TSTP Solution File: LAT088-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT088-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 18:31:59 EDT 2022
% Result : Unsatisfiable 0.17s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 33
% Syntax : Number of formulae : 126 ( 99 unt; 3 typ; 0 def)
% Number of atoms : 157 ( 151 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 46 ( 17 ~; 13 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 139 ( 127 !; 0 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_type,type,
a: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( ( join(meet(A,B),meet(B,join(A,B))) = B )
<=> ( join(meet(A,B),meet(B,join(A,B))) = B ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B )
<=> ! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B )
<=> ! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wal_absorbtion_3) ).
tff(5,plain,
! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B )
| ( join(meet(join(meet(a,a),meet(a,a)),a),meet(a,join(join(meet(a,a),meet(a,a)),a))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
join(meet(join(meet(a,a),meet(a,a)),a),meet(a,join(join(meet(a,a),meet(a,a)),a))) = a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( join(join(meet(A,B),meet(C,A)),A) = A )
<=> ( join(join(meet(A,B),meet(C,A)),A) = A ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [B: $i,A: $i,C: $i] : ( join(join(meet(A,B),meet(C,A)),A) = A )
<=> ! [B: $i,A: $i,C: $i] : ( join(join(meet(A,B),meet(C,A)),A) = A ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( join(join(meet(A,B),meet(C,A)),A) = A )
<=> ! [B: $i,A: $i,C: $i] : ( join(join(meet(A,B),meet(C,A)),A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [B: $i,A: $i,C: $i] : ( join(join(meet(A,B),meet(C,A)),A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wal_absorbtion_5) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] : ( join(join(meet(A,B),meet(C,A)),A) = A ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( join(join(meet(A,B),meet(C,A)),A) = A ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( join(join(meet(A,B),meet(C,A)),A) = A ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( join(join(meet(A,B),meet(C,A)),A) = A )
| ( join(join(meet(a,a),meet(a,a)),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
join(join(meet(a,a),meet(a,a)),a) = a,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
meet(a,join(join(meet(a,a),meet(a,a)),a)) = meet(a,a),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
meet(a,a) = meet(a,join(join(meet(a,a),meet(a,a)),a)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)) = join(meet(join(meet(a,a),meet(a,a)),a),meet(a,join(join(meet(a,a),meet(a,a)),a))),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)) = a,
inference(transitivity,[status(thm)],[21,9]) ).
tff(23,plain,
^ [B: $i,A: $i] :
refl(
( ( join(meet(A,A),meet(B,join(A,A))) = A )
<=> ( join(meet(A,A),meet(B,join(A,A))) = A ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A )
<=> ! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A )
<=> ! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wal_absorbtion_2) ).
tff(27,plain,
! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A )
| ( join(meet(a,a),meet(join(a,a),join(a,a))) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
join(meet(a,a),meet(join(a,a),join(a,a))) = a,
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
meet(join(meet(a,a),meet(join(a,a),join(a,a))),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))) = meet(a,a),
inference(monotonicity,[status(thm)],[31,22]) ).
tff(33,plain,
meet(a,a) = meet(join(meet(a,a),meet(join(a,a),join(a,a))),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
meet(meet(a,a),meet(a,a)) = meet(meet(join(meet(a,a),meet(join(a,a),join(a,a))),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))),meet(a,a)),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
meet(meet(join(meet(a,a),meet(join(a,a),join(a,a))),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))),meet(a,a)) = meet(meet(a,a),meet(a,a)),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( meet(meet(join(A,B),join(C,A)),A) = A )
<=> ( meet(meet(join(A,B),join(C,A)),A) = A ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A )
<=> ! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A )
<=> ! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wal_absorbtion_4) ).
tff(40,plain,
! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A )
| ( meet(meet(join(meet(a,a),meet(join(a,a),join(a,a))),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))),meet(a,a)) = meet(a,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
meet(meet(join(meet(a,a),meet(join(a,a),join(a,a))),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))),meet(a,a)) = meet(a,a),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
meet(a,a) = meet(meet(join(meet(a,a),meet(join(a,a),join(a,a))),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))),meet(a,a)),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
meet(a,join(join(meet(a,a),meet(a,a)),a)) = meet(meet(a,a),meet(a,a)),
inference(transitivity,[status(thm)],[19,45,35]) ).
