TSTP Solution File: LAT036-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT036-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:31:49 EDT 2022
% Result : Unsatisfiable 1.13s 0.98s
% Output : Proof 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 43
% Syntax : Number of formulae : 102 ( 69 unt; 6 typ; 0 def)
% Number of atoms : 133 ( 127 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 48 ( 16 ~; 12 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 139 ( 127 !; 0 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(k_type,type,
k: $i > $i ).
tff(aa_type,type,
aa: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(cc_type,type,
cc: $i ).
tff(bb_type,type,
bb: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
tff(5,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(k(aa),meet(aa,k(meet(bb,cc)))) = join(meet(aa,k(meet(bb,cc))),k(aa)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
join(k(aa),meet(aa,k(meet(bb,cc)))) = join(meet(aa,k(meet(bb,cc))),k(aa)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V: $i,U: $i] :
refl(
( ( k(meet(U,V)) = join(k(U),k(V)) )
<=> ( k(meet(U,V)) = join(k(U),k(V)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [V: $i,U: $i] : ( k(meet(U,V)) = join(k(U),k(V)) )
<=> ! [V: $i,U: $i] : ( k(meet(U,V)) = join(k(U),k(V)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V: $i,U: $i] : ( k(meet(U,V)) = join(k(U),k(V)) )
<=> ! [V: $i,U: $i] : ( k(meet(U,V)) = join(k(U),k(V)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [V: $i,U: $i] : ( k(meet(U,V)) = join(k(U),k(V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_on_meet) ).
tff(14,plain,
! [V: $i,U: $i] : ( k(meet(U,V)) = join(k(U),k(V)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [V: $i,U: $i] : ( k(meet(U,V)) = join(k(U),k(V)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V: $i,U: $i] : ( k(meet(U,V)) = join(k(U),k(V)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [V: $i,U: $i] : ( k(meet(U,V)) = join(k(U),k(V)) )
| ( k(meet(bb,cc)) = join(k(bb),k(cc)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
k(meet(bb,cc)) = join(k(bb),k(cc)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
join(k(bb),k(cc)) = k(meet(bb,cc)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
meet(aa,join(k(bb),k(cc))) = meet(aa,k(meet(bb,cc))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
join(k(aa),meet(aa,join(k(bb),k(cc)))) = join(k(aa),meet(aa,k(meet(bb,cc)))),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
<=> ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dist_join) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
| ( join(k(aa),meet(aa,join(k(bb),k(cc)))) = meet(join(k(aa),aa),join(k(aa),join(k(bb),k(cc)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
join(k(aa),meet(aa,join(k(bb),k(cc)))) = meet(join(k(aa),aa),join(k(aa),join(k(bb),k(cc)))),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
meet(join(k(aa),aa),join(k(aa),join(k(bb),k(cc)))) = join(k(aa),meet(aa,join(k(bb),k(cc)))),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(k(aa),aa) = join(aa,k(aa)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
join(k(aa),aa) = join(aa,k(aa)),
inference(unit_resolution,[status(thm)],[32,7]) ).
tff(34,plain,
join(aa,k(aa)) = join(k(aa),aa),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
meet(join(aa,k(aa)),join(k(aa),join(k(bb),k(cc)))) = meet(join(k(aa),aa),join(k(aa),join(k(bb),k(cc)))),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( join(k(k(aa)),join(k(aa),join(k(bb),k(cc)))) = join(k(aa),join(k(bb),k(cc))) )
<=> ( join(k(k(aa)),join(k(aa),join(k(bb),k(cc)))) = join(k(aa),join(k(bb),k(cc))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
join(k(k(aa)),join(k(aa),join(k(bb),k(cc)))) = join(k(aa),join(k(bb),k(cc))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs3) ).
tff(38,plain,
join(k(k(aa)),join(k(aa),join(k(bb),k(cc)))) = join(k(aa),join(k(bb),k(cc))),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ( join(k(k(k(bb))),join(k(aa),join(k(bb),k(cc)))) = join(k(aa),join(k(bb),k(cc))) )
<=> ( join(k(k(k(bb))),join(k(aa),join(k(bb),k(cc)))) = join(k(aa),join(k(bb),k(cc))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
join(k(k(k(bb))),join(k(aa),join(k(bb),k(cc)))) = join(k(aa),join(k(bb),k(cc))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs4) ).
