%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT090-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 Jun 21 05:13:51 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 27
% Syntax : Number of formulae : 94 ( 73 unt; 0 typ; 0 def)
% Number of atoms : 125 ( 119 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 14 ~; 10 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 133 ( 121 !; 0 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_type,type,
a: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,plain,
! [B: $i,A: $i,C: $i] : ( join(join(meet(A,B),meet(C,A)),A) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( join(join(meet(A,B),meet(C,A)),A) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( join(join(meet(A,B),meet(C,A)),A) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( join(join(meet(A,B),meet(C,A)),A) = A )
| ( join(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
join(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a) = a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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(14,plain,
! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A )
| ( meet(meet(join(a,a),join(a,a)),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
meet(meet(join(a,a),join(a,a)),a) = a,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
a = meet(meet(join(a,a),join(a,a)),a),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
join(meet(a,a),a) = join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)) = join(meet(a,a),a),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),join(meet(a,a),meet(a,a))) = meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))) = meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),join(meet(a,a),meet(a,a))),
inference(symmetry,[status(thm)],[22]) ).
tff(24,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(25,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)],[24]) ).
tff(26,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(27,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(28,plain,
! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B )
| ( join(meet(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))),meet(meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))),join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))))) = meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
join(meet(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))),meet(meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))),join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))))) = meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,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(34,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)],[33]) ).
tff(35,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(36,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(37,plain,
! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
( ~ ! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A )
| ( join(meet(meet(a,a),meet(a,a)),meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),join(meet(a,a),meet(a,a)))) = meet(a,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
join(meet(meet(a,a),meet(a,a)),meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),join(meet(a,a),meet(a,a)))) = meet(a,a),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i] : ( join(meet(A,B),meet(B,join(A,B))) = B )
| ( join(meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a),meet(a,join(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
join(meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a),meet(a,join(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a))) = a,
inference(unit_resolution,[status(thm)],[42,30]) ).
tff(44,plain,
meet(a,join(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a)) = meet(a,a),
inference(monotonicity,[status(thm)],[9]) ).
tff(45,plain,
meet(a,a) = meet(a,join(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a)),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
join(meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a),meet(a,a)) = join(meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a),meet(a,join(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a))),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
join(meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a),meet(a,a)) = a,
inference(transitivity,[status(thm)],[46,43]) ).
tff(48,plain,
( ~ ! [B: $i,A: $i] : ( join(meet(A,A),meet(B,join(A,A))) = A )
| ( join(meet(a,a),meet(join(meet(join(a,a),join(a,a)),meet(join(a,a),join(a,a))),join(a,a))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
join(meet(a,a),meet(join(meet(join(a,a),join(a,a)),meet(join(a,a),join(a,a))),join(a,a))) = a,
inference(unit_resolution,[status(thm)],[48,39]) ).
tff(50,plain,
meet(join(meet(a,a),meet(join(meet(join(a,a),join(a,a)),meet(join(a,a),join(a,a))),join(a,a))),join(meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a),meet(a,a))) = meet(a,a),
inference(monotonicity,[status(thm)],[49,47]) ).
tff(51,plain,
meet(a,a) = meet(join(meet(a,a),meet(join(meet(join(a,a),join(a,a)),meet(join(a,a),join(a,a))),join(a,a))),join(meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a),meet(a,a))),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
meet(meet(a,a),meet(a,a)) = meet(meet(join(meet(a,a),meet(join(meet(join(a,a),join(a,a)),meet(join(a,a),join(a,a))),join(a,a))),join(meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a),meet(a,a))),meet(a,a)),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
meet(meet(join(meet(a,a),meet(join(meet(join(a,a),join(a,a)),meet(join(a,a),join(a,a))),join(a,a))),join(meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a),meet(a,a))),meet(a,a)) = meet(meet(a,a),meet(a,a)),
inference(symmetry,[status(thm)],[52]) ).
tff(54,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(meet(join(a,a),join(a,a)),meet(join(a,a),join(a,a))),join(a,a))),join(meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a),meet(a,a))),meet(a,a)) = meet(a,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
meet(meet(join(meet(a,a),meet(join(meet(join(a,a),join(a,a)),meet(join(a,a),join(a,a))),join(a,a))),join(meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a),meet(a,a))),meet(a,a)) = meet(a,a),
inference(unit_resolution,[status(thm)],[54,16]) ).
