%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT138-1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 13.05s 13.25s
% Output : Proof 13.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 45
% Syntax : Number of formulae : 156 ( 119 unt; 0 typ; 0 def)
% Number of atoms : 207 ( 199 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 70 ( 26 ~; 22 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 206 ( 189 !; 0 ?; 206 :)
% 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(( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
tff(5,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),join(meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),join(b,meet(a,c)))) = meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
meet(meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),join(meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),join(b,meet(a,c)))) = meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(14,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),join(b,meet(a,c))) = join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
join(meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),join(b,meet(a,c))) = join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = join(meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),join(b,meet(a,c))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
meet(meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) = meet(meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),join(meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),join(b,meet(a,c)))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(22,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)],[21]) ).
tff(23,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(24,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
tff(25,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
meet(join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,b)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
meet(a,join(a,b)) = a,
inference(unit_resolution,[status(thm)],[30,7]) ).
tff(32,plain,
meet(meet(a,join(a,b)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) = meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,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(34,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)],[33]) ).
tff(35,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(36,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(37,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,join(a,b)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) = meet(a,meet(join(a,b),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
meet(meet(a,join(a,b)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) = meet(a,meet(join(a,b),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
meet(a,meet(join(a,b),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(meet(a,join(a,b)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,meet(a,c))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
meet(a,join(a,meet(a,c))) = a,
inference(unit_resolution,[status(thm)],[43,7]) ).
tff(45,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(46,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)],[45]) ).
tff(47,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(48,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
tff(49,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(a,meet(a,c)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
join(a,meet(a,c)) = a,
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
a = join(a,meet(a,c)),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
meet(a,a) = meet(a,join(a,meet(a,c))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
meet(a,a) = a,
inference(transitivity,[status(thm)],[55,44]) ).
tff(57,plain,
meet(meet(a,a),meet(join(a,b),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(a,meet(join(a,b),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,a),meet(join(a,b),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(a,meet(a,meet(join(a,b),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
meet(meet(a,a),meet(join(a,b),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(a,meet(a,meet(join(a,b),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))),
inference(unit_resolution,[status(thm)],[58,39]) ).
tff(60,plain,
meet(a,meet(a,meet(join(a,b),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) = meet(meet(a,a),meet(join(a,b),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) = meet(meet(a,join(a,b)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
inference(symmetry,[status(thm)],[32]) ).
tff(62,plain,
meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) = meet(a,meet(join(a,b),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(transitivity,[status(thm)],[61,41]) ).
tff(63,plain,
meet(a,meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(a,meet(a,meet(join(a,b),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
meet(a,meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
inference(transitivity,[status(thm)],[63,60,57,42,32]) ).
tff(65,plain,
meet(join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),meet(a,meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) = meet(join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
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(join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),a),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),meet(a,meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
meet(meet(join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),a),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),meet(a,meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))),
inference(unit_resolution,[status(thm)],[66,39]) ).
tff(68,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),a) = meet(a,join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
meet(join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),a) = meet(a,join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))),
inference(unit_resolution,[status(thm)],[68,27]) ).
tff(70,plain,
meet(a,join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) = meet(join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),a),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
join(join(b,meet(a,c)),meet(a,meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) = join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(monotonicity,[status(thm)],[64]) ).
tff(72,plain,
join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = join(join(b,meet(a,c)),meet(a,meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
meet(a,join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) = meet(a,join(join(b,meet(a,c)),meet(a,meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))))),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
meet(a,join(join(b,meet(a,c)),meet(a,meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))))) = meet(a,join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
join(join(a,meet(a,c)),b) = join(a,b),
inference(monotonicity,[status(thm)],[53]) ).
tff(76,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(77,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)],[76]) ).
tff(78,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(79,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(80,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(a,meet(a,c)),b) = join(a,join(meet(a,c),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
join(join(a,meet(a,c)),b) = join(a,join(meet(a,c),b)),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
join(a,join(meet(a,c),b)) = join(join(a,meet(a,c)),b),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(a,c),b) = join(b,meet(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
join(meet(a,c),b) = join(b,meet(a,c)),
inference(unit_resolution,[status(thm)],[86,16]) ).
tff(88,plain,
join(b,meet(a,c)) = join(meet(a,c),b),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
join(a,join(b,meet(a,c))) = join(a,join(meet(a,c),b)),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
join(a,join(b,meet(a,c))) = join(a,b),
inference(transitivity,[status(thm)],[89,85,75]) ).
