%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM561+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:21:24 AM UTC 2025
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 31 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 112 ( 43 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 160 ( 90 ~; 36 |; 15 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 15 !; 8 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xx_type,type,
xx: $i ).
tff(xF_type,type,
xF: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(1,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) )
<=> ~ ( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) )
<=> ~ ~ ( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) ) )),
rewrite(( ~ ~ ( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [W0: $i] :
~ ( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
~ ( ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) )
| aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(7,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) ),
inference(or_elim,[status(thm)],[6]) ).
tff(8,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) ),
inference(modus_ponens,[status(thm)],[7,5]) ).
tff(9,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) ),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
~ ? [W0: $i] :
( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) ),
inference(modus_ponens,[status(thm)],[10,5]) ).
tff(12,plain,
^ [W0: $i] :
refl($oeq(~ ( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) ),
~ ( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) ))),
inference(bind,[status(th)],[]) ).
tff(13,plain,
! [W0: $i] :
~ ( aElementOf0(W0,szDzozmdt0(xF))
& ( sdtlpdtrp0(xF,W0) = sdtlpdtrp0(xF,xx) ) ),
inference(nnf-neg,[status(sab)],[11,12]) ).
tff(14,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) ),
inference(modus_ponens,[status(thm)],[13,4]) ).
tff(15,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) ),
inference(modus_ponens,[status(thm)],[14,2]) ).
tff(16,plain,
( aElementOf0(xx,szDzozmdt0(xF))
<=> aElementOf0(xx,szDzozmdt0(xF)) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
aElementOf0(xx,szDzozmdt0(xF)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2911_02) ).
tff(18,plain,
aElementOf0(xx,szDzozmdt0(xF)),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) )
| ~ aElementOf0(xx,szDzozmdt0(xF)) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) )
| ~ aElementOf0(xx,szDzozmdt0(xF)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ( ~ aElementOf0(xx,szDzozmdt0(xF))
| $false )
<=> ~ aElementOf0(xx,szDzozmdt0(xF)) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( sdtlpdtrp0(xF,xx) = sdtlpdtrp0(xF,xx) )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ( sdtlpdtrp0(xF,xx) != sdtlpdtrp0(xF,xx) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ( sdtlpdtrp0(xF,xx) != sdtlpdtrp0(xF,xx) )
<=> $false ),
inference(transitivity,[status(thm)],[23,21]) ).
tff(25,plain,
( ( ~ aElementOf0(xx,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,xx) != sdtlpdtrp0(xF,xx) ) )
<=> ( ~ aElementOf0(xx,szDzozmdt0(xF))
| $false ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ aElementOf0(xx,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,xx) != sdtlpdtrp0(xF,xx) ) )
<=> ~ aElementOf0(xx,szDzozmdt0(xF)) ),
inference(transitivity,[status(thm)],[25,20]) ).
tff(27,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) )
| ~ aElementOf0(xx,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,xx) != sdtlpdtrp0(xF,xx) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) )
| ~ aElementOf0(xx,szDzozmdt0(xF)) ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) )
| ~ aElementOf0(xx,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,xx) != sdtlpdtrp0(xF,xx) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) )
| ~ aElementOf0(xx,szDzozmdt0(xF)) ) ),
inference(transitivity,[status(thm)],[27,19]) ).
tff(29,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) )
| ~ aElementOf0(xx,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,xx) != sdtlpdtrp0(xF,xx) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xF))
| ( sdtlpdtrp0(xF,W0) != sdtlpdtrp0(xF,xx) ) )
| ~ aElementOf0(xx,szDzozmdt0(xF)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
$false,
inference(unit_resolution,[status(thm)],[30,18,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM561+2 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n005.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 01:26:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% See solution above
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------