%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT143-1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:13:54 AM UTC 2025
% Result : Unsatisfiable 6.03s 6.24s
% Output : Proof 6.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 63
% Syntax : Number of formulae : 227 ( 172 unt; 0 typ; 0 def)
% Number of atoms : 296 ( 288 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 106 ( 44 ~; 40 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 7 ( 7 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 247 ( 230 !; 0 ?; 247 :)
% Comments :
%------------------------------------------------------------------------------
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(c_type,type,
c: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(5,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c)))) = meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c)))) = meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(14,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))) = meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
meet(join(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))) = meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(a,b)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(a,b)) = meet(join(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),a) = meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),a) = meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),
inference(unit_resolution,[status(thm)],[20,16]) ).
tff(22,plain,
meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))) = meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),a),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(a,b)) = meet(meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),a),join(a,b)),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
meet(meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),a),join(a,b)) = meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(a,b)),
inference(symmetry,[status(thm)],[23]) ).
tff(25,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(26,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)],[25]) ).
tff(27,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(28,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
tff(29,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),a),join(a,b)) = meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),meet(a,join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
meet(meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),a),join(a,b)) = meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),meet(a,join(a,b))),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),meet(a,join(a,b))) = meet(meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),a),join(a,b)),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(36,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)],[35]) ).
tff(37,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(38,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
tff(39,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,b)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
meet(a,join(a,b)) = a,
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),meet(a,join(a,b))) = meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),a),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),a) = meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),meet(a,join(a,b))),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))) = meet(join(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))),
inference(transitivity,[status(thm)],[22,45,34,24,19]) ).
tff(47,plain,
join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c)))) = join(meet(join(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))),meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c)))),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
join(meet(join(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))),meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c)))) = join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c)))),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(join(meet(a,b),meet(a,c)),join(join(meet(a,b),meet(a,c)),meet(c,join(a,b)))) = join(meet(a,b),meet(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
meet(join(meet(a,b),meet(a,c)),join(join(meet(a,b),meet(a,c)),meet(c,join(a,b)))) = join(meet(a,b),meet(a,c)),
inference(unit_resolution,[status(thm)],[49,41]) ).
tff(51,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(52,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)],[51]) ).
tff(53,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(54,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
tff(55,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(a,b),meet(a,c)),meet(c,join(a,b))) = join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
join(join(meet(a,b),meet(a,c)),meet(c,join(a,b))) = join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))) = join(join(meet(a,b),meet(a,c)),meet(c,join(a,b))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
meet(join(meet(a,b),meet(a,c)),join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))) = meet(join(meet(a,b),meet(a,c)),join(join(meet(a,b),meet(a,c)),meet(c,join(a,b)))),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),join(meet(a,b),meet(a,c))) = meet(join(meet(a,b),meet(a,c)),join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),join(meet(a,b),meet(a,c))) = meet(join(meet(a,b),meet(a,c)),join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),
inference(unit_resolution,[status(thm)],[62,16]) ).
tff(64,plain,
meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),join(meet(a,b),meet(a,c))) = join(meet(a,b),meet(a,c)),
inference(transitivity,[status(thm)],[63,61,50]) ).
tff(65,plain,
meet(a,meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),join(meet(a,b),meet(a,c)))) = meet(a,join(meet(a,b),meet(a,c))),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c))) = meet(a,meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),join(meet(a,b),meet(a,c)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c))) = meet(a,meet(join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),join(meet(a,b),meet(a,c)))),
inference(unit_resolution,[status(thm)],[66,31]) ).
tff(68,plain,
meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c))) = meet(a,join(meet(a,b),meet(a,c))),
inference(transitivity,[status(thm)],[67,65]) ).
tff(69,plain,
meet(join(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))) = meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),
inference(transitivity,[status(thm)],[18,23,33,44,21]) ).
tff(70,plain,
join(meet(join(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))),meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c)))) = join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,join(meet(a,b),meet(a,c)))),
inference(monotonicity,[status(thm)],[69,68]) ).
