%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM441+6 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:20:59 AM UTC 2025
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of formulae : 69 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 1163 ( 48 equ)
% Maximal formula atoms : 64 ( 16 avg)
% Number of connectives : 1323 ( 256 ~; 215 |; 612 &)
% ( 141 <=>; 99 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 10 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 27 ( 27 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 281 ( 233 !; 42 ?; 281 :)
% Comments :
%------------------------------------------------------------------------------
tff(isOpen0_type,type,
isOpen0: $i > $o ).
tff(sdtslmnbsdt0_type,type,
sdtslmnbsdt0: ( $i * $i ) > $i ).
tff(stldt0_type,type,
stldt0: $i > $i ).
tff(xB_type,type,
xB: $i ).
tff(xA_type,type,
xA: $i ).
tff(sdtbsmnsldt0_type,type,
sdtbsmnsldt0: ( $i * $i ) > $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(aInteger0_type,type,
aInteger0: $i > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(cS1395_type,type,
cS1395: $i ).
tff(szAzrzSzezqlpdtcmdtrp0_type,type,
szAzrzSzezqlpdtcmdtrp0: ( $i * $i ) > $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(aDivisorOf0_type,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(isClosed0_type,type,
isClosed0: $i > $o ).
tff(1,plain,
( ( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) )
<=> ( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0: $i] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& aElementOf0(W0,stldt0(xA))
& aElementOf0(W0,stldt0(xB)) ) )
& ( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
tff(3,plain,
stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtslmnbsdt0(stldt0(xA),stldt0(xB)) = stldt0(sdtbsmnsldt0(xA,xB)),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB)))
<=> isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
<=> isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB))) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
<=> ~ isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB))) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
<=> ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
( ~ ( ( aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0: $i] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) ) )
=> ( ( ( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) ) )
=> ( ! [W0: $i] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [W1: $i] :
( aInteger0(W1)
& ( W1 != sz00 )
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2: $i] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) ) )
=> ( ! [W2: $i] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(sdtbsmnsldt0(xA,xB))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sdtbsmnsldt0(xA,xB))) ) ) ) )
| isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ) )
| isClosed0(sdtbsmnsldt0(xA,xB)) ) )
<=> ~ ( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| isClosed0(sdtbsmnsldt0(xA,xB))
| ! [W0: $i] :
( ~ aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
| ? [W1: $i] :
( aInteger0(W1)
& ( W1 != sz00 )
& ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sdtbsmnsldt0(xA,xB)))
| ~ ( aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2: $i] :
( ( ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( aInteger0(W2)
& ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ~ ( aInteger0(W2)
& ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) ) ) )
| aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) ) )
| ! [W2: $i] :
( ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| aElementOf0(W2,stldt0(sdtbsmnsldt0(xA,xB))) ) ) ) )
| ~ ( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) ) )
| ~ ( aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0: $i] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
~ ( ( aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0: $i] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) ) )
=> ( ( ( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) ) )
=> ( ! [W0: $i] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [W1: $i] :
( aInteger0(W1)
& ( W1 != sz00 )
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2: $i] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) ) )
=> ( ! [W2: $i] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(sdtbsmnsldt0(xA,xB))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sdtbsmnsldt0(xA,xB))) ) ) ) )
| isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ) )
| isClosed0(sdtbsmnsldt0(xA,xB)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(12,plain,
~ ( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| isClosed0(sdtbsmnsldt0(xA,xB))
| ! [W0: $i] :
( ~ aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
| ? [W1: $i] :
( aInteger0(W1)
& ( W1 != sz00 )
& ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sdtbsmnsldt0(xA,xB)))
| ~ ( aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2: $i] :
( ( ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( aInteger0(W2)
& ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ~ ( aInteger0(W2)
& ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) ) ) )
| aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) ) )
| ! [W2: $i] :
( ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| aElementOf0(W2,stldt0(sdtbsmnsldt0(xA,xB))) ) ) ) )
| ~ ( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) ) )
| ~ ( aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0: $i] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(or_elim,[status(thm)],[12]) ).
tff(14,plain,
~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
~ isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB))),
inference(modus_ponens,[status(thm)],[14,8]) ).
tff(16,plain,
( aSubsetOf0(stldt0(xB),cS1395)
<=> aSubsetOf0(stldt0(xB),cS1395) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0: $i] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& aElementOf0(W0,stldt0(xA))
& aElementOf0(W0,stldt0(xB)) ) ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(18,plain,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0: $i] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) ) ),
inference(and_elim,[status(thm)],[17]) ).
tff(19,plain,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0: $i] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) ) ),
inference(and_elim,[status(thm)],[18]) ).