tff(47,plain,
( ~ ! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A )
| ( join(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a)))) = meet(a,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
join(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a)))) = meet(a,a),
inference(unit_resolution,[status(thm)],[47,29]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B )
| ( join(meet(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a)))),meet(meet(a,join(meet(a,a),meet(a,a))),join(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a)))))) = meet(a,join(meet(a,a),meet(a,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
join(meet(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a)))),meet(meet(a,join(meet(a,a),meet(a,a))),join(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a)))))) = meet(a,join(meet(a,a),meet(a,a))),
inference(unit_resolution,[status(thm)],[49,7]) ).
tff(51,plain,
meet(a,a) = meet(meet(a,a),meet(a,a)),
inference(transitivity,[status(thm)],[45,35]) ).
tff(52,plain,
join(meet(a,a),meet(a,join(meet(a,a),meet(a,a)))) = join(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a)))),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
join(meet(a,a),meet(a,join(meet(a,a),meet(a,a)))) = meet(a,a),
inference(transitivity,[status(thm)],[52,48]) ).
tff(54,plain,
meet(meet(a,a),join(meet(a,a),meet(a,join(meet(a,a),meet(a,a))))) = meet(meet(a,a),meet(a,a)),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
meet(meet(a,a),meet(a,a)) = meet(meet(a,a),join(meet(a,a),meet(a,join(meet(a,a),meet(a,a))))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A )
| ( meet(meet(join(meet(a,a),meet(join(a,a),join(a,a))),join(meet(a,a),meet(a,a))),meet(a,a)) = meet(a,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
meet(meet(join(meet(a,a),meet(join(a,a),join(a,a))),join(meet(a,a),meet(a,a))),meet(a,a)) = meet(a,a),
inference(unit_resolution,[status(thm)],[56,42]) ).
tff(58,plain,
meet(join(meet(a,a),meet(join(a,a),join(a,a))),join(meet(a,a),meet(a,a))) = meet(a,join(meet(a,a),meet(a,a))),
inference(monotonicity,[status(thm)],[31]) ).
tff(59,plain,
meet(a,join(meet(a,a),meet(a,a))) = meet(join(meet(a,a),meet(join(a,a),join(a,a))),join(meet(a,a),meet(a,a))),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
meet(meet(a,join(meet(a,a),meet(a,a))),join(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a))))) = meet(meet(join(meet(a,a),meet(join(a,a),join(a,a))),join(meet(a,a),meet(a,a))),meet(a,a)),
inference(monotonicity,[status(thm)],[59,48]) ).
tff(61,plain,
meet(meet(a,join(meet(a,a),meet(a,a))),join(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a))))) = meet(meet(a,a),join(meet(a,a),meet(a,join(meet(a,a),meet(a,a))))),
inference(transitivity,[status(thm)],[60,57,45,35,55]) ).
tff(62,plain,
meet(meet(a,a),meet(a,join(meet(a,a),meet(a,a)))) = meet(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a)))),
inference(monotonicity,[status(thm)],[51]) ).
tff(63,plain,
meet(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a)))) = meet(meet(a,a),meet(a,join(meet(a,a),meet(a,a)))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
join(meet(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a)))),meet(meet(a,join(meet(a,a),meet(a,a))),join(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a)))))) = join(meet(meet(a,a),meet(a,join(meet(a,a),meet(a,a)))),meet(meet(a,a),join(meet(a,a),meet(a,join(meet(a,a),meet(a,a)))))),
inference(monotonicity,[status(thm)],[63,61]) ).
tff(65,plain,
join(meet(meet(a,a),meet(a,join(meet(a,a),meet(a,a)))),meet(meet(a,a),join(meet(a,a),meet(a,join(meet(a,a),meet(a,a)))))) = join(meet(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a)))),meet(meet(a,join(meet(a,a),meet(a,a))),join(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a)))))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
^ [B: $i,A: $i] :
refl(
( ( join(meet(A,B),meet(A,join(A,B))) = A )
<=> ( join(meet(A,B),meet(A,join(A,B))) = A ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A )
<=> ! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A )
<=> ! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,axiom,
! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wal_absorbtion_1) ).
