%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM558+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:21:23 AM UTC 2025
% Result : Theorem 0.18s 0.49s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 52
% Syntax : Number of formulae : 140 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 1416 ( 209 equ)
% Maximal formula atoms : 48 ( 10 avg)
% Number of connectives : 2247 (1022 ~; 798 |; 211 &)
% ( 148 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 51 ( 51 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 249 ( 235 !; 1 ?; 249 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xx_type,type,
xx: $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(xy_type,type,
xy: $i ).
tff(xQ_type,type,
xQ: $i ).
tff(xP_type,type,
xP: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(xS_type,type,
xS: $i ).
tff(xT_type,type,
xT: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(xk_type,type,
xk: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(tptp_fun_W1_12_type,type,
tptp_fun_W1_12: $i > $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(1,plain,
( ( xP = sdtpldt0(sdtmndt0(xQ,xy),xx) )
<=> ( xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aSet0(sdtmndt0(xQ,xy))
& ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(xQ,xy))
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != xy ) ) )
& aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) )
& ( xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).
tff(3,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtpldt0(sdtmndt0(xQ,xy),xx) = xP,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( aElementOf0(xx,sdtpldt0(sdtmndt0(xQ,xy),xx))
<=> aElementOf0(xx,xP) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( aElementOf0(xx,xP)
<=> aElementOf0(xx,sdtpldt0(sdtmndt0(xQ,xy),xx)) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
^ [W0: $i] :
refl(( ~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) )
<=> ~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) )
<=> ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [W0: $i] :
trans(trans(monotonicity(trans(monotonicity(rewrite(( ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) )
<=> ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )),
( ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) )),
rewrite(( ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> ~ ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) )),
( ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> ~ ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) )),
( ( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) )
<=> ( aElementOf0(W0,xP)
<=> ~ ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) ) )),
rewrite(( ( aElementOf0(W0,xP)
<=> ~ ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) )
<=> ~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) ) )),
( ( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) )
<=> ~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) ) )),
rewrite(( ~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) )
<=> ~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) ) )),
( ( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) )
<=> ~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) )
<=> ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) )
<=> ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( aSet0(sdtmndt0(xQ,xy))
& ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(xQ,xy))
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != xy ) ) )
& aSet0(xP)
& ! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(14,plain,
! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) ),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) ),
inference(modus_ponens,[status(thm)],[14,12]) ).
tff(16,plain,
! [W0: $i] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) ),
inference(modus_ponens,[status(thm)],[16,11]) ).
tff(18,plain,
! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) ),
inference(modus_ponens,[status(thm)],[17,9]) ).
tff(19,plain,
( ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) )
| ( aElement0(xx)
<=> aElementOf0(xx,xP) ) )
<=> ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) )
| ( aElement0(xx)
<=> aElementOf0(xx,xP) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ~ ~ ( aElement0(xx)
<=> aElementOf0(xx,xP) )
<=> ( aElement0(xx)
<=> aElementOf0(xx,xP) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ( aElement0(xx)
<=> aElementOf0(xx,xP) )
<=> ~ ( aElement0(xx)
<=> aElementOf0(xx,xP) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( ~ aElement0(xx)
<=> aElementOf0(xx,xP) )
<=> ~ ( aElement0(xx)
<=> aElementOf0(xx,xP) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ( ~ aElement0(xx)
| $false )
<=> ~ aElement0(xx) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( aElementOf0(xx,sdtmndt0(xQ,xy))
| $true )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( xx = xx )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ( aElementOf0(xx,sdtmndt0(xQ,xy))
| ( xx = xx ) )
<=> ( aElementOf0(xx,sdtmndt0(xQ,xy))
| $true ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ( aElementOf0(xx,sdtmndt0(xQ,xy))
| ( xx = xx ) )
<=> $true ),
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,plain,
( ~ ( aElementOf0(xx,sdtmndt0(xQ,xy))
| ( xx = xx ) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ~ ( aElementOf0(xx,sdtmndt0(xQ,xy))
| ( xx = xx ) )
<=> $false ),
inference(transitivity,[status(thm)],[29,24]) ).
tff(31,plain,
( ( ~ aElement0(xx)
| ~ ( aElementOf0(xx,sdtmndt0(xQ,xy))
| ( xx = xx ) ) )
<=> ( ~ aElement0(xx)
| $false ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ aElement0(xx)
| ~ ( aElementOf0(xx,sdtmndt0(xQ,xy))
| ( xx = xx ) ) )
<=> ~ aElement0(xx) ),
inference(transitivity,[status(thm)],[31,23]) ).
tff(33,plain,
( ( ( ~ aElement0(xx)
| ~ ( aElementOf0(xx,sdtmndt0(xQ,xy))
| ( xx = xx ) ) )
<=> aElementOf0(xx,xP) )
<=> ( ~ aElement0(xx)
<=> aElementOf0(xx,xP) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ( ~ aElement0(xx)
| ~ ( aElementOf0(xx,sdtmndt0(xQ,xy))
| ( xx = xx ) ) )
<=> aElementOf0(xx,xP) )
<=> ~ ( aElement0(xx)
<=> aElementOf0(xx,xP) ) ),
inference(transitivity,[status(thm)],[33,22]) ).