tff(20,plain,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0: $i] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) ) ),
inference(and_elim,[status(thm)],[19]) ).
tff(21,plain,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0: $i] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) ),
inference(and_elim,[status(thm)],[20]) ).
tff(22,plain,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0: $i] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) ) ),
inference(and_elim,[status(thm)],[21]) ).
tff(23,plain,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB)) ),
inference(and_elim,[status(thm)],[22]) ).
tff(24,plain,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395) ),
inference(and_elim,[status(thm)],[23]) ).
tff(25,plain,
aSubsetOf0(stldt0(xB),cS1395),
inference(and_elim,[status(thm)],[24]) ).
tff(26,plain,
aSubsetOf0(stldt0(xB),cS1395),
inference(modus_ponens,[status(thm)],[25,16]) ).
tff(27,plain,
( aSubsetOf0(stldt0(xA),cS1395)
<=> aSubsetOf0(stldt0(xA),cS1395) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) ) ),
inference(and_elim,[status(thm)],[24]) ).
tff(29,plain,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) ) ),
inference(and_elim,[status(thm)],[28]) ).
tff(30,plain,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& aSet0(cS1395) ),
inference(and_elim,[status(thm)],[29]) ).
tff(31,plain,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) ) ),
inference(and_elim,[status(thm)],[30]) ).
tff(32,plain,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB)) ),
inference(and_elim,[status(thm)],[31]) ).
tff(33,plain,
( aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395) ),
inference(and_elim,[status(thm)],[32]) ).
tff(34,plain,
aSubsetOf0(stldt0(xA),cS1395),
inference(and_elim,[status(thm)],[33]) ).
tff(35,plain,
aSubsetOf0(stldt0(xA),cS1395),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
( isOpen0(stldt0(xB))
<=> isOpen0(stldt0(xB)) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
( aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xA)
& ! [W0: $i] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xB)
& ! [W0: $i] :
( aElementOf0(W0,xB)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> ? [W1: $i] :
( aInteger0(W1)
& ( W1 != sz00 )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2: $i] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& ! [W2: $i] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA)) ) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
=> ? [W1: $i] :
( aInteger0(W1)
& ( W1 != sz00 )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2: $i] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& ! [W2: $i] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xB)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xB)) ) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1826) ).
tff(38,plain,
( aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xA)
& ! [W0: $i] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xB)
& ! [W0: $i] :
( aElementOf0(W0,xB)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> ? [W1: $i] :
( aInteger0(W1)
& ( W1 != sz00 )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2: $i] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& ! [W2: $i] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA)) ) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
=> ? [W1: $i] :
( aInteger0(W1)
& ( W1 != sz00 )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2: $i] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& ! [W2: $i] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xB)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xB)) ) )
& isOpen0(stldt0(xB)) ),
inference(and_elim,[status(thm)],[37]) ).
tff(39,plain,
isOpen0(stldt0(xB)),
inference(and_elim,[status(thm)],[38]) ).
tff(40,plain,
isOpen0(stldt0(xB)),
inference(modus_ponens,[status(thm)],[39,36]) ).
tff(41,plain,
( isOpen0(stldt0(xA))
<=> isOpen0(stldt0(xA)) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xA)
& ! [W0: $i] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xB)
& ! [W0: $i] :
( aElementOf0(W0,xB)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> ? [W1: $i] :
( aInteger0(W1)
& ( W1 != sz00 )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2: $i] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& ! [W2: $i] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA)) ) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
=> ? [W1: $i] :
( aInteger0(W1)
& ( W1 != sz00 )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2: $i] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& ! [W2: $i] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xB)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xB)) ) ) ),
inference(and_elim,[status(thm)],[38]) ).
tff(43,plain,
( aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xA)
& ! [W0: $i] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xB)
& ! [W0: $i] :
( aElementOf0(W0,xB)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> ? [W1: $i] :
( aInteger0(W1)
& ( W1 != sz00 )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2: $i] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& ! [W2: $i] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA)) ) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) ) ),
inference(and_elim,[status(thm)],[42]) ).
tff(44,plain,
( aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xA)
& ! [W0: $i] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xB)
& ! [W0: $i] :
( aElementOf0(W0,xB)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> ? [W1: $i] :
( aInteger0(W1)
& ( W1 != sz00 )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2: $i] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& ! [W2: $i] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA)) ) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB)) ),
inference(and_elim,[status(thm)],[43]) ).
