TSTP Solution File: RNG126+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : RNG126+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:55:28 EDT 2023
% Result : Theorem 35.16s 5.63s
% Output : CNFRefutation 35.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 21
% Syntax : Number of formulae : 121 ( 33 unt; 0 def)
% Number of atoms : 540 ( 80 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 678 ( 259 ~; 245 |; 136 &)
% ( 15 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% 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 : 240 ( 0 sgn; 170 !; 42 ?)
% 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(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
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] :
( slsdtgt0(X0) = X1
<=> ( ! [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] :
( ( sz00 != X0
& aElementOf0(X0,xI) )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& sz00 != xu
& aElementOf0(xu,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
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,[],[f48]) ).
fof(f53,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X3] :
( aElementOf0(X3,X0)
=> aElementOf0(sdtpldt0(X1,X3),X0) ) ) )
& aSet0(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f57,plain,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(flattening,[],[f49]) ).
fof(f70,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f71,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f70]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f88,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ aElementOf0(X1,X0) )
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f99,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f100,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( doDivides0(X1,X0)
& aElement0(X1) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f102,plain,
! [X0,X1] :
( ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> ( ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f103,plain,
! [X0,X1] :
( ! [X2] :
( aGcdOfAnd0(X2,X0,X1)
<=> ( ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f102]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( slsdtgt0(X0) = X1
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f108,plain,
( ! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| sz00 = X0
| ~ aElementOf0(X0,xI) )
& sz00 != xu
& aElementOf0(xu,xI) ),
inference(ennf_transformation,[],[f45]) ).
fof(f109,plain,
( ! [X0] :
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
| sz00 = X0
| ~ aElementOf0(X0,xI) )
& sz00 != xu
& aElementOf0(xu,xI) ),
inference(flattening,[],[f108]) ).
fof(f129,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f130,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(flattening,[],[f129]) ).
fof(f131,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtasdt0(X5,X4),X0)
| ~ aElement0(X5) )
& ! [X6] :
( aElementOf0(sdtpldt0(X4,X6),X0)
| ~ aElementOf0(X6,X0) ) )
| ~ aElementOf0(X4,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(rectify,[],[f130]) ).
fof(f132,plain,
! [X0] :
( ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& aElementOf0(X1,X0) )
=> ( ( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,sK10(X0)),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(sK10(X0),X3),X0)
& aElementOf0(X3,X0) ) )
& aElementOf0(sK10(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f133,plain,
! [X0] :
( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,sK10(X0)),X0)
& aElement0(X2) )
=> ( ~ aElementOf0(sdtasdt0(sK11(X0),sK10(X0)),X0)
& aElement0(sK11(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f134,plain,
! [X0] :
( ? [X3] :
( ~ aElementOf0(sdtpldt0(sK10(X0),X3),X0)
& aElementOf0(X3,X0) )
=> ( ~ aElementOf0(sdtpldt0(sK10(X0),sK12(X0)),X0)
& aElementOf0(sK12(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f135,plain,
! [X0] :
( ( aIdeal0(X0)
| ( ( ( ~ aElementOf0(sdtasdt0(sK11(X0),sK10(X0)),X0)
& aElement0(sK11(X0)) )
| ( ~ aElementOf0(sdtpldt0(sK10(X0),sK12(X0)),X0)
& aElementOf0(sK12(X0),X0) ) )
& aElementOf0(sK10(X0),X0) )
| ~ aSet0(X0) )
& ( ( ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtasdt0(X5,X4),X0)
| ~ aElement0(X5) )
& ! [X6] :
( aElementOf0(sdtpldt0(X4,X6),X0)
| ~ aElementOf0(X6,X0) ) )
| ~ aElementOf0(X4,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f131,f134,f133,f132]) ).
fof(f143,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aElement0(X2) ) )
& ( ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f144,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aElement0(X2) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aElement0(X3) )
| ~ doDivides0(X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(rectify,[],[f143]) ).