tff(71,plain,
join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,join(meet(a,b),meet(a,c)))) = join(meet(join(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))),meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c)))),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(join(meet(a,b),meet(a,c)),join(join(meet(a,b),meet(a,c)),a)) = join(meet(a,b),meet(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
meet(join(meet(a,b),meet(a,c)),join(join(meet(a,b),meet(a,c)),a)) = join(meet(a,b),meet(a,c)),
inference(unit_resolution,[status(thm)],[72,41]) ).
tff(74,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(75,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)],[74]) ).
tff(76,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(77,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(78,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(meet(a,b),meet(a,c)),a) = join(a,join(meet(a,b),meet(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
join(join(meet(a,b),meet(a,c)),a) = join(a,join(meet(a,b),meet(a,c))),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
join(a,join(meet(a,b),meet(a,c))) = join(join(meet(a,b),meet(a,c)),a),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(a,meet(a,b)),meet(a,c)) = join(a,join(meet(a,b),meet(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
join(join(a,meet(a,b)),meet(a,c)) = join(a,join(meet(a,b),meet(a,c))),
inference(unit_resolution,[status(thm)],[84,57]) ).
tff(86,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(a,meet(a,b)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
join(a,meet(a,b)) = a,
inference(unit_resolution,[status(thm)],[86,7]) ).
tff(88,plain,
join(join(a,meet(a,b)),meet(a,c)) = join(a,meet(a,c)),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
join(a,meet(a,c)) = join(join(a,meet(a,b)),meet(a,c)),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(a,meet(a,c)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
join(a,meet(a,c)) = a,
inference(unit_resolution,[status(thm)],[90,7]) ).
tff(92,plain,
a = join(a,meet(a,c)),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
a = join(join(meet(a,b),meet(a,c)),a),
inference(transitivity,[status(thm)],[92,89,85,83]) ).
tff(94,plain,
meet(join(meet(a,b),meet(a,c)),a) = meet(join(meet(a,b),meet(a,c)),join(join(meet(a,b),meet(a,c)),a)),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(a,b),meet(a,c)),a) = meet(a,join(meet(a,b),meet(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
meet(join(meet(a,b),meet(a,c)),a) = meet(a,join(meet(a,b),meet(a,c))),
inference(unit_resolution,[status(thm)],[95,16]) ).
tff(97,plain,
meet(a,join(meet(a,b),meet(a,c))) = meet(join(meet(a,b),meet(a,c)),a),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
meet(a,join(meet(a,b),meet(a,c))) = join(meet(a,b),meet(a,c)),
inference(transitivity,[status(thm)],[97,94,73]) ).
tff(99,plain,
join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,join(meet(a,b),meet(a,c)))) = join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c))),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c))) = join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,join(meet(a,b),meet(a,c)))),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,b),meet(a,join(meet(a,b),meet(a,c)))) = join(meet(a,join(meet(a,b),meet(a,c))),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
join(meet(a,b),meet(a,join(meet(a,b),meet(a,c)))) = join(meet(a,join(meet(a,b),meet(a,c))),meet(a,b)),
inference(unit_resolution,[status(thm)],[101,80]) ).
tff(103,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(c,a) = meet(a,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
meet(c,a) = meet(a,c),
inference(unit_resolution,[status(thm)],[103,16]) ).
tff(105,plain,
meet(c,meet(a,join(a,b))) = meet(c,a),
inference(monotonicity,[status(thm)],[43]) ).
tff(106,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(c,a),join(a,b)) = meet(c,meet(a,join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
meet(meet(c,a),join(a,b)) = meet(c,meet(a,join(a,b))),
inference(unit_resolution,[status(thm)],[106,31]) ).
tff(108,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,a) = join(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
join(b,a) = join(a,b),
inference(unit_resolution,[status(thm)],[108,80]) ).
tff(110,plain,
meet(a,c) = meet(c,a),
inference(symmetry,[status(thm)],[104]) ).
tff(111,plain,
meet(meet(a,c),join(b,a)) = meet(meet(c,a),join(a,b)),
inference(monotonicity,[status(thm)],[110,109]) ).
tff(112,plain,
meet(meet(a,c),join(b,a)) = meet(a,c),
inference(transitivity,[status(thm)],[111,107,105,104]) ).
tff(113,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,a) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
meet(b,a) = meet(a,b),
inference(unit_resolution,[status(thm)],[113,16]) ).
