%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM549+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.22s 0.50s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 40
% Syntax : Number of formulae : 104 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 685 ( 187 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 1141 ( 598 ~; 389 |; 51 &)
% ( 84 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 38 ( 38 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 196 ( 171 !; 11 ?; 196 :)
% 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(slcrc0_type,type,
slcrc0: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(xS_type,type,
xS: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xk_type,type,
xk: $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xT_type,type,
xT: $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/sandbox2/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) ) ) )
| ~ ( ~ ( ~ aSet0(xQ)
| ( xQ = slcrc0 )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slcrc0 )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(xQ)
| ( xQ = slcrc0 )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slcrc0 )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) ) ) ) ),
inference(rewrite,[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) ) ) )
<=> ~ ( ~ ( ~ aSet0(xQ)
| ( xQ = slcrc0 )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slcrc0 )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,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) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(xQ)
| ( xQ = slcrc0 )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slcrc0 )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,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) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(xQ)
| ( xQ = slcrc0 )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slcrc0 )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) ) ) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,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(25,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ( W0 = slcrc0 )
| ~ aSet0(W0)
| aElementOf0(tptp_fun_W1_0(W0),W0) )
| ~ ( ( W0 != slcrc0 )
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] : ~ aElementOf0(W1,W0) ) ) )
| ~ ( ~ ( ~ aSet0(xQ)
| ( xQ = slcrc0 )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slcrc0 )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ ( ~ ( ~ aSet0(xQ)
| ( xQ = slcrc0 )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slcrc0 )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) ) ),
inference(unit_resolution,[status(thm)],[25,19]) ).
tff(27,plain,
( ~ ( ~ aSet0(xQ)
| ( xQ = slcrc0 )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ ( ( xQ != slcrc0 )
| ~ ( ~ aSet0(xQ)
| ~ ! [W1: $i] : ~ aElementOf0(W1,xQ) ) )
| ~ aSet0(xQ)
| ( xQ = slcrc0 )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(tautology,[status(thm)],[]) ).
tff(28,plain,
( ~ aSet0(xQ)
| ( xQ = slcrc0 )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( aSet0(xQ)
<=> aSet0(xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xQ,xS)
& ( sbrdtbr0(xQ) = xk )
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
tff(31,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xQ,xS)
& ( sbrdtbr0(xQ) = xk ) ),
inference(and_elim,[status(thm)],[30]) ).
tff(32,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xQ,xS) ),
inference(and_elim,[status(thm)],[31]) ).
tff(33,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) ) ),
inference(and_elim,[status(thm)],[32]) ).
tff(34,plain,
aSet0(xQ),
inference(and_elim,[status(thm)],[33]) ).
tff(35,plain,
aSet0(xQ),
inference(modus_ponens,[status(thm)],[34,29]) ).
tff(36,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
^ [W0: $i] :
rewrite(( ( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
tff(42,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(xQ)
| ( ( sbrdtbr0(xQ) = sz00 )
<=> ( xQ = slcrc0 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(xQ)
| ( ( sbrdtbr0(xQ) = sz00 )
<=> ( xQ = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(xQ)
| ( ( sbrdtbr0(xQ) = sz00 )
<=> ( xQ = slcrc0 ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
| ~ aSet0(xQ)
| ( ( sbrdtbr0(xQ) = sz00 )
<=> ( xQ = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( ( sbrdtbr0(xQ) = sz00 )
<=> ( xQ = slcrc0 ) ),
inference(unit_resolution,[status(thm)],[48,45,35]) ).
tff(50,plain,
( ( sbrdtbr0(xQ) = xk )
<=> ( sbrdtbr0(xQ) = xk ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
sbrdtbr0(xQ) = xk,
inference(and_elim,[status(thm)],[31]) ).
tff(52,plain,
sbrdtbr0(xQ) = xk,
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
( ( sbrdtbr0(xQ) = sz00 )
<=> ( xk = sz00 ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( xk = sz00 )
<=> ( sbrdtbr0(xQ) = sz00 ) ),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
( ( xk != sz00 )
<=> ( sbrdtbr0(xQ) != sz00 ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( xk != sz00 )
<=> ( xk != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
( aSet0(xS)
& aSet0(xT)
& ( xk != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
tff(58,plain,
xk != sz00,
inference(and_elim,[status(thm)],[57]) ).
tff(59,plain,
xk != sz00,
inference(modus_ponens,[status(thm)],[58,56]) ).
tff(60,plain,
sbrdtbr0(xQ) != sz00,
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ~ ( ( sbrdtbr0(xQ) = sz00 )
<=> ( xQ = slcrc0 ) )
| ( sbrdtbr0(xQ) = sz00 )
| ( xQ != slcrc0 ) ),
inference(tautology,[status(thm)],[]) ).
tff(62,plain,
xQ != slcrc0,
inference(unit_resolution,[status(thm)],[61,60,49]) ).
tff(63,plain,
( ~ ( ~ aSet0(xQ)
| ( xQ = slcrc0 )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ~ aSet0(xQ)
| ( xQ = slcrc0 )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(tautology,[status(thm)],[]) ).
tff(64,plain,
( ~ ( ~ aSet0(xQ)
| ( xQ = slcrc0 )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) )
| ( xQ = slcrc0 )
| aElementOf0(tptp_fun_W1_0(xQ),xQ) ),
inference(unit_resolution,[status(thm)],[63,35]) ).
tff(65,plain,
aElementOf0(tptp_fun_W1_0(xQ),xQ),
inference(unit_resolution,[status(thm)],[64,62,28]) ).
tff(66,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(67,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)],[66]) ).
tff(68,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(69,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)],[68]) ).
tff(70,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)],[69,67]) ).
tff(71,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(72,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(73,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)],[72]) ).
tff(74,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(75,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,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(80,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(81,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)],[80,79]) ).
tff(82,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xQ) ),
inference(unit_resolution,[status(thm)],[81,78,35]) ).
tff(83,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(84,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(85,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)],[84,83]) ).
tff(86,plain,
aElement0(tptp_fun_W1_0(xQ)),
inference(unit_resolution,[status(thm)],[85,82,65]) ).
tff(87,plain,
^ [W0: $i] :
refl(( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
<=> ( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,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(90,plain,
( ! [W0: $i] :
~ ( aElement0(W0)
& aElementOf0(W0,xQ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) )
<=> ~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,axiom,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(93,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[93,91]) ).
tff(95,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[94,91]) ).
tff(96,plain,
~ ? [W0: $i] :
( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
^ [W0: $i] :
refl($oeq(~ ( aElement0(W0)
& aElementOf0(W0,xQ) ),
~ ( aElement0(W0)
& aElementOf0(W0,xQ) ))),
inference(bind,[status(th)],[]) ).
tff(98,plain,
! [W0: $i] :
~ ( aElement0(W0)
& aElementOf0(W0,xQ) ),
inference(nnf-neg,[status(sab)],[96,97]) ).
tff(99,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[98,90]) ).
tff(100,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ aElementOf0(W0,xQ) ),
inference(modus_ponens,[status(thm)],[99,88]) ).
tff(101,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(102,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(103,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)],[102,101]) ).
tff(104,plain,
$false,
inference(unit_resolution,[status(thm)],[103,100,65,86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM549+3 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 01:26:31 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.50 % SZS status Theorem
% 0.22/0.50 % SZS output start Proof
% See solution above
% 0.22/0.51 % E exiting
%------------------------------------------------------------------------------