tff(70,plain,
! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
( ~ ! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A )
| ( join(meet(meet(a,a),meet(a,join(meet(a,a),meet(a,a)))),meet(meet(a,a),join(meet(a,a),meet(a,join(meet(a,a),meet(a,a)))))) = meet(a,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
join(meet(meet(a,a),meet(a,join(meet(a,a),meet(a,a)))),meet(meet(a,a),join(meet(a,a),meet(a,join(meet(a,a),meet(a,a)))))) = meet(a,a),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
meet(a,a) = join(meet(meet(a,a),meet(a,join(meet(a,a),meet(a,a)))),meet(meet(a,a),join(meet(a,a),meet(a,join(meet(a,a),meet(a,a)))))),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
meet(a,a) = meet(a,join(meet(a,a),meet(a,a))),
inference(transitivity,[status(thm)],[75,65,50]) ).
tff(77,plain,
join(meet(a,a),meet(a,a)) = join(meet(meet(a,a),meet(a,a)),meet(a,join(meet(a,a),meet(a,a)))),
inference(monotonicity,[status(thm)],[51,76]) ).
tff(78,plain,
join(meet(a,a),meet(a,a)) = meet(a,a),
inference(transitivity,[status(thm)],[77,48]) ).
tff(79,plain,
meet(join(meet(a,a),meet(a,a)),a) = meet(meet(a,a),a),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
join(meet(join(meet(a,a),meet(a,a)),a),meet(a,join(join(meet(a,a),meet(a,a)),a))) = join(meet(meet(a,a),a),meet(meet(a,a),meet(a,a))),
inference(monotonicity,[status(thm)],[79,46]) ).
tff(81,plain,
join(meet(meet(a,a),a),meet(meet(a,a),meet(a,a))) = join(meet(join(meet(a,a),meet(a,a)),a),meet(a,join(join(meet(a,a),meet(a,a)),a))),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B )
| ( join(meet(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)),meet(meet(a,a),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)))) = meet(a,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
join(meet(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)),meet(meet(a,a),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)))) = meet(a,a),
inference(unit_resolution,[status(thm)],[82,7]) ).
tff(84,plain,
meet(meet(a,a),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))) = meet(meet(a,a),a),
inference(monotonicity,[status(thm)],[22]) ).
tff(85,plain,
meet(meet(a,a),a) = meet(meet(a,a),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
meet(join(meet(a,a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))) = meet(join(meet(a,a),meet(a,a)),a),
inference(monotonicity,[status(thm)],[22]) ).
tff(87,plain,
meet(join(meet(a,a),meet(a,a)),a) = meet(join(meet(a,a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
meet(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)) = meet(meet(join(meet(a,a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))),meet(a,a)),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
meet(meet(join(meet(a,a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))),meet(a,a)) = meet(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A )
| ( meet(meet(join(meet(a,a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))),meet(a,a)) = meet(a,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
meet(meet(join(meet(a,a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))),meet(a,a)) = meet(a,a),
inference(unit_resolution,[status(thm)],[90,42]) ).
tff(92,plain,
meet(a,a) = meet(meet(join(meet(a,a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a))),meet(a,a)),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
meet(a,a) = meet(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)),
inference(transitivity,[status(thm)],[92,89]) ).
tff(94,plain,
join(meet(a,a),meet(meet(a,a),a)) = join(meet(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)),meet(meet(a,a),join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)))),
inference(monotonicity,[status(thm)],[93,85]) ).
tff(95,plain,
join(meet(a,a),meet(meet(a,a),a)) = meet(a,a),
inference(transitivity,[status(thm)],[94,83]) ).
tff(96,plain,
meet(meet(a,a),join(meet(a,a),meet(meet(a,a),a))) = meet(meet(a,a),meet(a,a)),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
meet(meet(a,a),meet(a,a)) = meet(meet(a,a),join(meet(a,a),meet(meet(a,a),a))),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
meet(meet(a,a),a) = meet(join(meet(a,a),meet(a,a)),a),
inference(symmetry,[status(thm)],[79]) ).
tff(99,plain,
( ~ ! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A )
| ( join(meet(join(meet(a,a),meet(a,a)),a),meet(join(meet(a,a),meet(a,a)),join(join(meet(a,a),meet(a,a)),a))) = join(meet(a,a),meet(a,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
join(meet(join(meet(a,a),meet(a,a)),a),meet(join(meet(a,a),meet(a,a)),join(join(meet(a,a),meet(a,a)),a))) = join(meet(a,a),meet(a,a)),
inference(unit_resolution,[status(thm)],[99,72]) ).
tff(101,plain,
meet(join(meet(a,a),meet(a,a)),join(join(meet(a,a),meet(a,a)),a)) = meet(join(meet(a,a),meet(a,a)),a),
inference(monotonicity,[status(thm)],[18]) ).
