TSTP Solution File: LAT253-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT253-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 : Sat Sep 17 18:32:27 EDT 2022
% Result : Unsatisfiable 6.25s 4.24s
% Output : Proof 6.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 73
% Syntax : Number of formulae : 200 ( 131 unt; 7 typ; 0 def)
% Number of atoms : 342 ( 326 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 227 ( 96 ~; 87 |; 0 &)
% ( 44 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 276 ( 251 !; 0 ?; 276 :)
% Comments :
%------------------------------------------------------------------------------
tff(zero_type,type,
zero: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(one_type,type,
one: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( meet(X,complement(X)) = zero )
<=> ( meet(X,complement(X)) = zero ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( meet(X,complement(X)) = zero )
<=> ! [X: $i] : ( meet(X,complement(X)) = zero ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( meet(X,complement(X)) = zero )
<=> ! [X: $i] : ( meet(X,complement(X)) = zero ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( meet(X,complement(X)) = zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
tff(5,plain,
! [X: $i] : ( meet(X,complement(X)) = zero ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( meet(X,complement(X)) = zero ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( meet(X,complement(X)) = zero ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( meet(X,complement(X)) = zero )
| ( meet(a,complement(a)) = zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
meet(a,complement(a)) = zero,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(14,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(a),meet(complement(a),a)) = complement(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
join(complement(a),meet(complement(a),a)) = complement(a),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
<=> ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
<=> ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(23,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(complement(a),a) = meet(a,complement(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
meet(complement(a),a) = meet(a,complement(a)),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
meet(a,complement(a)) = meet(complement(a),a),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( ( meet(b,a) = a )
<=> ( meet(b,a) = a ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
meet(b,a) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
tff(31,plain,
meet(b,a) = a,
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,b) = meet(b,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
meet(a,b) = meet(b,a),
inference(unit_resolution,[status(thm)],[32,25]) ).
tff(34,plain,
meet(a,b) = a,
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
meet(meet(a,b),complement(a)) = meet(a,complement(a)),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
tff(40,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,b),complement(a)) = meet(a,meet(b,complement(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
meet(meet(a,b),complement(a)) = meet(a,meet(b,complement(a))),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
meet(a,meet(b,complement(a))) = meet(meet(a,b),complement(a)),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
tff(50,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,complement(a))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
meet(a,join(a,complement(a))) = a,
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
^ [X: $i] :
refl(
( ( join(X,complement(X)) = one )
<=> ( join(X,complement(X)) = one ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [X: $i] : ( join(X,complement(X)) = one )
<=> ! [X: $i] : ( join(X,complement(X)) = one ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [X: $i] : ( join(X,complement(X)) = one )
<=> ! [X: $i] : ( join(X,complement(X)) = one ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
! [X: $i] : ( join(X,complement(X)) = one ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_join) ).
tff(59,plain,
! [X: $i] : ( join(X,complement(X)) = one ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [X: $i] : ( join(X,complement(X)) = one ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [X: $i] : ( join(X,complement(X)) = one ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [X: $i] : ( join(X,complement(X)) = one )
| ( join(a,complement(a)) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
join(a,complement(a)) = one,
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
one = join(a,complement(a)),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
meet(a,one) = meet(a,join(a,complement(a))),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
meet(a,one) = a,
inference(transitivity,[status(thm)],[65,54]) ).
tff(67,plain,
meet(meet(a,one),meet(b,complement(a))) = meet(a,meet(b,complement(a))),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,one),meet(b,complement(a))) = meet(a,meet(one,meet(b,complement(a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
meet(meet(a,one),meet(b,complement(a))) = meet(a,meet(one,meet(b,complement(a)))),
inference(unit_resolution,[status(thm)],[68,42]) ).
tff(70,plain,
meet(a,meet(one,meet(b,complement(a)))) = meet(meet(a,one),meet(b,complement(a))),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
^ [X: $i] :
refl(
( ( meet(X,X) = X )
<=> ( meet(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
! [X: $i] : ( meet(X,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
tff(75,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(a,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
meet(a,a) = a,
inference(unit_resolution,[status(thm)],[78,77]) ).
