%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG126+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 02:39:15 PM UTC 2026
% Result : Theorem 85.18s 13.18s
% Output : CNFRefutation 85.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 70 ( 17 unt; 0 def)
% Number of atoms : 437 ( 131 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 535 ( 168 ~; 147 |; 183 &)
% ( 21 <=>; 16 =>; 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 : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 11 con; 0-2 aty)
% Number of variables : 196 ( 0 sgn 139 !; 57 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f34,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( doDivides0(X1,X0)
& aElement0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDvs) ).
fof(f39,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xb))
<=> ? [X1] :
( sdtasdt0(xb,X1) = X0
& aElement0(X1) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(f45,axiom,
( ! [X0] :
( ( X0 != sz00
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xu
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
fof(f46,axiom,
( aDivisorOf0(xu,xb)
& doDivides0(xu,xb)
& ? [X0] :
( sdtasdt0(xu,X0) = xb
& aElement0(X0) )
& aDivisorOf0(xu,xa)
& doDivides0(xu,xa)
& ? [X0] :
( sdtasdt0(xu,X0) = xa
& aElement0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2373) ).
fof(f47,axiom,
? [X0] :
( sdtasdt0(xu,X0) = xc
& aElement0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2744) ).
fof(f48,conjecture,
( ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
=> ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xb))
<=> ? [X1] :
( sdtasdt0(xb,X1) = X0
& aElement0(X1) ) )
=> ( aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [X0,X1] :
( sdtpldt0(X0,X1) = xc
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
=> ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xb))
<=> ? [X1] :
( sdtasdt0(xb,X1) = X0
& aElement0(X1) ) )
=> ( aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [X0,X1] :
( sdtpldt0(X0,X1) = xc
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f58,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X7] :
( aElementOf0(X7,xI)
<=> ? [X8,X9] :
( sdtpldt0(X8,X9) = X7
& aElementOf0(X9,slsdtgt0(xb))
& aElementOf0(X8,slsdtgt0(xa)) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xb))
<=> ? [X6] :
( sdtasdt0(xb,X6) = X5
& aElement0(X6) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xa))
<=> ? [X4] :
( sdtasdt0(xa,X4) = X3
& aElement0(X4) ) )
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
inference(rectify,[],[f42]) ).
fof(f61,plain,
( ! [X2] :
( ( sz00 != X2
& ( aElementOf0(X2,xI)
| ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xu
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(rectify,[],[f45]) ).
fof(f62,plain,
( aDivisorOf0(xu,xb)
& doDivides0(xu,xb)
& ? [X1] :
( xb = sdtasdt0(xu,X1)
& aElement0(X1) )
& aDivisorOf0(xu,xa)
& doDivides0(xu,xa)
& ? [X0] :
( sdtasdt0(xu,X0) = xa
& aElement0(X0) ) ),
inference(rectify,[],[f46]) ).
fof(f63,plain,
~ ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
=> ( ! [X2] :
( aElementOf0(X2,slsdtgt0(xb))
<=> ? [X3] :
( sdtasdt0(xb,X3) = X2
& aElement0(X3) ) )
=> ( aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [X4,X5] :
( sdtpldt0(X4,X5) = xc
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) ) ),
inference(rectify,[],[f49]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f76]) ).
fof(f107,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( doDivides0(X1,X0)
& aElement0(X1) ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f116,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X7] :
( aElementOf0(X7,xI)
<=> ? [X8,X9] :
( sdtpldt0(X8,X9) = X7
& aElementOf0(X9,slsdtgt0(xb))
& aElementOf0(X8,slsdtgt0(xa)) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xb))
<=> ? [X6] :
( sdtasdt0(xb,X6) = X5
& aElement0(X6) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xa))
<=> ? [X4] :
( sdtasdt0(xa,X4) = X3
& aElement0(X4) ) )
& aIdeal0(xI)
& ! [X0] :
( ~ aElementOf0(X0,xI)
| ( ! [X2] :
( ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X0),xI) )
& ! [X1] :
( ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
inference(ennf_transformation,[],[f58]) ).