tff(91,plain,
meet(c,join(a,join(b,meet(a,c)))) = meet(c,join(a,b)),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
join(meet(a,join(b,meet(a,c))),meet(c,join(a,join(b,meet(a,c))))) = join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,join(b,meet(a,c)))))) = meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,join(b,meet(a,c))))))) = join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,join(b,meet(a,c))))))),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
join(join(b,meet(a,c)),meet(a,meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) = join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,join(b,meet(a,c))))))),
inference(transitivity,[status(thm)],[71,95]) ).
tff(97,plain,
meet(a,join(join(b,meet(a,c)),meet(a,meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))))) = meet(a,join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,join(b,meet(a,c)))))))),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
meet(a,join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,join(b,meet(a,c)))))))) = meet(a,join(join(b,meet(a,c)),meet(a,meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))))),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,meet(X,join(meet(X,Y),meet(Z,join(X,Y)))))) )
<=> ( meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,meet(X,join(meet(X,Y),meet(Z,join(X,Y)))))) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,meet(X,join(meet(X,Y),meet(Z,join(X,Y)))))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,meet(X,join(meet(X,Y),meet(Z,join(X,Y)))))) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,meet(X,join(meet(X,Y),meet(Z,join(X,Y)))))) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,meet(X,join(meet(X,Y),meet(Z,join(X,Y)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,meet(X,join(meet(X,Y),meet(Z,join(X,Y)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H7) ).
tff(103,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,meet(X,join(meet(X,Y),meet(Z,join(X,Y)))))) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,meet(X,join(meet(X,Y),meet(Z,join(X,Y)))))) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,meet(X,join(meet(X,Y),meet(Z,join(X,Y)))))) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(X,join(Y,meet(X,Z))) = meet(X,join(Y,meet(X,join(meet(X,Y),meet(Z,join(X,Y)))))) )
| ( meet(a,join(join(b,meet(a,c)),meet(a,c))) = meet(a,join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,join(b,meet(a,c)))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
meet(a,join(join(b,meet(a,c)),meet(a,c))) = meet(a,join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,join(b,meet(a,c)))))))),
inference(unit_resolution,[status(thm)],[106,105]) ).
tff(108,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(join(b,meet(a,c)),meet(join(b,meet(a,c)),meet(a,c))) = join(b,meet(a,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
join(join(b,meet(a,c)),meet(join(b,meet(a,c)),meet(a,c))) = join(b,meet(a,c)),
inference(unit_resolution,[status(thm)],[108,51]) ).
tff(110,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(b,meet(a,c)),meet(a,c)) = meet(meet(a,c),join(b,meet(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
meet(join(b,meet(a,c)),meet(a,c)) = meet(meet(a,c),join(b,meet(a,c))),
inference(unit_resolution,[status(thm)],[110,27]) ).
tff(112,plain,
meet(meet(a,c),join(b,meet(a,c))) = meet(join(b,meet(a,c)),meet(a,c)),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
meet(meet(a,c),join(b,meet(a,c))) = meet(meet(a,c),join(meet(a,c),b)),
inference(monotonicity,[status(thm)],[88]) ).
tff(114,plain,
meet(meet(a,c),join(meet(a,c),b)) = meet(meet(a,c),join(b,meet(a,c))),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(a,c),join(meet(a,c),b)) = meet(a,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
meet(meet(a,c),join(meet(a,c),b)) = meet(a,c),
inference(unit_resolution,[status(thm)],[115,7]) ).
tff(117,plain,
meet(a,c) = meet(meet(a,c),join(meet(a,c),b)),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
meet(a,c) = meet(join(b,meet(a,c)),meet(a,c)),
inference(transitivity,[status(thm)],[117,114,112]) ).
tff(119,plain,
join(join(b,meet(a,c)),meet(a,c)) = join(join(b,meet(a,c)),meet(join(b,meet(a,c)),meet(a,c))),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
join(join(b,meet(a,c)),meet(a,c)) = join(b,meet(a,c)),
inference(transitivity,[status(thm)],[119,109]) ).
