TSTP Solution File: LAT382+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT382+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 18:33:38 EDT 2022
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 74
% Syntax : Number of formulae : 153 ( 31 unt; 12 typ; 0 def)
% Number of atoms : 1932 ( 52 equ)
% Maximal formula atoms : 48 ( 13 avg)
% Number of connectives : 3619 (1893 ~;1453 |; 117 &)
% ( 109 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 65 ( 65 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 8 >; 9 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 492 ( 474 !; 0 ?; 492 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(xv_type,type,
xv: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xT_type,type,
xT: $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(aLowerBoundOfIn0_type,type,
aLowerBoundOfIn0: ( $i * $i * $i ) > $o ).
tff(xS_type,type,
xS: $i ).
tff(aInfimumOfIn0_type,type,
aInfimumOfIn0: ( $i * $i * $i ) > $o ).
tff(tptp_fun_W3_4_type,type,
tptp_fun_W3_4: ( $i * $i * $i ) > $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(xu_type,type,
xu: $i ).
tff(1,plain,
( aSet0(xT)
<=> aSet0(xT) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
aSet0(xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__773) ).
tff(3,plain,
aSet0(xT),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[9,7]) ).
tff(11,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( ( ~ aInfimumOfIn0(W2,W1,W0)
| ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
& ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( ( ~ aInfimumOfIn0(W2,W1,W0)
| ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
& ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( ( ~ aInfimumOfIn0(W2,W1,W0)
| ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
& ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( ( ~ aInfimumOfIn0(W2,W1,W0)
| ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
& ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( ( ~ aInfimumOfIn0(W2,W1,W0)
| ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
& ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( ( ~ aInfimumOfIn0(W2,W1,W0)
| ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
& ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W2: $i] :
rewrite(
( ( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( aLowerBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W3,W2) ) ) )
<=> ( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ))),
( ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( aLowerBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W3,W2) ) ) )
<=> ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) )),
( ( aSubsetOf0(W1,W0)
=> ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( aLowerBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W3,W2) ) ) ) )
<=> ( aSubsetOf0(W1,W0)
=> ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) )),
rewrite(
( ( aSubsetOf0(W1,W0)
=> ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) )
<=> ( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) )),
( ( aSubsetOf0(W1,W0)
=> ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( aLowerBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W3,W2) ) ) ) )
<=> ( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ))),
( ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( aLowerBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W3,W2) ) ) ) )
<=> ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( aLowerBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W3,W2) ) ) ) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )),
rewrite(
( ( aSet0(W0)
=> ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( aLowerBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W3,W2) ) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( aLowerBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W3,W2) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
=> ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( aLowerBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W3,W2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInf) ).
tff(19,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( ( ~ aInfimumOfIn0(W2,W1,W0)
| ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
& ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
( ( ~ aInfimumOfIn0(W2,W1,W0)
| ( aElementOf0(W2,W0)
& aLowerBoundOfIn0(W2,W1,W0)
& ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
& ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[22,12]) ).
tff(24,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) )
| ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[23,10]) ).
tff(25,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,5]) ).
tff(26,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( ~ aSet0(xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,xT)
| ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )
<=> ( ~ aSet0(xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,xT)
| ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,xT)
| ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,xT)
| ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,W0)
| ! [W2: $i] :
~ ( ~ ( aInfimumOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,W0),W1,W0)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,W0),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,W0)
| ~ ( ~ aElementOf0(W2,W0)
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,W0)
| sdtlseqdt0(W3,W2) ) ) ) ) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[31,25,3]) ).
tff(33,plain,
( aSubsetOf0(xS,xT)
<=> aSubsetOf0(xS,xT) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
aSubsetOf0(xS,xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__773_01) ).
tff(35,plain,
aSubsetOf0(xS,xT),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) )
| ~ aSubsetOf0(xS,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) )
| ~ aSubsetOf0(xS,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( ~ aSubsetOf0(xS,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) )
<=> ( ~ aSubsetOf0(xS,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) )
| ~ aSubsetOf0(xS,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) )
| ~ aSubsetOf0(xS,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) )
| ~ aSubsetOf0(xS,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) )
| ~ aSubsetOf0(xS,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,plain,
( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) )
| ~ aSubsetOf0(xS,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| aInfimumOfIn0(W2,W1,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,W1,xT),W1,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,W1,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,W1,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,W1,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,W1,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) )
| ~ aSubsetOf0(xS,xT)
| ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) ),
inference(unit_resolution,[status(thm)],[41,35,32]) ).