tff(115,plain,
join(meet(b,a),meet(meet(a,c),join(b,a))) = join(meet(a,b),meet(a,c)),
inference(monotonicity,[status(thm)],[114,112]) ).
tff(116,plain,
meet(a,join(meet(b,a),meet(meet(a,c),join(b,a)))) = meet(a,join(meet(a,b),meet(a,c))),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
meet(a,join(meet(a,b),meet(a,c))) = meet(a,join(meet(b,a),meet(meet(a,c),join(b,a)))),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
meet(a,b) = meet(b,a),
inference(symmetry,[status(thm)],[114]) ).
tff(119,plain,
join(meet(a,b),meet(a,join(meet(a,b),meet(a,c)))) = join(meet(b,a),meet(a,join(meet(b,a),meet(meet(a,c),join(b,a))))),
inference(monotonicity,[status(thm)],[118,117]) ).
tff(120,plain,
join(meet(b,a),meet(a,join(meet(b,a),meet(meet(a,c),join(b,a))))) = join(meet(a,b),meet(a,join(meet(a,b),meet(a,c)))),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( join(meet(X,Y),meet(Y,Z)) = join(meet(X,Y),meet(Y,join(meet(X,Y),meet(Z,join(X,Y))))) )
<=> ( join(meet(X,Y),meet(Y,Z)) = join(meet(X,Y),meet(Y,join(meet(X,Y),meet(Z,join(X,Y))))) ) )),
inference(bind,[status(th)],[]) ).
tff(122,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Y,Z)) = join(meet(X,Y),meet(Y,join(meet(X,Y),meet(Z,join(X,Y))))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Y,Z)) = join(meet(X,Y),meet(Y,join(meet(X,Y),meet(Z,join(X,Y))))) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Y,Z)) = join(meet(X,Y),meet(Y,join(meet(X,Y),meet(Z,join(X,Y))))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Y,Z)) = join(meet(X,Y),meet(Y,join(meet(X,Y),meet(Z,join(X,Y))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Y,Z)) = join(meet(X,Y),meet(Y,join(meet(X,Y),meet(Z,join(X,Y))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H24) ).
tff(125,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Y,Z)) = join(meet(X,Y),meet(Y,join(meet(X,Y),meet(Z,join(X,Y))))) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Y,Z)) = join(meet(X,Y),meet(Y,join(meet(X,Y),meet(Z,join(X,Y))))) ),
inference(skolemize,[status(sab)],[125]) ).
tff(127,plain,
! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Y,Z)) = join(meet(X,Y),meet(Y,join(meet(X,Y),meet(Z,join(X,Y))))) ),
inference(modus_ponens,[status(thm)],[126,122]) ).
tff(128,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Y,Z)) = join(meet(X,Y),meet(Y,join(meet(X,Y),meet(Z,join(X,Y))))) )
| ( join(meet(b,a),meet(a,meet(a,c))) = join(meet(b,a),meet(a,join(meet(b,a),meet(meet(a,c),join(b,a))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
join(meet(b,a),meet(a,meet(a,c))) = join(meet(b,a),meet(a,join(meet(b,a),meet(meet(a,c),join(b,a))))),
inference(unit_resolution,[status(thm)],[128,127]) ).
tff(130,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(a,c),join(meet(a,c),meet(c,join(a,b)))) = meet(a,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
meet(meet(a,c),join(meet(a,c),meet(c,join(a,b)))) = meet(a,c),
inference(unit_resolution,[status(thm)],[130,41]) ).
tff(132,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,c),join(meet(a,c),meet(c,join(a,b)))) = meet(a,meet(c,join(meet(a,c),meet(c,join(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
meet(meet(a,c),join(meet(a,c),meet(c,join(a,b)))) = meet(a,meet(c,join(meet(a,c),meet(c,join(a,b))))),
inference(unit_resolution,[status(thm)],[132,31]) ).
tff(134,plain,
meet(a,meet(c,join(meet(a,c),meet(c,join(a,b))))) = meet(meet(a,c),join(meet(a,c),meet(c,join(a,b)))),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,meet(a,b))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
meet(a,join(a,meet(a,b))) = a,
inference(unit_resolution,[status(thm)],[135,41]) ).
