TSTP Solution File: LAT241-10 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT241-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:32:24 EDT 2022
% Result : Unsatisfiable 138.44s 86.92s
% Output : Proof 138.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 77
% Syntax : Number of formulae : 220 ( 157 unt; 8 typ; 0 def)
% Number of atoms : 291 ( 278 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 100 ( 33 ~; 29 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 299 ( 273 !; 0 ?; 299 :)
% Comments :
%------------------------------------------------------------------------------
tff(complement_type,type,
complement: $i > $i ).
tff(a_type,type,
a: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(zero_type,type,
zero: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(one_type,type,
one: $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ifeq(A,A,B,C) = B )
<=> ( ifeq(A,A,B,C) = B ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(zero,zero,complement(a),join(complement(b),complement(a))) = complement(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
ifeq(zero,zero,complement(a),join(complement(b),complement(a))) = complement(a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(
( ( meet(X,complement(X)) = zero )
<=> ( meet(X,complement(X)) = zero ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] : ( meet(X,complement(X)) = zero )
<=> ! [X: $i] : ( meet(X,complement(X)) = zero ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( meet(X,complement(X)) = zero )
<=> ! [X: $i] : ( meet(X,complement(X)) = zero ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X: $i] : ( meet(X,complement(X)) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_meet) ).
tff(14,plain,
! [X: $i] : ( meet(X,complement(X)) = zero ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( meet(X,complement(X)) = zero ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( meet(X,complement(X)) = zero ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( meet(X,complement(X)) = zero )
| ( meet(a,complement(a)) = zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
meet(a,complement(a)) = zero,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(20,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)],[19]) ).
tff(21,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(22,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
tff(23,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,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(27,plain,
join(complement(a),meet(complement(a),a)) = complement(a),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(29,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)],[28]) ).
tff(30,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(31,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
tff(32,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,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(36,plain,
meet(complement(a),a) = meet(a,complement(a)),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
meet(a,complement(a)) = meet(complement(a),a),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
zero = meet(a,complement(a)),
inference(symmetry,[status(thm)],[18]) ).
tff(39,plain,
zero = meet(complement(a),a),
inference(transitivity,[status(thm)],[38,37]) ).
tff(40,plain,
join(complement(a),zero) = join(complement(a),meet(complement(a),a)),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(42,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)],[41]) ).
tff(43,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(44,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
tff(45,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(zero,complement(a)) = join(complement(a),zero) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
join(zero,complement(a)) = join(complement(a),zero),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(complement(a),meet(complement(a),complement(b))) = complement(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
join(complement(a),meet(complement(a),complement(b))) = complement(a),
inference(unit_resolution,[status(thm)],[50,25]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(complement(a),complement(b)) = meet(complement(b),complement(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
meet(complement(a),complement(b)) = meet(complement(b),complement(a)),
inference(unit_resolution,[status(thm)],[52,34]) ).
tff(54,plain,
meet(complement(b),complement(a)) = meet(complement(a),complement(b)),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
join(complement(a),meet(complement(b),complement(a))) = join(complement(a),meet(complement(a),complement(b))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
join(complement(a),meet(complement(b),complement(a))) = complement(a),
inference(transitivity,[status(thm)],[55,51]) ).
tff(57,plain,
join(zero,join(complement(a),meet(complement(b),complement(a)))) = join(zero,complement(a)),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,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(59,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)],[58]) ).
tff(60,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(61,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
tff(62,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(zero,complement(a)),meet(complement(b),complement(a))) = join(zero,join(complement(a),meet(complement(b),complement(a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
join(join(zero,complement(a)),meet(complement(b),complement(a))) = join(zero,join(complement(a),meet(complement(b),complement(a)))),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
join(complement(a),zero) = join(zero,complement(a)),
inference(symmetry,[status(thm)],[49]) ).