tff(41,plain,
join(k(k(k(bb))),join(k(aa),join(k(bb),k(cc)))) = join(k(aa),join(k(bb),k(cc))),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
join(k(k(aa)),join(k(k(k(bb))),join(k(aa),join(k(bb),k(cc))))) = join(k(k(aa)),join(k(aa),join(k(bb),k(cc)))),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,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(44,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)],[43]) ).
tff(45,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(46,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(47,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(k(k(aa)),k(k(k(bb)))),join(k(aa),join(k(bb),k(cc)))) = join(k(k(aa)),join(k(k(k(bb))),join(k(aa),join(k(bb),k(cc))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
join(join(k(k(aa)),k(k(k(bb)))),join(k(aa),join(k(bb),k(cc)))) = join(k(k(aa)),join(k(k(k(bb))),join(k(aa),join(k(bb),k(cc))))),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),join(k(bb),k(cc))) = join(join(k(k(aa)),k(k(k(bb)))),join(k(aa),join(k(bb),k(cc)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),join(k(bb),k(cc))) = join(join(k(k(aa)),k(k(k(bb)))),join(k(aa),join(k(bb),k(cc)))),
inference(unit_resolution,[status(thm)],[52,49]) ).
tff(54,plain,
join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),join(k(bb),k(cc))) = join(k(aa),join(k(bb),k(cc))),
inference(transitivity,[status(thm)],[53,51,42,38]) ).
tff(55,plain,
( ( join(k(k(aa)),join(aa,k(aa))) = join(aa,k(aa)) )
<=> ( join(k(k(aa)),join(aa,k(aa))) = join(aa,k(aa)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
join(k(k(aa)),join(aa,k(aa))) = join(aa,k(aa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs1) ).
tff(57,plain,
join(k(k(aa)),join(aa,k(aa))) = join(aa,k(aa)),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
( ( join(k(k(k(bb))),join(aa,k(aa))) = join(aa,k(aa)) )
<=> ( join(k(k(k(bb))),join(aa,k(aa))) = join(aa,k(aa)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
join(k(k(k(bb))),join(aa,k(aa))) = join(aa,k(aa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs2) ).
tff(60,plain,
join(k(k(k(bb))),join(aa,k(aa))) = join(aa,k(aa)),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
join(k(k(aa)),join(k(k(k(bb))),join(aa,k(aa)))) = join(k(k(aa)),join(aa,k(aa))),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(k(k(aa)),k(k(k(bb)))),join(aa,k(aa))) = join(k(k(aa)),join(k(k(k(bb))),join(aa,k(aa)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
join(join(k(k(aa)),k(k(k(bb)))),join(aa,k(aa))) = join(k(k(aa)),join(k(k(k(bb))),join(aa,k(aa)))),
inference(unit_resolution,[status(thm)],[62,49]) ).
tff(64,plain,
join(join(k(k(aa)),k(k(k(bb)))),join(k(aa),aa)) = join(join(k(k(aa)),k(k(k(bb)))),join(aa,k(aa))),
inference(monotonicity,[status(thm)],[33]) ).
tff(65,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),aa) = join(join(k(k(aa)),k(k(k(bb)))),join(k(aa),aa)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),aa) = join(join(k(k(aa)),k(k(k(bb)))),join(k(aa),aa)),
inference(unit_resolution,[status(thm)],[65,49]) ).
tff(67,plain,
join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),aa) = join(aa,k(aa)),
inference(transitivity,[status(thm)],[66,64,63,61,57]) ).
tff(68,plain,
meet(join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),aa),join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),join(k(bb),k(cc)))) = meet(join(aa,k(aa)),join(k(aa),join(k(bb),k(cc)))),
inference(monotonicity,[status(thm)],[67,54]) ).
tff(69,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) )
| ( join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),meet(aa,join(k(bb),k(cc)))) = meet(join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),aa),join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),join(k(bb),k(cc)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),meet(aa,join(k(bb),k(cc)))) = meet(join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),aa),join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),join(k(bb),k(cc)))),
inference(unit_resolution,[status(thm)],[69,28]) ).
tff(71,plain,
meet(aa,k(meet(bb,cc))) = meet(aa,join(k(bb),k(cc))),
inference(symmetry,[status(thm)],[20]) ).
