%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT388+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:14:37 AM UTC 2025
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 37 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 935 ( 1 equ)
% Maximal formula atoms : 44 ( 25 avg)
% Number of connectives : 1604 ( 801 ~; 614 |; 155 &)
% ( 25 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 11 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 95 ( 95 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 17 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 155 ( 139 !; 9 ?; 155 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(tptp_fun_W1_17_type,type,
tptp_fun_W1_17: $i > $i ).
tff(xp_type,type,
xp: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xS_type,type,
xS: $i ).
tff(aUpperBoundOfIn0_type,type,
aUpperBoundOfIn0: ( $i * $i * $i ) > $o ).
tff(xT_type,type,
xT: $i ).
tff(tptp_fun_W1_15_type,type,
tptp_fun_W1_15: $i > $i ).
tff(aSupremumOfIn0_type,type,
aSupremumOfIn0: ( $i * $i * $i ) > $o ).
tff(aFixedPointOf0_type,type,
aFixedPointOf0: ( $i * $i ) > $o ).
tff(xf_type,type,
xf: $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(1,plain,
( aSupremumOfIn0(xp,xT,xS)
<=> aSupremumOfIn0(xp,xT,xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aElementOf0(xp,szDzozmdt0(xf))
& ( sdtlpdtrp0(xf,xp) = xp )
& aFixedPointOf0(xp,xf)
& ! [W0: $i] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(W0,xp) )
& aUpperBoundOfIn0(xp,xT,xS)
& ! [W0: $i] :
( ( ( aElementOf0(W0,xS)
& ! [W1: $i] :
( aElementOf0(W1,xT)
=> sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
=> sdtlseqdt0(xp,W0) )
& aSupremumOfIn0(xp,xT,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1330) ).
tff(3,plain,
aSupremumOfIn0(xp,xT,xS),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aSupremumOfIn0(xp,xT,xS),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( aSupremumOfIn0(xp,xT,xS)
| ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,xS) )
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,xS)
| ~ aElementOf0(tptp_fun_W1_17(xp),xS)
| sdtlseqdt0(xp,tptp_fun_W1_17(xp)) ) )
| ~ aSupremumOfIn0(xp,xT,xS) ),
inference(tautology,[status(thm)],[]) ).
tff(6,plain,
( aSupremumOfIn0(xp,xT,xS)
| ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,xS) )
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,xS)
| ~ aElementOf0(tptp_fun_W1_17(xp),xS)
| sdtlseqdt0(xp,tptp_fun_W1_17(xp)) ) ) ),
inference(unit_resolution,[status(thm)],[5,4]) ).
tff(7,plain,
^ [W0: $i] :
rewrite(( ~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) )
<=> ~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) )
<=> ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [W0: $i] :
refl(( ~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) )
<=> ~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) )
<=> ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [W0: $i] :
rewrite(( ~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) )
<=> ~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) )
<=> ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) )
<=> ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) ) ),
inference(transitivity,[status(thm)],[12,10]) ).
tff(14,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) )
<=> ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) ) )),
rewrite(( ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) )
<=> ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) )),
( ( ~ aElementOf0(W0,xS)
| ( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) )
| ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) )
<=> ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) )),
rewrite(( ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) )
<=> ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) )),
( ( ~ aElementOf0(W0,xS)
| ( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) )
| ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) )
<=> ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) )),
( ( ~ aSupremumOfIn0(W0,xT,xS)
& ( ~ aElementOf0(W0,xS)
| ( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) )
| ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) )
<=> ( ~ aSupremumOfIn0(W0,xT,xS)
& ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) ) )),
rewrite(( ( ~ aSupremumOfIn0(W0,xT,xS)
& ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) )
<=> ~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) ) )),
( ( ~ aSupremumOfIn0(W0,xT,xS)
& ( ~ aElementOf0(W0,xS)
| ( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) )
| ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) )
<=> ~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [W0: $i] :
( ~ aSupremumOfIn0(W0,xT,xS)
& ( ~ aElementOf0(W0,xS)
| ( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) )
| ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) )
<=> ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
^ [W0: $i] :
rewrite(( ( ~ aSupremumOfIn0(W0,xT,xS)
& ( ~ aElementOf0(W0,xS)
| ( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) )
| ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) )
<=> ( ~ aSupremumOfIn0(W0,xT,xS)
& ( ~ aElementOf0(W0,xS)
| ( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) )
| ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [W0: $i] :
( ~ aSupremumOfIn0(W0,xT,xS)
& ( ~ aElementOf0(W0,xS)
| ( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) )
| ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) )
<=> ! [W0: $i] :
( ~ aSupremumOfIn0(W0,xT,xS)
& ( ~ aElementOf0(W0,xS)
| ( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) )
| ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,xS)
| ( aElementOf0(W0,xS)
& ( ( aElementOf0(W0,xS)
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,xS) )
| sdtlseqdt0(W0,W1) ) ) )
<=> ~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,xS)
| ( aElementOf0(W0,xS)
& ( ( aElementOf0(W0,xS)
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,xS) )
| sdtlseqdt0(W0,W1) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ? [W0: $i] :
( ( aElementOf0(W0,xS)
& ( ( aElementOf0(W0,xS)
& ! [W1: $i] :
( aElementOf0(W1,xT)
=> sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
& ! [W1: $i] :
( ( aElementOf0(W1,xS)
& ! [W2: $i] :
( aElementOf0(W2,xT)
=> sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,xS) )
=> sdtlseqdt0(W0,W1) ) )
| aSupremumOfIn0(W0,xT,xS) )
<=> ~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,xS)
| ( aElementOf0(W0,xS)
& ( ( aElementOf0(W0,xS)
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,xS) )
| sdtlseqdt0(W0,W1) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
~ ? [W0: $i] :
( ( aElementOf0(W0,xS)
& ( ( aElementOf0(W0,xS)
& ! [W1: $i] :
( aElementOf0(W1,xT)
=> sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
& ! [W1: $i] :
( ( aElementOf0(W1,xS)
& ! [W2: $i] :
( aElementOf0(W2,xT)
=> sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,xS) )
=> sdtlseqdt0(W0,W1) ) )
| aSupremumOfIn0(W0,xT,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(21,plain,
~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,xS)
| ( aElementOf0(W0,xS)
& ( ( aElementOf0(W0,xS)
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,xS) )
| sdtlseqdt0(W0,W1) ) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,xS)
| ( aElementOf0(W0,xS)
& ( ( aElementOf0(W0,xS)
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,xS) )
| sdtlseqdt0(W0,W1) ) ) ),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,xS)
| ( aElementOf0(W0,xS)
& ( ( aElementOf0(W0,xS)
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,xS) )
| sdtlseqdt0(W0,W1) ) ) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,xS)
| ( aElementOf0(W0,xS)
& ( ( aElementOf0(W0,xS)
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,xS) )
| sdtlseqdt0(W0,W1) ) ) ),
inference(modus_ponens,[status(thm)],[23,18]) ).
tff(25,plain,
^ [W0: $i] :
nnf_neg(refl($oeq(~ aSupremumOfIn0(W0,xT,xS),~ aSupremumOfIn0(W0,xT,xS))),
nnf_neg(refl($oeq(~ aElementOf0(W0,xS),~ aElementOf0(W0,xS))),
nnf_neg(nnf_neg(refl($oeq(~ aElementOf0(W0,xS),~ aElementOf0(W0,xS))),
sk($oeq(~ ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ),
~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ))),
$oeq(~ ( aElementOf0(W0,xS)
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) ),
( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) ))),refl($oeq(~ aUpperBoundOfIn0(W0,xT,xS),~ aUpperBoundOfIn0(W0,xT,xS))),
$oeq(~ ( ( aElementOf0(W0,xS)
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) ),
( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) ))),
trans(sk($oeq(~ ! [W1: $i] :
( ~ ( aElementOf0(W1,xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,xS) )
| sdtlseqdt0(W0,W1) ),
~ ( ~ ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) )
| sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ))),
nnf_neg(nnf_neg(monotonicity(refl($oeq(aElementOf0(tptp_fun_W1_17(W0),xS),aElementOf0(tptp_fun_W1_17(W0),xS))),
nnf_pos(proof_bind(^ [W2: $i] :
refl($oeq(( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ),
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )))),
$oeq(! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ),
! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ))),
refl($oeq(aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS),aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS))),
$oeq(( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ),
( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ))),
$oeq(~ ~ ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ),
( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ))),refl($oeq(~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)),~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)))),
$oeq(~ ( ~ ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) )
| sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ),
( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ))),
$oeq(~ ! [W1: $i] :
( ~ ( aElementOf0(W1,xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,xS) )
| sdtlseqdt0(W0,W1) ),
( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ))),
$oeq(~ ( aElementOf0(W0,xS)
& ( ( aElementOf0(W0,xS)
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,xS) )
| sdtlseqdt0(W0,W1) ) ),
( ~ aElementOf0(W0,xS)
| ( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) )
| ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ))),
$oeq(~ ( aSupremumOfIn0(W0,xT,xS)
| ( aElementOf0(W0,xS)
& ( ( aElementOf0(W0,xS)
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,xS) )
| sdtlseqdt0(W0,W1) ) ) ),
( ~ aSupremumOfIn0(W0,xT,xS)
& ( ~ aElementOf0(W0,xS)
| ( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) )
| ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) ))),
inference(bind,[status(th)],[]) ).