fof(f117,plain,
( ! [X2] :
( sz00 = X2
| ( ~ aElementOf0(X2,xI)
& ! [X3,X4] :
( sdtpldt0(X3,X4) != X2
| ~ aElementOf0(X4,slsdtgt0(xb))
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xu
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(ennf_transformation,[],[f61]) ).
fof(f118,plain,
( ! [X2] :
( sz00 = X2
| ( ~ aElementOf0(X2,xI)
& ! [X3,X4] :
( sdtpldt0(X3,X4) != X2
| ~ aElementOf0(X4,slsdtgt0(xb))
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xu
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
( ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
& ! [X2] :
( aElementOf0(X2,slsdtgt0(xb))
<=> ? [X3] :
( sdtasdt0(xb,X3) = X2
& aElement0(X3) ) )
& ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X4,X5] :
( sdtpldt0(X4,X5) != xc
| ~ aElementOf0(X5,slsdtgt0(xb))
| ~ aElementOf0(X4,slsdtgt0(xa)) ) ),
inference(ennf_transformation,[],[f63]) ).
fof(f120,plain,
( ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
& ! [X2] :
( aElementOf0(X2,slsdtgt0(xb))
<=> ? [X3] :
( sdtasdt0(xb,X3) = X2
& aElement0(X3) ) )
& ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X4,X5] :
( sdtpldt0(X4,X5) != xc
| ~ aElementOf0(X5,slsdtgt0(xb))
| ~ aElementOf0(X4,slsdtgt0(xa)) ) ),
inference(flattening,[],[f119]) ).
fof(f149,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( doDivides0(X1,X0)
& aElement0(X1) ) )
& ( ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f107]) ).
fof(f150,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( doDivides0(X1,X0)
& aElement0(X1) ) )
& ( ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(flattening,[],[f149]) ).
fof(f166,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X7] :
( ( ~ aElementOf0(X7,xI)
| ? [X8,X9] :
( sdtpldt0(X8,X9) = X7
& aElementOf0(X9,slsdtgt0(xb))
& aElementOf0(X8,slsdtgt0(xa)) ) )
& ( ! [X8,X9] :
( sdtpldt0(X8,X9) != X7
| ~ aElementOf0(X9,slsdtgt0(xb))
| ~ aElementOf0(X8,slsdtgt0(xa)) )
| aElementOf0(X7,xI) ) )
& ! [X5] :
( ( ~ aElementOf0(X5,slsdtgt0(xb))
| ? [X6] :
( sdtasdt0(xb,X6) = X5
& aElement0(X6) ) )
& ( ! [X6] :
( sdtasdt0(xb,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,slsdtgt0(xb)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xa))
| ? [X4] :
( sdtasdt0(xa,X4) = X3
& aElement0(X4) ) )
& ( ! [X4] :
( sdtasdt0(xa,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X0] :
( ~ aElementOf0(X0,xI)
| ( ! [X2] :
( ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X0),xI) )
& ! [X1] :
( ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
inference(nnf_transformation,[],[f116]) ).
fof(f167,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X9] :
( ( ~ aElementOf0(X9,xI)
| ? [X12,X13] :
( sdtpldt0(X12,X13) = X9
& aElementOf0(X13,slsdtgt0(xb))
& aElementOf0(X12,slsdtgt0(xa)) ) )
& ( ! [X10,X11] :
( sdtpldt0(X10,X11) != X9
| ~ aElementOf0(X11,slsdtgt0(xb))
| ~ aElementOf0(X10,slsdtgt0(xa)) )
| aElementOf0(X9,xI) ) )
& ! [X6] :
( ( ~ aElementOf0(X6,slsdtgt0(xb))
| ? [X8] :
( sdtasdt0(xb,X8) = X6
& aElement0(X8) ) )
& ( ! [X7] :
( sdtasdt0(xb,X7) != X6
| ~ aElement0(X7) )
| aElementOf0(X6,slsdtgt0(xb)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xa))
| ? [X5] :
( sdtasdt0(xa,X5) = X3
& aElement0(X5) ) )
& ( ! [X4] :
( sdtasdt0(xa,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X0] :
( ~ aElementOf0(X0,xI)
| ( ! [X2] :
( ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X0),xI) )
& ! [X1] :
( ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
inference(rectify,[],[f166]) ).