tff(80,plain,
meet(meet(a,a),meet(one,meet(b,complement(a)))) = meet(a,meet(one,meet(b,complement(a)))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,a),meet(one,meet(b,complement(a)))) = meet(a,meet(a,meet(one,meet(b,complement(a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
meet(meet(a,a),meet(one,meet(b,complement(a)))) = meet(a,meet(a,meet(one,meet(b,complement(a))))),
inference(unit_resolution,[status(thm)],[81,42]) ).
tff(83,plain,
meet(a,meet(a,meet(one,meet(b,complement(a))))) = meet(meet(a,a),meet(one,meet(b,complement(a)))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
meet(a,meet(b,complement(a))) = meet(meet(a,one),meet(b,complement(a))),
inference(symmetry,[status(thm)],[67]) ).
tff(85,plain,
meet(a,complement(a)) = meet(meet(a,b),complement(a)),
inference(symmetry,[status(thm)],[35]) ).
tff(86,plain,
zero = meet(a,complement(a)),
inference(symmetry,[status(thm)],[9]) ).
tff(87,plain,
zero = meet(a,meet(one,meet(b,complement(a)))),
inference(transitivity,[status(thm)],[86,85,44,84,69]) ).
tff(88,plain,
meet(a,zero) = meet(a,meet(a,meet(one,meet(b,complement(a))))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(zero,a) = meet(a,zero) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
meet(zero,a) = meet(a,zero),
inference(unit_resolution,[status(thm)],[89,25]) ).
tff(91,plain,
( ~ ! [X: $i] : ( meet(X,complement(X)) = zero )
| ( meet(b,complement(b)) = zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
meet(b,complement(b)) = zero,
inference(unit_resolution,[status(thm)],[91,7]) ).
tff(93,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(complement(b),b) = meet(b,complement(b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
meet(complement(b),b) = meet(b,complement(b)),
inference(unit_resolution,[status(thm)],[93,25]) ).
tff(95,plain,
meet(complement(b),b) = zero,
inference(transitivity,[status(thm)],[94,92]) ).
tff(96,plain,
meet(meet(complement(b),b),a) = meet(zero,a),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(complement(b),b),a) = meet(complement(b),meet(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
meet(meet(complement(b),b),a) = meet(complement(b),meet(b,a)),
inference(unit_resolution,[status(thm)],[97,42]) ).
tff(99,plain,
meet(complement(b),meet(b,a)) = meet(meet(complement(b),b),a),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
a = meet(b,a),
inference(symmetry,[status(thm)],[31]) ).
tff(101,plain,
meet(complement(b),a) = meet(complement(b),meet(b,a)),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
meet(complement(b),a) = meet(complement(a),a),
inference(transitivity,[status(thm)],[101,99,96,90,88,83,80,70,67,45,35,28]) ).
tff(103,plain,
join(complement(a),meet(complement(b),a)) = join(complement(a),meet(complement(a),a)),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
join(complement(a),meet(complement(b),a)) = complement(a),
inference(transitivity,[status(thm)],[103,18]) ).
tff(105,plain,
meet(a,join(complement(a),meet(complement(b),a))) = meet(a,complement(a)),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(a,meet(a,complement(a))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
join(a,meet(a,complement(a))) = a,
inference(unit_resolution,[status(thm)],[106,16]) ).
tff(108,plain,
meet(complement(b),join(a,meet(a,complement(a)))) = meet(complement(b),a),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
join(complement(a),meet(complement(b),join(a,meet(a,complement(a))))) = join(complement(a),meet(complement(b),a)),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
meet(a,join(complement(a),meet(complement(b),join(a,meet(a,complement(a)))))) = meet(a,join(complement(a),meet(complement(b),a))),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
^ [Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( meet(X,join(Y,meet(Z,join(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))) )
<=> ( meet(X,join(Y,meet(Z,join(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))) ) )),
inference(bind,[status(th)],]) ).
tff(112,plain,
( ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))) )
<=> ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))) )
<=> ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,axiom,
! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H76) ).
tff(115,plain,
! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))) ),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))) ),
inference(modus_ponens,[status(thm)],[116,112]) ).
tff(118,plain,
( ~ ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(Y,U)))) = meet(X,join(Y,meet(Z,join(U,meet(X,Y))))) )
| ( meet(a,join(complement(a),meet(complement(b),join(complement(a),a)))) = meet(a,join(complement(a),meet(complement(b),join(a,meet(a,complement(a)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
meet(a,join(complement(a),meet(complement(b),join(complement(a),a)))) = meet(a,join(complement(a),meet(complement(b),join(a,meet(a,complement(a)))))),
inference(unit_resolution,[status(thm)],[118,117]) ).
