%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG126+1 : 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 : n016.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 02:39:14 PM UTC 2026
% Result : Theorem 5.38s 2.27s
% Output : CNFRefutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 109 ( 34 unt; 0 def)
% Number of atoms : 479 ( 70 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 605 ( 235 ~; 229 |; 113 &)
% ( 15 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 200 ( 0 sgn 172 !; 28 ?; 25 :)
% 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(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f33,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(f34,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( doDivides0(X1,X0)
& aElement0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDvs) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> ( ! [X3] :
( ( aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X0) )
=> doDivides0(X3,X2) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefGCD) ).
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f39,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(f41,axiom,
aGcdOfAnd0(xc,xa,xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2129) ).
fof(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(f45,axiom,
( ! [X0] :
( ( X0 != sz00
& aElementOf0(X0,xI) )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
fof(f46,axiom,
( aDivisorOf0(xu,xb)
& aDivisorOf0(xu,xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2373) ).
fof(f47,axiom,
doDivides0(xu,xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2744) ).
fof(f48,conjecture,
aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f50,plain,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(flattening,[],[f49]) ).
fof(f52,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f58,plain,
( ! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(ennf_transformation,[],[f45]) ).
fof(f59,plain,
( ! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(flattening,[],[f58]) ).
fof(f64,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> ( ! [X3] :
( ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0)
| doDivides0(X3,X2) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f65,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> ( ! [X3] :
( ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0)
| doDivides0(X3,X2) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) ) ),
inference(flattening,[],[f64]) ).
fof(f69,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( ~ aElementOf0(X1,X0)
| ( ! [X3] :
( ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f72,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f75,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( doDivides0(X1,X0)
& aElement0(X1) ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) ) ) ),
inference(flattening,[],[f76]) ).
fof(f82,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f83,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f82]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ( ~ aGcdOfAnd0(X2,X0,X1)
| ( ! [X3] :
( ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0)
| doDivides0(X3,X2) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) )
& ( ? [X3] :
( aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X0)
& ~ doDivides0(X3,X2) )
| ~ aDivisorOf0(X2,X1)
| ~ aDivisorOf0(X2,X0)
| aGcdOfAnd0(X2,X0,X1) ) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f100,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ( ~ aGcdOfAnd0(X2,X0,X1)
| ( ! [X3] :
( ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0)
| doDivides0(X3,X2) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) )
& ( ? [X3] :
( aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X0)
& ~ doDivides0(X3,X2) )
| ~ aDivisorOf0(X2,X1)
| ~ aDivisorOf0(X2,X0)
| aGcdOfAnd0(X2,X0,X1) ) ) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ( ~ aGcdOfAnd0(X2,X0,X1)
| ( ! [X4] :
( ~ aDivisorOf0(X4,X1)
| ~ aDivisorOf0(X4,X0)
| doDivides0(X4,X2) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) )
& ( ? [X3] :
( aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X0)
& ~ doDivides0(X3,X2) )
| ~ aDivisorOf0(X2,X1)
| ~ aDivisorOf0(X2,X0)
| aGcdOfAnd0(X2,X0,X1) ) ) ),
inference(rectify,[],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ( ~ aGcdOfAnd0(X2,X0,X1)
| ( ! [X4] :
( ~ aDivisorOf0(X4,X1)
| ~ aDivisorOf0(X4,X0)
| doDivides0(X4,X2) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) )
& ( ( aDivisorOf0(sK3(X0,X1,X2),X1)
& aDivisorOf0(sK3(X0,X1,X2),X0)
& ~ doDivides0(sK3(X0,X1,X2),X2) )
| ~ aDivisorOf0(X2,X1)
| ~ aDivisorOf0(X2,X0)
| aGcdOfAnd0(X2,X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f101]) ).
fof(f103,plain,
! [X0] :
( ( ~ aIdeal0(X0)
| ( ! [X1] :
( ~ aElementOf0(X1,X0)
| ( ! [X3] :
( ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ( ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) )
| ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f104,plain,
! [X0] :
( ( ~ aIdeal0(X0)
| ( ! [X1] :
( ~ aElementOf0(X1,X0)
| ( ! [X3] :
( ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ( ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) )
| ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
! [X0] :
( ( ~ aIdeal0(X0)
| ( ! [X4] :
( ~ aElementOf0(X4,X0)
| ( ! [X6] :
( ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),X0) )
& ! [X5] :
( ~ aElementOf0(X5,X0)
| aElementOf0(sdtpldt0(X4,X5),X0) ) ) )
& aSet0(X0) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ( ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) )
| ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X0] :
( ( ~ aIdeal0(X0)
| ( ! [X4] :
( ~ aElementOf0(X4,X0)
| ( ! [X6] :
( ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),X0) )
& ! [X5] :
( ~ aElementOf0(X5,X0)
| aElementOf0(sdtpldt0(X4,X5),X0) ) ) )
& aSet0(X0) ) )
& ( ( aElementOf0(sK4(X0),X0)
& ( ( aElement0(sK6(X0))
& ~ aElementOf0(sdtasdt0(sK6(X0),sK4(X0)),X0) )
| ( aElementOf0(sK5(X0),X0)
& ~ aElementOf0(sdtpldt0(sK4(X0),sK5(X0)),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X1,sK4(X0)),skolemize(X2,sK5(X0)),skolemize(X3,sK6(X0))],[f105]) ).