tff(56,plain,
meet(a,a) = meet(meet(join(meet(a,a),meet(join(meet(join(a,a),join(a,a)),meet(join(a,a),join(a,a))),join(a,a))),join(meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a),meet(a,a))),meet(a,a)),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
meet(a,a) = meet(meet(a,a),meet(a,a)),
inference(transitivity,[status(thm)],[56,53]) ).
tff(58,plain,
join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))) = join(meet(meet(a,a),meet(a,a)),meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),join(meet(a,a),meet(a,a)))),
inference(monotonicity,[status(thm)],[57,23]) ).
tff(59,plain,
join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))) = meet(a,a),
inference(transitivity,[status(thm)],[58,41]) ).
tff(60,plain,
meet(meet(a,a),join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))))) = meet(meet(a,a),meet(a,a)),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
meet(meet(a,a),meet(a,a)) = meet(meet(a,a),join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))))),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( meet(meet(join(A,B),join(C,A)),A) = A )
| ( meet(meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))),meet(a,a)) = meet(a,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
meet(meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))),meet(a,a)) = meet(a,a),
inference(unit_resolution,[status(thm)],[62,16]) ).
tff(64,plain,
meet(meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))),join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))))) = meet(meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))),meet(a,a)),
inference(monotonicity,[status(thm)],[59]) ).
tff(65,plain,
meet(meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))),join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))))) = meet(meet(a,a),join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))))),
inference(transitivity,[status(thm)],[64,63,56,53,61]) ).
tff(66,plain,
join(meet(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))),meet(meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))),join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))))) = join(meet(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))),meet(meet(a,a),join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))))),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
join(meet(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))),meet(meet(a,a),join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))))) = join(meet(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))),meet(meet(join(meet(a,a),a),join(meet(a,a),meet(a,a))),join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))))),
inference(symmetry,[status(thm)],[66]) ).
tff(68,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(69,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)],[68]) ).
tff(70,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(71,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(72,plain,
! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
( ~ ! [B: $i,A: $i] : ( join(meet(A,B),meet(A,join(A,B))) = A )
| ( join(meet(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))),meet(meet(a,a),join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))))) = meet(a,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
join(meet(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))),meet(meet(a,a),join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))))) = meet(a,a),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
meet(a,a) = join(meet(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))),meet(meet(a,a),join(meet(a,a),meet(join(meet(a,a),a),join(meet(a,a),meet(a,a)))))),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
meet(a,a) = meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),join(meet(a,a),meet(a,a))),
inference(transitivity,[status(thm)],[77,67,32,23]) ).
tff(79,plain,
join(meet(a,a),meet(a,a)) = join(meet(meet(a,a),meet(a,a)),meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),join(meet(a,a),meet(a,a)))),
inference(monotonicity,[status(thm)],[57,78]) ).
tff(80,plain,
join(meet(meet(a,a),meet(a,a)),meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),join(meet(a,a),meet(a,a)))) = join(meet(a,a),meet(a,a)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
meet(a,a) = join(meet(meet(a,a),meet(a,a)),meet(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),join(meet(a,a),meet(a,a)))),
inference(symmetry,[status(thm)],[41]) ).
tff(82,plain,
meet(a,a) = join(meet(a,a),meet(a,a)),
inference(transitivity,[status(thm)],[81,80]) ).
tff(83,plain,
join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)) = join(join(meet(a,a),meet(a,a)),a),
inference(monotonicity,[status(thm)],[82,18]) ).
tff(84,plain,
join(join(meet(a,a),meet(a,a)),a) = join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),
inference(symmetry,[status(thm)],[83]) ).
tff(85,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(86,plain,
join(join(meet(a,a),meet(a,a)),a) = a,
inference(unit_resolution,[status(thm)],[85,7]) ).
tff(87,plain,
a = join(join(meet(a,a),meet(a,a)),a),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
a = join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),
inference(transitivity,[status(thm)],[87,84]) ).
tff(89,plain,
join(a,a) = join(join(meet(a,a),meet(meet(join(a,a),join(a,a)),a)),a),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
join(a,a) = a,
inference(transitivity,[status(thm)],[89,9]) ).
tff(91,plain,
( ( join(a,a) != a )
<=> ( join(a,a) != a ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,axiom,
join(a,a) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_normal_axioms_3) ).
tff(93,plain,
join(a,a) != a,
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
$false,
inference(unit_resolution,[status(thm)],[93,90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT090-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:33:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% See solution above
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------