tff(120,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(complement(b),join(complement(b),b)) = complement(b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
meet(complement(b),join(complement(b),b)) = complement(b),
inference(unit_resolution,[status(thm)],[120,52]) ).
tff(122,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
<=> ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
<=> ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(126,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(complement(b),b) = join(b,complement(b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
join(complement(b),b) = join(b,complement(b)),
inference(unit_resolution,[status(thm)],[129,128]) ).
tff(131,plain,
join(b,complement(b)) = join(complement(b),b),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
( ~ ! [X: $i] : ( join(X,complement(X)) = one )
| ( join(b,complement(b)) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
join(b,complement(b)) = one,
inference(unit_resolution,[status(thm)],[132,61]) ).
tff(134,plain,
one = join(b,complement(b)),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(complement(a),a) = join(a,complement(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(136,plain,
join(complement(a),a) = join(a,complement(a)),
inference(unit_resolution,[status(thm)],[135,128]) ).
tff(137,plain,
join(complement(a),a) = join(complement(b),b),
inference(transitivity,[status(thm)],[136,63,134,131]) ).
tff(138,plain,
meet(complement(b),join(complement(a),a)) = meet(complement(b),join(complement(b),b)),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
meet(complement(b),join(complement(a),a)) = complement(b),
inference(transitivity,[status(thm)],[138,121]) ).
tff(140,plain,
join(complement(a),meet(complement(b),join(complement(a),a))) = join(complement(a),complement(b)),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
join(complement(a),complement(b)) = join(complement(a),meet(complement(b),join(complement(a),a))),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(complement(a),complement(b)) = join(complement(b),complement(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
join(complement(a),complement(b)) = join(complement(b),complement(a)),
inference(unit_resolution,[status(thm)],[142,128]) ).
tff(144,plain,
join(complement(b),complement(a)) = join(complement(a),complement(b)),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
join(complement(b),complement(a)) = join(complement(a),meet(complement(b),join(complement(a),a))),
inference(transitivity,[status(thm)],[144,141]) ).
tff(146,plain,
meet(a,join(complement(b),complement(a))) = meet(a,join(complement(a),meet(complement(b),join(complement(a),a)))),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(transitivity,[status(thm)],[146,119,110,105,9]) ).
tff(148,plain,
( ( complement(a) = join(complement(b),complement(a)) )
<=> ( join(complement(b),complement(a)) = complement(a) ) ),
inference(commutativity,[status(thm)],]) ).
tff(149,plain,
( ( join(complement(b),complement(a)) = complement(a) )
<=> ( complement(a) = join(complement(b),complement(a)) ) ),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
( ( join(complement(b),complement(a)) != complement(a) )
<=> ( complement(a) != join(complement(b),complement(a)) ) ),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
( ( join(complement(b),complement(a)) != complement(a) )
<=> ( join(complement(b),complement(a)) != complement(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,axiom,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
tff(153,plain,
join(complement(b),complement(a)) != complement(a),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
complement(a) != join(complement(b),complement(a)),
inference(modus_ponens,[status(thm)],[153,150]) ).
tff(155,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(b),meet(complement(b),join(complement(b),complement(a)))) = complement(b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
join(complement(b),meet(complement(b),join(complement(b),complement(a)))) = complement(b),
inference(unit_resolution,[status(thm)],[155,16]) ).
tff(157,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(complement(b),join(complement(b),complement(a))) = complement(b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
meet(complement(b),join(complement(b),complement(a))) = complement(b),
inference(unit_resolution,[status(thm)],[157,52]) ).
tff(159,plain,
complement(b) = meet(complement(b),join(complement(b),complement(a))),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
join(complement(b),complement(b)) = join(complement(b),meet(complement(b),join(complement(b),complement(a)))),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
join(complement(b),complement(b)) = complement(b),
inference(transitivity,[status(thm)],[160,156]) ).
tff(162,plain,
join(b,join(complement(b),complement(b))) = join(b,complement(b)),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(164,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[163]) ).
tff(165,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(166,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
tff(167,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[167]) ).
tff(169,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[168,164]) ).
