%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG090+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:24:09 AM UTC 2025
% Result : Theorem 4.40s 4.60s
% Output : Proof 4.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 87
% Syntax : Number of formulae : 225 ( 64 unt; 0 typ; 0 def)
% Number of atoms : 2246 ( 176 equ)
% Maximal formula atoms : 56 ( 9 avg)
% Number of connectives : 4176 (2232 ~;1638 |; 143 &)
% ( 130 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 77 ( 77 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 671 ( 640 !; 0 ?; 671 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(xl_type,type,
xl: $i ).
tff(xm_type,type,
xm: $i ).
tff(xk_type,type,
xk: $i ).
tff(xy_type,type,
xy: $i ).
tff(xx_type,type,
xx: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xJ_type,type,
xJ: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
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(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/sandbox/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/sandbox/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) ) ) )
| aSet0(xJ) ),
inference(tautology,[status(thm)],[]) ).
tff(40,plain,
aSet0(xJ),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,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(42,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)],[41]) ).
tff(43,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(44,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)],[43]) ).
tff(45,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)],[44,42]) ).
tff(46,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(47,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(48,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)],[47]) ).
tff(49,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
tff(50,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ),
inference(unit_resolution,[status(thm)],[56,53,40]) ).
tff(58,plain,
( aElementOf0(xl,xJ)
<=> aElementOf0(xl,xJ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& ( xx = sdtpldt0(xk,xl) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__934) ).
tff(60,plain,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ) ),
inference(and_elim,[status(thm)],[59]) ).
tff(61,plain,
aElementOf0(xl,xJ),
inference(and_elim,[status(thm)],[60]) ).
tff(62,plain,
aElementOf0(xl,xJ),
inference(modus_ponens,[status(thm)],[61,58]) ).
tff(63,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xl)
| ~ aElementOf0(xl,xJ) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xl)
| ~ aElementOf0(xl,xJ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xl)
| ~ aElementOf0(xl,xJ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xl)
| ~ aElementOf0(xl,xJ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
aElement0(xl),
inference(unit_resolution,[status(thm)],[65,62,57]) ).
tff(67,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(68,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(69,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)],[68]) ).
tff(70,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)],[69,67]) ).
tff(71,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(72,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)],[71,70]) ).
tff(73,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)],[72,22]) ).
tff(74,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(75,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)],[74,73]) ).
tff(76,plain,
( aIdeal0(xI)
<=> aIdeal0(xI) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
aIdeal0(xI),
inference(and_elim,[status(thm)],[33]) ).
tff(78,plain,
aIdeal0(xI),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,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(80,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)],[79,78]) ).
tff(81,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)],[80,75]) ).
tff(82,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) ) ) )
| aSet0(xI) ),
inference(tautology,[status(thm)],[]) ).
tff(83,plain,
aSet0(xI),
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ),
inference(unit_resolution,[status(thm)],[86,53,83]) ).
tff(88,plain,
( aElementOf0(sdtpldt0(xk,xm),xI)
<=> aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,axiom,
( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__994) ).
tff(90,plain,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(and_elim,[status(thm)],[89]) ).
tff(91,plain,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(modus_ponens,[status(thm)],[90,88]) ).
tff(92,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(sdtpldt0(xk,xm))
| ~ aElementOf0(sdtpldt0(xk,xm),xI) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(sdtpldt0(xk,xm))
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(sdtpldt0(xk,xm))
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(sdtpldt0(xk,xm))
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
aElement0(sdtpldt0(xk,xm)),
inference(unit_resolution,[status(thm)],[94,91,87]) ).
tff(96,plain,
( aElementOf0(xn,xJ)
<=> aElementOf0(xn,xJ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
( aElementOf0(xm,xI)
& aElementOf0(xn,xJ)
& ( xy = sdtpldt0(xm,xn) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__967) ).
tff(98,plain,
( aElementOf0(xm,xI)
& aElementOf0(xn,xJ) ),
inference(and_elim,[status(thm)],[97]) ).