fof(f113,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& ( ~ aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f114,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& ( ~ aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X5] :
( ( ~ aElementOf0(X5,X1)
| ? [X7] :
( sdtasdt0(X0,X7) = X5
& aElement0(X7) ) )
& ( ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ? [X4] :
( sdtasdt0(X0,X4) = X2
& aElement0(X4) ) )
& ( ~ aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(rectify,[],[f114]) ).
fof(f116,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X5] :
( ( ~ aElementOf0(X5,X1)
| ( sdtasdt0(X0,sK14(X0,X5)) = X5
& aElement0(sK14(X0,X5)) ) )
& ( ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,X1) ) )
& aSet0(X1) ) )
& ( ( ( aElementOf0(sK12(X0,X1),X1)
| ( sK12(X0,X1) = sdtasdt0(X0,sK13(X0,X1))
& aElement0(sK13(X0,X1)) ) )
& ( ~ aElementOf0(sK12(X0,X1),X1)
| ! [X3] :
( sdtasdt0(X0,X3) != sK12(X0,X1)
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X2,sK12(X0,X1)),skolemize(X4,sK13(X0,X1)),skolemize(X7,sK14(X0,X5))],[f115]) ).
fof(f118,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( doDivides0(X1,X0)
& aElement0(X1) ) )
& ( ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f119,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( doDivides0(X1,X0)
& aElement0(X1) ) )
& ( ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(flattening,[],[f118]) ).
fof(f120,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ( ( ~ doDivides0(X0,X1)
| ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aElement0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f77]) ).
fof(f121,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ( ( ~ doDivides0(X0,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X1
& aElement0(X3) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aElement0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(rectify,[],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ( ( ~ doDivides0(X0,X1)
| ( sdtasdt0(X0,sK17(X0,X1)) = X1
& aElement0(sK17(X0,X1)) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aElement0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X3,sK17(X0,X1))],[f121]) ).
fof(f124,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f125,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f127,plain,
aGcdOfAnd0(xc,xa,xb),
inference(cnf_transformation,[],[f41]) ).
fof(f128,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f42]) ).
fof(f129,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f42]) ).
fof(f138,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f59]) ).
fof(f139,plain,
aDivisorOf0(xu,xb),
inference(cnf_transformation,[],[f46]) ).
fof(f141,plain,
doDivides0(xu,xc),
inference(cnf_transformation,[],[f47]) ).
fof(f142,plain,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f50]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aGcdOfAnd0(X2,X0,X1)
| aDivisorOf0(X2,X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f157,plain,
! [X0,X6,X4] :
( ~ aIdeal0(X0)
| ~ aElementOf0(X4,X0)
| ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f177,plain,
! [X0,X1,X5] :
( ~ aElement0(X0)
| slsdtgt0(X0) != X1
| ~ aElementOf0(X5,X1)
| sdtasdt0(X0,sK14(X0,X5)) = X5 ),
inference(cnf_transformation,[],[f116]) ).
fof(f178,plain,
! [X0,X1,X5] :
( ~ aElement0(X0)
| slsdtgt0(X0) != X1
| ~ aElementOf0(X5,X1)
| aElement0(sK14(X0,X5)) ),
inference(cnf_transformation,[],[f116]) ).
fof(f179,plain,
! [X0,X1,X6,X5] :
( ~ aElement0(X0)
| slsdtgt0(X0) != X1
| sdtasdt0(X0,X6) != X5
| ~ aElement0(X6)
| aElementOf0(X5,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f189,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aDivisorOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f191,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ~ doDivides0(X0,X1)
| sdtasdt0(X0,sK17(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f122]) ).
fof(f192,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ~ doDivides0(X0,X1)
| aElement0(sK17(X0,X1)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f197,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f210,plain,
! [X0,X1,X6] :
( ~ aElement0(X0)
| slsdtgt0(X0) != X1
| ~ aElement0(X6)
| aElementOf0(sdtasdt0(X0,X6),X1) ),
inference(equality_resolution,[],[f179]) ).
