%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM443+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 : Fri Sep 25 02:24:29 PM UTC 2026
% Result : Theorem 1.38s 1.76s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 20 unt; 0 def)
% Number of atoms : 374 ( 52 equ)
% Maximal formula atoms : 34 ( 7 avg)
% Number of connectives : 467 ( 141 ~; 127 |; 177 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 64 !; 24 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X0,X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
=> sdteqdtlpzmzozddtrp0(X1,X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModSym) ).
fof(f22,axiom,
! [X0,X1,X2,X3] :
( ( aInteger0(X3)
& X2 != sz00
& aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( ( sdteqdtlpzmzozddtrp0(X1,X3,X2)
& sdteqdtlpzmzozddtrp0(X0,X1,X2) )
=> sdteqdtlpzmzozddtrp0(X0,X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModTrn) ).
fof(f41,axiom,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1962) ).
fof(f42,axiom,
( aInteger0(xc)
& aInteger0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2010) ).
fof(f43,conjecture,
( ( sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& ? [X0] :
( sdtasdt0(xq,X0) = sdtpldt0(xc,smndt0(xb))
& aInteger0(X0) )
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( ( ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) ) )
& aInteger0(X0) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( ( ! [X0] :
( ( ( ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) ) )
& aInteger0(X0) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f44,negated_conjecture,
~ ( ( sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& ? [X0] :
( sdtasdt0(xq,X0) = sdtpldt0(xc,smndt0(xb))
& aInteger0(X0) )
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( ( ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) ) )
& aInteger0(X0) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( ( ! [X0] :
( ( ( ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) ) )
& aInteger0(X0) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ ( ( sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& ? [X3] :
( sdtpldt0(xc,smndt0(xb)) = sdtasdt0(xq,X3)
& aInteger0(X3) )
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( ( ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| ? [X2] :
( sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,X2)
& aInteger0(X2) ) )
& aInteger0(X0) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( ( ! [X4] :
( ( ( ( sdteqdtlpzmzozddtrp0(X4,xa,xq)
| aDivisorOf0(xq,sdtpldt0(X4,smndt0(xa)))
| ? [X6] :
( sdtpldt0(X4,smndt0(xa)) = sdtasdt0(xq,X6)
& aInteger0(X6) ) )
& aInteger0(X4) )
=> aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( sdteqdtlpzmzozddtrp0(X4,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X4,smndt0(xa)))
& ? [X5] :
( sdtasdt0(xq,X5) = sdtpldt0(X4,smndt0(xa))
& aInteger0(X5) )
& aInteger0(X4) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
=> ( aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ),
inference(rectify,[],[f44]) ).
fof(f52,plain,
( sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& ? [X3] :
( sdtpldt0(xc,smndt0(xb)) = sdtasdt0(xq,X3)
& aInteger0(X3) )
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X4] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X4,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X4,smndt0(xa)))
& ! [X6] :
( sdtpldt0(X4,smndt0(xa)) != sdtasdt0(xq,X6)
| ~ aInteger0(X6) ) )
| ~ aInteger0(X4)
| aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X4,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X4,smndt0(xa)))
& ? [X5] :
( sdtasdt0(xq,X5) = sdtpldt0(X4,smndt0(xa))
& aInteger0(X5) )
& aInteger0(X4) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f53,plain,
( sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& ? [X3] :
( sdtpldt0(xc,smndt0(xb)) = sdtasdt0(xq,X3)
& aInteger0(X3) )
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X4] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X4,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X4,smndt0(xa)))
& ! [X6] :
( sdtpldt0(X4,smndt0(xa)) != sdtasdt0(xq,X6)
| ~ aInteger0(X6) ) )
| ~ aInteger0(X4)
| aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X4,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X4,smndt0(xa)))
& ? [X5] :
( sdtasdt0(xq,X5) = sdtpldt0(X4,smndt0(xa))
& aInteger0(X5) )
& aInteger0(X4) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(flattening,[],[f52]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( ~ aInteger0(X3)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X0,X3,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( ~ aInteger0(X3)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X0,X3,X2) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X1,X0,X2) ),
inference(ennf_transformation,[],[f21]) ).