tff(43,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( aInfimumOfIn0(xv,xS,xT)
| ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xv,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xv,xS,xT),xv) ) )
| ~ ( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( aInfimumOfIn0(xv,xS,xT)
| ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xv,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xv,xS,xT),xv) ) )
| ~ ( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ ( ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xv,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xv,xS,xT),xv) ) )
| ~ ( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ) )
<=> ~ ( ~ ( aInfimumOfIn0(xv,xS,xT)
| ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xv,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xv,xS,xT),xv) ) )
| ~ ( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xv,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xv,xS,xT),xv) ) )
| ~ ( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( aInfimumOfIn0(xv,xS,xT)
| ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xv,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xv,xS,xT),xv) ) )
| ~ ( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xv,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xv,xS,xT),xv) ) )
| ~ ( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( aInfimumOfIn0(xv,xS,xT)
| ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xv,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xv,xS,xT),xv) ) )
| ~ ( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[45,43]) ).
tff(47,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xv,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xv,xS,xT),xv) ) )
| ~ ( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( aInfimumOfIn0(xv,xS,xT)
| ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xv,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xv,xS,xT),xv) ) )
| ~ ( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ ( ~ ( aInfimumOfIn0(xv,xS,xT)
| ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xv,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xv,xS,xT),xv) ) )
| ~ ( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ) ),
inference(unit_resolution,[status(thm)],[48,42]) ).
tff(50,plain,
( ~ ( aInfimumOfIn0(xv,xS,xT)
| ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xv,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xv,xS,xT),xv) ) )
| ~ ( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) )
| ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(51,plain,
( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( aInfimumOfIn0(xv,xS,xT)
<=> aInfimumOfIn0(xv,xS,xT) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
( aInfimumOfIn0(xu,xS,xT)
& aInfimumOfIn0(xv,xS,xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__792) ).
tff(54,plain,
aInfimumOfIn0(xv,xS,xT),
inference(and_elim,[status(thm)],[53]) ).
tff(55,plain,
aInfimumOfIn0(xv,xS,xT),
inference(modus_ponens,[status(thm)],[54,52]) ).
tff(56,plain,
( ~ ( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) )
| ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(57,plain,
( ~ ( ~ aInfimumOfIn0(xv,xS,xT)
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) )
| ~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ) ),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
~ ( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ),
inference(unit_resolution,[status(thm)],[57,51]) ).
tff(59,plain,
( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) )
| aElementOf0(xv,xT) ),
inference(tautology,[status(thm)],]) ).
tff(60,plain,
aElementOf0(xv,xT),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
rewrite(
( ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(70,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ),
inference(unit_resolution,[status(thm)],[76,73,3]) ).
tff(78,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xv)
| ~ aElementOf0(xv,xT) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xv)
| ~ aElementOf0(xv,xT) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xv)
| ~ aElementOf0(xv,xT) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xv)
| ~ aElementOf0(xv,xT) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
aElement0(xv),
inference(unit_resolution,[status(thm)],[80,77,60]) ).
tff(82,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( aInfimumOfIn0(xu,xS,xT)
| ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xu,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xu,xS,xT),xu) ) )
| ~ ( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( aInfimumOfIn0(xu,xS,xT)
| ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xu,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xu,xS,xT),xu) ) )
| ~ ( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ~ ( ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xu,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xu,xS,xT),xu) ) )
| ~ ( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ) )
<=> ~ ( ~ ( aInfimumOfIn0(xu,xS,xT)
| ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xu,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xu,xS,xT),xu) ) )
| ~ ( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xu,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xu,xS,xT),xu) ) )
| ~ ( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( aInfimumOfIn0(xu,xS,xT)
| ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xu,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xu,xS,xT),xu) ) )
| ~ ( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xu,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xu,xS,xT),xu) ) )
| ~ ( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ) ) )
<=> ( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( aInfimumOfIn0(xu,xS,xT)
| ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xu,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xu,xS,xT),xu) ) )
| ~ ( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xu,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xu,xS,xT),xu) ) )
| ~ ( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(W2,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(W2,xS,xT),W2) ) )
| ~ ( ~ aInfimumOfIn0(W2,xS,xT)
| ~ ( ~ aElementOf0(W2,xT)
| ~ aLowerBoundOfIn0(W2,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,W2) ) ) ) )
| ~ ( ~ ( aInfimumOfIn0(xu,xS,xT)
| ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xu,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xu,xS,xT),xu) ) )
| ~ ( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
~ ( ~ ( aInfimumOfIn0(xu,xS,xT)
| ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xu,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xu,xS,xT),xu) ) )
| ~ ( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ) ),
inference(unit_resolution,[status(thm)],[87,42]) ).
tff(89,plain,
( ~ ( aInfimumOfIn0(xu,xS,xT)
| ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ( ~ aLowerBoundOfIn0(tptp_fun_W3_4(xu,xS,xT),xS,xT)
| sdtlseqdt0(tptp_fun_W3_4(xu,xS,xT),xu) ) )
| ~ ( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) )
| ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(90,plain,
( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ),
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
( aInfimumOfIn0(xu,xS,xT)
<=> aInfimumOfIn0(xu,xS,xT) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
aInfimumOfIn0(xu,xS,xT),
inference(and_elim,[status(thm)],[53]) ).