tff(137,plain,
a = join(a,meet(a,b)),
inference(symmetry,[status(thm)],[87]) ).
tff(138,plain,
meet(a,a) = meet(a,join(a,meet(a,b))),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
meet(a,a) = a,
inference(transitivity,[status(thm)],[138,136]) ).
tff(140,plain,
meet(meet(a,a),meet(c,join(meet(a,c),meet(c,join(a,b))))) = meet(a,meet(c,join(meet(a,c),meet(c,join(a,b))))),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,a),meet(c,join(meet(a,c),meet(c,join(a,b))))) = meet(a,meet(a,meet(c,join(meet(a,c),meet(c,join(a,b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
meet(meet(a,a),meet(c,join(meet(a,c),meet(c,join(a,b))))) = meet(a,meet(a,meet(c,join(meet(a,c),meet(c,join(a,b)))))),
inference(unit_resolution,[status(thm)],[141,31]) ).
tff(143,plain,
meet(a,meet(a,meet(c,join(meet(a,c),meet(c,join(a,b)))))) = meet(meet(a,a),meet(c,join(meet(a,c),meet(c,join(a,b))))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
meet(a,c) = meet(meet(a,c),join(meet(a,c),meet(c,join(a,b)))),
inference(symmetry,[status(thm)],[131]) ).
tff(145,plain,
meet(a,c) = meet(a,meet(c,join(meet(a,c),meet(c,join(a,b))))),
inference(transitivity,[status(thm)],[144,133]) ).
tff(146,plain,
meet(a,meet(a,c)) = meet(a,meet(a,meet(c,join(meet(a,c),meet(c,join(a,b)))))),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
meet(a,meet(a,c)) = meet(a,c),
inference(transitivity,[status(thm)],[146,143,140,134,131]) ).
tff(148,plain,
join(meet(b,a),meet(a,meet(a,c))) = join(meet(a,b),meet(a,c)),
inference(monotonicity,[status(thm)],[114,147]) ).
tff(149,plain,
join(meet(a,b),meet(a,c)) = join(meet(b,a),meet(a,meet(a,c))),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
join(meet(a,b),meet(a,c)) = join(meet(a,join(meet(a,b),meet(a,c))),meet(a,b)),
inference(transitivity,[status(thm)],[149,129,120,102]) ).
tff(151,plain,
join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c))) = join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,join(meet(a,b),meet(a,c))),meet(a,b))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,join(meet(a,b),meet(a,c))),meet(a,b))) = join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c))),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
join(meet(a,join(meet(a,b),meet(a,c))),meet(a,b)) = join(meet(a,b),meet(a,join(meet(a,b),meet(a,c)))),
inference(symmetry,[status(thm)],[102]) ).
tff(154,plain,
join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,join(meet(a,b),meet(a,c))),meet(a,b))) = join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,join(meet(a,b),meet(a,c))))),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,join(meet(a,b),meet(a,c))))) = join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,join(meet(a,b),meet(a,c))),meet(a,b))),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b)),meet(a,join(meet(a,b),meet(a,c)))) = join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,join(meet(a,b),meet(a,c))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
join(join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b)),meet(a,join(meet(a,b),meet(a,c)))) = join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,join(meet(a,b),meet(a,c))))),
inference(unit_resolution,[status(thm)],[156,57]) ).
tff(158,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b)),meet(a,join(meet(a,b),meet(a,c)))) = join(meet(a,join(meet(a,b),meet(a,c))),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
join(join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b)),meet(a,join(meet(a,b),meet(a,c)))) = join(meet(a,join(meet(a,b),meet(a,c))),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b))),
inference(unit_resolution,[status(thm)],[158,80]) ).
tff(160,plain,
join(meet(a,join(meet(a,b),meet(a,c))),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b))) = join(join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b)),meet(a,join(meet(a,b),meet(a,c)))),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))) = join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,plain,
join(meet(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))) = join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b)),
inference(unit_resolution,[status(thm)],[161,80]) ).
