TSTP Solution File: LCL164-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL164-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 04:55:09 EDT 2022
% Result : Unsatisfiable 0.16s 0.37s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 58
% Syntax : Number of formulae : 151 ( 102 unt; 8 typ; 0 def)
% Number of atoms : 206 ( 194 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 77 ( 25 ~; 21 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 155 ( 140 !; 0 ?; 155 :)
% Comments :
%------------------------------------------------------------------------------
tff(truth_type,type,
truth: $i ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(x_type,type,
x: $i ).
tff(y_type,type,
y: $i ).
tff(not_type,type,
not: $i > $i ).
tff(xor_type,type,
xor: ( $i * $i ) > $i ).
tff(falsehood_type,type,
falsehood: $i ).
tff(and_star_type,type,
and_star: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( xor(X,not(truth)) = X )
<=> ( xor(X,not(truth)) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( xor(X,not(truth)) = X )
<=> ! [X: $i] : ( xor(X,not(truth)) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(
( ( xor(X,falsehood) = X )
<=> ( xor(X,not(truth)) = X ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] : ( xor(X,falsehood) = X )
<=> ! [X: $i] : ( xor(X,not(truth)) = X ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] : ( xor(X,falsehood) = X )
<=> ! [X: $i] : ( xor(X,falsehood) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [X: $i] : ( xor(X,falsehood) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_2) ).
tff(7,plain,
! [X: $i] : ( xor(X,falsehood) = X ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i] : ( xor(X,not(truth)) = X ),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
! [X: $i] : ( xor(X,not(truth)) = X ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] : ( xor(X,not(truth)) = X ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i] : ( xor(X,not(truth)) = X )
| ( xor(truth,not(truth)) = truth ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
xor(truth,not(truth)) = truth,
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
^ [X: $i] :
refl(
( ( and_star(xor(truth,X),X) = not(truth) )
<=> ( and_star(xor(truth,X),X) = not(truth) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X: $i] : ( and_star(xor(truth,X),X) = not(truth) )
<=> ! [X: $i] : ( and_star(xor(truth,X),X) = not(truth) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
^ [X: $i] :
rewrite(
( ( and_star(xor(truth,X),X) = falsehood )
<=> ( and_star(xor(truth,X),X) = not(truth) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X: $i] : ( and_star(xor(truth,X),X) = falsehood )
<=> ! [X: $i] : ( and_star(xor(truth,X),X) = not(truth) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i] : ( and_star(xor(truth,X),X) = falsehood )
<=> ! [X: $i] : ( and_star(xor(truth,X),X) = falsehood ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [X: $i] : ( and_star(xor(truth,X),X) = falsehood ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_6) ).
tff(19,plain,
! [X: $i] : ( and_star(xor(truth,X),X) = falsehood ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X: $i] : ( and_star(xor(truth,X),X) = not(truth) ),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
! [X: $i] : ( and_star(xor(truth,X),X) = not(truth) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [X: $i] : ( and_star(xor(truth,X),X) = not(truth) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ~ ! [X: $i] : ( and_star(xor(truth,X),X) = not(truth) )
| ( and_star(xor(truth,xor(truth,and_star(y,xor(truth,x)))),xor(truth,and_star(y,xor(truth,x)))) = not(truth) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
and_star(xor(truth,xor(truth,and_star(y,xor(truth,x)))),xor(truth,and_star(y,xor(truth,x)))) = not(truth),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
not(truth) = and_star(xor(truth,xor(truth,and_star(y,xor(truth,x)))),xor(truth,and_star(y,xor(truth,x)))),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
xor(truth,not(truth)) = xor(truth,and_star(xor(truth,xor(truth,and_star(y,xor(truth,x)))),xor(truth,and_star(y,xor(truth,x))))),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
xor(truth,and_star(xor(truth,xor(truth,and_star(y,xor(truth,x)))),xor(truth,and_star(y,xor(truth,x))))) = xor(truth,not(truth)),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ~ ! [X: $i] : ( and_star(xor(truth,X),X) = not(truth) )
| ( and_star(xor(truth,xor(truth,xor(truth,and_star(y,xor(truth,x))))),xor(truth,xor(truth,and_star(y,xor(truth,x))))) = not(truth) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
and_star(xor(truth,xor(truth,xor(truth,and_star(y,xor(truth,x))))),xor(truth,xor(truth,and_star(y,xor(truth,x))))) = not(truth),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
and_star(xor(truth,xor(truth,xor(truth,and_star(y,xor(truth,x))))),xor(truth,xor(truth,and_star(y,xor(truth,x))))) = and_star(xor(truth,xor(truth,and_star(y,xor(truth,x)))),xor(truth,and_star(y,xor(truth,x)))),
inference(transitivity,[status(thm)],[29,25]) ).
