%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG089+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:24:09 AM UTC 2025
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 42
% Syntax : Number of formulae : 98 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 1416 ( 1 equ)
% Maximal formula atoms : 56 ( 14 avg)
% Number of connectives : 3093 (1789 ~;1174 |; 72 &)
% ( 49 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 412 ( 406 !; 0 ?; 412 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xJ_type,type,
xJ: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xl_type,type,
xl: $i ).
tff(xz_type,type,
xz: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aIdeal0_type,type,
aIdeal0: $i > $o ).
tff(tptp_fun_W2_9_type,type,
tptp_fun_W2_9: $i > $i ).
tff(tptp_fun_W1_8_type,type,
tptp_fun_W1_8: $i > $i ).
tff(tptp_fun_W2_10_type,type,
tptp_fun_W2_10: $i > $i ).
tff(xI_type,type,
xI: $i ).
tff(xk_type,type,
xk: $i ).
tff(xx_type,type,
xx: $i ).
tff(sdtpldt1_type,type,
sdtpldt1: ( $i * $i ) > $i ).
tff(xy_type,type,
xy: $i ).
tff(1,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
refl(( ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
<=> ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )),
rewrite(( ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
<=> ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )),
( ( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ( ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
rewrite(( ( ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
( ( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(( ( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
<=> ! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [W0: $i] :
rewrite(( ( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
<=> ( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
<=> ! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
tff(16,plain,
! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) )
| ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ) )
<=> ~ ( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) )
| ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) )
| ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) )
| ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) )
| ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(31,plain,
( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( aIdeal0(xJ)
<=> aIdeal0(xJ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
tff(34,plain,
aIdeal0(xJ),
inference(and_elim,[status(thm)],[33]) ).
tff(35,plain,
aIdeal0(xJ),
inference(modus_ponens,[status(thm)],[34,32]) ).
tff(36,plain,
( ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) )
| ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(37,plain,
( ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) )
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ),
inference(unit_resolution,[status(thm)],[37,31]) ).
tff(39,plain,
( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) )
| ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(40,plain,
! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
( aElementOf0(xl,xJ)
<=> aElementOf0(xl,xJ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& ( xx = sdtpldt0(xk,xl) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).
tff(43,plain,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ) ),
inference(and_elim,[status(thm)],[42]) ).
tff(44,plain,
aElementOf0(xl,xJ),
inference(and_elim,[status(thm)],[43]) ).
tff(45,plain,
aElementOf0(xl,xJ),
inference(modus_ponens,[status(thm)],[44,41]) ).
tff(46,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) )
| ~ aElementOf0(xl,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(xl,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) )
| ~ aElementOf0(xl,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(xl,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) )
| ~ aElementOf0(xl,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(xl,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) )
| ~ aElementOf0(xl,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(xl,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) ) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(xl,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) ) ),
inference(unit_resolution,[status(thm)],[48,45,40]) ).
tff(50,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(xl,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) )
| ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(51,plain,
! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( aElement0(xz)
<=> aElement0(xz) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
( aElementOf0(xx,sdtpldt1(xI,xJ))
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
tff(54,plain,
aElement0(xz),
inference(and_elim,[status(thm)],[53]) ).
tff(55,plain,
aElement0(xz),
inference(modus_ponens,[status(thm)],[54,52]) ).
tff(56,plain,
( ( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xl),xJ) )
<=> ( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xl),xJ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(unit_resolution,[status(thm)],[58,55,51]) ).
tff(60,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) )
| ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ) )
<=> ~ ( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) )
| ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) )
| ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[62,60]) ).
tff(64,plain,
( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) )
| ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
~ ( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[65,22]) ).
tff(67,plain,
( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) )
| ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) )
| ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(68,plain,
( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
( aIdeal0(xI)
<=> aIdeal0(xI) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
aIdeal0(xI),
inference(and_elim,[status(thm)],[33]) ).
tff(71,plain,
aIdeal0(xI),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) )
| ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(73,plain,
( ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) )
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ),
inference(unit_resolution,[status(thm)],[73,68]) ).
tff(75,plain,
( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) )
| ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(76,plain,
! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
( aElementOf0(xk,xI)
<=> aElementOf0(xk,xI) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
aElementOf0(xk,xI),
inference(and_elim,[status(thm)],[43]) ).
tff(79,plain,
aElementOf0(xk,xI),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) )
| ~ aElementOf0(xk,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(xk,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) )
| ~ aElementOf0(xk,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(xk,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) )
| ~ aElementOf0(xk,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(xk,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) )
| ~ aElementOf0(xk,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(xk,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) ) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(xk,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) ) ),
inference(unit_resolution,[status(thm)],[82,79,76]) ).
tff(84,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(xk,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) )
| ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) ) ),
inference(tautology,[status(thm)],[]) ).
tff(85,plain,
! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) ),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
( ( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xk),xI) )
<=> ( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xk),xI) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(unit_resolution,[status(thm)],[88,55,85]) ).
tff(90,plain,
( ~ ~ ( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) )
<=> ( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) )
<=> ~ ( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) )
<=> ~ ~ ( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) )
<=> ( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ) ),
inference(transitivity,[status(thm)],[92,90]) ).
tff(94,plain,
( ~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) )
<=> ~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,axiom,
~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(96,plain,
~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(modus_ponens,[status(thm)],[96,93]) ).
tff(98,plain,
$false,
inference(unit_resolution,[status(thm)],[97,89,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG089+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 03:19:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% See solution above
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------