%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM441+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:40:32 PM UTC 2026
% Result : Theorem 1.23s 0.62s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 12 unt; 5 def)
% Number of atoms : 832 ( 53 equ)
% Maximal formula atoms : 74 ( 17 avg)
% Number of connectives : 1066 ( 281 ~; 236 |; 485 &)
% ( 37 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 11 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 6 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-2 aty)
% Number of variables : 208 ( 175 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f38,axiom,
! [W0,W1] :
( ( isOpen0(W1)
& isOpen0(W0)
& aSubsetOf0(W1,cS1395)
& aSubsetOf0(W0,cS1395) )
=> isOpen0(sdtslmnbsdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
=> ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xB))
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xB)) )
& ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
=> ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA))
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xA)) )
& ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [W0] :
( aElementOf0(W0,xB)
=> aElementOf0(W0,cS1395) )
& aSet0(xB)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [W0] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,cS1395) )
& aSet0(xA)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aElementOf0(W0,stldt0(xB))
& aElementOf0(W0,stldt0(xA))
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) )
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& aSet0(stldt0(xA)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,conjecture,
( ( ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
=> ( isClosed0(sdtbsmnsldt0(xA,xB))
| ( ( ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [W1] :
( ( ( ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sdtbsmnsldt0(xA,xB)))
| ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(sdtbsmnsldt0(xA,xB))) ) ) )
& W1 != sz00
& aInteger0(W1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
~ ( ( ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
=> ( isClosed0(sdtbsmnsldt0(xA,xB))
| ( ( ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [W1] :
( ( ( ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sdtbsmnsldt0(xA,xB)))
| ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(sdtbsmnsldt0(xA,xB))) ) ) )
& W1 != sz00
& aInteger0(W1) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f206,plain,
! [W0,W1] :
( isOpen0(sdtslmnbsdt0(W0,W1))
| ~ isOpen0(W1)
| ~ isOpen0(W0)
| ~ aSubsetOf0(W1,cS1395)
| ~ aSubsetOf0(W0,cS1395) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f207,plain,
! [X0,X1] :
( isOpen0(sdtslmnbsdt0(X0,X1))
| ~ isOpen0(X1)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[status(thm)],[f206]) ).
fof(f208,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [W0] :
( ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xB))
& ! [W2] :
( aElementOf0(W2,stldt0(xB))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [W0] :
( ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA))
& ! [W2] :
( aElementOf0(W2,stldt0(xA))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xB) )
& aSet0(xB)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xA) )
& aSet0(xA)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f209,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [W0] :
( ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xB))
& ! [W2] :
( aElementOf0(W2,stldt0(xB))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [W0] :
( ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA))
& ! [W2] :
( aElementOf0(W2,stldt0(xA))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xB) )
& aSet0(xB)
& ! [W0] :
( ( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) ) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xA) )
& aSet0(xA)
& ! [W0] :
( ( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) ) )
& aSet0(cS1395) ),
inference(NNF_transformation,[status(thm)],[f208]) ).
fof(f210,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [W0] :
( ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xB))
& ! [W2] :
( aElementOf0(W2,stldt0(xB))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ! [W2] :
( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [W0] :
( ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA))
& ! [W2] :
( aElementOf0(W2,stldt0(xA))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ! [W2] :
( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xB) )
& aSet0(xB)
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ! [W0] :
( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xA) )
& aSet0(xA)
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ! [W0] :
( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) )
& aSet0(cS1395) ),
inference(miniscoping,[status(thm)],[f209]) ).
fof(f211,plain,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [W0] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,sK16_skl(W0)),stldt0(xB))
& ! [W2] :
( aElementOf0(W2,stldt0(xB))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,sK16_skl(W0))) )
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,sK16_skl(W0)))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,sK16_skl(W0))
& ~ aDivisorOf0(sK16_skl(W0),sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(sK16_skl(W0),W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ! [W2] :
( ( sdteqdtlpzmzozddtrp0(W2,W0,sK16_skl(W0))
& aDivisorOf0(sK16_skl(W0),sdtpldt0(W2,smndt0(W0)))
& sdtasdt0(sK16_skl(W0),sK17_skl(W2,W0)) = sdtpldt0(W2,smndt0(W0))
& aInteger0(sK17_skl(W2,W0))
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,sK16_skl(W0))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,sK16_skl(W0)))
& sK16_skl(W0) != sz00
& aInteger0(sK16_skl(W0)) )
| ~ aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [W0] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,sK14_skl(W0)),stldt0(xA))
& ! [W2] :
( aElementOf0(W2,stldt0(xA))
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,sK14_skl(W0))) )
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,sK14_skl(W0)))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,sK14_skl(W0))
& ~ aDivisorOf0(sK14_skl(W0),sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(sK14_skl(W0),W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ! [W2] :
( ( sdteqdtlpzmzozddtrp0(W2,W0,sK14_skl(W0))
& aDivisorOf0(sK14_skl(W0),sdtpldt0(W2,smndt0(W0)))
& sdtasdt0(sK14_skl(W0),sK15_skl(W2,W0)) = sdtpldt0(W2,smndt0(W0))
& aInteger0(sK15_skl(W2,W0))
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,sK14_skl(W0))) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,sK14_skl(W0)))
& sK14_skl(W0) != sz00
& aInteger0(sK14_skl(W0)) )
| ~ aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xB) )
& aSet0(xB)
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ! [W0] :
( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,xA) )
& aSet0(xA)
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ! [W0] :
( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) )
& aSet0(cS1395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl,sK17_skl]),skolemize(W1,sK14_skl(W0)),skolemize(W3,sK15_skl(W2,W0)),skolemize(W1,sK16_skl(W0)),skolemize(W3,sK17_skl(W2,W0))],[f210]) ).