tff(26,plain,
! [W0: $i] :
( ~ aSupremumOfIn0(W0,xT,xS)
& ( ~ aElementOf0(W0,xS)
| ( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) )
| ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) ),
inference(nnf-neg,[status(sab)],[24,25]) ).
tff(27,plain,
! [W0: $i] :
( ~ aSupremumOfIn0(W0,xT,xS)
& ( ~ aElementOf0(W0,xS)
| ( ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,xS) )
| ( aElementOf0(tptp_fun_W1_17(W0),xS)
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) ),
inference(modus_ponens,[status(thm)],[26,17]) ).
tff(28,plain,
! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) ),
inference(modus_ponens,[status(thm)],[27,15]) ).
tff(29,plain,
! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS) ) ) ),
inference(modus_ponens,[status(thm)],[28,13]) ).
tff(30,plain,
! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) ),
inference(modus_ponens,[status(thm)],[29,8]) ).
tff(31,plain,
( ( ~ ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) )
| ~ ( aSupremumOfIn0(xp,xT,xS)
| ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,xS) )
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,xS)
| ~ aElementOf0(tptp_fun_W1_17(xp),xS)
| sdtlseqdt0(xp,tptp_fun_W1_17(xp)) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) )
| ~ ( aSupremumOfIn0(xp,xT,xS)
| ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,xS) )
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,xS)
| ~ aElementOf0(tptp_fun_W1_17(xp),xS)
| sdtlseqdt0(xp,tptp_fun_W1_17(xp)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ( aSupremumOfIn0(xp,xT,xS)
| ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,xS) )
| ~ ( sdtlseqdt0(xp,tptp_fun_W1_17(xp))
| ~ aElementOf0(tptp_fun_W1_17(xp),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) ) ) ) )
<=> ~ ( aSupremumOfIn0(xp,xT,xS)
| ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,xS) )
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,xS)
| ~ aElementOf0(tptp_fun_W1_17(xp),xS)
| sdtlseqdt0(xp,tptp_fun_W1_17(xp)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) )
| ~ ( aSupremumOfIn0(xp,xT,xS)
| ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,xS) )
| ~ ( sdtlseqdt0(xp,tptp_fun_W1_17(xp))
| ~ aElementOf0(tptp_fun_W1_17(xp),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) )
| ~ ( aSupremumOfIn0(xp,xT,xS)
| ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,xS) )
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,xS)
| ~ aElementOf0(tptp_fun_W1_17(xp),xS)
| sdtlseqdt0(xp,tptp_fun_W1_17(xp)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) )
| ~ ( aSupremumOfIn0(xp,xT,xS)
| ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,xS) )
| ~ ( sdtlseqdt0(xp,tptp_fun_W1_17(xp))
| ~ aElementOf0(tptp_fun_W1_17(xp),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) )
| ~ ( aSupremumOfIn0(xp,xT,xS)
| ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,xS) )
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,xS)
| ~ aElementOf0(tptp_fun_W1_17(xp),xS)
| sdtlseqdt0(xp,tptp_fun_W1_17(xp)) ) ) ) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) )
| ~ ( aSupremumOfIn0(xp,xT,xS)
| ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,xS) )
| ~ ( sdtlseqdt0(xp,tptp_fun_W1_17(xp))
| ~ aElementOf0(tptp_fun_W1_17(xp),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,xS)
| ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ ( ~ aElementOf0(W0,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,xS) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),xS)
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) )
| ~ ( aSupremumOfIn0(xp,xT,xS)
| ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ ( ~ aElementOf0(xp,xS)
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,xS) )
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,xS)
| ~ aElementOf0(tptp_fun_W1_17(xp),xS)
| sdtlseqdt0(xp,tptp_fun_W1_17(xp)) ) ) ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,30,6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT388+4 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 20:52:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% See solution above
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------