tff(45,plain,
( aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xA)
& ! [W0: $i] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xB)
& ! [W0: $i] :
( aElementOf0(W0,xB)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> ? [W1: $i] :
( aInteger0(W1)
& ( W1 != sz00 )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2: $i] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& ! [W2: $i] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA)) ) )
& isOpen0(stldt0(xA))
& isClosed0(xA) ),
inference(and_elim,[status(thm)],[44]) ).
tff(46,plain,
( aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xA)
& ! [W0: $i] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [W0: $i] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xB)
& ! [W0: $i] :
( aElementOf0(W0,xB)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& ! [W0: $i] :
( aElementOf0(W0,stldt0(xA))
=> ? [W1: $i] :
( aInteger0(W1)
& ( W1 != sz00 )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2: $i] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3: $i] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& ! [W2: $i] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA)) ) )
& isOpen0(stldt0(xA)) ),
inference(and_elim,[status(thm)],[45]) ).
tff(47,plain,
isOpen0(stldt0(xA)),
inference(and_elim,[status(thm)],[46]) ).
tff(48,plain,
isOpen0(stldt0(xA)),
inference(modus_ponens,[status(thm)],[47,41]) ).
tff(49,plain,
^ [W0: $i,W1: $i] :
refl(( ( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) )
<=> ( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) )
<=> ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) )
<=> ~ ( ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) ) )),
( ~ ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) )
<=> ~ ~ ( ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) ) )),
rewrite(( ~ ~ ( ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) )
<=> ( ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) ) )),
( ~ ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) )
<=> ( ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) ) )),
( ( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) ) )
<=> ( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) ) )),
rewrite(( ( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) )
<=> ( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) ) )),
( ( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) ) )
<=> ( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0) )
<=> ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0) ) )),
( ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) )
<=> ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) ) )),
rewrite(( ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) )
<=> ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) ) )),
( ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) )
<=> ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) ) )),
( ( ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) )
=> isOpen0(sdtslmnbsdt0(W0,W1)) )
<=> ( ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) )
=> isOpen0(sdtslmnbsdt0(W0,W1)) ) )),
rewrite(( ( ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) )
=> isOpen0(sdtslmnbsdt0(W0,W1)) )
<=> ( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) ) ) )),
( ( ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) )
=> isOpen0(sdtslmnbsdt0(W0,W1)) )
<=> ( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [W0: $i,W1: $i] :
( ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) )
=> isOpen0(sdtslmnbsdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [W0: $i,W1: $i] :
( ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) )
=> isOpen0(sdtslmnbsdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mInterOpen) ).
tff(57,plain,
! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) ) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) ) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) ),
inference(modus_ponens,[status(thm)],[60,50]) ).
tff(62,plain,
( ( ~ ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) )
| ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ aSubsetOf0(stldt0(xB),cS1395)
| isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB)))
| ~ isOpen0(stldt0(xB))
| ~ isOpen0(stldt0(xA)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) )
| ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ aSubsetOf0(stldt0(xB),cS1395)
| isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB)))
| ~ isOpen0(stldt0(xB))
| ~ isOpen0(stldt0(xA)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB)))
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ isOpen0(stldt0(xB))
| ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ isOpen0(stldt0(xA)) )
<=> ( ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ aSubsetOf0(stldt0(xB),cS1395)
| isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB)))
| ~ isOpen0(stldt0(xB))
| ~ isOpen0(stldt0(xA)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( ~ ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) )
| isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB)))
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ isOpen0(stldt0(xB))
| ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ isOpen0(stldt0(xA)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) )
| ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ aSubsetOf0(stldt0(xB),cS1395)
| isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB)))
| ~ isOpen0(stldt0(xB))
| ~ isOpen0(stldt0(xA)) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) )
| isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB)))
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ isOpen0(stldt0(xB))
| ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ isOpen0(stldt0(xA)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) )
| ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ aSubsetOf0(stldt0(xB),cS1395)
| isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB)))
| ~ isOpen0(stldt0(xB))
| ~ isOpen0(stldt0(xA)) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) )
| isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB)))
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ isOpen0(stldt0(xB))
| ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ isOpen0(stldt0(xA)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [W0: $i,W1: $i] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ aSubsetOf0(W1,cS1395)
| ~ isOpen0(W1)
| ~ aSubsetOf0(W0,cS1395)
| ~ isOpen0(W0) )
| ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ aSubsetOf0(stldt0(xB),cS1395)
| isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB)))
| ~ isOpen0(stldt0(xB))
| ~ isOpen0(stldt0(xA)) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB))),
inference(unit_resolution,[status(thm)],[67,61,48,40,35,26]) ).
tff(69,plain,
$false,
inference(unit_resolution,[status(thm)],[68,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM441+6 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 01:08:09 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% See solution above
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------