tff(35,plain,
( ( ( ~ aElement0(xx)
| ~ ( aElementOf0(xx,sdtmndt0(xQ,xy))
| ( xx = xx ) ) )
<=> aElementOf0(xx,xP) )
<=> ~ ( aElement0(xx)
<=> aElementOf0(xx,xP) ) ),
inference(transitivity,[status(thm)],[34,21]) ).
tff(36,plain,
( ~ ( ( ~ aElement0(xx)
| ~ ( aElementOf0(xx,sdtmndt0(xQ,xy))
| ( xx = xx ) ) )
<=> aElementOf0(xx,xP) )
<=> ~ ~ ( aElement0(xx)
<=> aElementOf0(xx,xP) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ~ ( ( ~ aElement0(xx)
| ~ ( aElementOf0(xx,sdtmndt0(xQ,xy))
| ( xx = xx ) ) )
<=> aElementOf0(xx,xP) )
<=> ( aElement0(xx)
<=> aElementOf0(xx,xP) ) ),
inference(transitivity,[status(thm)],[36,20]) ).
tff(38,plain,
( ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) )
| ~ ( ( ~ aElement0(xx)
| ~ ( aElementOf0(xx,sdtmndt0(xQ,xy))
| ( xx = xx ) ) )
<=> aElementOf0(xx,xP) ) )
<=> ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) )
| ( aElement0(xx)
<=> aElementOf0(xx,xP) ) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) )
| ~ ( ( ~ aElement0(xx)
| ~ ( aElementOf0(xx,sdtmndt0(xQ,xy))
| ( xx = xx ) ) )
<=> aElementOf0(xx,xP) ) )
<=> ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) )
| ( aElement0(xx)
<=> aElementOf0(xx,xP) ) ) ),
inference(transitivity,[status(thm)],[38,19]) ).
tff(40,plain,
( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) )
| ~ ( ( ~ aElement0(xx)
| ~ ( aElementOf0(xx,sdtmndt0(xQ,xy))
| ( xx = xx ) ) )
<=> aElementOf0(xx,xP) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) )
<=> aElementOf0(W0,xP) )
| ( aElement0(xx)
<=> aElementOf0(xx,xP) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( aElement0(xx)
<=> aElementOf0(xx,xP) ),
inference(unit_resolution,[status(thm)],[41,18]) ).
tff(43,plain,
( aSet0(xS)
<=> aSet0(xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
( aSet0(xS)
& aSet0(xT)
& ( xk != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
tff(45,plain,
( aSet0(xS)
& aSet0(xT) ),
inference(and_elim,[status(thm)],[44]) ).
tff(46,plain,
aSet0(xS),
inference(and_elim,[status(thm)],[45]) ).
tff(47,plain,
aSet0(xS),
inference(modus_ponens,[status(thm)],[46,43]) ).
tff(48,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(49,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)],[48]) ).
tff(50,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(51,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)],[50]) ).
tff(52,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)],[51,49]) ).
tff(53,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(54,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(55,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)],[54]) ).
tff(56,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(57,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xS)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xS)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xS)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xS)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) ),
inference(unit_resolution,[status(thm)],[63,60,47]) ).
tff(65,plain,
( aElementOf0(xx,xS)
<=> aElementOf0(xx,xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).
tff(67,plain,
aElementOf0(xx,xS),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) )
| aElement0(xx)
| ~ aElementOf0(xx,xS) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) )
| aElement0(xx)
| ~ aElementOf0(xx,xS) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) )
| aElement0(xx)
| ~ aElementOf0(xx,xS) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) )
| aElement0(xx)
| ~ aElementOf0(xx,xS) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
aElement0(xx),
inference(unit_resolution,[status(thm)],[70,67,64]) ).
tff(72,plain,
( ~ ( aElement0(xx)
<=> aElementOf0(xx,xP) )
| ~ aElement0(xx)
| aElementOf0(xx,xP) ),
inference(tautology,[status(thm)],[]) ).
tff(73,plain,
aElementOf0(xx,xP),
inference(unit_resolution,[status(thm)],[72,71,42]) ).
tff(74,plain,
aElementOf0(xx,sdtpldt0(sdtmndt0(xQ,xy),xx)),
inference(modus_ponens,[status(thm)],[73,7]) ).
tff(75,plain,
^ [W0: $i] :
refl(( ~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[78,76]) ).