fof(f241,plain,
isOpen0(stldt0(xA)),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f260,plain,
isOpen0(stldt0(xB)),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f262,plain,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aElementOf0(W0,stldt0(xB))
& aElementOf0(W0,stldt0(xA))
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& aSet0(stldt0(xA)) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f263,plain,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [W0] :
( ( ~ aElementOf0(W0,stldt0(xB))
| ~ aElementOf0(W0,stldt0(xA))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ( aElementOf0(W0,stldt0(xB))
& aElementOf0(W0,stldt0(xA))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& ! [W0] :
( ( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) ) )
& ! [W0] :
( ( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) ) )
& ! [W0] :
( ( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( ( ( ~ aElementOf0(W0,xB)
& ~ aElementOf0(W0,xA) )
| ~ aInteger0(W0)
| aElementOf0(W0,sdtbsmnsldt0(xA,xB)) )
& ( ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) ) )
& aSet0(cS1395)
& ! [W0] :
( ( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) ) )
& aSet0(cS1395)
& ! [W0] :
( ( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) ) )
& aSet0(stldt0(xA)) ),
inference(NNF_transformation,[status(thm)],[f262]) ).
fof(f264,plain,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [W0] :
( ~ aElementOf0(W0,stldt0(xB))
| ~ aElementOf0(W0,stldt0(xA))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [W0] :
( ( aElementOf0(W0,stldt0(xB))
& aElementOf0(W0,stldt0(xA))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [W0] :
( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [W0] :
( ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& ~ aElementOf0(W0,xA) )
| ~ aInteger0(W0)
| aElementOf0(W0,sdtbsmnsldt0(xA,xB)) )
& ! [W0] :
( ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ! [W0] :
( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,xB)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xB)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xB)) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
| ~ aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ~ aInteger0(W0)
| aElementOf0(W0,cS1395) )
& ! [W0] :
( aInteger0(W0)
| ~ aElementOf0(W0,cS1395) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,xA)
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(xA)) )
& ! [W0] :
( ( ~ aElementOf0(W0,xA)
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(xA)) )
& aSet0(stldt0(xA)) ),
inference(miniscoping,[status(thm)],[f263]) ).
fof(f273,plain,
aSubsetOf0(stldt0(xA),cS1395),
inference(cnf_transformation,[status(thm)],[f264]) ).
fof(f282,plain,
aSubsetOf0(stldt0(xB),cS1395),
inference(cnf_transformation,[status(thm)],[f264]) ).
fof(f302,plain,
stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)),
inference(cnf_transformation,[status(thm)],[f264]) ).
fof(f303,plain,
( ~ isClosed0(sdtbsmnsldt0(xA,xB))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ? [W0] :
( ! [W1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sdtbsmnsldt0(xA,xB)))
& ? [W2] :
( ~ aElementOf0(W2,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
| W1 = sz00
| ~ aInteger0(W1) )
& aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f304,plain,
( ~ isClosed0(sdtbsmnsldt0(xA,xB))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ? [W0] :
( ! [W1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sdtbsmnsldt0(xA,xB)))
& ? [W2] :
( ~ aElementOf0(W2,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
| W1 = sz00
| ~ aInteger0(W1) )
& aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [W0] :
( ( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( ( ( ~ aElementOf0(W0,xB)
& ~ aElementOf0(W0,xA) )
| ~ aInteger0(W0)
| aElementOf0(W0,sdtbsmnsldt0(xA,xB)) )
& ( ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) ),
inference(NNF_transformation,[status(thm)],[f303]) ).
fof(f305,plain,
( ~ isClosed0(sdtbsmnsldt0(xA,xB))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ? [W0] :
( ! [W1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sdtbsmnsldt0(xA,xB)))
& ? [W2] :
( ~ aElementOf0(W2,stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,W0,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ! [W2] :
( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
| W1 = sz00
| ~ aInteger0(W1) )
& aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [W0] :
( ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& ~ aElementOf0(W0,xA) )
| ~ aInteger0(W0)
| aElementOf0(W0,sdtbsmnsldt0(xA,xB)) )
& ! [W0] :
( ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) )
& aSet0(sdtbsmnsldt0(xA,xB)) ),
inference(miniscoping,[status(thm)],[f304]) ).