tff(99,plain,
aElementOf0(xn,xJ),
inference(and_elim,[status(thm)],[98]) ).
tff(100,plain,
aElementOf0(xn,xJ),
inference(modus_ponens,[status(thm)],[99,96]) ).
tff(101,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xn)
| ~ aElementOf0(xn,xJ) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xn)
| ~ aElementOf0(xn,xJ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xn)
| ~ aElementOf0(xn,xJ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xn)
| ~ aElementOf0(xn,xJ) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
aElement0(xn),
inference(unit_resolution,[status(thm)],[103,100,57]) ).
tff(105,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(106,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
<=> ~ ( ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
<=> ~ ~ ( ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(( ~ ~ ( ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
<=> ( ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0)
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
rewrite(( ( ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0)
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(108,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
<=> ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) ) )),
( ( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
rewrite(( ( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
( ( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(111,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
tff(113,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[113,109]) ).
tff(115,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
inference(skolemize,[status(sab)],[114]) ).
tff(116,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[115,108]) ).
tff(117,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[116,106]) ).
tff(118,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) )
| ~ aElement0(sdtpldt0(xk,xm)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) )
| ~ aElement0(sdtpldt0(xk,xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
( ( ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) )
| ~ aElement0(xn)
| ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xk,xm)) )
<=> ( ~ aElement0(xl)
| ~ aElement0(xn)
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) )
| ~ aElement0(sdtpldt0(xk,xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) )
| ~ aElement0(xn)
| ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xk,xm)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) )
| ~ aElement0(sdtpldt0(xk,xm)) ) ),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) )
| ~ aElement0(xn)
| ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xk,xm)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) )
| ~ aElement0(sdtpldt0(xk,xm)) ) ),
inference(transitivity,[status(thm)],[120,118]) ).
tff(122,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) )
| ~ aElement0(xn)
| ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xk,xm)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) )
| ~ aElement0(sdtpldt0(xk,xm)) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
( ~ aElement0(xl)
| ~ aElement0(xn)
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) )
| ~ aElement0(sdtpldt0(xk,xm)) ),
inference(unit_resolution,[status(thm)],[123,117]) ).
tff(125,plain,
sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(unit_resolution,[status(thm)],[124,104,95,66]) ).
tff(126,plain,
( aElementOf0(xk,xI)
<=> aElementOf0(xk,xI) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
aElementOf0(xk,xI),
inference(and_elim,[status(thm)],[60]) ).
tff(128,plain,
aElementOf0(xk,xI),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xk)
| ~ aElementOf0(xk,xI) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xk)
| ~ aElementOf0(xk,xI) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xk)
| ~ aElementOf0(xk,xI) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xk)
| ~ aElementOf0(xk,xI) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
aElement0(xk),
inference(unit_resolution,[status(thm)],[131,128,87]) ).
tff(133,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(134,plain,
( ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[133]) ).
tff(135,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(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) ) )),
( ( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0)
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) )),
rewrite(( ( ~ aElement0(W1)
| ~ aElement0(W0)
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(136,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aElement0(W0)
& aElement0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(139,plain,
( ! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,axiom,
! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
tff(141,plain,
! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[141,137]) ).
tff(143,plain,
! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[142]) ).
tff(144,plain,
! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[143,136]) ).
tff(145,plain,
! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[144,134]) ).
tff(146,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| ( sdtpldt0(xl,xk) = sdtpldt0(xk,xl) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| ( sdtpldt0(xl,xk) = sdtpldt0(xk,xl) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
( ( ( sdtpldt0(xl,xk) = sdtpldt0(xk,xl) )
| ~ aElement0(xk)
| ~ aElement0(xl) )
<=> ( ~ aElement0(xl)
| ~ aElement0(xk)
| ( sdtpldt0(xl,xk) = sdtpldt0(xk,xl) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(xl,xk) = sdtpldt0(xk,xl) )
| ~ aElement0(xk)
| ~ aElement0(xl) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| ( sdtpldt0(xl,xk) = sdtpldt0(xk,xl) ) ) ),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(xl,xk) = sdtpldt0(xk,xl) )
| ~ aElement0(xk)
| ~ aElement0(xl) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| ( sdtpldt0(xl,xk) = sdtpldt0(xk,xl) ) ) ),
inference(transitivity,[status(thm)],[148,146]) ).