tff(121,plain,
meet(a,join(join(b,meet(a,c)),meet(a,c))) = meet(a,join(b,meet(a,c))),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
meet(a,join(b,meet(a,c))) = meet(a,join(join(b,meet(a,c)),meet(a,c))),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(meet(a,join(b,meet(a,c))),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) = meet(a,join(b,meet(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
meet(meet(a,join(b,meet(a,c))),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) = meet(a,join(b,meet(a,c))),
inference(unit_resolution,[status(thm)],[123,7]) ).
tff(125,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,join(b,meet(a,c))),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) = meet(a,meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
meet(meet(a,join(b,meet(a,c))),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) = meet(a,meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(unit_resolution,[status(thm)],[125,39]) ).
tff(127,plain,
meet(a,meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(meet(a,join(b,meet(a,c))),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
meet(a,meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),a),
inference(transitivity,[status(thm)],[127,124,122,107,98,74,70]) ).
tff(129,plain,
meet(meet(a,meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(meet(join(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),a),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
meet(a,join(b,meet(a,c))) = meet(meet(a,join(b,meet(a,c))),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
inference(symmetry,[status(thm)],[124]) ).
tff(131,plain,
meet(a,join(b,meet(a,c))) = meet(a,meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(transitivity,[status(thm)],[130,126]) ).
tff(132,plain,
meet(meet(a,join(b,meet(a,c))),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(meet(a,meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,join(b,meet(a,c))),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(a,meet(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
meet(meet(a,join(b,meet(a,c))),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(a,meet(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))),
inference(unit_resolution,[status(thm)],[133,39]) ).
tff(135,plain,
meet(a,meet(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) = meet(meet(a,join(b,meet(a,c))),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(b,meet(a,c)),a),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) = meet(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
meet(meet(join(b,meet(a,c)),a),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) = meet(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(unit_resolution,[status(thm)],[136,39]) ).
tff(138,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(b,meet(a,c)),a) = meet(a,join(b,meet(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
meet(join(b,meet(a,c)),a) = meet(a,join(b,meet(a,c))),
inference(unit_resolution,[status(thm)],[138,27]) ).
tff(140,plain,
meet(meet(join(b,meet(a,c)),a),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) = meet(meet(a,join(b,meet(a,c))),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
meet(meet(a,join(b,meet(a,c))),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) = meet(meet(join(b,meet(a,c)),a),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
meet(a,join(b,meet(a,c))) = meet(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(transitivity,[status(thm)],[130,141,137]) ).
tff(143,plain,
meet(a,meet(a,join(b,meet(a,c)))) = meet(a,meet(join(b,meet(a,c)),meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
meet(a,meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(a,join(b,meet(a,c))),
inference(transitivity,[status(thm)],[127,124]) ).
tff(145,plain,
meet(a,meet(a,meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) = meet(a,meet(a,join(b,meet(a,c)))),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,a),meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(a,meet(a,meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,plain,
meet(meet(a,a),meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(a,meet(a,meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))))),
inference(unit_resolution,[status(thm)],[146,39]) ).
tff(148,plain,
meet(a,join(a,meet(a,c))) = meet(a,a),
inference(symmetry,[status(thm)],[55]) ).
tff(149,plain,
a = meet(a,join(a,meet(a,c))),
inference(symmetry,[status(thm)],[44]) ).
tff(150,plain,
a = meet(a,a),
inference(transitivity,[status(thm)],[149,148]) ).
tff(151,plain,
meet(a,meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))) = meet(meet(a,a),meet(join(b,meet(a,c)),join(meet(a,join(b,meet(a,c))),meet(c,join(a,b))))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
meet(a,join(b,meet(a,c))) = meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
inference(transitivity,[status(thm)],[130,126,151,147,145,143,135,132,129,67,65,29,20,9]) ).
tff(153,plain,
( ( meet(a,join(b,meet(a,c))) != meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) )
<=> ( meet(a,join(b,meet(a,c))) != meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(154,axiom,
meet(a,join(b,meet(a,c))) != meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_H6) ).
tff(155,plain,
meet(a,join(b,meet(a,c))) != meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
$false,
inference(unit_resolution,[status(thm)],[155,152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : LAT138-1 : TPTP v9.0.0. Released v3.1.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Jun 19 19:39:32 EDT 2025
% 0.15/0.37 % CPUTime :
% 13.05/13.25 % SZS status Unsatisfiable
% 13.05/13.25 % SZS output start Proof
% See solution above
% 13.05/13.27 % E exiting
%------------------------------------------------------------------------------