tff(31,plain,
xor(truth,and_star(xor(truth,xor(truth,xor(truth,and_star(y,xor(truth,x))))),xor(truth,xor(truth,and_star(y,xor(truth,x)))))) = xor(truth,and_star(xor(truth,xor(truth,and_star(y,xor(truth,x)))),xor(truth,and_star(y,xor(truth,x))))),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
^ [Y: $i,X: $i] :
refl(
( ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
<=> ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
<=> ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
tff(36,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
| ( implies(xor(truth,xor(truth,xor(truth,and_star(y,xor(truth,x))))),xor(truth,and_star(y,xor(truth,x)))) = xor(truth,and_star(xor(truth,xor(truth,xor(truth,and_star(y,xor(truth,x))))),xor(truth,xor(truth,and_star(y,xor(truth,x)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
implies(xor(truth,xor(truth,xor(truth,and_star(y,xor(truth,x))))),xor(truth,and_star(y,xor(truth,x)))) = xor(truth,and_star(xor(truth,xor(truth,xor(truth,and_star(y,xor(truth,x))))),xor(truth,xor(truth,and_star(y,xor(truth,x)))))),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
| ( implies(y,x) = xor(truth,and_star(y,xor(truth,x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
implies(y,x) = xor(truth,and_star(y,xor(truth,x))),
inference(unit_resolution,[status(thm)],[41,38]) ).
tff(43,plain,
^ [Y: $i,X: $i] :
refl(
( ( xor(X,Y) = xor(Y,X) )
<=> ( xor(X,Y) = xor(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
<=> ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
<=> ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutativity) ).
tff(47,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(xor(truth,xor(truth,and_star(y,xor(truth,x)))),truth) = xor(truth,xor(truth,xor(truth,and_star(y,xor(truth,x))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
xor(xor(truth,xor(truth,and_star(y,xor(truth,x)))),truth) = xor(truth,xor(truth,xor(truth,and_star(y,xor(truth,x))))),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(xor(truth,and_star(y,xor(truth,x))),truth) = xor(truth,xor(truth,and_star(y,xor(truth,x)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
xor(xor(truth,and_star(y,xor(truth,x))),truth) = xor(truth,xor(truth,and_star(y,xor(truth,x)))),
inference(unit_resolution,[status(thm)],[52,49]) ).
tff(54,plain,
xor(xor(xor(truth,and_star(y,xor(truth,x))),truth),truth) = xor(xor(truth,xor(truth,and_star(y,xor(truth,x)))),truth),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
^ [Y: $i,X: $i] :
refl(
( ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
<=> ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
<=> ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
<=> ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_7) ).
tff(59,plain,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
| ( xor(xor(truth,and_star(y,xor(truth,x))),xor(truth,truth)) = xor(xor(xor(truth,and_star(y,xor(truth,x))),truth),truth) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
xor(xor(truth,and_star(y,xor(truth,x))),xor(truth,truth)) = xor(xor(xor(truth,and_star(y,xor(truth,x))),truth),truth),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
^ [X: $i] :
refl(
( ( xor(X,X) = not(truth) )
<=> ( xor(X,X) = not(truth) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [X: $i] : ( xor(X,X) = not(truth) )
<=> ! [X: $i] : ( xor(X,X) = not(truth) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
^ [X: $i] :
rewrite(
( ( xor(X,X) = falsehood )
<=> ( xor(X,X) = not(truth) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [X: $i] : ( xor(X,X) = falsehood )
<=> ! [X: $i] : ( xor(X,X) = not(truth) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [X: $i] : ( xor(X,X) = falsehood )
<=> ! [X: $i] : ( xor(X,X) = falsehood ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,axiom,
! [X: $i] : ( xor(X,X) = falsehood ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_3) ).
tff(70,plain,
! [X: $i] : ( xor(X,X) = falsehood ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [X: $i] : ( xor(X,X) = not(truth) ),
inference(modus_ponens,[status(thm)],[70,67]) ).
tff(72,plain,
! [X: $i] : ( xor(X,X) = not(truth) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [X: $i] : ( xor(X,X) = not(truth) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
( ~ ! [X: $i] : ( xor(X,X) = not(truth) )
| ( xor(truth,truth) = not(truth) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
xor(truth,truth) = not(truth),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
not(truth) = xor(truth,truth),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
xor(xor(truth,and_star(y,xor(truth,x))),not(truth)) = xor(xor(truth,and_star(y,xor(truth,x))),xor(truth,truth)),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(xor(truth,and_star(y,xor(truth,x))),not(truth)) = xor(not(truth),xor(truth,and_star(y,xor(truth,x)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
xor(xor(truth,and_star(y,xor(truth,x))),not(truth)) = xor(not(truth),xor(truth,and_star(y,xor(truth,x)))),
inference(unit_resolution,[status(thm)],[78,49]) ).