tff(68,plain,
join(join(complement(a),zero),meet(complement(b),complement(a))) = join(join(zero,complement(a)),meet(complement(b),complement(a))),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(complement(a),zero),meet(complement(b),complement(a))) = join(complement(a),join(zero,meet(complement(b),complement(a)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
join(join(complement(a),zero),meet(complement(b),complement(a))) = join(complement(a),join(zero,meet(complement(b),complement(a)))),
inference(unit_resolution,[status(thm)],[69,64]) ).
tff(71,plain,
join(complement(a),join(zero,meet(complement(b),complement(a)))) = join(join(complement(a),zero),meet(complement(b),complement(a))),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ( meet(b,a) = a )
<=> ( meet(b,a) = a ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
meet(b,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
tff(74,plain,
meet(b,a) = a,
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,b) = meet(b,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
meet(a,b) = meet(b,a),
inference(unit_resolution,[status(thm)],[75,34]) ).
tff(77,plain,
meet(a,b) = a,
inference(transitivity,[status(thm)],[76,74]) ).
tff(78,plain,
meet(meet(a,b),complement(a)) = meet(a,complement(a)),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,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(80,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)],[79]) ).
tff(81,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(82,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
tff(83,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,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(87,plain,
meet(meet(a,b),complement(a)) = meet(a,meet(b,complement(a))),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
meet(a,meet(b,complement(a))) = meet(meet(a,b),complement(a)),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
^ [Y: $i,X: $i] :
refl(
( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],]) ).
tff(90,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)],[89]) ).
tff(91,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(92,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
tff(93,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,complement(a))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
meet(a,join(a,complement(a))) = a,
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
^ [X: $i] :
refl(
( ( join(X,complement(X)) = one )
<=> ( join(X,complement(X)) = one ) )),
inference(bind,[status(th)],]) ).
tff(99,plain,
( ! [X: $i] : ( join(X,complement(X)) = one )
<=> ! [X: $i] : ( join(X,complement(X)) = one ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [X: $i] : ( join(X,complement(X)) = one )
<=> ! [X: $i] : ( join(X,complement(X)) = one ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,axiom,
! [X: $i] : ( join(X,complement(X)) = one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_join) ).
tff(102,plain,
! [X: $i] : ( join(X,complement(X)) = one ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [X: $i] : ( join(X,complement(X)) = one ),
inference(skolemize,[status(sab)],[102]) ).
tff(104,plain,
! [X: $i] : ( join(X,complement(X)) = one ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
( ~ ! [X: $i] : ( join(X,complement(X)) = one )
| ( join(a,complement(a)) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
join(a,complement(a)) = one,
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,plain,
one = join(a,complement(a)),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
meet(a,one) = meet(a,join(a,complement(a))),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
meet(a,one) = a,
inference(transitivity,[status(thm)],[108,97]) ).
tff(110,plain,
meet(meet(a,one),meet(b,complement(a))) = meet(a,meet(b,complement(a))),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,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(112,plain,
meet(meet(a,one),meet(b,complement(a))) = meet(a,meet(one,meet(b,complement(a)))),
inference(unit_resolution,[status(thm)],[111,85]) ).
tff(113,plain,
meet(a,meet(one,meet(b,complement(a)))) = meet(meet(a,one),meet(b,complement(a))),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
^ [X: $i] :
refl(
( ( meet(X,X) = X )
<=> ( meet(X,X) = X ) )),
inference(bind,[status(th)],]) ).
tff(115,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,plain,
( ! [X: $i] : ( meet(X,X) = X )
<=> ! [X: $i] : ( meet(X,X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,axiom,
! [X: $i] : ( meet(X,X) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
tff(118,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [X: $i] : ( meet(X,X) = X ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
( ~ ! [X: $i] : ( meet(X,X) = X )
| ( meet(a,a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
meet(a,a) = a,
inference(unit_resolution,[status(thm)],[121,120]) ).
tff(123,plain,
meet(meet(a,a),meet(one,meet(b,complement(a)))) = meet(a,meet(one,meet(b,complement(a)))),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,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(125,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)],[124,85]) ).
tff(126,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)],[125]) ).
tff(127,plain,
meet(a,meet(b,complement(a))) = meet(meet(a,one),meet(b,complement(a))),
inference(symmetry,[status(thm)],[110]) ).