fof(f168,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X9] :
( ( ~ aElementOf0(X9,xI)
| ( sdtpldt0(sK29(X9),sK30(X9)) = X9
& aElementOf0(sK30(X9),slsdtgt0(xb))
& aElementOf0(sK29(X9),slsdtgt0(xa)) ) )
& ( ! [X10,X11] :
( sdtpldt0(X10,X11) != X9
| ~ aElementOf0(X11,slsdtgt0(xb))
| ~ aElementOf0(X10,slsdtgt0(xa)) )
| aElementOf0(X9,xI) ) )
& ! [X6] :
( ( ~ aElementOf0(X6,slsdtgt0(xb))
| ( sdtasdt0(xb,sK28(X6)) = X6
& aElement0(sK28(X6)) ) )
& ( ! [X7] :
( sdtasdt0(xb,X7) != X6
| ~ aElement0(X7) )
| aElementOf0(X6,slsdtgt0(xb)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xa))
| ( sdtasdt0(xa,sK27(X3)) = X3
& aElement0(sK27(X3)) ) )
& ( ! [X4] :
( sdtasdt0(xa,X4) != X3
| ~ aElement0(X4) )
| aElementOf0(X3,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X0] :
( ~ aElementOf0(X0,xI)
| ( ! [X2] :
( ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X0),xI) )
& ! [X1] :
( ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27,sK28,sK29,sK30]),skolemize(X5,sK27(X3)),skolemize(X8,sK28(X6)),skolemize(X12,sK29(X9)),skolemize(X13,sK30(X9))],[f167]) ).
fof(f173,plain,
( ! [X2] :
( sz00 = X2
| ( ~ aElementOf0(X2,xI)
& ! [X3,X4] :
( sdtpldt0(X3,X4) != X2
| ~ aElementOf0(X4,slsdtgt0(xb))
| ~ aElementOf0(X3,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& xu = sdtpldt0(sK40,sK41)
& aElementOf0(sK41,slsdtgt0(xb))
& aElementOf0(sK40,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41]),skolemize(X0,sK40),skolemize(X1,sK41)],[f118]) ).
fof(f174,plain,
( aDivisorOf0(xu,xb)
& doDivides0(xu,xb)
& xb = sdtasdt0(xu,sK43)
& aElement0(sK43)
& aDivisorOf0(xu,xa)
& doDivides0(xu,xa)
& xa = sdtasdt0(xu,sK42)
& aElement0(sK42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42,sK43]),skolemize(X0,sK42),skolemize(X1,sK43)],[f62]) ).
fof(f175,plain,
( xc = sdtasdt0(xu,sK44)
& aElement0(sK44) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(X0,sK44)],[f47]) ).
fof(f176,plain,
( ! [X0] :
( ( ~ aElementOf0(X0,slsdtgt0(xa))
| ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
& ( ! [X1] :
( sdtasdt0(xa,X1) != X0
| ~ aElement0(X1) )
| aElementOf0(X0,slsdtgt0(xa)) ) )
& ! [X2] :
( ( ~ aElementOf0(X2,slsdtgt0(xb))
| ? [X3] :
( sdtasdt0(xb,X3) = X2
& aElement0(X3) ) )
& ( ! [X3] :
( sdtasdt0(xb,X3) != X2
| ~ aElement0(X3) )
| aElementOf0(X2,slsdtgt0(xb)) ) )
& ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X4,X5] :
( sdtpldt0(X4,X5) != xc
| ~ aElementOf0(X5,slsdtgt0(xb))
| ~ aElementOf0(X4,slsdtgt0(xa)) ) ),
inference(nnf_transformation,[],[f120]) ).
fof(f177,plain,
( ! [X5] :
( ( ~ aElementOf0(X5,slsdtgt0(xa))
| ? [X7] :
( sdtasdt0(xa,X7) = X5
& aElement0(X7) ) )
& ( ! [X6] :
( sdtasdt0(xa,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,slsdtgt0(xa)) ) )
& ! [X2] :
( ( ~ aElementOf0(X2,slsdtgt0(xb))
| ? [X4] :
( sdtasdt0(xb,X4) = X2
& aElement0(X4) ) )
& ( ! [X3] :
( sdtasdt0(xb,X3) != X2
| ~ aElement0(X3) )
| aElementOf0(X2,slsdtgt0(xb)) ) )
& ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X0,X1] :
( sdtpldt0(X0,X1) != xc
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(rectify,[],[f176]) ).