tff(170,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(b,complement(b)),complement(b)) = join(b,join(complement(b),complement(b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
join(join(b,complement(b)),complement(b)) = join(b,join(complement(b),complement(b))),
inference(unit_resolution,[status(thm)],[170,169]) ).
tff(172,plain,
join(a,complement(a)) = join(b,complement(b)),
inference(transitivity,[status(thm)],[63,134]) ).
tff(173,plain,
join(join(a,complement(a)),complement(b)) = join(join(b,complement(b)),complement(b)),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(a,complement(a)),complement(b)) = join(a,join(complement(a),complement(b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(175,plain,
join(join(a,complement(a)),complement(b)) = join(a,join(complement(a),complement(b))),
inference(unit_resolution,[status(thm)],[174,169]) ).
tff(176,plain,
join(a,join(complement(a),complement(b))) = join(join(a,complement(a)),complement(b)),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
join(a,join(complement(b),complement(a))) = join(a,join(complement(a),complement(b))),
inference(monotonicity,[status(thm)],[144]) ).
tff(178,plain,
join(a,join(complement(b),complement(a))) = one,
inference(transitivity,[status(thm)],[177,176,173,171,162,133]) ).
tff(179,plain,
^ [Y: $i,X: $i] :
refl(
( ( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) )
<=> ( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ) )),
inference(bind,[status(th)],]) ).
tff(180,plain,
( ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) )
<=> ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ) ),
inference(quant_intro,[status(thm)],[179]) ).
tff(181,plain,
( ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) )
<=> ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(182,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ( meet(X,Y) != zero )
| ( join(X,Y) != one ) )
<=> ( ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ) )),
( ( ( meet(X,Y) != zero )
| ( join(X,Y) != one )
| ( complement(X) = Y ) )
<=> ( ( join(X,Y) != one )
| ( meet(X,Y) != zero )
| ( complement(X) = Y ) ) )),
rewrite(
( ( ( join(X,Y) != one )
| ( meet(X,Y) != zero )
| ( complement(X) = Y ) )
<=> ( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ) )),
( ( ( meet(X,Y) != zero )
| ( join(X,Y) != one )
| ( complement(X) = Y ) )
<=> ( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ) )),
inference(bind,[status(th)],]) ).
tff(183,plain,
( ! [Y: $i,X: $i] :
( ( meet(X,Y) != zero )
| ( join(X,Y) != one )
| ( complement(X) = Y ) )
<=> ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ) ),
inference(quant_intro,[status(thm)],[182]) ).
tff(184,axiom,
! [Y: $i,X: $i] :
( ( meet(X,Y) != zero )
| ( join(X,Y) != one )
| ( complement(X) = Y ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).
tff(185,plain,
! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[185,181]) ).
tff(187,plain,
! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ),
inference(skolemize,[status(sab)],[186]) ).
tff(188,plain,
! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) ),
inference(modus_ponens,[status(thm)],[187,180]) ).
tff(189,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) )
| ( complement(a) = join(complement(b),complement(a)) )
| ( join(a,join(complement(b),complement(a))) != one )
| ( meet(a,join(complement(b),complement(a))) != zero ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) )
| ( complement(a) = join(complement(b),complement(a)) )
| ( join(a,join(complement(b),complement(a))) != one )
| ( meet(a,join(complement(b),complement(a))) != zero ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(190,plain,
( ~ ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) )
| ( complement(a) = join(complement(b),complement(a)) )
| ( join(a,join(complement(b),complement(a))) != one )
| ( meet(a,join(complement(b),complement(a))) != zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(191,plain,
( ~ ! [Y: $i,X: $i] :
( ( complement(X) = Y )
| ( join(X,Y) != one )
| ( meet(X,Y) != zero ) )
| ( complement(a) = join(complement(b),complement(a)) )
| ( join(a,join(complement(b),complement(a))) != one )
| ( meet(a,join(complement(b),complement(a))) != zero ) ),
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,plain,
( ( complement(a) = join(complement(b),complement(a)) )
| ( join(a,join(complement(b),complement(a))) != one )
| ( meet(a,join(complement(b),complement(a))) != zero ) ),
inference(unit_resolution,[status(thm)],[191,188]) ).
tff(193,plain,
$false,
inference(unit_resolution,[status(thm)],[192,178,154,147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT253-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 12:49:04 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.
% 6.25/4.24 % SZS status Unsatisfiable
% 6.25/4.24 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------