fof(f145,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aElement0(X3) )
=> ( sdtasdt0(X0,sK17(X0,X1)) = X1
& aElement0(sK17(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f146,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aElement0(X2) ) )
& ( ( sdtasdt0(X0,sK17(X0,X1)) = X1
& aElement0(sK17(X0,X1)) )
| ~ doDivides0(X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f144,f145]) ).
fof(f147,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1) )
& ( ( doDivides0(X1,X0)
& aElement0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f101]) ).
fof(f148,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ doDivides0(X1,X0)
| ~ aElement0(X1) )
& ( ( doDivides0(X1,X0)
& aElement0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( ! [X2] :
( ( aGcdOfAnd0(X2,X0,X1)
| ? [X3] :
( ~ doDivides0(X3,X2)
& aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X0) )
| ~ aDivisorOf0(X2,X1)
| ~ aDivisorOf0(X2,X0) )
& ( ( ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) )
| ~ aGcdOfAnd0(X2,X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f150,plain,
! [X0,X1] :
( ! [X2] :
( ( aGcdOfAnd0(X2,X0,X1)
| ? [X3] :
( ~ doDivides0(X3,X2)
& aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X0) )
| ~ aDivisorOf0(X2,X1)
| ~ aDivisorOf0(X2,X0) )
& ( ( ! [X3] :
( doDivides0(X3,X2)
| ~ aDivisorOf0(X3,X1)
| ~ aDivisorOf0(X3,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) )
| ~ aGcdOfAnd0(X2,X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f149]) ).
fof(f151,plain,
! [X0,X1] :
( ! [X2] :
( ( aGcdOfAnd0(X2,X0,X1)
| ? [X3] :
( ~ doDivides0(X3,X2)
& aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X0) )
| ~ aDivisorOf0(X2,X1)
| ~ aDivisorOf0(X2,X0) )
& ( ( ! [X4] :
( doDivides0(X4,X2)
| ~ aDivisorOf0(X4,X1)
| ~ aDivisorOf0(X4,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) )
| ~ aGcdOfAnd0(X2,X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(rectify,[],[f150]) ).
fof(f152,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ doDivides0(X3,X2)
& aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X0) )
=> ( ~ doDivides0(sK18(X0,X1,X2),X2)
& aDivisorOf0(sK18(X0,X1,X2),X1)
& aDivisorOf0(sK18(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f153,plain,
! [X0,X1] :
( ! [X2] :
( ( aGcdOfAnd0(X2,X0,X1)
| ( ~ doDivides0(sK18(X0,X1,X2),X2)
& aDivisorOf0(sK18(X0,X1,X2),X1)
& aDivisorOf0(sK18(X0,X1,X2),X0) )
| ~ aDivisorOf0(X2,X1)
| ~ aDivisorOf0(X2,X0) )
& ( ( ! [X4] :
( doDivides0(X4,X2)
| ~ aDivisorOf0(X4,X1)
| ~ aDivisorOf0(X4,X0) )
& aDivisorOf0(X2,X1)
& aDivisorOf0(X2,X0) )
| ~ aGcdOfAnd0(X2,X0,X1) ) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f151,f152]) ).
fof(f155,plain,
! [X0] :
( ! [X1] :
( ( slsdtgt0(X0) = X1
| ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| ~ aElementOf0(X2,X1) ) )
& aSet0(X1) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f106]) ).
fof(f156,plain,
! [X0] :
( ! [X1] :
( ( slsdtgt0(X0) = X1
| ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) )
| ~ aElementOf0(X2,X1) ) )
& aSet0(X1) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f155]) ).
fof(f157,plain,
! [X0] :
( ! [X1] :
( ( slsdtgt0(X0) = X1
| ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( sdtasdt0(X0,X4) = X2
& aElement0(X4) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X7] :
( sdtasdt0(X0,X7) = X5
& aElement0(X7) )
| ~ aElementOf0(X5,X1) ) )
& aSet0(X1) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(rectify,[],[f156]) ).
