TSTP Solution File: LAT388+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT388+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 18:33:41 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 30
% Syntax : Number of formulae : 56 ( 10 unt; 14 typ; 0 def)
% Number of atoms : 872 ( 1 equ)
% Maximal formula atoms : 22 ( 20 avg)
% Number of connectives : 1361 ( 626 ~; 497 |; 205 &)
% ( 24 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 18 ( 10 >; 8 *; 0 +; 0 <<)
% Number of predicates : 20 ( 17 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 172 ( 146 !; 19 ?; 172 :)
% 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(xT_type,type,
xT: $i ).
tff(aUpperBoundOfIn0_type,type,
aUpperBoundOfIn0: ( $i * $i * $i ) > $o ).
tff(cS1142_type,type,
cS1142: $i > $i ).
tff(xf_type,type,
xf: $i ).
tff(tptp_fun_W1_15_type,type,
tptp_fun_W1_15: $i > $i ).
tff(aSupremumOfIn0_type,type,
aSupremumOfIn0: ( $i * $i * $i ) > $o ).
tff(xS_type,type,
xS: $i ).
tff(aFixedPointOf0_type,type,
aFixedPointOf0: ( $i * $i ) > $o ).
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,cS1142(xf)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aSupremumOfIn0(xp,xT,xS)
<=> aSupremumOfIn0(xp,xT,xS) ),
inference(rewrite,[status(thm)],]) ).
tff(3,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/sandbox2/benchmark/theBenchmark.p',m__1330) ).
tff(4,plain,
aSupremumOfIn0(xp,xT,xS),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aSupremumOfIn0(xp,xT,xS),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
aSupremumOfIn0(xp,xT,cS1142(xf)),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( aSupremumOfIn0(xp,xT,cS1142(xf))
| ~ ( ~ aElementOf0(xp,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(xp,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(xp,tptp_fun_W1_17(xp))
| ~ aElementOf0(tptp_fun_W1_17(xp),cS1142(xf))
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) ) ) )
| ~ aSupremumOfIn0(xp,xT,cS1142(xf)) ),
inference(tautology,[status(thm)],]) ).
tff(8,plain,
( aSupremumOfIn0(xp,xT,cS1142(xf))
| ~ ( ~ aElementOf0(xp,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(xp,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(xp,tptp_fun_W1_17(xp))
| ~ aElementOf0(tptp_fun_W1_17(xp),cS1142(xf))
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) ) ) ) ),
inference(unit_resolution,[status(thm)],[7,6]) ).
tff(9,plain,
^ [W0: $i] :
rewrite(
( ~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) )
<=> ~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) )
<=> ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [W0: $i] :
refl(
( ~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) )
<=> ~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) )
<=> ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
^ [W0: $i] :
rewrite(
( ~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) )
<=> ~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) )
<=> ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) )
<=> ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) ) ),
inference(transitivity,[status(thm)],[14,12]) ).
tff(16,plain,
^ [W0: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
<=> ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) ) )),
rewrite(
( ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) )
<=> ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) )),
( ( ~ aElementOf0(W0,cS1142(xf))
| ( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) )
<=> ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) )),
rewrite(
( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) )
<=> ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) )),
( ( ~ aElementOf0(W0,cS1142(xf))
| ( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) )
<=> ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) )),
( ( ~ aSupremumOfIn0(W0,xT,cS1142(xf))
& ( ~ aElementOf0(W0,cS1142(xf))
| ( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) )
<=> ( ~ aSupremumOfIn0(W0,xT,cS1142(xf))
& ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) ) )),
rewrite(
( ( ~ aSupremumOfIn0(W0,xT,cS1142(xf))
& ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) )
<=> ~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) ) )),
( ( ~ aSupremumOfIn0(W0,xT,cS1142(xf))
& ( ~ aElementOf0(W0,cS1142(xf))
| ( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) )
<=> ~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [W0: $i] :
( ~ aSupremumOfIn0(W0,xT,cS1142(xf))
& ( ~ aElementOf0(W0,cS1142(xf))
| ( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) )
<=> ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSupremumOfIn0(W0,xT,cS1142(xf))
& ( ~ aElementOf0(W0,cS1142(xf))
| ( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) )
<=> ( ~ aSupremumOfIn0(W0,xT,cS1142(xf))
& ( ~ aElementOf0(W0,cS1142(xf))
| ( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [W0: $i] :
( ~ aSupremumOfIn0(W0,xT,cS1142(xf))
& ( ~ aElementOf0(W0,cS1142(xf))
| ( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) )
<=> ! [W0: $i] :
( ~ aSupremumOfIn0(W0,xT,cS1142(xf))
& ( ~ aElementOf0(W0,cS1142(xf))
| ( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,cS1142(xf))
| ( aElementOf0(W0,cS1142(xf))
& ( ( aElementOf0(W0,cS1142(xf))
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,cS1142(xf)) )
| sdtlseqdt0(W0,W1) ) ) )
<=> ~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,cS1142(xf))
| ( aElementOf0(W0,cS1142(xf))
& ( ( aElementOf0(W0,cS1142(xf))
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,cS1142(xf)) )
| sdtlseqdt0(W0,W1) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
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) ) ) )
<=> ~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,cS1142(xf))
| ( aElementOf0(W0,cS1142(xf))
& ( ( aElementOf0(W0,cS1142(xf))
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,cS1142(xf)) )
| sdtlseqdt0(W0,W1) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
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) ) ) )
<=> ~ ? [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(23,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(24,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/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(25,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)],[24,23]) ).