tff(128,plain,
meet(a,complement(a)) = meet(meet(a,b),complement(a)),
inference(symmetry,[status(thm)],[78]) ).
tff(129,plain,
zero = meet(a,meet(one,meet(b,complement(a)))),
inference(transitivity,[status(thm)],[38,128,87,127,112]) ).
tff(130,plain,
meet(a,zero) = meet(a,meet(a,meet(one,meet(b,complement(a))))),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
( ~ ! [X: $i] : ( meet(X,complement(X)) = zero )
| ( meet(b,complement(b)) = zero ) ),
inference(quant_inst,[status(thm)],]) ).
tff(132,plain,
meet(b,complement(b)) = zero,
inference(unit_resolution,[status(thm)],[131,16]) ).
tff(133,plain,
meet(a,meet(b,complement(b))) = meet(a,zero),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,b),complement(b)) = meet(a,meet(b,complement(b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
meet(meet(a,b),complement(b)) = meet(a,meet(b,complement(b))),
inference(unit_resolution,[status(thm)],[134,85]) ).
tff(136,plain,
meet(b,a) = meet(a,b),
inference(symmetry,[status(thm)],[76]) ).
tff(137,plain,
a = meet(b,a),
inference(symmetry,[status(thm)],[74]) ).
tff(138,plain,
a = meet(a,b),
inference(transitivity,[status(thm)],[137,136]) ).
tff(139,plain,
meet(a,complement(b)) = meet(meet(a,b),complement(b)),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
meet(a,complement(b)) = zero,
inference(transitivity,[status(thm)],[139,135,133,130,126,123,113,110,88,78,18]) ).
tff(141,plain,
join(meet(a,complement(b)),meet(complement(b),complement(a))) = join(zero,meet(complement(b),complement(a))),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
join(complement(a),join(meet(a,complement(b)),meet(complement(b),complement(a)))) = join(complement(a),join(zero,meet(complement(b),complement(a)))),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
join(complement(a),join(meet(a,complement(b)),meet(complement(b),complement(a)))) = complement(a),
inference(transitivity,[status(thm)],[142,71,68,66,57,49,40,27]) ).
tff(144,plain,
meet(a,join(complement(a),join(meet(a,complement(b)),meet(complement(b),complement(a))))) = meet(a,complement(a)),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,plain,
^ [Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,U)))) )
<=> ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,U)))) ) )),
inference(bind,[status(th)],]) ).
tff(146,plain,
( ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,U)))) )
<=> ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,U)))) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,plain,
( ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,U)))) )
<=> ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,U)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,axiom,
! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,U)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H51) ).
tff(149,plain,
! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,U)))) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,U)))) ),
inference(skolemize,[status(sab)],[149]) ).
tff(151,plain,
! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,U)))) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
( ~ ! [Z: $i,Y: $i,U: $i,X: $i] : ( meet(X,join(Y,meet(Z,join(X,U)))) = meet(X,join(Y,join(meet(X,Z),meet(Z,U)))) )
| ( meet(a,join(complement(a),meet(complement(b),join(a,complement(a))))) = meet(a,join(complement(a),join(meet(a,complement(b)),meet(complement(b),complement(a))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
meet(a,join(complement(a),meet(complement(b),join(a,complement(a))))) = meet(a,join(complement(a),join(meet(a,complement(b)),meet(complement(b),complement(a))))),
inference(unit_resolution,[status(thm)],[152,151]) ).
tff(154,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(155,plain,
meet(complement(b),join(complement(b),b)) = complement(b),
inference(unit_resolution,[status(thm)],[154,95]) ).
tff(156,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(157,plain,
join(complement(b),b) = join(b,complement(b)),
inference(unit_resolution,[status(thm)],[156,47]) ).
tff(158,plain,
join(b,complement(b)) = join(complement(b),b),
inference(symmetry,[status(thm)],[157]) ).
tff(159,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(160,plain,
meet(complement(b),join(complement(b),complement(a))) = complement(b),
inference(unit_resolution,[status(thm)],[159,95]) ).