tff(150,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(xl,xk) = sdtpldt0(xk,xl) )
| ~ aElement0(xk)
| ~ aElement0(xl) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| ( sdtpldt0(xl,xk) = sdtpldt0(xk,xl) ) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
( ~ aElement0(xl)
| ~ aElement0(xk)
| ( sdtpldt0(xl,xk) = sdtpldt0(xk,xl) ) ),
inference(unit_resolution,[status(thm)],[151,145]) ).
tff(153,plain,
sdtpldt0(xl,xk) = sdtpldt0(xk,xl),
inference(unit_resolution,[status(thm)],[152,66,132]) ).
tff(154,plain,
sdtpldt0(sdtpldt0(xl,xk),xm) = sdtpldt0(sdtpldt0(xk,xl),xm),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
( aElementOf0(xm,xI)
<=> aElementOf0(xm,xI) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,plain,
aElementOf0(xm,xI),
inference(and_elim,[status(thm)],[98]) ).
tff(157,plain,
aElementOf0(xm,xI),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xm)
| ~ aElementOf0(xm,xI) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xm)
| ~ aElementOf0(xm,xI) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xm)
| ~ aElementOf0(xm,xI) ),
inference(quant_inst,[status(thm)],[]) ).
tff(160,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xm)
| ~ aElementOf0(xm,xI) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
aElement0(xm),
inference(unit_resolution,[status(thm)],[160,157,87]) ).
tff(162,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xl,xk),xm) = sdtpldt0(xl,sdtpldt0(xk,xm)) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xl,xk),xm) = sdtpldt0(xl,sdtpldt0(xk,xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,plain,
( ( ( sdtpldt0(sdtpldt0(xl,xk),xm) = sdtpldt0(xl,sdtpldt0(xk,xm)) )
| ~ aElement0(xm)
| ~ aElement0(xk)
| ~ aElement0(xl) )
<=> ( ~ aElement0(xl)
| ~ aElement0(xk)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xl,xk),xm) = sdtpldt0(xl,sdtpldt0(xk,xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xl,xk),xm) = sdtpldt0(xl,sdtpldt0(xk,xm)) )
| ~ aElement0(xm)
| ~ aElement0(xk)
| ~ aElement0(xl) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xl,xk),xm) = sdtpldt0(xl,sdtpldt0(xk,xm)) ) ) ),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xl,xk),xm) = sdtpldt0(xl,sdtpldt0(xk,xm)) )
| ~ aElement0(xm)
| ~ aElement0(xk)
| ~ aElement0(xl) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xl,xk),xm) = sdtpldt0(xl,sdtpldt0(xk,xm)) ) ) ),
inference(transitivity,[status(thm)],[164,162]) ).
tff(166,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xl,xk),xm) = sdtpldt0(xl,sdtpldt0(xk,xm)) )
| ~ aElement0(xm)
| ~ aElement0(xk)
| ~ aElement0(xl) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xl,xk),xm) = sdtpldt0(xl,sdtpldt0(xk,xm)) ) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
sdtpldt0(sdtpldt0(xl,xk),xm) = sdtpldt0(xl,sdtpldt0(xk,xm)),
inference(unit_resolution,[status(thm)],[167,117,66,132,161]) ).
