%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM443+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 01:40:33 PM UTC 2026
% Result : Theorem 0.22s 1.07s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 84 ( 18 unt; 12 def)
% Number of atoms : 405 ( 53 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 471 ( 150 ~; 140 |; 149 &)
% ( 13 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 12 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 92 ( 72 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0,W1,W2] :
( ( W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
=> sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [W0,W1,W2,W3] :
( ( aInteger0(W3)
& W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( ( sdteqdtlpzmzozddtrp0(W1,W3,W2)
& sdteqdtlpzmzozddtrp0(W0,W1,W2) )
=> sdteqdtlpzmzozddtrp0(W0,W3,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
( aInteger0(xc)
& aInteger0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
( ( sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xc,smndt0(xb))
& aInteger0(W0) )
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0] :
( ( ( ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ? [W1] :
( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa))
& aInteger0(W1) ) )
& aInteger0(W0) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ? [W1] :
( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa))
& aInteger0(W1) )
& aInteger0(W0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( ( ! [W0] :
( ( ( ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ? [W1] :
( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa))
& aInteger0(W1) ) )
& aInteger0(W0) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ? [W1] :
( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa))
& aInteger0(W1) )
& aInteger0(W0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ ( ( sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xc,smndt0(xb))
& aInteger0(W0) )
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0] :
( ( ( ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ? [W1] :
( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa))
& aInteger0(W1) ) )
& aInteger0(W0) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ? [W1] :
( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa))
& aInteger0(W1) )
& aInteger0(W0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( ( ! [W0] :
( ( ( ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ? [W1] :
( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa))
& aInteger0(W1) ) )
& aInteger0(W0) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ? [W1] :
( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa))
& aInteger0(W1) )
& aInteger0(W0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f49,plain,
aInteger0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f50,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f51,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [W0,W1] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f53,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f84,plain,
! [W0] :
( ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) )
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f85,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(NNF_transformation,[status(thm)],[f84]) ).
fof(f86,plain,
! [W0] :
( ( ! [W1] :
( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ! [W1] :
( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(miniscoping,[status(thm)],[f85]) ).
fof(f87,plain,
! [W0] :
( ( ! [W1] :
( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ! [W1] :
( ( sdtasdt0(W1,sK0_skl(W1,W0)) = W0
& aInteger0(sK0_skl(W1,W0))
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W2,sK0_skl(W1,W0))],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( aInteger0(X1)
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f99,plain,
! [W0,W1,W2] :
( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f100,plain,
! [X0,X1,X2] :
( sdteqdtlpzmzozddtrp0(X1,X0,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| X2 = sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [W0,W1,W2,W3] :
( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W3)
| W2 = sz00
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f102,plain,
! [X0,X1,X2,X3] :
( sdteqdtlpzmzozddtrp0(X0,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X3)
| X2 = sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f216,plain,
aInteger0(xa),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f218,plain,
xq != sz00,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f219,plain,
aInteger0(xb),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f220,plain,
aInteger0(xc),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f221,plain,
( ~ aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1] :
( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa))
| ~ aInteger0(W1) ) )
| ~ aInteger0(W0) )
& ( ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ? [W1] :
( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa))
& aInteger0(W1) )
& aInteger0(W0) )
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xc,smndt0(xb))
& aInteger0(W0) )
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1] :
( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa))
| ~ aInteger0(W1) ) )
| ~ aInteger0(W0) )
& ( ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ? [W1] :
( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa))
& aInteger0(W1) )
& aInteger0(W0) )
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f222,plain,
( ~ aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0] :
( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1] :
( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa))
| ~ aInteger0(W1) ) )
| ~ aInteger0(W0) )
& ! [W0] :
( ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ? [W1] :
( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa))
& aInteger0(W1) )
& aInteger0(W0) )
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xc,smndt0(xb))
& aInteger0(W0) )
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0] :
( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1] :
( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa))
| ~ aInteger0(W1) ) )
| ~ aInteger0(W0) )
& ! [W0] :
( ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ? [W1] :
( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa))
& aInteger0(W1) )
& aInteger0(W0) )
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(miniscoping,[status(thm)],[f221]) ).
fof(f223,plain,
( ~ aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0] :
( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1] :
( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa))
| ~ aInteger0(W1) ) )
| ~ aInteger0(W0) )
& ! [W0] :
( ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdtasdt0(xq,sK17_skl(W0)) = sdtpldt0(W0,smndt0(xa))
& aInteger0(sK17_skl(W0))
& aInteger0(W0) )
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdtasdt0(xq,sK16_skl) = sdtpldt0(xc,smndt0(xb))
& aInteger0(sK16_skl)
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0] :
( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1] :
( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa))
| ~ aInteger0(W1) ) )
| ~ aInteger0(W0) )
& ! [W0] :
( ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdtasdt0(xq,sK15_skl(W0)) = sdtpldt0(W0,smndt0(xa))
& aInteger0(sK15_skl(W0))
& aInteger0(W0) )
| ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl,sK17_skl]),skolemize(W1,sK15_skl(W0)),skolemize(W0,sK16_skl),skolemize(W1,sK17_skl(W0))],[f222]) ).
fof(f229,plain,
! [X0] :
( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[status(thm)],[f223]) ).
fof(f232,plain,
! [X0] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(thm)],[f223]) ).
fof(f233,plain,
~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(cnf_transformation,[status(thm)],[f223]) ).
fof(f237,plain,
aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb))),
inference(cnf_transformation,[status(thm)],[f223]) ).
fof(f238,plain,
sdteqdtlpzmzozddtrp0(xc,xb,xq),
inference(cnf_transformation,[status(thm)],[f223]) ).