tff(163,plain,
join(meet(a,join(meet(a,b),meet(a,c))),join(meet(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))))) = join(meet(a,join(meet(a,b),meet(a,c))),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b))),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(a,join(meet(a,b),meet(a,c))),meet(a,b)),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))) = join(meet(a,join(meet(a,b),meet(a,c))),join(meet(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
join(join(meet(a,join(meet(a,b),meet(a,c))),meet(a,b)),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))) = join(meet(a,join(meet(a,b),meet(a,c))),join(meet(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))))),
inference(unit_resolution,[status(thm)],[164,57]) ).
tff(166,plain,
join(join(meet(a,b),meet(a,c)),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))) = join(join(meet(a,join(meet(a,b),meet(a,c))),meet(a,b)),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))),
inference(monotonicity,[status(thm)],[150]) ).
tff(167,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(join(meet(a,b),meet(a,c)),meet(join(meet(a,b),meet(a,c)),meet(a,b))) = join(meet(a,b),meet(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
join(join(meet(a,b),meet(a,c)),meet(join(meet(a,b),meet(a,c)),meet(a,b))) = join(meet(a,b),meet(a,c)),
inference(unit_resolution,[status(thm)],[167,7]) ).
tff(169,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(a,b),meet(a,c)),meet(a,b)) = meet(meet(a,b),join(meet(a,b),meet(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
meet(join(meet(a,b),meet(a,c)),meet(a,b)) = meet(meet(a,b),join(meet(a,b),meet(a,c))),
inference(unit_resolution,[status(thm)],[169,16]) ).
tff(171,plain,
meet(meet(a,b),join(meet(a,b),meet(a,c))) = meet(join(meet(a,b),meet(a,c)),meet(a,b)),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(a,b),join(meet(a,b),meet(a,c))) = meet(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
meet(meet(a,b),join(meet(a,b),meet(a,c))) = meet(a,b),
inference(unit_resolution,[status(thm)],[172,41]) ).
tff(174,plain,
meet(a,b) = meet(meet(a,b),join(meet(a,b),meet(a,c))),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
meet(a,b) = meet(join(meet(a,b),meet(a,c)),meet(a,b)),
inference(transitivity,[status(thm)],[174,171]) ).
tff(176,plain,
join(join(meet(a,b),meet(a,c)),meet(a,b)) = join(join(meet(a,b),meet(a,c)),meet(join(meet(a,b),meet(a,c)),meet(a,b))),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
join(join(meet(a,b),meet(a,c)),meet(a,b)) = join(meet(a,b),meet(a,c)),
inference(transitivity,[status(thm)],[176,168]) ).
tff(178,plain,
join(join(join(meet(a,b),meet(a,c)),meet(a,b)),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))) = join(join(meet(a,b),meet(a,c)),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(join(meet(a,b),meet(a,c)),meet(a,b)),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))) = join(join(meet(a,b),meet(a,c)),join(meet(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(180,plain,
join(join(join(meet(a,b),meet(a,c)),meet(a,b)),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))) = join(join(meet(a,b),meet(a,c)),join(meet(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))))),
inference(unit_resolution,[status(thm)],[179,57]) ).
tff(181,plain,
join(join(meet(a,b),meet(a,c)),join(meet(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))))) = join(join(join(meet(a,b),meet(a,c)),meet(a,b)),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b)) = join(meet(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))))),
inference(symmetry,[status(thm)],[162]) ).
tff(183,plain,
join(join(meet(a,b),meet(a,c)),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b))) = join(join(meet(a,b),meet(a,c)),join(meet(a,b),meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))))),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
join(meet(b,a),meet(a,join(meet(b,a),meet(meet(a,c),join(b,a))))) = join(meet(b,a),meet(a,meet(a,c))),
inference(symmetry,[status(thm)],[129]) ).
tff(185,plain,
join(meet(a,join(meet(a,b),meet(a,c))),meet(a,b)) = join(meet(a,b),meet(a,c)),
inference(transitivity,[status(thm)],[153,119,184,148]) ).
tff(186,plain,
join(join(meet(a,join(meet(a,b),meet(a,c))),meet(a,b)),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b))) = join(join(meet(a,b),meet(a,c)),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b))),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,plain,
join(join(meet(a,b),meet(a,join(meet(a,b),meet(a,c)))),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b))) = join(join(meet(a,join(meet(a,b),meet(a,c))),meet(a,b)),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b))),
inference(monotonicity,[status(thm)],[102]) ).