tff(169,plain,
sdtpldt0(xl,sdtpldt0(xk,xm)) = sdtpldt0(sdtpldt0(xl,xk),xm),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xk,xm))
| ( sdtpldt0(xl,sdtpldt0(xk,xm)) = sdtpldt0(sdtpldt0(xk,xm),xl) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xk,xm))
| ( sdtpldt0(xl,sdtpldt0(xk,xm)) = sdtpldt0(sdtpldt0(xk,xm),xl) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,plain,
( ( ( sdtpldt0(xl,sdtpldt0(xk,xm)) = sdtpldt0(sdtpldt0(xk,xm),xl) )
| ~ aElement0(sdtpldt0(xk,xm))
| ~ aElement0(xl) )
<=> ( ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xk,xm))
| ( sdtpldt0(xl,sdtpldt0(xk,xm)) = sdtpldt0(sdtpldt0(xk,xm),xl) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(xl,sdtpldt0(xk,xm)) = sdtpldt0(sdtpldt0(xk,xm),xl) )
| ~ aElement0(sdtpldt0(xk,xm))
| ~ aElement0(xl) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xk,xm))
| ( sdtpldt0(xl,sdtpldt0(xk,xm)) = sdtpldt0(sdtpldt0(xk,xm),xl) ) ) ),
inference(monotonicity,[status(thm)],[171]) ).
tff(173,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(xl,sdtpldt0(xk,xm)) = sdtpldt0(sdtpldt0(xk,xm),xl) )
| ~ aElement0(sdtpldt0(xk,xm))
| ~ aElement0(xl) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xk,xm))
| ( sdtpldt0(xl,sdtpldt0(xk,xm)) = sdtpldt0(sdtpldt0(xk,xm),xl) ) ) ),
inference(transitivity,[status(thm)],[172,170]) ).
tff(174,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(xl,sdtpldt0(xk,xm)) = sdtpldt0(sdtpldt0(xk,xm),xl) )
| ~ aElement0(sdtpldt0(xk,xm))
| ~ aElement0(xl) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xk,xm))
| ( sdtpldt0(xl,sdtpldt0(xk,xm)) = sdtpldt0(sdtpldt0(xk,xm),xl) ) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
sdtpldt0(xl,sdtpldt0(xk,xm)) = sdtpldt0(sdtpldt0(xk,xm),xl),
inference(unit_resolution,[status(thm)],[175,145,66,95]) ).
tff(177,plain,
sdtpldt0(sdtpldt0(xk,xm),xl) = sdtpldt0(xl,sdtpldt0(xk,xm)),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
sdtpldt0(sdtpldt0(xk,xm),xl) = sdtpldt0(sdtpldt0(xk,xl),xm),
inference(transitivity,[status(thm)],[177,169,154]) ).
tff(179,plain,
sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn) = sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn) = sdtpldt0(sdtpldt0(sdtpldt0(xk,xm),xl),xn),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
^ [W0: $i,W1: $i] :
refl(( ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(182,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[181]) ).
tff(183,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(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) ) )),
( ( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(( ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(184,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[183]) ).
tff(185,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(187,plain,
( ! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[186]) ).
tff(188,axiom,
! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(189,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[189,185]) ).
tff(191,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(skolemize,[status(sab)],[190]) ).
tff(192,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[191,184]) ).
tff(193,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[192,182]) ).
tff(194,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| aElement0(sdtpldt0(xk,xl)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| aElement0(sdtpldt0(xk,xl)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(195,plain,
( ( aElement0(sdtpldt0(xk,xl))
| ~ aElement0(xl)
| ~ aElement0(xk) )
<=> ( ~ aElement0(xl)
| ~ aElement0(xk)
| aElement0(sdtpldt0(xk,xl)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(196,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(xk,xl))
| ~ aElement0(xl)
| ~ aElement0(xk) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| aElement0(sdtpldt0(xk,xl)) ) ),
inference(monotonicity,[status(thm)],[195]) ).
tff(197,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(xk,xl))
| ~ aElement0(xl)
| ~ aElement0(xk) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| aElement0(sdtpldt0(xk,xl)) ) ),
inference(transitivity,[status(thm)],[196,194]) ).
tff(198,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(xk,xl))
| ~ aElement0(xl)
| ~ aElement0(xk) ),
inference(quant_inst,[status(thm)],[]) ).