fof(f158,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( sdtasdt0(X0,X4) = X2
& aElement0(X4) )
| aElementOf0(X2,X1) ) )
=> ( ( ! [X3] :
( sdtasdt0(X0,X3) != sK19(X0,X1)
| ~ aElement0(X3) )
| ~ aElementOf0(sK19(X0,X1),X1) )
& ( ? [X4] :
( sdtasdt0(X0,X4) = sK19(X0,X1)
& aElement0(X4) )
| aElementOf0(sK19(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f159,plain,
! [X0,X1] :
( ? [X4] :
( sdtasdt0(X0,X4) = sK19(X0,X1)
& aElement0(X4) )
=> ( sK19(X0,X1) = sdtasdt0(X0,sK20(X0,X1))
& aElement0(sK20(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
! [X0,X5] :
( ? [X7] :
( sdtasdt0(X0,X7) = X5
& aElement0(X7) )
=> ( sdtasdt0(X0,sK21(X0,X5)) = X5
& aElement0(sK21(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f161,plain,
! [X0] :
( ! [X1] :
( ( slsdtgt0(X0) = X1
| ( ( ! [X3] :
( sdtasdt0(X0,X3) != sK19(X0,X1)
| ~ aElement0(X3) )
| ~ aElementOf0(sK19(X0,X1),X1) )
& ( ( sK19(X0,X1) = sdtasdt0(X0,sK20(X0,X1))
& aElement0(sK20(X0,X1)) )
| aElementOf0(sK19(X0,X1),X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) ) )
& ( ( sdtasdt0(X0,sK21(X0,X5)) = X5
& aElement0(sK21(X0,X5)) )
| ~ aElementOf0(X5,X1) ) )
& aSet0(X1) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20,sK21])],[f157,f160,f159,f158]) ).
fof(f175,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f187,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f211,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f213,plain,
! [X0,X4,X5] :
( aElementOf0(sdtasdt0(X5,X4),X0)
| ~ aElement0(X5)
| ~ aElementOf0(X4,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f233,plain,
! [X0,X1] :
( aElement0(sK17(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f234,plain,
! [X0,X1] :
( sdtasdt0(X0,sK17(X0,X1)) = X1
| ~ doDivides0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f236,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aDivisorOf0(X1,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f240,plain,
! [X2,X0,X1] :
( aDivisorOf0(X2,X1)
| ~ aGcdOfAnd0(X2,X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f248,plain,
! [X0,X1,X5] :
( aElement0(sK21(X0,X5))
| ~ aElementOf0(X5,X1)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f249,plain,
! [X0,X1,X5] :
( sdtasdt0(X0,sK21(X0,X5)) = X5
| ~ aElementOf0(X5,X1)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f250,plain,
! [X0,X1,X6,X5] :
( aElementOf0(X5,X1)
| sdtasdt0(X0,X6) != X5
| ~ aElement0(X6)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f255,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f256,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f258,plain,
aGcdOfAnd0(xc,xa,xb),
inference(cnf_transformation,[],[f41]) ).
fof(f259,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f42]) ).
fof(f260,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f42]) ).
fof(f267,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f109]) ).
fof(f272,plain,
doDivides0(xu,xc),
inference(cnf_transformation,[],[f47]) ).
fof(f273,plain,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f57]) ).
fof(f281,plain,
! [X0,X1,X6] :
( aElementOf0(sdtasdt0(X0,X6),X1)
| ~ aElement0(X6)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f250]) ).
fof(f282,plain,
! [X0,X6] :
( aElementOf0(sdtasdt0(X0,X6),slsdtgt0(X0))
| ~ aElement0(X6)
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f281]) ).
fof(f283,plain,
! [X0,X5] :
( sdtasdt0(X0,sK21(X0,X5)) = X5
| ~ aElementOf0(X5,slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f249]) ).
fof(f284,plain,
! [X0,X5] :
( aElement0(sK21(X0,X5))
| ~ aElementOf0(X5,slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f248]) ).
cnf(c_60,plain,
( ~ aElement0(X0)
| ~ aElement0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f175]) ).
cnf(c_72,plain,
( ~ aElementOf0(X0,X1)
| ~ aSet0(X1)
| aElement0(X0) ),
inference(cnf_transformation,[],[f187]) ).