fof(f211,plain,
! [X0,X6] :
( ~ aElement0(X0)
| ~ aElement0(X6)
| aElementOf0(sdtasdt0(X0,X6),slsdtgt0(X0)) ),
inference(equality_resolution,[],[f210]) ).
fof(f212,plain,
! [X0,X5] :
( ~ aElement0(X0)
| ~ aElementOf0(X5,slsdtgt0(X0))
| aElement0(sK14(X0,X5)) ),
inference(equality_resolution,[],[f178]) ).
fof(f213,plain,
! [X0,X5] :
( ~ aElement0(X0)
| ~ aElementOf0(X5,slsdtgt0(X0))
| sdtasdt0(X0,sK14(X0,X5)) = X5 ),
inference(equality_resolution,[],[f177]) ).
tcf(c_49,plain,
aElement0(xa),
inference(cnf_transformation,[],[f125]) ).
tcf(c_50,plain,
aElement0(xb),
inference(cnf_transformation,[],[f124]) ).
tcf(c_52,plain,
aGcdOfAnd0(xc,xa,xb),
inference(cnf_transformation,[],[f127]) ).
tcf(c_53,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f129]) ).
tcf(c_54,plain,
sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
inference(cnf_transformation,[],[f128]) ).
tcf(c_61,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f138]) ).
tcf(c_65,plain,
aDivisorOf0(xu,xb),
inference(cnf_transformation,[],[f139]) ).
tcf(c_66,plain,
doDivides0(xu,xc),
inference(cnf_transformation,[],[f141]) ).
tcf(c_67,negated_conjecture,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f142]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( aDivisorOf0(X0,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aGcdOfAnd0(X0,X1,X2) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtasdt0(X2,X0),X1)
| ~ aIdeal0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X0,X1),slsdtgt0(X0))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( aElement0(sK14(X1,X0))
| ~ aElement0(X1)
| ~ aElementOf0(X0,slsdtgt0(X1)) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X1,sK14(X1,X0)) = X0 )
| ~ aElement0(X1)
| ~ aElementOf0(X0,slsdtgt0(X1)) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aElement0(X1)
| ~ aDivisorOf0(X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( aElement0(sK17(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,sK17(X0,X1)) = X1 )
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_724,plain,
~ aElementOf0(xc,xI),
inference(demodulation,[status(thm)],[c_67,c_54]) ).
tcf(c_1487,plain,
! [X0: $i,X1: $i] :
( aElement0(sK17(X1,X0))
| ~ aElement0(X1)
| ~ aElement0(X0)
| ( X1 != xu )
| ( X0 != xc ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_117]) ).
tcf(c_1488,plain,
( aElement0(sK17(xu,xc))
| ~ aElement0(xu)
| ~ aElement0(xc) ),
inference(unflattening,[status(thm)],[c_1487]) ).
tcf(c_5881,plain,
( aElement0(xu)
| ~ aElement0(xb) ),
inference(superposition,[status(thm)],[c_65,c_114]) ).
tcf(c_5882,plain,
aElement0(xu),
inference(forward_subsumption_resolution,[status(thm)],[c_5881,c_50]) ).
tcf(c_6196,plain,
( aDivisorOf0(xc,xa)
| ~ aElement0(xb)
| ~ aElement0(xa) ),
inference(superposition,[status(thm)],[c_52,c_77]) ).
tcf(c_6197,plain,
aDivisorOf0(xc,xa),
inference(forward_subsumption_resolution,[status(thm)],[c_6196,c_50,c_49]) ).
tcf(c_6219,plain,
( aElement0(xc)
| ~ aElement0(xa) ),
inference(superposition,[status(thm)],[c_6197,c_114]) ).
tcf(c_6220,plain,
aElement0(xc),
inference(forward_subsumption_resolution,[status(thm)],[c_6219,c_49]) ).
tcf(c_6370,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xu) = sdtasdt0(xu,X0) )
| ~ aElement0(X0) ),
inference(superposition,[status(thm)],[c_5882,c_122]) ).
tcf(c_7086,plain,
( ( sdtasdt0(xu,sK17(xu,xc)) = xc )
| ~ aElement0(xu)
| ~ aElement0(xc) ),
inference(superposition,[status(thm)],[c_66,c_118]) ).
tcf(c_7113,plain,
sdtasdt0(xu,sK17(xu,xc)) = xc,
inference(forward_subsumption_resolution,[status(thm)],[c_7086,c_5882,c_6220]) ).
tcf(c_8705,plain,
( aElementOf0(xc,slsdtgt0(xu))
| ~ aElement0(xu)
| ~ aElement0(sK17(xu,xc)) ),
inference(superposition,[status(thm)],[c_7113,c_106]) ).