tff(199,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xk)
| aElement0(sdtpldt0(xk,xl)) ),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
( ~ aElement0(xl)
| ~ aElement0(xk)
| aElement0(sdtpldt0(xk,xl)) ),
inference(unit_resolution,[status(thm)],[199,193]) ).
tff(201,plain,
aElement0(sdtpldt0(xk,xl)),
inference(unit_resolution,[status(thm)],[200,66,132]) ).
tff(202,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) )
| ~ aElement0(xm)
| ~ aElement0(xn)
| ~ aElement0(sdtpldt0(xk,xl)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) )
| ~ aElement0(xm)
| ~ aElement0(xn)
| ~ aElement0(sdtpldt0(xk,xl)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(203,plain,
( ( ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) )
| ~ aElement0(xn)
| ~ aElement0(xm)
| ~ aElement0(sdtpldt0(xk,xl)) )
<=> ( ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) )
| ~ aElement0(xm)
| ~ aElement0(xn)
| ~ aElement0(sdtpldt0(xk,xl)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(204,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) )
| ~ aElement0(xn)
| ~ aElement0(xm)
| ~ aElement0(sdtpldt0(xk,xl)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) )
| ~ aElement0(xm)
| ~ aElement0(xn)
| ~ aElement0(sdtpldt0(xk,xl)) ) ),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) )
| ~ aElement0(xn)
| ~ aElement0(xm)
| ~ aElement0(sdtpldt0(xk,xl)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) )
| ~ aElement0(xm)
| ~ aElement0(xn)
| ~ aElement0(sdtpldt0(xk,xl)) ) ),
inference(transitivity,[status(thm)],[204,202]) ).
tff(206,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) )
| ~ aElement0(xn)
| ~ aElement0(xm)
| ~ aElement0(sdtpldt0(xk,xl)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(207,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) )
| ~ aElement0(xm)
| ~ aElement0(xn)
| ~ aElement0(sdtpldt0(xk,xl)) ),
inference(modus_ponens,[status(thm)],[206,205]) ).
tff(208,plain,
( ( sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) )
| ~ aElement0(xm)
| ~ aElement0(xn)
| ~ aElement0(sdtpldt0(xk,xl)) ),
inference(unit_resolution,[status(thm)],[207,117]) ).
tff(209,plain,
sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)),
inference(unit_resolution,[status(thm)],[208,161,104,201]) ).
tff(210,plain,
sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) = sdtpldt0(sdtpldt0(sdtpldt0(xk,xl),xm),xn),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
( ( xy = sdtpldt0(xm,xn) )
<=> ( xy = sdtpldt0(xm,xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(212,plain,
xy = sdtpldt0(xm,xn),
inference(and_elim,[status(thm)],[97]) ).
tff(213,plain,
xy = sdtpldt0(xm,xn),
inference(modus_ponens,[status(thm)],[212,211]) ).
tff(214,plain,
sdtpldt0(xm,xn) = xy,
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
( ( xx = sdtpldt0(xk,xl) )
<=> ( xx = sdtpldt0(xk,xl) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(216,plain,
xx = sdtpldt0(xk,xl),
inference(and_elim,[status(thm)],[59]) ).
tff(217,plain,
xx = sdtpldt0(xk,xl),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
sdtpldt0(xk,xl) = xx,
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) = sdtpldt0(xx,xy),
inference(monotonicity,[status(thm)],[218,214]) ).
tff(220,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(transitivity,[status(thm)],[220,210,180,125]) ).
tff(222,plain,
( ( sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) )
<=> ( sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(223,axiom,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(224,plain,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(modus_ponens,[status(thm)],[223,222]) ).
tff(225,plain,
$false,
inference(unit_resolution,[status(thm)],[224,221]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG090+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 03:20:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.40/4.60 % SZS status Theorem
% 4.40/4.60 % SZS output start Proof
% See solution above
% 4.47/4.63 % E exiting
%------------------------------------------------------------------------------