fof(f68,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X1,X0,X2) ),
inference(flattening,[],[f67]) ).
fof(f107,plain,
( sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& ? [X6] :
( sdtpldt0(xc,smndt0(xb)) = sdtasdt0(xq,X6)
& aInteger0(X6) )
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X3] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X3,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& ! [X5] :
( sdtasdt0(xq,X5) != sdtpldt0(X3,smndt0(xa))
| ~ aInteger0(X5) ) )
| ~ aInteger0(X3)
| aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X3,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& ? [X4] :
( sdtasdt0(xq,X4) = sdtpldt0(X3,smndt0(xa))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ? [X1] :
( sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa))
& aInteger0(X1) )
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(rectify,[],[f53]) ).
fof(f108,plain,
( sdteqdtlpzmzozddtrp0(xc,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdtpldt0(xc,smndt0(xb)) = sdtasdt0(xq,sK6)
& aInteger0(sK6)
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X3] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X3,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& ! [X5] :
( sdtasdt0(xq,X5) != sdtpldt0(X3,smndt0(xa))
| ~ aInteger0(X5) ) )
| ~ aInteger0(X3)
| aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X3,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& sdtpldt0(X3,smndt0(xa)) = sdtasdt0(xq,sK5(X3))
& aInteger0(sK5(X3))
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( ( ~ sdteqdtlpzmzozddtrp0(X0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ! [X2] :
( sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2)
| ~ aInteger0(X2) ) )
| ~ aInteger0(X0)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( sdteqdtlpzmzozddtrp0(X0,xa,xq)
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,sK4(X0))
& aInteger0(sK4(X0))
& aInteger0(X0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X1,sK4(X0)),skolemize(X4,sK5(X3)),skolemize(X6,sK6)],[f107]) ).
fof(f144,plain,
sz00 != xq,
inference(cnf_transformation,[],[f41]) ).
fof(f145,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f41]) ).
fof(f146,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f41]) ).
fof(f147,plain,
aInteger0(xc),
inference(cnf_transformation,[],[f42]) ).
fof(f148,plain,
aInteger0(xb),
inference(cnf_transformation,[],[f42]) ).
fof(f149,plain,
sdteqdtlpzmzozddtrp0(xc,xb,xq),
inference(cnf_transformation,[],[f108]) ).
fof(f154,plain,
~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(cnf_transformation,[],[f108]) ).
fof(f155,plain,
! [X3] :
( ~ sdteqdtlpzmzozddtrp0(X3,xa,xq)
| ~ aInteger0(X3)
| aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f158,plain,
! [X3] :
( ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdteqdtlpzmzozddtrp0(X3,xa,xq) ),
inference(cnf_transformation,[],[f108]) ).
fof(f174,plain,
aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(cnf_transformation,[],[f108]) ).
fof(f193,plain,
! [X2,X3,X0,X1] :
( ~ aInteger0(X3)
| sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X0,X3,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f194,plain,
! [X2,X0,X1] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X1,X0,X2) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_49,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f146]) ).
tcf(c_50,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f145]) ).
tcf(c_51,plain,
xq != sz00,
inference(cnf_transformation,[],[f144]) ).
tcf(c_52,plain,
aInteger0(xb),
inference(cnf_transformation,[],[f148]) ).
tcf(c_53,plain,
aInteger0(xc),
inference(cnf_transformation,[],[f147]) ).
tcf(c_54,negated_conjecture,
aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(cnf_transformation,[],[f174]) ).
tcf(c_70,negated_conjecture,
! [X0: $i] :
( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_73,negated_conjecture,
! [X0: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,xa,xq) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_74,negated_conjecture,
~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(cnf_transformation,[],[f154]) ).