fof(f248,plain,
aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(cnf_transformation,[status(thm)],[f223]) ).
fof(f287,plain,
( aInteger0(xq)
| ~ aInteger0(sdtpldt0(xc,smndt0(xb))) ),
inference(resolution,[status(thm)],[f237,f88]) ).
fof(f288,definition,
( sQ0_spl
<=> aInteger0(sdtpldt0(xc,smndt0(xb))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( sQ0_spl
| ~ aInteger0(sdtpldt0(xc,smndt0(xb))) ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f291,definition,
( sQ1_spl
<=> aInteger0(xq) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f287,f288,f291]) ).
fof(f295,plain,
( sQ0_spl
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xc) ),
inference(resolution,[status(thm)],[f290,f53]) ).
fof(f296,definition,
( sQ2_spl
<=> aInteger0(xc) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( sQ2_spl
| ~ aInteger0(xc) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,definition,
( sQ3_spl
<=> aInteger0(smndt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( sQ3_spl
| ~ aInteger0(smndt0(xb)) ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f302,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f295,f296,f299,f288]) ).
fof(f303,plain,
( sQ3_spl
| ~ aInteger0(xb) ),
inference(resolution,[status(thm)],[f301,f51]) ).
fof(f304,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f219]) ).
fof(f305,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f304]) ).
fof(f306,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f220]) ).
fof(f307,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f306]) ).
fof(f313,definition,
( sQ5_spl
<=> aInteger0(xb) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( sQ5_spl
| ~ aInteger0(xb) ),
inference(component_clause,[status(thm)],[f313]) ).
fof(f392,definition,
( sQ20_spl
<=> aInteger0(sz10) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f394,plain,
( sQ20_spl
| ~ aInteger0(sz10) ),
inference(component_clause,[status(thm)],[f392]) ).
fof(f428,plain,
sdteqdtlpzmzozddtrp0(xc,xa,xq),
inference(resolution,[status(thm)],[f229,f248]) ).
fof(f494,definition,
( sQ35_spl
<=> aInteger0(xa) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( sQ35_spl
| ~ aInteger0(xa) ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,definition,
( sQ36_spl
<=> xq = sz00 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( ~ sQ36_spl
| xq = sz00 ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f501,plain,
( ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aInteger0(xb) ),
inference(resolution,[status(thm)],[f232,f233]) ).
fof(f509,definition,
( sQ37_spl
<=> sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f512,plain,
( ~ sQ37_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f501,f313,f509]) ).
fof(f517,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f498,f218]) ).
fof(f518,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f519,plain,
( sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f496,f216]) ).
fof(f520,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f539,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f315,f219]) ).
fof(f540,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f625,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f394,f49]) ).
fof(f626,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f625]) ).
fof(f637,plain,
( sdteqdtlpzmzozddtrp0(xb,xc,xq)
| xq = sz00
| ~ aInteger0(xq)
| ~ aInteger0(xb)
| ~ aInteger0(xc) ),
inference(resolution,[status(thm)],[f100,f238]) ).
fof(f643,definition,
( sQ60_spl
<=> sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f644,plain,
( ~ sQ60_spl
| sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
inference(component_clause,[status(thm)],[f643]) ).
fof(f646,plain,
( sQ60_spl
| sQ36_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f637,f296,f313,f291,f497,f643]) ).
fof(f648,plain,
! [X0] :
( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(X0,xc,xq)
| ~ aInteger0(xa)
| xq = sz00
| ~ aInteger0(xq)
| ~ aInteger0(xc)
| ~ aInteger0(X0) ),
inference(resolution,[status(thm)],[f102,f428]) ).
fof(f651,definition,
! [X0] :
( sQ61_spl
<=> ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(X0,xc,xq)
| ~ aInteger0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f652,plain,
! [X0] :
( ~ sQ61_spl
| sdteqdtlpzmzozddtrp0(X0,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(X0,xc,xq)
| ~ aInteger0(X0) ),
inference(component_clause,[status(thm)],[f651]) ).
fof(f654,plain,
( ~ sQ35_spl
| sQ36_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f648,f651,f296,f291,f497,f494]) ).
fof(f679,plain,
( ~ sQ60_spl
| ~ sQ61_spl
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aInteger0(xb) ),
inference(resolution,[status(thm)],[f652,f644]) ).
fof(f682,plain,
( ~ sQ60_spl
| ~ sQ61_spl
| sQ37_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f679,f313,f509,f651,f643]) ).
fof(f688,plain,
$false,
inference(sat_refutation,[status(thm)],[f294,f302,f305,f307,f512,f518,f520,f540,f626,f646,f654,f682]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM443+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/1.02 % Computer : n010.cluster.edu
% 0.18/1.02 % Model : x86_64 x86_64
% 0.18/1.02 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/1.02 % Memory : 8046.5625MB
% 0.18/1.02 % OS : Linux 6.8.0-71-generic
% 0.18/1.02 % CPULimit : 300
% 0.18/1.02 % WCLimit : 300
% 0.18/1.02 % DateTime : Mon Sep 21 02:30:25 UTC 2026
% 0.18/1.02 % CPUTime :
% 0.18/1.04 % Drodi V4.1.1
% 0.22/1.07 % Refutation found
% 0.22/1.07 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/1.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/1.10 % Elapsed time: 0.073249 seconds
% 0.22/1.10 % CPU time: 0.275967 seconds
% 0.22/1.10 % Total memory used: 79.042 MB
% 0.22/1.10 % Net memory used: 78.841 MB
%------------------------------------------------------------------------------