tff(161,plain,
join(b,meet(complement(b),join(complement(b),complement(a)))) = join(b,complement(b)),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
join(b,meet(complement(b),join(complement(b),complement(a)))) = join(complement(b),b),
inference(transitivity,[status(thm)],[161,158]) ).
tff(163,plain,
meet(complement(b),join(b,meet(complement(b),join(complement(b),complement(a))))) = meet(complement(b),join(complement(b),b)),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
join(b,complement(b)) = join(b,meet(complement(b),join(complement(b),complement(a)))),
inference(symmetry,[status(thm)],[161]) ).
tff(165,plain,
( ~ ! [X: $i] : ( join(X,complement(X)) = one )
| ( join(b,complement(b)) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(166,plain,
join(b,complement(b)) = one,
inference(unit_resolution,[status(thm)],[165,104]) ).
tff(167,plain,
one = join(b,complement(b)),
inference(symmetry,[status(thm)],[166]) ).
tff(168,plain,
join(a,complement(a)) = join(b,meet(complement(b),join(complement(b),complement(a)))),
inference(transitivity,[status(thm)],[106,167,164]) ).
tff(169,plain,
meet(complement(b),join(a,complement(a))) = meet(complement(b),join(b,meet(complement(b),join(complement(b),complement(a))))),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
meet(complement(b),join(a,complement(a))) = complement(b),
inference(transitivity,[status(thm)],[169,163,155]) ).
tff(171,plain,
join(complement(a),meet(complement(b),join(a,complement(a)))) = join(complement(a),complement(b)),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
join(complement(a),complement(b)) = join(complement(a),meet(complement(b),join(a,complement(a)))),
inference(symmetry,[status(thm)],[171]) ).
tff(173,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(174,plain,
join(complement(a),complement(b)) = join(complement(b),complement(a)),
inference(unit_resolution,[status(thm)],[173,47]) ).
tff(175,plain,
join(complement(b),complement(a)) = join(complement(a),complement(b)),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
join(complement(b),complement(a)) = join(complement(a),meet(complement(b),join(a,complement(a)))),
inference(transitivity,[status(thm)],[175,172]) ).
tff(177,plain,
meet(a,join(complement(b),complement(a))) = meet(a,join(complement(a),meet(complement(b),join(a,complement(a))))),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
meet(a,join(complement(b),complement(a))) = zero,
inference(transitivity,[status(thm)],[177,153,144,18]) ).
tff(179,plain,
ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))) = ifeq(zero,zero,complement(a),join(complement(b),complement(a))),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(one,one,ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))) = ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(181,plain,
ifeq(one,one,ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))) = ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))),
inference(unit_resolution,[status(thm)],[180,7]) ).
tff(182,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(183,plain,
join(complement(b),meet(complement(b),join(complement(b),complement(a)))) = complement(b),
inference(unit_resolution,[status(thm)],[182,25]) ).
tff(184,plain,
complement(b) = meet(complement(b),join(complement(b),complement(a))),
inference(symmetry,[status(thm)],[160]) ).
tff(185,plain,
join(complement(b),complement(b)) = join(complement(b),meet(complement(b),join(complement(b),complement(a)))),
inference(monotonicity,[status(thm)],[184]) ).
tff(186,plain,
join(complement(b),complement(b)) = complement(b),
inference(transitivity,[status(thm)],[185,183]) ).
tff(187,plain,
join(b,join(complement(b),complement(b))) = join(b,complement(b)),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,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(189,plain,
join(join(b,complement(b)),complement(b)) = join(b,join(complement(b),complement(b))),
inference(unit_resolution,[status(thm)],[188,64]) ).
tff(190,plain,
join(a,complement(a)) = join(b,complement(b)),
inference(transitivity,[status(thm)],[106,167]) ).
tff(191,plain,
join(join(a,complement(a)),complement(b)) = join(join(b,complement(b)),complement(b)),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,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(193,plain,
join(join(a,complement(a)),complement(b)) = join(a,join(complement(a),complement(b))),
inference(unit_resolution,[status(thm)],[192,64]) ).