tff(80,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) ) )),
trans(monotonicity(rewrite(( ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) )
<=> ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) )),
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) )
<=> ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )),
rewrite(( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) )
<=> ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )),
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) )
<=> ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )),
( ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) )),
rewrite(( ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) )),
( ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
^ [W0: $i] :
rewrite(( ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) )
| ( sbrdtbr0(W0) != xk )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
<=> ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) )
| ( sbrdtbr0(W0) != xk )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
<=> ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ~ ( ( aSubsetOf0(W0,xT)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
<=> ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ~ ( ( aSubsetOf0(W0,xT)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
^ [W0: $i] :
rewrite(( ( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
<=> ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ~ ( ( aSubsetOf0(W0,xT)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
<=> ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ~ ( ( aSubsetOf0(W0,xT)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
& ! [W0: $i] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ~ ( ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
=> ( ~ ? [W0: $i] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
| ( slbdtsldtrb0(xS,xk) = slcrc0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2227) ).
tff(88,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
& ! [W0: $i] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
inference(and_elim,[status(thm)],[87]) ).
tff(89,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
& ! [W0: $i] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(and_elim,[status(thm)],[88]) ).
tff(90,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ) ),
inference(and_elim,[status(thm)],[89]) ).
tff(91,plain,
! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(and_elim,[status(thm)],[90]) ).
tff(92,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ~ ( ( aSubsetOf0(W0,xT)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(modus_ponens,[status(thm)],[91,86]) ).
tff(93,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ~ ( ( aSubsetOf0(W0,xT)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(modus_ponens,[status(thm)],[92,84]) ).
tff(94,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) )
| ( sbrdtbr0(W0) != xk )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[94,83]) ).
tff(96,plain,
! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[95,81]) ).
tff(97,plain,
! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[96,79]) ).
tff(98,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) )
| ~ ( ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),xT) ) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) )
| ~ ( ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),xT) ) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ~ ( ~ ( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ( aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT)
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),xT) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) )
| ~ ( ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),xT) ) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ( aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT)
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),xT) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) )
| ~ ( ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),xT) ) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) ) ) ) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ( aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT)
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),xT) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) )
| ~ ( ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),xT) ) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) ) ) ) ),
inference(transitivity,[status(thm)],[100,98]) ).
tff(102,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ( aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT)
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),xT) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) )
| ~ ( ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),xT) ) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) ) ) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
~ ( ~ ( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) )
| ~ ( ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),xT) ) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) ) ),
inference(unit_resolution,[status(thm)],[103,97]) ).
tff(105,plain,
( ~ ( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) )
| ~ ( ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ~ ( ~ aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(tptp_fun_W1_12(sdtpldt0(sdtmndt0(xQ,xy),xx)),xT) ) )
| aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) )
| ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) ),
inference(tautology,[status(thm)],[]) ).
tff(106,plain,
( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) ),
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,plain,
( aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,xk))
<=> aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(108,plain,
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
<=> aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,xk)) ),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
<=> aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,axiom,
( ! [W0: $i] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xP,xS)
& ( sbrdtbr0(xP) = xk )
& aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2378) ).
tff(111,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(and_elim,[status(thm)],[110]) ).
tff(112,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(modus_ponens,[status(thm)],[111,109]) ).
tff(113,plain,
aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,xk)),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )),
inference(bind,[status(th)],[]) ).
tff(115,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )),
inference(bind,[status(th)],[]) ).
tff(118,plain,
( ! [W0: $i] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
! [W0: $i] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ),
inference(and_elim,[status(thm)],[89]) ).
tff(120,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ),
inference(skolemize,[status(sab)],[121]) ).
tff(123,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ),
inference(modus_ponens,[status(thm)],[122,115]) ).
tff(124,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
| ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,xk))
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk)) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
| ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,xk))
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
| ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,xk))
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
| ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,xk))
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk)) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xS,xk))
| aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk)) ),
inference(unit_resolution,[status(thm)],[126,123]) ).
tff(128,plain,
aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk)),
inference(unit_resolution,[status(thm)],[127,113]) ).
tff(129,plain,
( ~ ( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) )
| ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ) ),
inference(tautology,[status(thm)],[]) ).
tff(130,plain,
~ ( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT) ),
inference(unit_resolution,[status(thm)],[129,128,106]) ).
tff(131,plain,
( ~ aSet0(sdtpldt0(sdtmndt0(xQ,xy),xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xQ,xy),xx),xT)
| ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) ) ),
inference(tautology,[status(thm)],[]) ).
tff(132,plain,
! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) ),
inference(unit_resolution,[status(thm)],[131,130]) ).
tff(133,plain,
( ~ aElementOf0(xx,xT)
<=> ~ aElementOf0(xx,xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,axiom,
~ aElementOf0(xx,xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(135,plain,
~ aElementOf0(xx,xT),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(xx,xT) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(xx,xT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(xx,xT) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(W1,xT) )
| ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xQ,xy),xx))
| aElementOf0(xx,xT) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
~ aElementOf0(xx,sdtpldt0(sdtmndt0(xQ,xy),xx)),
inference(unit_resolution,[status(thm)],[138,135,132]) ).
tff(140,plain,
$false,
inference(unit_resolution,[status(thm)],[139,74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM558+3 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 01:25:50 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.49 % SZS status Theorem
% 0.18/0.49 % SZS output start Proof
% See solution above
% 0.18/0.52 % E exiting
%------------------------------------------------------------------------------