fof(f306,plain,
( ~ isClosed0(sdtbsmnsldt0(xA,xB))
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK18_skl,W1),stldt0(sdtbsmnsldt0(xA,xB)))
& ~ aElementOf0(sK20_skl(W1),stldt0(sdtbsmnsldt0(xA,xB)))
& aElementOf0(sK20_skl(W1),szAzrzSzezqlpdtcmdtrp0(sK18_skl,W1))
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sK18_skl,W1))
| ( ~ sdteqdtlpzmzozddtrp0(W2,sK18_skl,W1)
& ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(sK18_skl)))
& ! [W3] :
( sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(sK18_skl))
| ~ aInteger0(W3) ) )
| ~ aInteger0(W2) )
& ! [W2] :
( ( sdteqdtlpzmzozddtrp0(W2,sK18_skl,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(sK18_skl)))
& sdtasdt0(W1,sK19_skl(W2,W1)) = sdtpldt0(W2,smndt0(sK18_skl))
& aInteger0(sK19_skl(W2,W1))
& aInteger0(W2) )
| ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sK18_skl,W1)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK18_skl,W1)) )
| W1 = sz00
| ~ aInteger0(W1) )
& aElementOf0(sK18_skl,stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
| ~ aInteger0(W0)
| aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& ! [W0] :
( ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) )
| ~ aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB))) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( ( ~ aElementOf0(W0,xB)
& ~ aElementOf0(W0,xA) )
| ~ aInteger0(W0)
| aElementOf0(W0,sdtbsmnsldt0(xA,xB)) )
& ! [W0] :
( ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) )
| ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) )
& aSet0(sdtbsmnsldt0(xA,xB)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl,sK19_skl,sK20_skl]),skolemize(W0,sK18_skl),skolemize(W3,sK19_skl(W2,W1)),skolemize(W2,sK20_skl(W1))],[f305]) ).
fof(f329,plain,
~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(cnf_transformation,[status(thm)],[f306]) ).
fof(f1019,definition,
( sQ64_spl
<=> isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1020,plain,
( ~ sQ64_spl
| isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ),
inference(component_clause,[status(thm)],[f1019]) ).
fof(f1341,definition,
( sQ98_spl
<=> aSubsetOf0(stldt0(xB),cS1395) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1343,plain,
( sQ98_spl
| ~ aSubsetOf0(stldt0(xB),cS1395) ),
inference(component_clause,[status(thm)],[f1341]) ).
fof(f1348,definition,
( sQ100_spl
<=> aSubsetOf0(stldt0(xA),cS1395) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1350,plain,
( sQ100_spl
| ~ aSubsetOf0(stldt0(xA),cS1395) ),
inference(component_clause,[status(thm)],[f1348]) ).
fof(f1355,plain,
( sQ100_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1350,f273]) ).
fof(f1356,plain,
sQ100_spl,
inference(contradiction_clause,[status(thm)],[f1355]) ).
fof(f1357,plain,
( sQ98_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1343,f282]) ).
fof(f1358,plain,
sQ98_spl,
inference(contradiction_clause,[status(thm)],[f1357]) ).
fof(f1732,definition,
( sQ152_spl
<=> isOpen0(stldt0(xA)) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1734,plain,
( sQ152_spl
| ~ isOpen0(stldt0(xA)) ),
inference(component_clause,[status(thm)],[f1732]) ).
fof(f2025,definition,
( sQ184_spl
<=> isOpen0(stldt0(xB)) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f2027,plain,
( sQ184_spl
| ~ isOpen0(stldt0(xB)) ),
inference(component_clause,[status(thm)],[f2025]) ).
fof(f2115,plain,
( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| ~ isOpen0(stldt0(xB))
| ~ isOpen0(stldt0(xA))
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ aSubsetOf0(stldt0(xA),cS1395) ),
inference(paramodulation,[status(thm)],[f302,f207]) ).
fof(f2118,plain,
( sQ64_spl
| ~ sQ184_spl
| ~ sQ152_spl
| ~ sQ98_spl
| ~ sQ100_spl ),
inference(split_clause,[status(thm)],[f2115,f1348,f1341,f1732,f2025,f1019]) ).
fof(f2124,plain,
( sQ152_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1734,f241]) ).
fof(f2125,plain,
sQ152_spl,
inference(contradiction_clause,[status(thm)],[f2124]) ).
fof(f2126,plain,
( sQ184_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2027,f260]) ).
fof(f2127,plain,
sQ184_spl,
inference(contradiction_clause,[status(thm)],[f2126]) ).
fof(f2128,plain,
( ~ sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1020,f329]) ).
fof(f2129,plain,
~ sQ64_spl,
inference(contradiction_clause,[status(thm)],[f2128]) ).
fof(f2130,plain,
$false,
inference(sat_refutation,[status(thm)],[f1356,f1358,f2118,f2125,f2127,f2129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM441+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:24:41 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 1.23/0.62 % Refutation found
% 1.23/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.23/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.23/0.65 % Elapsed time: 0.273493 seconds
% 1.23/0.65 % CPU time: 1.807173 seconds
% 1.23/0.65 % Total memory used: 134.141 MB
% 1.23/0.65 % Net memory used: 132.151 MB
%------------------------------------------------------------------------------