tff(194,plain,
join(a,join(complement(a),complement(b))) = join(join(a,complement(a)),complement(b)),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
join(a,join(complement(b),complement(a))) = join(a,join(complement(a),complement(b))),
inference(monotonicity,[status(thm)],[175]) ).
tff(196,plain,
join(a,join(complement(b),complement(a))) = one,
inference(transitivity,[status(thm)],[195,194,191,189,187,166]) ).
tff(197,plain,
ifeq(join(a,join(complement(b),complement(a))),one,ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))) = ifeq(one,one,ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
^ [Y: $i,X: $i] :
refl(
( ( ifeq(join(X,Y),one,ifeq(meet(X,Y),zero,complement(X),Y),Y) = Y )
<=> ( ifeq(join(X,Y),one,ifeq(meet(X,Y),zero,complement(X),Y),Y) = Y ) )),
inference(bind,[status(th)],]) ).
tff(199,plain,
( ! [Y: $i,X: $i] : ( ifeq(join(X,Y),one,ifeq(meet(X,Y),zero,complement(X),Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( ifeq(join(X,Y),one,ifeq(meet(X,Y),zero,complement(X),Y),Y) = Y ) ),
inference(quant_intro,[status(thm)],[198]) ).
tff(200,plain,
( ! [Y: $i,X: $i] : ( ifeq(join(X,Y),one,ifeq(meet(X,Y),zero,complement(X),Y),Y) = Y )
<=> ! [Y: $i,X: $i] : ( ifeq(join(X,Y),one,ifeq(meet(X,Y),zero,complement(X),Y),Y) = Y ) ),
inference(rewrite,[status(thm)],]) ).
tff(201,axiom,
! [Y: $i,X: $i] : ( ifeq(join(X,Y),one,ifeq(meet(X,Y),zero,complement(X),Y),Y) = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_join_complement) ).
tff(202,plain,
! [Y: $i,X: $i] : ( ifeq(join(X,Y),one,ifeq(meet(X,Y),zero,complement(X),Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
! [Y: $i,X: $i] : ( ifeq(join(X,Y),one,ifeq(meet(X,Y),zero,complement(X),Y),Y) = Y ),
inference(skolemize,[status(sab)],[202]) ).
tff(204,plain,
! [Y: $i,X: $i] : ( ifeq(join(X,Y),one,ifeq(meet(X,Y),zero,complement(X),Y),Y) = Y ),
inference(modus_ponens,[status(thm)],[203,199]) ).
tff(205,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq(join(X,Y),one,ifeq(meet(X,Y),zero,complement(X),Y),Y) = Y )
| ( ifeq(join(a,join(complement(b),complement(a))),one,ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))) = join(complement(b),complement(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(206,plain,
ifeq(join(a,join(complement(b),complement(a))),one,ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))) = join(complement(b),complement(a)),
inference(unit_resolution,[status(thm)],[205,204]) ).
tff(207,plain,
join(complement(b),complement(a)) = ifeq(join(a,join(complement(b),complement(a))),one,ifeq(meet(a,join(complement(b),complement(a))),zero,complement(a),join(complement(b),complement(a))),join(complement(b),complement(a))),
inference(symmetry,[status(thm)],[206]) ).
tff(208,plain,
join(complement(b),complement(a)) = complement(a),
inference(transitivity,[status(thm)],[207,197,181,179,9]) ).
tff(209,plain,
( ( join(complement(b),complement(a)) != complement(a) )
<=> ( join(complement(b),complement(a)) != complement(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(210,axiom,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
tff(211,plain,
join(complement(b),complement(a)) != complement(a),
inference(modus_ponens,[status(thm)],[210,209]) ).
tff(212,plain,
$false,
inference(unit_resolution,[status(thm)],[211,208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT241-10 : TPTP v8.1.0. Released v7.5.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 12:54:36 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.
% 138.44/86.92 % SZS status Unsatisfiable
% 138.44/86.92 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------