%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM532+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 05:21:18 AM UTC 2025
% Result : Theorem 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 46 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 650 ( 0 equ)
% Maximal formula atoms : 36 ( 14 avg)
% Number of connectives : 1306 ( 717 ~; 499 |; 33 &)
% ( 45 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 183 ( 176 !; 0 ?; 183 :)
% Comments :
%------------------------------------------------------------------------------
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xA_type,type,
xA: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(1,plain,
( ~ aSubsetOf0(xA,xA)
<=> ~ aSubsetOf0(xA,xA) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ aSubsetOf0(xA,xA),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(3,plain,
~ aSubsetOf0(xA,xA),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( aSet0(xA)
<=> aSet0(xA) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
aSet0(xA),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__467) ).
tff(6,plain,
aSet0(xA),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ~ ( aSubsetOf0(xA,xA)
| ~ aSet0(xA) )
| aSubsetOf0(xA,xA)
| ~ aSet0(xA) ),
inference(tautology,[status(thm)],[]) ).
tff(8,plain,
~ ( aSubsetOf0(xA,xA)
| ~ aSet0(xA) ),
inference(unit_resolution,[status(thm)],[7,6,3]) ).
tff(9,plain,
( ~ ( aSubsetOf0(xA,xA)
| ~ aSet0(xA) )
| ~ ( aSet0(xA)
| ~ aSubsetOf0(xA,xA) )
| aSubsetOf0(xA,xA)
| ~ aSet0(xA) ),
inference(tautology,[status(thm)],[]) ).
tff(10,plain,
( ~ ( aSubsetOf0(xA,xA)
| ~ aSet0(xA) )
| ~ ( aSet0(xA)
| ~ aSubsetOf0(xA,xA) ) ),
inference(unit_resolution,[status(thm)],[9,8]) ).
tff(11,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(transitivity,[status(thm)],[16,14]) ).
tff(18,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ))),
( ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
rewrite(( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
tff(26,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[29,19]) ).
tff(31,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[30,17]) ).
tff(32,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[31,12]) ).
tff(33,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xA)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xA)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( ~ aSet0(xA)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xA)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) ) )
<=> ( ~ aSet0(xA)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xA)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xA)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xA)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xA)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xA)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xA)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xA)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xA)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xA)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) ),
inference(unit_resolution,[status(thm)],[38,32,6]) ).
tff(40,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xA)
| ~ aSet0(xA) )
| ~ ( aSet0(xA)
| ~ aSubsetOf0(xA,xA) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xA)
| ~ aSet0(xA) )
| ~ ( aSet0(xA)
| ~ aSubsetOf0(xA,xA) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ( ~ ( ~ aSet0(xA)
| aSubsetOf0(xA,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xA),xA)
| aElementOf0(tptp_fun_W2_1(xA,xA),xA) ) )
| ~ ( ~ aSubsetOf0(xA,xA)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xA) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(xA,xA)
| ~ aSet0(xA) )
| ~ ( aSet0(xA)
| ~ aSubsetOf0(xA,xA) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) )
| ~ ( ~ ( ~ aSet0(xA)
| aSubsetOf0(xA,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xA),xA)
| aElementOf0(tptp_fun_W2_1(xA,xA),xA) ) )
| ~ ( ~ aSubsetOf0(xA,xA)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xA) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xA)
| ~ aSet0(xA) )
| ~ ( aSet0(xA)
| ~ aSubsetOf0(xA,xA) ) ) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) )
| ~ ( ~ ( ~ aSet0(xA)
| aSubsetOf0(xA,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xA),xA)
| aElementOf0(tptp_fun_W2_1(xA,xA),xA) ) )
| ~ ( ~ aSubsetOf0(xA,xA)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xA) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xA)
| ~ aSet0(xA) )
| ~ ( aSet0(xA)
| ~ aSubsetOf0(xA,xA) ) ) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) )
| ~ ( ~ ( ~ aSet0(xA)
| aSubsetOf0(xA,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xA),xA)
| aElementOf0(tptp_fun_W2_1(xA,xA),xA) ) )
| ~ ( ~ aSubsetOf0(xA,xA)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xA) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xA),W1)
| aElementOf0(tptp_fun_W2_1(W1,xA),xA) ) )
| ~ ( ~ aSubsetOf0(W1,xA)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xA) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xA)
| ~ aSet0(xA) )
| ~ ( aSet0(xA)
| ~ aSubsetOf0(xA,xA) ) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
$false,
inference(unit_resolution,[status(thm)],[45,39,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM532+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 01:25:05 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.38 % SZS status Theorem
% 0.21/0.38 % SZS output start Proof
% See solution above
% 0.21/0.39 % E exiting
%------------------------------------------------------------------------------