%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM432+3 : 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 05:20:58 AM UTC 2025
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 48 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 221 ( 42 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 280 ( 133 ~; 84 |; 34 &)
% ( 26 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 26 ( 26 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 65 ( 47 !; 9 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
tff(aInteger0_type,type,
aInteger0: $i > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xn_type,type,
xn: $i ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(xc_type,type,
xc: $i ).
tff(xb_type,type,
xb: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xq_type,type,
xq: $i ).
tff(xa_type,type,
xa: $i ).
tff(aDivisorOf0_type,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(1,plain,
( aInteger0(xm)
<=> aInteger0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aInteger0(xm)
& ( sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__899) ).
tff(3,plain,
aInteger0(xm),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aInteger0(xm),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( aInteger0(xn)
<=> aInteger0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
( aInteger0(xn)
& ( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__876) ).
tff(7,plain,
aInteger0(xn),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
aInteger0(xn),
inference(modus_ponens,[status(thm)],[7,5]) ).
tff(9,plain,
^ [W0: $i,W1: $i] :
refl(( ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aInteger0(W0)
& aInteger0(W1) )
<=> ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1) )
<=> ~ ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
rewrite(( ~ ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1) )
<=> ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
rewrite(( ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [W0: $i,W1: $i] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [W0: $i,W1: $i] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
tff(17,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[20,10]) ).
tff(22,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xn,xm))
| ~ aInteger0(xm)
| ~ aInteger0(xn) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xn,xm))
| ~ aInteger0(xm)
| ~ aInteger0(xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xn,xm))
| ~ aInteger0(xm)
| ~ aInteger0(xn) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xn,xm))
| ~ aInteger0(xm)
| ~ aInteger0(xn) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
aInteger0(sdtpldt0(xn,xm)),
inference(unit_resolution,[status(thm)],[24,21,8,4]) ).
tff(26,plain,
^ [W0: $i] :
refl(( ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) )
<=> ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) )
<=> ~ ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) ) )),
( ~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) )
<=> ~ ~ ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) ) )),
rewrite(( ~ ~ ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) )
<=> ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) ) )),
( ~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) )
<=> ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [W0: $i] :
~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) )
<=> ~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
~ ( ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| sdteqdtlpzmzozddtrp0(xa,xc,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(32,plain,
~ ( ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc))) ),
inference(or_elim,[status(thm)],[31]) ).
tff(33,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) ),
inference(or_elim,[status(thm)],[32]) ).
tff(34,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) ),
inference(modus_ponens,[status(thm)],[33,30]) ).
tff(35,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) ),
inference(modus_ponens,[status(thm)],[35,30]) ).
tff(37,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) ),
inference(modus_ponens,[status(thm)],[36,30]) ).
tff(38,plain,
^ [W0: $i] :
refl($oeq(~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) ),
~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) ))),
inference(bind,[status(th)],[]) ).
tff(39,plain,
! [W0: $i] :
~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc)) ) ),
inference(nnf-neg,[status(sab)],[37,38]) ).
tff(40,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) ),
inference(modus_ponens,[status(thm)],[39,29]) ).
tff(41,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) ),
inference(modus_ponens,[status(thm)],[40,27]) ).
tff(42,plain,
( ( sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)) )
<=> ( sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__924) ).
tff(44,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) )
| ~ aInteger0(sdtpldt0(xn,xm))
| ( sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) )
| ~ aInteger0(sdtpldt0(xn,xm))
| ( sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) )
| ~ aInteger0(sdtpldt0(xn,xm))
| ( sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xc)) ) )
| ~ aInteger0(sdtpldt0(xn,xm))
| ( sdtasdt0(xq,sdtpldt0(xn,xm)) != sdtpldt0(xa,smndt0(xc)) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,44,41,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM432+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 01:05:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% See solution above
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------