tff(93,plain,
aInfimumOfIn0(xu,xS,xT),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
( ~ ( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) )
| ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(95,plain,
( ~ ( ~ aInfimumOfIn0(xu,xS,xT)
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) )
| ~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ) ),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
~ ( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ),
inference(unit_resolution,[status(thm)],[95,90]) ).
tff(97,plain,
( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) )
| aElementOf0(xu,xT) ),
inference(tautology,[status(thm)],]) ).
tff(98,plain,
aElementOf0(xu,xT),
inference(unit_resolution,[status(thm)],[97,96]) ).
tff(99,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xu)
| ~ aElementOf0(xu,xT) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xu)
| ~ aElementOf0(xu,xT) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xu)
| ~ aElementOf0(xu,xT) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xu)
| ~ aElementOf0(xu,xT) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
aElement0(xu),
inference(unit_resolution,[status(thm)],[101,77,98]) ).
tff(103,plain,
( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) )
| aLowerBoundOfIn0(xv,xS,xT) ),
inference(tautology,[status(thm)],]) ).
tff(104,plain,
aLowerBoundOfIn0(xv,xS,xT),
inference(unit_resolution,[status(thm)],[103,58]) ).
tff(105,plain,
( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) )
| ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ) ),
inference(tautology,[status(thm)],]) ).
tff(106,plain,
! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) ),
inference(unit_resolution,[status(thm)],[105,96]) ).
tff(107,plain,
( ( ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) )
| ~ aLowerBoundOfIn0(xv,xS,xT)
| sdtlseqdt0(xv,xu) )
<=> ( ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) )
| ~ aLowerBoundOfIn0(xv,xS,xT)
| sdtlseqdt0(xv,xu) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) )
| ~ aLowerBoundOfIn0(xv,xS,xT)
| sdtlseqdt0(xv,xu) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
( ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) )
| ~ aLowerBoundOfIn0(xv,xS,xT)
| sdtlseqdt0(xv,xu) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
sdtlseqdt0(xv,xu),
inference(unit_resolution,[status(thm)],[109,106,104]) ).
tff(111,plain,
( ~ aElementOf0(xv,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) )
| ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ) ),
inference(tautology,[status(thm)],]) ).
tff(112,plain,
! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) ),
inference(unit_resolution,[status(thm)],[111,58]) ).
tff(113,plain,
( ~ aElementOf0(xu,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT)
| ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xu) )
| aLowerBoundOfIn0(xu,xS,xT) ),
inference(tautology,[status(thm)],]) ).
tff(114,plain,
aLowerBoundOfIn0(xu,xS,xT),
inference(unit_resolution,[status(thm)],[113,96]) ).
tff(115,plain,
( ( ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) )
| ~ aLowerBoundOfIn0(xu,xS,xT)
| sdtlseqdt0(xu,xv) )
<=> ( ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) )
| ~ aLowerBoundOfIn0(xu,xS,xT)
| sdtlseqdt0(xu,xv) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,plain,
( ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) )
| ~ aLowerBoundOfIn0(xu,xS,xT)
| sdtlseqdt0(xu,xv) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
( ~ ! [W3: $i] :
( ~ aLowerBoundOfIn0(W3,xS,xT)
| sdtlseqdt0(W3,xv) )
| ~ aLowerBoundOfIn0(xu,xS,xT)
| sdtlseqdt0(xu,xv) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
sdtlseqdt0(xu,xv),
inference(unit_resolution,[status(thm)],[117,114,112]) ).
tff(119,plain,
( ( xu != xv )
<=> ( xu != xv ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,axiom,
xu != xv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(121,plain,
xu != xv,
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
<=> ( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ~ ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
rewrite(
( ~ ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
trans(
monotonicity(
rewrite(
( ( aElement0(W0)
& aElement0(W1) )
<=> ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(
( ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(
( ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) ) )),
( ( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(125,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) )
<=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) )),
( ( ( aElement0(W0)
& aElement0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ( ( aElement0(W0)
& aElement0(W1) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) ) )),
rewrite(
( ( ( aElement0(W0)
& aElement0(W1) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) ) )),
( ( ( aElement0(W0)
& aElement0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(128,plain,
( ! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,axiom,
! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mASymm) ).
tff(130,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[130,126]) ).
tff(132,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[132,125]) ).
tff(134,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[133,123]) ).
tff(135,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xu)
| ~ sdtlseqdt0(xv,xu)
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xu)
| ~ sdtlseqdt0(xv,xu)
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,plain,
( ( ( xu = xv )
| ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu) )
<=> ( ( xu = xv )
| ~ aElement0(xu)
| ~ sdtlseqdt0(xv,xu)
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xu)
| ~ sdtlseqdt0(xv,xu)
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) ) ),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xu)
| ~ sdtlseqdt0(xv,xu)
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) ) ),
inference(transitivity,[status(thm)],[137,135]) ).
tff(139,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xu)
| ~ sdtlseqdt0(xv,xu)
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
$false,
inference(unit_resolution,[status(thm)],[140,134,121,118,110,102,81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT382+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n029.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 16:55:13 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------