fof(f178,plain,
( ! [X5] :
( ( ~ aElementOf0(X5,slsdtgt0(xa))
| ( sdtasdt0(xa,sK46(X5)) = X5
& aElement0(sK46(X5)) ) )
& ( ! [X6] :
( sdtasdt0(xa,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,slsdtgt0(xa)) ) )
& ! [X2] :
( ( ~ aElementOf0(X2,slsdtgt0(xb))
| ( sdtasdt0(xb,sK45(X2)) = X2
& aElement0(sK45(X2)) ) )
& ( ! [X3] :
( sdtasdt0(xb,X3) != X2
| ~ aElement0(X3) )
| aElementOf0(X2,slsdtgt0(xb)) ) )
& ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X0,X1] :
( sdtpldt0(X0,X1) != xc
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45,sK46]),skolemize(X4,sK45(X2)),skolemize(X7,sK46(X5))],[f177]) ).
fof(f190,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f252,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aDivisorOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f150]) ).
fof(f271,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f293,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f168]) ).
fof(f305,plain,
! [X2,X0] :
( ~ aElementOf0(X0,xI)
| ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X0),xI) ),
inference(cnf_transformation,[],[f168]) ).
fof(f334,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f173]) ).
fof(f342,plain,
aDivisorOf0(xu,xa),
inference(cnf_transformation,[],[f174]) ).
fof(f346,plain,
xc = sdtasdt0(xu,sK44),
inference(cnf_transformation,[],[f175]) ).
fof(f347,plain,
aElement0(sK44),
inference(cnf_transformation,[],[f175]) ).
fof(f354,plain,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f178]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aElement0(X1)
| ~ aDivisorOf0(X0,X1) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_140,plain,
aElement0(xa),
inference(cnf_transformation,[],[f271]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X1,X0),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_177,plain,
sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
inference(cnf_transformation,[],[f293]) ).
tcf(c_204,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f334]) ).
tcf(c_211,plain,
aDivisorOf0(xu,xa),
inference(cnf_transformation,[],[f342]) ).
tcf(c_216,plain,
aElement0(sK44),
inference(cnf_transformation,[],[f347]) ).
tcf(c_217,plain,
sdtasdt0(xu,sK44) = xc,
inference(cnf_transformation,[],[f346]) ).
tcf(c_219,negated_conjecture,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f354]) ).
tcf(c_7684,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_7686,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_7691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,X2)
| ~ aElementOf0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_10181,plain,
! [X0: $i,X1: $i] :
( ( xc = X0 )
| ( xc != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_7686]) ).
tcf(c_10259,plain,
! [X0: $i] :
( aElement0(xu)
| ~ aElement0(X0)
| ~ aDivisorOf0(xu,X0) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_10262,plain,
( aElement0(xu)
| ~ aElement0(xa)
| ~ aDivisorOf0(xu,xa) ),
inference(instantiation,[status(thm)],[c_10259]) ).
tcf(c_11818,plain,
xc = xc,
inference(instantiation,[status(thm)],[c_7684]) ).
tcf(c_16113,plain,
! [X0: $i] :
( ( xc = X0 )
| ( xc != xc )
| ( X0 != xc ) ),
inference(instantiation,[status(thm)],[c_10181]) ).
tcf(c_20631,plain,
( ( xc = sdtasdt0(xu,sK44) )
| ( xc != xc )
| ( sdtasdt0(xu,sK44) != xc ) ),
inference(instantiation,[status(thm)],[c_16113]) ).
tcf(c_30527,plain,
! [X0: $i] :
( ( xc = X0 )
| ( xc != sdtasdt0(xu,sK44) )
| ( X0 != sdtasdt0(xu,sK44) ) ),
inference(instantiation,[status(thm)],[c_10181]) ).