tff(188,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(a,b),meet(a,join(meet(a,b),meet(a,c)))),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b))) = join(meet(a,b),join(meet(a,join(meet(a,b),meet(a,c))),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
join(join(meet(a,b),meet(a,join(meet(a,b),meet(a,c)))),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b))) = join(meet(a,b),join(meet(a,join(meet(a,b),meet(a,c))),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b)))),
inference(unit_resolution,[status(thm)],[188,57]) ).
tff(190,plain,
join(meet(a,b),join(meet(a,join(meet(a,b),meet(a,c))),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b)))) = join(join(meet(a,b),meet(a,join(meet(a,b),meet(a,c)))),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b))),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,join(meet(a,b),meet(a,c))))) = join(join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b)),meet(a,join(meet(a,b),meet(a,c)))),
inference(symmetry,[status(thm)],[157]) ).
tff(192,plain,
meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))) = join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),join(meet(a,b),meet(a,c)))),
inference(symmetry,[status(thm)],[9]) ).
tff(193,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(c,join(a,b)),join(meet(a,b),meet(a,c))) = join(join(meet(a,b),meet(a,c)),meet(c,join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(194,plain,
join(meet(c,join(a,b)),join(meet(a,b),meet(a,c))) = join(join(meet(a,b),meet(a,c)),meet(c,join(a,b))),
inference(unit_resolution,[status(thm)],[193,80]) ).
tff(195,plain,
join(meet(a,b),meet(a,c)) = join(meet(b,a),meet(a,c)),
inference(monotonicity,[status(thm)],[118]) ).
tff(196,plain,
join(meet(b,a),meet(a,c)) = join(meet(a,b),meet(a,c)),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(meet(X,Y),meet(Y,Z)) = join(meet(X,Y),meet(Y,join(meet(X,Y),meet(Z,join(X,Y))))) )
| ( join(meet(b,a),meet(a,c)) = join(meet(b,a),meet(a,join(meet(b,a),meet(c,join(b,a))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(198,plain,
join(meet(b,a),meet(a,c)) = join(meet(b,a),meet(a,join(meet(b,a),meet(c,join(b,a))))),
inference(unit_resolution,[status(thm)],[197,127]) ).
tff(199,plain,
join(meet(b,a),meet(a,join(meet(b,a),meet(c,join(b,a))))) = join(meet(b,a),meet(a,c)),
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
join(meet(a,b),meet(a,join(meet(b,a),meet(c,join(b,a))))) = join(meet(b,a),meet(a,join(meet(b,a),meet(c,join(b,a))))),
inference(monotonicity,[status(thm)],[118]) ).
tff(201,plain,
join(meet(a,b),meet(a,join(meet(b,a),meet(c,join(b,a))))) = join(meet(a,b),meet(a,c)),
inference(transitivity,[status(thm)],[200,199,196]) ).
tff(202,plain,
join(meet(c,join(a,b)),join(meet(a,b),meet(a,join(meet(b,a),meet(c,join(b,a)))))) = join(meet(c,join(a,b)),join(meet(a,b),meet(a,c))),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(meet(c,join(a,b)),meet(a,b)),meet(a,join(meet(b,a),meet(c,join(b,a))))) = join(meet(c,join(a,b)),join(meet(a,b),meet(a,join(meet(b,a),meet(c,join(b,a)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,plain,
join(join(meet(c,join(a,b)),meet(a,b)),meet(a,join(meet(b,a),meet(c,join(b,a))))) = join(meet(c,join(a,b)),join(meet(a,b),meet(a,join(meet(b,a),meet(c,join(b,a)))))),
inference(unit_resolution,[status(thm)],[203,57]) ).
tff(205,plain,
meet(c,join(b,a)) = meet(c,join(a,b)),
inference(monotonicity,[status(thm)],[109]) ).
tff(206,plain,
join(meet(b,a),meet(c,join(b,a))) = join(meet(a,b),meet(c,join(a,b))),
inference(monotonicity,[status(thm)],[114,205]) ).
tff(207,plain,
join(meet(a,b),meet(c,join(a,b))) = join(meet(b,a),meet(c,join(b,a))),
inference(symmetry,[status(thm)],[206]) ).