tcf(c_8709,plain,
( aElementOf0(xc,slsdtgt0(xu))
| ~ aElement0(sK17(xu,xc)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8705,c_5882]) ).
tcf(c_10340,plain,
aElementOf0(xc,slsdtgt0(xu)),
inference(global_subsumption_just,[status(thm)],[c_8709,c_1488,c_5882,c_6220,c_8709]) ).
tcf(c_10343,plain,
( ( sdtasdt0(xu,sK14(xu,xc)) = xc )
| ~ aElement0(xu) ),
inference(superposition,[status(thm)],[c_10340,c_108]) ).
tcf(c_10344,plain,
( aElement0(sK14(xu,xc))
| ~ aElement0(xu) ),
inference(superposition,[status(thm)],[c_10340,c_107]) ).
tcf(c_10345,plain,
aElement0(sK14(xu,xc)),
inference(forward_subsumption_resolution,[status(thm)],[c_10344,c_5882]) ).
tcf(c_10346,plain,
sdtasdt0(xu,sK14(xu,xc)) = xc,
inference(forward_subsumption_resolution,[status(thm)],[c_10343,c_5882]) ).
tcf(c_18967,plain,
sdtasdt0(sK14(xu,xc),xu) = sdtasdt0(xu,sK14(xu,xc)),
inference(superposition,[status(thm)],[c_10345,c_6370]) ).
tcf(c_19019,plain,
sdtasdt0(sK14(xu,xc),xu) = xc,
inference(light_normalisation,[status(thm)],[c_18967,c_10346]) ).
tcf(c_20643,plain,
! [X0: $i] :
( aElementOf0(xc,X0)
| ~ aIdeal0(X0)
| ~ aElementOf0(xu,X0)
| ~ aElement0(sK14(xu,xc)) ),
inference(superposition,[status(thm)],[c_19019,c_89]) ).
tcf(c_20646,plain,
! [X0: $i] :
( aElementOf0(xc,X0)
| ~ aIdeal0(X0)
| ~ aElementOf0(xu,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20643,c_10345]) ).
tcf(c_22291,plain,
( aElementOf0(xc,xI)
| ~ aIdeal0(xI) ),
inference(superposition,[status(thm)],[c_61,c_20646]) ).
tcf(c_22292,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_22291,c_724,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG126+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n016.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 : Thu Sep 24 08:27:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 5.38/2.27 % SZS status Started for theBenchmark.p
% 5.38/2.27 % SZS status Theorem for theBenchmark.p
% 5.38/2.27
% 5.38/2.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.38/2.27
% 5.38/2.27 % ------ iProver source info
% 5.38/2.27
% 5.38/2.27 % git: date: 2026-07-19 20:42:38 +0200
% 5.38/2.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.38/2.27 % git: non_committed_changes: false
% 5.38/2.27
% 5.38/2.27 % ------ Parsing...
% 5.38/2.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.38/2.27
% 5.38/2.27 % ------ Preprocessing... sup_sim: 2 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 %
% 5.38/2.27
% 5.38/2.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.38/2.27
% 5.38/2.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.38/2.27 % ------ Proving...
% 5.38/2.27 % ------ Problem Properties
% 5.38/2.27
% 5.38/2.27 %
% 5.38/2.27 % clauses 82
% 5.38/2.27 % conjectures 0
% 5.38/2.27 % EPR 23
% 5.38/2.27 % Horn 63
% 5.38/2.27 % unary 18
% 5.38/2.27 % binary 9
% 5.38/2.27 % lits 258
% 5.38/2.27 % lits eq 40
% 5.38/2.27 % fd_pure 0
% 5.38/2.27 % fd_pseudo 0
% 5.38/2.27 % fd_cond 5
% 5.38/2.27 % fd_pseudo_cond 8
% 5.38/2.27 % AC symbols 0
% 5.38/2.27
% 5.38/2.27 % ------ Schedule dynamic 5 is on
% 5.38/2.27
% 5.38/2.27 % ------ no conjectures: strip conj schedule
% 5.38/2.27
% 5.38/2.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 5.38/2.27
% 5.38/2.27
% 5.38/2.27 % ------
% 5.38/2.27 % Current options:
% 5.38/2.27 % ------
% 5.38/2.27
% 5.38/2.27
% 5.38/2.27 %
% 5.38/2.27
% 5.38/2.27 % ------ Proving...
% 5.38/2.27 %
% 5.38/2.27
% 5.38/2.27 % SZS status Theorem for theBenchmark.p
% 5.38/2.27
% 5.38/2.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.38/2.28
% 5.38/2.28
%------------------------------------------------------------------------------