%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM427+3 : 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 05:20:57 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 41 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 142 ( 41 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 176 ( 88 ~; 51 |; 17 &)
% ( 17 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 13 ( 13 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 26 !; 9 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(aInteger0_type,type,
aInteger0: $i > $o ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(xn_type,type,
xn: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xb_type,type,
xb: $i ).
tff(xa_type,type,
xa: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xq_type,type,
xq: $i ).
tff(aDivisorOf0_type,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(1,plain,
( aInteger0(xn)
<=> aInteger0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aInteger0(xn)
& ( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__747) ).
tff(3,plain,
aInteger0(xn),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aInteger0(xn),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
^ [W0: $i] :
refl(( ( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
<=> ( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
<=> ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
<=> ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
^ [W0: $i] :
rewrite(( ( aInteger0(W0)
=> aInteger0(smndt0(W0)) )
<=> ( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) )
<=> ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,axiom,
! [W0: $i] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
tff(11,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[13,6]) ).
tff(15,plain,
( ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xn))
| ~ aInteger0(xn) )
<=> ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xn))
| ~ aInteger0(xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xn))
| ~ aInteger0(xn) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xn))
| ~ aInteger0(xn) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
aInteger0(smndt0(xn)),
inference(unit_resolution,[status(thm)],[17,14,4]) ).
tff(19,plain,
^ [W0: $i] :
refl(( ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) )
<=> ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) )
<=> ~ ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) ) )),
( ~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) )
<=> ~ ~ ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) ) )),
rewrite(( ~ ~ ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) )
<=> ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) ) )),
( ~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) )
<=> ( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [W0: $i] :
~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) )
<=> ~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
~ ( ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) )
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(25,plain,
~ ( ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) )
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ),
inference(or_elim,[status(thm)],[24]) ).
tff(26,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) ),
inference(or_elim,[status(thm)],[25]) ).
tff(27,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[26,23]) ).
tff(28,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[28,23]) ).
tff(30,plain,
~ ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[29,23]) ).
tff(31,plain,
^ [W0: $i] :
refl($oeq(~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) ),
~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) ))),
inference(bind,[status(th)],[]) ).
tff(32,plain,
! [W0: $i] :
~ ( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ) ),
inference(nnf-neg,[status(sab)],[30,31]) ).
tff(33,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[32,22]) ).
tff(34,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[33,20]) ).
tff(35,plain,
( ( sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)) )
<=> ( sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__767) ).
tff(37,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) )
| ~ aInteger0(smndt0(xn))
| ( sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) )
| ~ aInteger0(smndt0(xn))
| ( sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) )
| ~ aInteger0(smndt0(xn))
| ( sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa)) ) )
| ~ aInteger0(smndt0(xn))
| ( sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,37,34,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM427+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:03:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% See solution above
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------