tff(72,plain,
( ~ ! [V: $i,U: $i] : ( k(meet(U,V)) = join(k(U),k(V)) )
| ( k(meet(k(aa),k(k(bb)))) = join(k(k(aa)),k(k(k(bb)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
k(meet(k(aa),k(k(bb)))) = join(k(k(aa)),k(k(k(bb)))),
inference(unit_resolution,[status(thm)],[72,16]) ).
tff(74,plain,
^ [V: $i,U: $i] :
refl(
( ( k(join(U,V)) = meet(k(U),k(V)) )
<=> ( k(join(U,V)) = meet(k(U),k(V)) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) )
<=> ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) )
<=> ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,axiom,
! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_on_join) ).
tff(78,plain,
! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
( ~ ! [V: $i,U: $i] : ( k(join(U,V)) = meet(k(U),k(V)) )
| ( k(join(aa,k(bb))) = meet(k(aa),k(k(bb))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
k(join(aa,k(bb))) = meet(k(aa),k(k(bb))),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
k(k(join(aa,k(bb)))) = k(meet(k(aa),k(k(bb)))),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
k(k(join(aa,k(bb)))) = join(k(k(aa)),k(k(k(bb)))),
inference(transitivity,[status(thm)],[83,73]) ).
tff(85,plain,
join(k(k(join(aa,k(bb)))),k(aa)) = join(join(k(k(aa)),k(k(k(bb)))),k(aa)),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
join(join(k(k(join(aa,k(bb)))),k(aa)),meet(aa,k(meet(bb,cc)))) = join(join(join(k(k(aa)),k(k(k(bb)))),k(aa)),meet(aa,join(k(bb),k(cc)))),
inference(monotonicity,[status(thm)],[85,71]) ).
tff(87,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(k(k(join(aa,k(bb)))),k(aa)),meet(aa,k(meet(bb,cc)))) = join(k(k(join(aa,k(bb)))),join(k(aa),meet(aa,k(meet(bb,cc))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
join(join(k(k(join(aa,k(bb)))),k(aa)),meet(aa,k(meet(bb,cc)))) = join(k(k(join(aa,k(bb)))),join(k(aa),meet(aa,k(meet(bb,cc))))),
inference(unit_resolution,[status(thm)],[87,49]) ).
tff(89,plain,
join(k(k(join(aa,k(bb)))),join(k(aa),meet(aa,k(meet(bb,cc))))) = join(join(k(k(join(aa,k(bb)))),k(aa)),meet(aa,k(meet(bb,cc)))),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
join(meet(aa,k(meet(bb,cc))),k(aa)) = join(k(aa),meet(aa,k(meet(bb,cc)))),
inference(symmetry,[status(thm)],[9]) ).
tff(91,plain,
join(k(k(join(aa,k(bb)))),join(meet(aa,k(meet(bb,cc))),k(aa))) = join(k(k(join(aa,k(bb)))),join(k(aa),meet(aa,k(meet(bb,cc))))),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
join(k(k(join(aa,k(bb)))),join(meet(aa,k(meet(bb,cc))),k(aa))) = join(meet(aa,k(meet(bb,cc))),k(aa)),
inference(transitivity,[status(thm)],[91,89,86,70,68,35,31,21,9]) ).
tff(93,plain,
( ( join(k(k(join(aa,k(bb)))),join(meet(aa,k(meet(bb,cc))),k(aa))) != join(meet(aa,k(meet(bb,cc))),k(aa)) )
<=> ( join(k(k(join(aa,k(bb)))),join(meet(aa,k(meet(bb,cc))),k(aa))) != join(meet(aa,k(meet(bb,cc))),k(aa)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,axiom,
join(k(k(join(aa,k(bb)))),join(meet(aa,k(meet(bb,cc))),k(aa))) != join(meet(aa,k(meet(bb,cc))),k(aa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rhs) ).
tff(95,plain,
join(k(k(join(aa,k(bb)))),join(meet(aa,k(meet(bb,cc))),k(aa))) != join(meet(aa,k(meet(bb,cc))),k(aa)),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
$false,
inference(unit_resolution,[status(thm)],[95,92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT036-1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 10:54:57 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.13/0.98 % SZS status Unsatisfiable
% 1.13/0.98 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------