tff(102,plain,
meet(join(meet(a,a),meet(a,a)),a) = meet(join(meet(a,a),meet(a,a)),join(join(meet(a,a),meet(a,a)),a)),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
join(meet(join(meet(a,a),meet(a,a)),a),meet(join(meet(a,a),meet(a,a)),a)) = join(meet(join(meet(a,a),meet(a,a)),a),meet(join(meet(a,a),meet(a,a)),join(join(meet(a,a),meet(a,a)),a))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
join(meet(join(meet(a,a),meet(a,a)),a),meet(join(meet(a,a),meet(a,a)),a)) = join(meet(a,a),meet(a,a)),
inference(transitivity,[status(thm)],[103,100]) ).
tff(105,plain,
meet(join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(join(meet(a,a),meet(a,a)),a))) = meet(a,join(meet(a,a),meet(a,a))),
inference(monotonicity,[status(thm)],[22,104]) ).
tff(106,plain,
meet(a,join(meet(a,a),meet(a,a))) = meet(join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(join(meet(a,a),meet(a,a)),a))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
meet(a,a) = meet(join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(join(meet(a,a),meet(a,a)),a))),
inference(transitivity,[status(thm)],[75,65,50,106]) ).
tff(108,plain,
meet(meet(a,a),meet(meet(a,a),a)) = meet(meet(join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(join(meet(a,a),meet(a,a)),a))),meet(join(meet(a,a),meet(a,a)),a)),
inference(monotonicity,[status(thm)],[107,98]) ).
tff(109,plain,
meet(meet(join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(join(meet(a,a),meet(a,a)),a))),meet(join(meet(a,a),meet(a,a)),a)) = meet(meet(a,a),meet(meet(a,a),a)),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A )
| ( meet(meet(join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(join(meet(a,a),meet(a,a)),a))),meet(join(meet(a,a),meet(a,a)),a)) = meet(join(meet(a,a),meet(a,a)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
meet(meet(join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(join(meet(a,a),meet(a,a)),a))),meet(join(meet(a,a),meet(a,a)),a)) = meet(join(meet(a,a),meet(a,a)),a),
inference(unit_resolution,[status(thm)],[110,42]) ).
tff(112,plain,
meet(join(meet(a,a),meet(a,a)),a) = meet(meet(join(meet(join(meet(a,a),meet(a,a)),a),meet(a,a)),join(meet(join(meet(a,a),meet(a,a)),a),meet(join(meet(a,a),meet(a,a)),a))),meet(join(meet(a,a),meet(a,a)),a)),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
meet(meet(a,a),a) = meet(meet(a,a),meet(meet(a,a),a)),
inference(transitivity,[status(thm)],[98,112,109]) ).
tff(114,plain,
join(meet(meet(a,a),a),meet(meet(a,a),meet(a,a))) = join(meet(meet(a,a),meet(meet(a,a),a)),meet(meet(a,a),join(meet(a,a),meet(meet(a,a),a)))),
inference(monotonicity,[status(thm)],[113,97]) ).
tff(115,plain,
join(meet(meet(a,a),meet(meet(a,a),a)),meet(meet(a,a),join(meet(a,a),meet(meet(a,a),a)))) = join(meet(meet(a,a),a),meet(meet(a,a),meet(a,a))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A )
| ( join(meet(meet(a,a),meet(meet(a,a),a)),meet(meet(a,a),join(meet(a,a),meet(meet(a,a),a)))) = meet(a,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
join(meet(meet(a,a),meet(meet(a,a),a)),meet(meet(a,a),join(meet(a,a),meet(meet(a,a),a)))) = meet(a,a),
inference(unit_resolution,[status(thm)],[116,72]) ).
tff(118,plain,
meet(a,a) = join(meet(meet(a,a),meet(meet(a,a),a)),meet(meet(a,a),join(meet(a,a),meet(meet(a,a),a)))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
meet(a,a) = a,
inference(transitivity,[status(thm)],[118,115,81,9]) ).
tff(120,plain,
( ( meet(a,a) != a )
<=> ( meet(a,a) != a ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,axiom,
meet(a,a) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_normal_axioms_1) ).
tff(122,plain,
meet(a,a) != a,
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
$false,
inference(unit_resolution,[status(thm)],[122,119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT088-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Sep 1 11:33:03 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.17/0.37 % SZS status Unsatisfiable
% 0.17/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------