tff(80,plain,
xor(not(truth),xor(truth,and_star(y,xor(truth,x)))) = xor(xor(truth,and_star(y,xor(truth,x))),not(truth)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
| ( xor(not(truth),xor(truth,and_star(y,xor(truth,x)))) = xor(xor(not(truth),truth),and_star(y,xor(truth,x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
xor(not(truth),xor(truth,and_star(y,xor(truth,x)))) = xor(xor(not(truth),truth),and_star(y,xor(truth,x))),
inference(unit_resolution,[status(thm)],[81,61]) ).
tff(83,plain,
xor(xor(not(truth),truth),and_star(y,xor(truth,x))) = xor(not(truth),xor(truth,and_star(y,xor(truth,x)))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(not(truth),truth) = xor(truth,not(truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
xor(not(truth),truth) = xor(truth,not(truth)),
inference(unit_resolution,[status(thm)],[84,49]) ).
tff(86,plain,
xor(truth,not(truth)) = xor(not(truth),truth),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
truth = xor(truth,not(truth)),
inference(symmetry,[status(thm)],[12]) ).
tff(88,plain,
truth = xor(not(truth),truth),
inference(transitivity,[status(thm)],[87,86]) ).
tff(89,plain,
xor(truth,and_star(y,xor(truth,x))) = xor(xor(not(truth),truth),and_star(y,xor(truth,x))),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [X: $i] : ( xor(X,not(truth)) = X )
| ( xor(y,not(truth)) = y ) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
xor(y,not(truth)) = y,
inference(unit_resolution,[status(thm)],[90,10]) ).
tff(92,plain,
xor(y,not(truth)) = xor(y,xor(truth,truth)),
inference(monotonicity,[status(thm)],[76]) ).
tff(93,plain,
xor(y,xor(truth,truth)) = xor(y,not(truth)),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) )
| ( xor(y,xor(truth,truth)) = xor(xor(y,truth),truth) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
xor(y,xor(truth,truth)) = xor(xor(y,truth),truth),
inference(unit_resolution,[status(thm)],[94,61]) ).
tff(96,plain,
xor(xor(y,truth),truth) = xor(y,xor(truth,truth)),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(xor(y,truth),truth) = xor(truth,xor(y,truth)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
xor(xor(y,truth),truth) = xor(truth,xor(y,truth)),
inference(unit_resolution,[status(thm)],[97,49]) ).
tff(99,plain,
xor(truth,xor(y,truth)) = xor(xor(y,truth),truth),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
xor(truth,xor(y,truth)) = y,
inference(transitivity,[status(thm)],[99,96,93,91]) ).
tff(101,plain,
implies(xor(truth,xor(y,truth)),x) = implies(y,x),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
| ( implies(xor(truth,xor(y,truth)),x) = xor(truth,and_star(xor(truth,xor(y,truth)),xor(truth,x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
implies(xor(truth,xor(y,truth)),x) = xor(truth,and_star(xor(truth,xor(y,truth)),xor(truth,x))),
inference(unit_resolution,[status(thm)],[102,38]) ).
tff(104,plain,
xor(truth,and_star(xor(truth,xor(y,truth)),xor(truth,x))) = implies(xor(truth,xor(y,truth)),x),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [Y: $i,X: $i] : ( xor(X,Y) = xor(Y,X) )
| ( xor(truth,x) = xor(x,truth) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
xor(truth,x) = xor(x,truth),
inference(unit_resolution,[status(thm)],[105,49]) ).
tff(107,plain,
^ [X: $i] :
refl(
( ( not(X) = xor(X,truth) )
<=> ( not(X) = xor(X,truth) ) )),
inference(bind,[status(th)],]) ).
tff(108,plain,
( ! [X: $i] : ( not(X) = xor(X,truth) )
<=> ! [X: $i] : ( not(X) = xor(X,truth) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,plain,
( ! [X: $i] : ( not(X) = xor(X,truth) )
<=> ! [X: $i] : ( not(X) = xor(X,truth) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,axiom,
! [X: $i] : ( not(X) = xor(X,truth) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_1) ).
