%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM551+1 : 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 05:21:22 AM UTC 2025
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of formulae : 73 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 483 ( 88 equ)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 790 ( 416 ~; 275 |; 42 &)
% ( 45 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 36 ( 36 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 152 ( 129 !; 11 ?; 152 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(tptp_fun_W1_0_type,type,
tptp_fun_W1_0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(xk_type,type,
xk: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(1,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
refl(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
<=> ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )),
rewrite(( ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
<=> ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )),
( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ( ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
rewrite(( ( ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(( ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) )
<=> ! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
tff(14,plain,
! [W0: $i] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1: $i] : aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W0: $i] :
( ( ( W0 != slcrc0 )
| ( aSet0(W0)
& ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
& ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
! [W0: $i] :
~ ( ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) )
| ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) ) ),
inference(modus_ponens,[status(thm)],[17,7]) ).
tff(19,plain,
! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[18,2]) ).
tff(20,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slcrc0 )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
~ ( ~ ( ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slcrc0 )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) ) ),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
( ~ ( ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slcrc0 )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) )
| ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(tautology,[status(thm)],[]) ).
tff(23,plain,
( ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
( ( xQ != slcrc0 )
<=> ( xQ != slcrc0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
xQ != slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2313) ).
tff(26,plain,
xQ != slcrc0,
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
( aSet0(xQ)
<=> aSet0(xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
( aSet0(xQ)
& isFinite0(xQ)
& ( sbrdtbr0(xQ) = xk ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
tff(29,plain,
( aSet0(xQ)
& isFinite0(xQ) ),
inference(and_elim,[status(thm)],[28]) ).
tff(30,plain,
aSet0(xQ),
inference(and_elim,[status(thm)],[29]) ).
tff(31,plain,
aSet0(xQ),
inference(modus_ponens,[status(thm)],[30,27]) ).
tff(32,plain,
( ~ ( ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(tautology,[status(thm)],[]) ).
tff(33,plain,
( ~ ( ( xQ = slcrc0 )
| ~ aSet0(xQ)
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(unit_resolution,[status(thm)],[32,31,26]) ).
tff(34,plain,
aElementOf0(tptp_fun_W1_0(xQ),xQ),
inference(unit_resolution,[status(thm)],[33,23]) ).
tff(35,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(36,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)],[35]) ).
tff(37,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(38,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)],[37]) ).
tff(39,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)],[38,36]) ).
tff(40,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(41,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(42,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)],[41]) ).
tff(43,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
tff(44,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xQ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) ),
inference(unit_resolution,[status(thm)],[50,47,31]) ).
tff(52,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) )
| aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) )
| aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) )
| aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) )
| aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
aElement0(tptp_fun_W1_0(xQ)),
inference(unit_resolution,[status(thm)],[54,51,34]) ).
tff(56,plain,
^ [W0: $i] :
refl(( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aElement0(W0)
& aElementOf0(W0,xQ) )
<=> ~ ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) )),
( ~ ( aElement0(W0)
& aElementOf0(W0,xQ) )
<=> ~ ~ ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) )),
rewrite(( ~ ~ ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) )),
( ~ ( aElement0(W0)
& aElementOf0(W0,xQ) )
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [W0: $i] :
~ ( aElement0(W0)
& aElementOf0(W0,xQ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) )
<=> ~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(62,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[62,60]) ).
tff(64,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[63,60]) ).
tff(65,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
^ [W0: $i] :
refl($oeq(~ ( aElement0(W0)
& aElementOf0(W0,xQ) ),
~ ( aElement0(W0)
& aElementOf0(W0,xQ) ))),
inference(bind,[status(th)],[]) ).
tff(67,plain,
! [W0: $i] :
~ ( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(nnf-neg,[status(sab)],[65,66]) ).
tff(68,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[67,59]) ).
tff(69,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[68,57]) ).
tff(70,plain,
( ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
| ~ aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) )
<=> ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
| ~ aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
| ~ aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
| ~ aElement0(tptp_fun_W1_0(xQ))
| ~ aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
$false,
inference(unit_resolution,[status(thm)],[72,69,34,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM551+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:24:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% See solution above
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------