,[status(thm)],[153,25]) ).
tff(155,plain,
implies(not(not(truth)),or(not(x),not(not(truth)))) = or(not(truth),or(not(x),not(not(truth)))),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth),implies(implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))))) = implies(truth,implies(not(not(truth)),or(not(x),not(not(truth))))),
inference(symmetry,[status(thm)],[141]) ).
tff(157,plain,
truth = implies(implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),truth),implies(implies(truth,implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))),implies(implies(implies(not(not(x)),or(not(not(x)),not(truth))),or(not(not(x)),not(truth))),implies(implies(not(not(truth)),or(not(x),not(not(truth)))),or(not(x),not(not(truth))))))),
inference(symmetry,[status(thm)],[128]) ).
tff(158,plain,
truth = implies(not(not(not(truth))),not(truth)),
inference(transitivity,[status(thm)],[157,156,143,155,152,149,126,124]) ).
tff(159,plain,
implies(truth,or(not(x),not(not(truth)))) = implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(truth),not(x)),implies(not(not(not(truth))),not(x)))),
inference(monotonicity,[status(thm)],[158,106]) ).
tff(160,plain,
or(not(x),not(not(truth))) = truth,
inference(transitivity,[status(thm)],[105,159,9]) ).
tff(161,plain,
not(or(not(x),not(not(truth)))) = not(truth),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
^ [Y: $i,X: $i] :
refl(
( ( and_star(X,Y) = not(or(not(X),not(Y))) )
<=> ( and_star(X,Y) = not(or(not(X),not(Y))) ) )),
inference(bind,[status(th)],]) ).
tff(163,plain,
( ! [Y: $i,X: $i] : ( and_star(X,Y) = not(or(not(X),not(Y))) )
<=> ! [Y: $i,X: $i] : ( and_star(X,Y) = not(or(not(X),not(Y))) ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,plain,
( ! [Y: $i,X: $i] : ( and_star(X,Y) = not(or(not(X),not(Y))) )
<=> ! [Y: $i,X: $i] : ( and_star(X,Y) = not(or(not(X),not(Y))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(165,axiom,
! [Y: $i,X: $i] : ( and_star(X,Y) = not(or(not(X),not(Y))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',and_star_definition) ).
tff(166,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = not(or(not(X),not(Y))) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = not(or(not(X),not(Y))) ),
inference(skolemize,[status(sab)],[166]) ).
tff(168,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = not(or(not(X),not(Y))) ),
inference(modus_ponens,[status(thm)],[167,163]) ).
tff(169,plain,
( ~ ! [Y: $i,X: $i] : ( and_star(X,Y) = not(or(not(X),not(Y))) )
| ( and_star(x,not(truth)) = not(or(not(x),not(not(truth)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(170,plain,
and_star(x,not(truth)) = not(or(not(x),not(not(truth)))),
inference(unit_resolution,[status(thm)],[169,168]) ).
tff(171,plain,
and_star(x,not(truth)) = not(truth),
inference(transitivity,[status(thm)],[170,161]) ).
tff(172,plain,
( ( and_star(x,falsehood) != falsehood )
<=> ( and_star(x,not(truth)) != not(truth) ) ),
inference(rewrite,[status(thm)],]) ).
tff(173,plain,
( ( and_star(x,falsehood) != falsehood )
<=> ( and_star(x,falsehood) != falsehood ) ),
inference(rewrite,[status(thm)],]) ).
tff(174,axiom,
and_star(x,falsehood) != falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
tff(175,plain,
and_star(x,falsehood) != falsehood,
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
and_star(x,not(truth)) != not(truth),
inference(modus_ponens,[status(thm)],[175,172]) ).
tff(177,plain,
$false,
inference(unit_resolution,[status(thm)],[176,171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL157-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 17:45:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 3.91/2.75 % SZS status Unsatisfiable
% 3.91/2.75 % SZS output start Proof
% See solution above
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