tff(26,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)],[25,22]) ).
tff(27,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)],[26,22]) ).
tff(28,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)],[27,22]) ).
tff(29,plain,
~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,cS1142(xf))
| ( aElementOf0(W0,cS1142(xf))
& ( ( aElementOf0(W0,cS1142(xf))
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,cS1142(xf)) )
| sdtlseqdt0(W0,W1) ) ) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,cS1142(xf))
| ( aElementOf0(W0,cS1142(xf))
& ( ( aElementOf0(W0,cS1142(xf))
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,cS1142(xf)) )
| sdtlseqdt0(W0,W1) ) ) ),
inference(modus_ponens,[status(thm)],[29,20]) ).
tff(31,plain,
~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,cS1142(xf))
| ( aElementOf0(W0,cS1142(xf))
& ( ( aElementOf0(W0,cS1142(xf))
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,cS1142(xf)) )
| sdtlseqdt0(W0,W1) ) ) ),
inference(modus_ponens,[status(thm)],[30,20]) ).
tff(32,plain,
~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,cS1142(xf))
| ( aElementOf0(W0,cS1142(xf))
& ( ( aElementOf0(W0,cS1142(xf))
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,cS1142(xf)) )
| sdtlseqdt0(W0,W1) ) ) ),
inference(modus_ponens,[status(thm)],[31,20]) ).
tff(33,plain,
~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,cS1142(xf))
| ( aElementOf0(W0,cS1142(xf))
& ( ( aElementOf0(W0,cS1142(xf))
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,cS1142(xf)) )
| sdtlseqdt0(W0,W1) ) ) ),
inference(modus_ponens,[status(thm)],[32,20]) ).
tff(34,plain,
~ ? [W0: $i] :
( aSupremumOfIn0(W0,xT,cS1142(xf))
| ( aElementOf0(W0,cS1142(xf))
& ( ( aElementOf0(W0,cS1142(xf))
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,cS1142(xf)) )
| sdtlseqdt0(W0,W1) ) ) ),
inference(modus_ponens,[status(thm)],[33,20]) ).