tcf(c_42087,plain,
( ( xc = sdtasdt0(sK44,xu) )
| ( xc != sdtasdt0(xu,sK44) )
| ( sdtasdt0(sK44,xu) != sdtasdt0(xu,sK44) ) ),
inference(instantiation,[status(thm)],[c_30527]) ).
tcf(c_42088,plain,
( ( sdtasdt0(sK44,xu) = sdtasdt0(xu,sK44) )
| ~ aElement0(sK44)
| ~ aElement0(xu) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_56991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,X3)
| ~ aElementOf0(sdtasdt0(X1,X2),xI)
| ( X3 != xI )
| ( X0 != sdtasdt0(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_7691]) ).
tcf(c_57924,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ aElementOf0(sdtasdt0(X1,X2),xI)
| ( X0 != sdtasdt0(X1,X2) )
| ( sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) != xI ) ),
inference(instantiation,[status(thm)],[c_56991]) ).
tcf(c_88249,plain,
! [X0: $i,X1: $i] :
( aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ aElementOf0(sdtasdt0(X0,X1),xI)
| ( xc != sdtasdt0(X0,X1) )
| ( sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) != xI ) ),
inference(instantiation,[status(thm)],[c_57924]) ).
tcf(c_101048,plain,
( aElementOf0(sdtasdt0(sK44,xu),xI)
| ~ aElement0(sK44)
| ~ aElementOf0(xu,xI) ),
inference(instantiation,[status(thm)],[c_165]) ).
tcf(c_104039,plain,
( aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ aElementOf0(sdtasdt0(sK44,xu),xI)
| ( xc != sdtasdt0(sK44,xu) )
| ( sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) != xI ) ),
inference(instantiation,[status(thm)],[c_88249]) ).
tcf(c_104040,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_104039,c_101048,c_42088,c_42087,c_20631,c_11818,c_10262,c_177,c_219,c_217,c_204,c_211,c_140,c_216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG126+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Thu Sep 24 08:22:05 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.32
% 0.04/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.04/0.32
% 0.07/0.32 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 85.18/13.18 % SZS status Started for theBenchmark.p
% 85.18/13.18 % SZS status Theorem for theBenchmark.p
% 85.18/13.18
% 85.18/13.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 85.18/13.18
% 85.18/13.18 % ------ iProver source info
% 85.18/13.18
% 85.18/13.18 % git: date: 2026-07-19 20:42:38 +0200
% 85.18/13.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 85.18/13.18 % git: non_committed_changes: false
% 85.18/13.18
% 85.18/13.18 % ------ Parsing...
% 85.18/13.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 85.18/13.18
% 85.18/13.18 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 85.18/13.18
% 85.18/13.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 85.18/13.18
% 85.18/13.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 85.18/13.18 % ------ Proving...
% 85.18/13.18 % ------ Problem Properties
% 85.18/13.18
% 85.18/13.18 %
% 85.18/13.18 % clauses 167
% 85.18/13.18 % conjectures 7
% 85.18/13.18 % EPR 46
% 85.18/13.18 % Horn 140
% 85.18/13.18 % unary 51
% 85.18/13.18 % binary 36
% 85.18/13.18 % lits 454
% 85.18/13.19 % lits eq 73
% 85.18/13.19 % fd_pure 0
% 85.18/13.19 % fd_pseudo 0
% 85.18/13.19 % fd_cond 5
% 85.18/13.19 % fd_pseudo_cond 11
% 85.18/13.19 % AC symbols 0
% 85.18/13.19
% 85.18/13.19 % ------ Input Options Time Limit: Unbounded
% 85.18/13.19
% 85.18/13.19
% 85.18/13.19 % ------
% 85.18/13.19 % Current options:
% 85.18/13.19 % ------
% 85.18/13.19
% 85.18/13.19
% 85.18/13.19 %
% 85.18/13.19
% 85.18/13.19 % ------ Proving...
% 85.18/13.19 %
% 85.18/13.19
% 85.18/13.19 % SZS status Theorem for theBenchmark.p
% 85.18/13.19
% 85.18/13.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 85.18/13.19
% 85.18/13.19
%------------------------------------------------------------------------------