%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM472+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:21:05 AM UTC 2025
% Result : Theorem 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 32 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 115 ( 43 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 162 ( 90 ~; 36 |; 17 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 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 : 10 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 15 !; 8 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(xm_type,type,
xm: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xl_type,type,
xl: $i ).
tff(1,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) )
<=> ~ ( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) ) )),
( ~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) )
<=> ~ ~ ( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) ) )),
( ~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [W0: $i] :
~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) )
<=> ~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
~ ( ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) )
| sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(7,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) ),
inference(or_elim,[status(thm)],[6]) ).
tff(8,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) ),
inference(modus_ponens,[status(thm)],[7,5]) ).
tff(9,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) ),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) ),
inference(modus_ponens,[status(thm)],[10,5]) ).
tff(12,plain,
^ [W0: $i] :
refl($oeq(~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) ),
~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) ))),
inference(bind,[status(th)],[]) ).
tff(13,plain,
! [W0: $i] :
~ ( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = sdtpldt0(xm,xn) ) ),
inference(nnf-neg,[status(sab)],[11,12]) ).
tff(14,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) ),
inference(modus_ponens,[status(thm)],[13,4]) ).
tff(15,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) ),
inference(modus_ponens,[status(thm)],[14,2]) ).
tff(16,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
tff(18,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[17]) ).
tff(19,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[18,16]) ).
tff(20,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( ~ aNaturalNumber0(xn)
| $false )
<=> ~ aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ( sdtpldt0(xm,xn) = sdtpldt0(xm,xn) )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn) )
<=> $false ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,plain,
( ( ~ aNaturalNumber0(xn)
| ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn) ) )
<=> ( ~ aNaturalNumber0(xn)
| $false ) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ( ~ aNaturalNumber0(xn)
| ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn) ) )
<=> ~ aNaturalNumber0(xn) ),
inference(transitivity,[status(thm)],[26,21]) ).
tff(28,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn)
| ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn)
| ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn) ) ),
inference(transitivity,[status(thm)],[28,20]) ).
tff(30,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn)
| ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( sdtpldt0(xm,W0) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM472+2 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 01:13:33 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.22/0.41 % SZS status Theorem
% 0.22/0.41 % SZS output start Proof
% See solution above
% 0.22/0.42 % E exiting
%------------------------------------------------------------------------------