tcf(c_79,negated_conjecture,
sdteqdtlpzmzozddtrp0(xc,xb,xq),
inference(cnf_transformation,[],[f149]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdteqdtlpzmzozddtrp0(X0,X3,X2)
| ( X2 = sz00 )
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdteqdtlpzmzozddtrp0(X1,X0,X2)
| ( X2 = sz00 )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_8311,plain,
sdteqdtlpzmzozddtrp0(xc,xa,xq),
inference(superposition,[status(thm)],[c_54,c_70]) ).
tcf(c_8326,plain,
( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
inference(superposition,[status(thm)],[c_73,c_74]) ).
tcf(c_8327,plain,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(forward_subsumption_resolution,[status(thm)],[c_8326,c_52]) ).
tcf(c_9589,plain,
! [X0: $i,X1: $i] :
( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(X1,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,xq) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_10841,plain,
! [X0: $i] :
( sdteqdtlpzmzozddtrp0(X0,xa,xq)
| ( xq = sz00 )
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(X0)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(X0,xc,xq) ),
inference(instantiation,[status(thm)],[c_9589]) ).
tcf(c_16681,plain,
( sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ( xq = sz00 )
| ~ aInteger0(xc)
| ~ aInteger0(xb)
| ~ aInteger0(xq) ),
inference(superposition,[status(thm)],[c_79,c_99]) ).
tcf(c_16693,plain,
sdteqdtlpzmzozddtrp0(xb,xc,xq),
inference(forward_subsumption_resolution,[status(thm)],[c_16681,c_51,c_53,c_52,c_50]) ).
tcf(c_18146,plain,
( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ( xq = sz00 )
| ~ aInteger0(xc)
| ~ aInteger0(xb)
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
inference(instantiation,[status(thm)],[c_10841]) ).
tcf(c_18153,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_18146,c_16693,c_8327,c_8311,c_51,c_49,c_50,c_52,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM443+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 04:00:28 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 1.38/1.76 % SZS status Started for theBenchmark.p
% 1.38/1.76 % SZS status Theorem for theBenchmark.p
% 1.38/1.76
% 1.38/1.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.38/1.76
% 1.38/1.76 % ------ iProver source info
% 1.38/1.76
% 1.38/1.76 % git: date: 2026-07-19 20:42:38 +0200
% 1.38/1.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.38/1.76 % git: non_committed_changes: false
% 1.38/1.76
% 1.38/1.76 % ------ Parsing...
% 1.38/1.76 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.38/1.76
% 1.38/1.76 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.38/1.76
% 1.38/1.76 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.38/1.76
% 1.38/1.76 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.38/1.76 % ------ Proving...
% 1.38/1.76 % ------ Problem Properties
% 1.38/1.76
% 1.38/1.76 %
% 1.38/1.76 % clauses 110
% 1.38/1.76 % conjectures 18
% 1.38/1.76 % EPR 24
% 1.38/1.76 % Horn 79
% 1.38/1.76 % unary 16
% 1.38/1.76 % binary 23
% 1.38/1.76 % lits 367
% 1.38/1.76 % lits eq 52
% 1.38/1.76 % fd_pure 0
% 1.38/1.76 % fd_pseudo 0
% 1.38/1.76 % fd_cond 14
% 1.38/1.76 % fd_pseudo_cond 8
% 1.38/1.76 % AC symbols 0
% 1.38/1.76
% 1.38/1.76 % ------ Schedule dynamic 5 is on
% 1.38/1.76
% 1.38/1.76 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.38/1.76
% 1.38/1.76
% 1.38/1.76 % ------
% 1.38/1.76 % Current options:
% 1.38/1.76 % ------
% 1.38/1.76
% 1.38/1.76
% 1.38/1.76 %
% 1.38/1.76
% 1.38/1.76 % ------ Proving...
% 1.38/1.76 %
% 1.38/1.76
% 1.38/1.76 % SZS status Theorem for theBenchmark.p
% 1.38/1.76
% 1.38/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.38/1.77
% 1.38/1.77
%------------------------------------------------------------------------------