tff(208,plain,
meet(a,join(meet(a,b),meet(c,join(a,b)))) = meet(a,join(meet(b,a),meet(c,join(b,a)))),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(meet(a,b),meet(c,join(a,b))),a) = meet(a,join(meet(a,b),meet(c,join(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(210,plain,
meet(join(meet(a,b),meet(c,join(a,b))),a) = meet(a,join(meet(a,b),meet(c,join(a,b)))),
inference(unit_resolution,[status(thm)],[209,16]) ).
tff(211,plain,
meet(join(meet(a,b),meet(c,join(a,b))),a) = meet(a,join(meet(b,a),meet(c,join(b,a)))),
inference(transitivity,[status(thm)],[210,208]) ).
tff(212,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(c,join(a,b)),meet(a,b)) = join(meet(a,b),meet(c,join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
join(meet(c,join(a,b)),meet(a,b)) = join(meet(a,b),meet(c,join(a,b))),
inference(unit_resolution,[status(thm)],[212,80]) ).
tff(214,plain,
join(meet(a,b),meet(c,join(a,b))) = join(meet(c,join(a,b)),meet(a,b)),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
join(join(meet(a,b),meet(c,join(a,b))),meet(join(meet(a,b),meet(c,join(a,b))),a)) = join(join(meet(c,join(a,b)),meet(a,b)),meet(a,join(meet(b,a),meet(c,join(b,a))))),
inference(monotonicity,[status(thm)],[214,211]) ).
tff(216,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(join(meet(a,b),meet(c,join(a,b))),meet(join(meet(a,b),meet(c,join(a,b))),a)) = join(meet(a,b),meet(c,join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
join(join(meet(a,b),meet(c,join(a,b))),meet(join(meet(a,b),meet(c,join(a,b))),a)) = join(meet(a,b),meet(c,join(a,b))),
inference(unit_resolution,[status(thm)],[216,7]) ).
tff(218,plain,
join(meet(a,b),meet(c,join(a,b))) = join(join(meet(a,b),meet(c,join(a,b))),meet(join(meet(a,b),meet(c,join(a,b))),a)),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
join(meet(b,a),meet(c,join(b,a))) = join(meet(a,b),join(meet(a,c),meet(c,join(a,b)))),
inference(transitivity,[status(thm)],[206,218,215,204,202,194,59]) ).
tff(220,plain,
meet(a,join(meet(b,a),meet(c,join(b,a)))) = meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
meet(a,join(meet(b,a),meet(c,join(b,a)))) = join(meet(a,join(meet(a,b),meet(a,c))),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b))),
inference(transitivity,[status(thm)],[220,192,47,70,99,151,154,191,159]) ).
tff(222,plain,
join(meet(b,a),meet(a,join(meet(b,a),meet(c,join(b,a))))) = join(meet(a,b),join(meet(a,join(meet(a,b),meet(a,c))),join(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,b)))),
inference(monotonicity,[status(thm)],[114,221]) ).
tff(223,plain,
meet(a,join(meet(a,b),meet(a,c))) = meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),
inference(transitivity,[status(thm)],[97,94,73,195,198,222,190,187,186,183,181,178,166,165,163,160,157,155,152,100,71,48,9]) ).
tff(224,plain,
( ( meet(a,join(meet(a,b),meet(a,c))) != meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))) )
<=> ( meet(a,join(meet(a,b),meet(a,c))) != meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(225,axiom,
meet(a,join(meet(a,b),meet(a,c))) != meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_H15) ).
tff(226,plain,
meet(a,join(meet(a,b),meet(a,c))) != meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),
inference(modus_ponens,[status(thm)],[225,224]) ).
tff(227,plain,
$false,
inference(unit_resolution,[status(thm)],[226,223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LAT143-1 : TPTP v9.0.0. Released v3.1.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.35 % Computer : n004.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Thu Jun 19 19:39:08 EDT 2025
% 0.12/0.35 % CPUTime :
% 6.03/6.24 % SZS status Unsatisfiable
% 6.03/6.24 % SZS output start Proof
% See solution above
% 6.03/6.27 % E exiting
%------------------------------------------------------------------------------