tff(111,plain,
! [X: $i] : ( not(X) = xor(X,truth) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [X: $i] : ( not(X) = xor(X,truth) ),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [X: $i] : ( not(X) = xor(X,truth) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
( ~ ! [X: $i] : ( not(X) = xor(X,truth) )
| ( not(y) = xor(y,truth) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
not(y) = xor(y,truth),
inference(unit_resolution,[status(thm)],[114,113]) ).
tff(116,plain,
xor(truth,not(y)) = xor(truth,xor(y,truth)),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
xor(truth,xor(y,truth)) = xor(truth,not(y)),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
and_star(xor(truth,xor(y,truth)),xor(truth,x)) = and_star(xor(truth,not(y)),xor(x,truth)),
inference(monotonicity,[status(thm)],[117,106]) ).
tff(119,plain,
and_star(xor(truth,not(y)),xor(x,truth)) = and_star(xor(truth,xor(y,truth)),xor(truth,x)),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
^ [Y: $i,X: $i] :
refl(
( ( and_star(X,Y) = and_star(Y,X) )
<=> ( and_star(X,Y) = and_star(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) )
<=> ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
( ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) )
<=> ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,axiom,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_commutativity) ).
tff(124,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
( ~ ! [Y: $i,X: $i] : ( and_star(X,Y) = and_star(Y,X) )
| ( and_star(xor(truth,not(y)),xor(x,truth)) = and_star(xor(x,truth),xor(truth,not(y))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
and_star(xor(truth,not(y)),xor(x,truth)) = and_star(xor(x,truth),xor(truth,not(y))),
inference(unit_resolution,[status(thm)],[127,126]) ).
tff(129,plain,
and_star(xor(x,truth),xor(truth,not(y))) = and_star(xor(truth,not(y)),xor(x,truth)),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
( ~ ! [X: $i] : ( not(X) = xor(X,truth) )
| ( not(x) = xor(x,truth) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
not(x) = xor(x,truth),
inference(unit_resolution,[status(thm)],[130,113]) ).
tff(132,plain,
and_star(not(x),xor(truth,not(y))) = and_star(xor(x,truth),xor(truth,not(y))),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
and_star(not(x),xor(truth,not(y))) = and_star(xor(truth,xor(y,truth)),xor(truth,x)),
inference(transitivity,[status(thm)],[132,129,119]) ).
tff(134,plain,
xor(truth,and_star(not(x),xor(truth,not(y)))) = xor(truth,and_star(xor(truth,xor(y,truth)),xor(truth,x))),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
( ~ ! [Y: $i,X: $i] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) )
| ( implies(not(x),not(y)) = xor(truth,and_star(not(x),xor(truth,not(y)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(136,plain,
implies(not(x),not(y)) = xor(truth,and_star(not(x),xor(truth,not(y)))),
inference(unit_resolution,[status(thm)],[135,38]) ).
tff(137,plain,
implies(not(x),not(y)) = xor(truth,xor(truth,xor(truth,and_star(y,xor(truth,x))))),
inference(transitivity,[status(thm)],[136,134,104,101,42,89,83,80,77,63,54,51]) ).
tff(138,plain,
implies(implies(not(x),not(y)),implies(y,x)) = implies(xor(truth,xor(truth,xor(truth,and_star(y,xor(truth,x))))),xor(truth,and_star(y,xor(truth,x)))),
inference(monotonicity,[status(thm)],[137,42]) ).
tff(139,plain,
implies(implies(not(x),not(y)),implies(y,x)) = truth,
inference(transitivity,[status(thm)],[138,40,31,27,12]) ).
tff(140,plain,
( ( implies(implies(not(x),not(y)),implies(y,x)) != truth )
<=> ( implies(implies(not(x),not(y)),implies(y,x)) != truth ) ),
inference(rewrite,[status(thm)],]) ).
tff(141,axiom,
implies(implies(not(x),not(y)),implies(y,x)) != truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).
tff(142,plain,
implies(implies(not(x),not(y)),implies(y,x)) != truth,
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
$false,
inference(unit_resolution,[status(thm)],[142,139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : LCL164-1 : TPTP v8.1.0. Released v1.0.0.
% 0.02/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n002.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Sep 1 18:36:45 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.32 Usage: tptp [options] [-file:]file
% 0.10/0.32 -h, -? prints this message.
% 0.10/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.32 -m, -model generate model.
% 0.10/0.32 -p, -proof generate proof.
% 0.10/0.32 -c, -core generate unsat core of named formulas.
% 0.10/0.32 -st, -statistics display statistics.
% 0.10/0.32 -t:timeout set timeout (in second).
% 0.10/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.32 -<param>:<value> configuration parameter and value.
% 0.10/0.32 -o:<output-file> file to place output in.
% 0.16/0.37 % SZS status Unsatisfiable
% 0.16/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------