tff(35,plain,
^ [W0: $i] :
nnf_neg(refl($oeq(~ aSupremumOfIn0(W0,xT,cS1142(xf)),~ aSupremumOfIn0(W0,xT,cS1142(xf)))),
nnf_neg(refl($oeq(~ aElementOf0(W0,cS1142(xf)),~ aElementOf0(W0,cS1142(xf)))),
nnf_neg(
nnf_neg(refl($oeq(~ aElementOf0(W0,cS1142(xf)),~ aElementOf0(W0,cS1142(xf)))),
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,cS1142(xf))
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) ),
( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) ))),
refl($oeq(~ aUpperBoundOfIn0(W0,xT,cS1142(xf)),~ aUpperBoundOfIn0(W0,xT,cS1142(xf)))),
$oeq(
~ ( ( aElementOf0(W0,cS1142(xf))
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) ),
( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) ))),
trans(
sk(
$oeq(
~ ! [W1: $i] :
( ~ ( aElementOf0(W1,cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,cS1142(xf)) )
| sdtlseqdt0(W0,W1) ),
~ ( ~ ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) )
| sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ))),
nnf_neg(
nnf_neg(
monotonicity(refl($oeq(aElementOf0(tptp_fun_W1_17(W0),cS1142(xf)),aElementOf0(tptp_fun_W1_17(W0),cS1142(xf)))),
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,cS1142(xf)),aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)))),
$oeq(
( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ),
( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ))),
$oeq(
~ ~ ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ),
( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ))),
refl($oeq(~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)),~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)))),
$oeq(
~ ( ~ ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) )
| sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ),
( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ))),
$oeq(
~ ! [W1: $i] :
( ~ ( aElementOf0(W1,cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,cS1142(xf)) )
| sdtlseqdt0(W0,W1) ),
( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ))),
$oeq(
~ ( aElementOf0(W0,cS1142(xf))
& ( ( aElementOf0(W0,cS1142(xf))
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,cS1142(xf)) )
| sdtlseqdt0(W0,W1) ) ),
( ~ aElementOf0(W0,cS1142(xf))
| ( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ))),
$oeq(
~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ( aElementOf0(W0,cS1142(xf))
& ( ( aElementOf0(W0,cS1142(xf))
& ! [W1: $i] :
( ~ aElementOf0(W1,xT)
| sdtlseqdt0(W1,W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
& ! [W1: $i] :
( ~ ( aElementOf0(W1,cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,W1) )
& aUpperBoundOfIn0(W1,xT,cS1142(xf)) )
| sdtlseqdt0(W0,W1) ) ) ),
( ~ aSupremumOfIn0(W0,xT,cS1142(xf))
& ( ~ aElementOf0(W0,cS1142(xf))
| ( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) ))),
inference(bind,[status(th)],]) ).
tff(36,plain,
! [W0: $i] :
( ~ aSupremumOfIn0(W0,xT,cS1142(xf))
& ( ~ aElementOf0(W0,cS1142(xf))
| ( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) ),
inference(nnf-neg,[status(sab)],[34,35]) ).
tff(37,plain,
! [W0: $i] :
( ~ aSupremumOfIn0(W0,xT,cS1142(xf))
& ( ~ aElementOf0(W0,cS1142(xf))
| ( ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
& ~ aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ( aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
& ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
& aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
& ~ sdtlseqdt0(W0,tptp_fun_W1_17(W0)) ) ) ),
inference(modus_ponens,[status(thm)],[36,19]) ).
tff(38,plain,
! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) ),
inference(modus_ponens,[status(thm)],[37,17]) ).
tff(39,plain,
! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) )
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf)) ) ) ),
inference(modus_ponens,[status(thm)],[38,15]) ).
tff(40,plain,
! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) ),
inference(modus_ponens,[status(thm)],[39,10]) ).
tff(41,plain,
( ~ ! [W0: $i] :
~ ( aSupremumOfIn0(W0,xT,cS1142(xf))
| ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(W0,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(W0),xT)
| sdtlseqdt0(tptp_fun_W1_15(W0),W0) ) )
| aUpperBoundOfIn0(W0,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(W0,tptp_fun_W1_17(W0))
| ~ aElementOf0(tptp_fun_W1_17(W0),cS1142(xf))
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(W0),xT,cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(W0)) ) ) ) )
| ~ ( aSupremumOfIn0(xp,xT,cS1142(xf))
| ~ ( ~ aElementOf0(xp,cS1142(xf))
| ~ ( ~ ( ~ aElementOf0(xp,cS1142(xf))
| ~ ( ~ aElementOf0(tptp_fun_W1_15(xp),xT)
| sdtlseqdt0(tptp_fun_W1_15(xp),xp) ) )
| aUpperBoundOfIn0(xp,xT,cS1142(xf)) )
| ~ ( sdtlseqdt0(xp,tptp_fun_W1_17(xp))
| ~ aElementOf0(tptp_fun_W1_17(xp),cS1142(xf))
| ~ aUpperBoundOfIn0(tptp_fun_W1_17(xp),xT,cS1142(xf))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xT)
| sdtlseqdt0(W2,tptp_fun_W1_17(xp)) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
$false,
inference(unit_resolution,[status(thm)],[41,40,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LAT388+4 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Sep 1 16:47:57 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------