cnf(c_101,plain,
( ~ aElementOf0(X0,X1)
| ~ aElement0(X2)
| ~ aIdeal0(X1)
| aElementOf0(sdtasdt0(X2,X0),X1) ),
inference(cnf_transformation,[],[f213]) ).
cnf(c_103,plain,
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[],[f211]) ).
cnf(c_119,plain,
( ~ doDivides0(X0,X1)
| ~ aElement0(X0)
| ~ aElement0(X1)
| sdtasdt0(X0,sK17(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f234]) ).
cnf(c_120,plain,
( ~ doDivides0(X0,X1)
| ~ aElement0(X0)
| ~ aElement0(X1)
| aElement0(sK17(X0,X1)) ),
inference(cnf_transformation,[],[f233]) ).
cnf(c_123,plain,
( ~ aDivisorOf0(X0,X1)
| ~ aElement0(X1)
| aElement0(X0) ),
inference(cnf_transformation,[],[f236]) ).
cnf(c_128,plain,
( ~ aGcdOfAnd0(X0,X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2)
| aDivisorOf0(X0,X2) ),
inference(cnf_transformation,[],[f240]) ).
cnf(c_135,plain,
( ~ aElement0(X0)
| ~ aElement0(X1)
| aElementOf0(sdtasdt0(X0,X1),slsdtgt0(X0)) ),
inference(cnf_transformation,[],[f282]) ).
cnf(c_136,plain,
( ~ aElementOf0(X0,slsdtgt0(X1))
| ~ aElement0(X1)
| sdtasdt0(X1,sK21(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f283]) ).
cnf(c_137,plain,
( ~ aElementOf0(X0,slsdtgt0(X1))
| ~ aElement0(X1)
| aElement0(sK21(X1,X0)) ),
inference(cnf_transformation,[],[f284]) ).
cnf(c_140,plain,
aElement0(xb),
inference(cnf_transformation,[],[f256]) ).
cnf(c_141,plain,
aElement0(xa),
inference(cnf_transformation,[],[f255]) ).
cnf(c_143,plain,
aGcdOfAnd0(xc,xa,xb),
inference(cnf_transformation,[],[f258]) ).
cnf(c_144,plain,
sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
inference(cnf_transformation,[],[f260]) ).
cnf(c_145,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f259]) ).
cnf(c_154,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f267]) ).
cnf(c_157,plain,
doDivides0(xu,xc),
inference(cnf_transformation,[],[f272]) ).
cnf(c_158,negated_conjecture,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f273]) ).
cnf(c_992,plain,
~ aElementOf0(xc,xI),
inference(demodulation,[status(thm)],[c_158,c_144]) ).
cnf(c_2239,plain,
( X0 != xu
| X1 != xc
| ~ aElement0(X0)
| ~ aElement0(X1)
| aElement0(sK17(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_120,c_157]) ).
cnf(c_2240,plain,
( ~ aElement0(xc)
| ~ aElement0(xu)
| aElement0(sK17(xu,xc)) ),
inference(unflattening,[status(thm)],[c_2239]) ).
cnf(c_7150,plain,
aSet0(xI),
inference(superposition,[status(thm)],[c_145,c_103]) ).
cnf(c_7254,plain,
( ~ aSet0(xI)
| aElement0(xu) ),
inference(superposition,[status(thm)],[c_154,c_72]) ).
cnf(c_7257,plain,
aElement0(xu),
inference(forward_subsumption_resolution,[status(thm)],[c_7254,c_7150]) ).
cnf(c_7966,plain,
( ~ aElement0(X0)
| sdtasdt0(X0,xu) = sdtasdt0(xu,X0) ),
inference(superposition,[status(thm)],[c_7257,c_60]) ).
cnf(c_8344,plain,
( ~ aElement0(xb)
| ~ aElement0(xa)
| aDivisorOf0(xc,xb) ),
inference(superposition,[status(thm)],[c_143,c_128]) ).
cnf(c_8345,plain,
aDivisorOf0(xc,xb),
inference(forward_subsumption_resolution,[status(thm)],[c_8344,c_141,c_140]) ).
cnf(c_8369,plain,
( ~ aElement0(xb)
| aElement0(xc) ),
inference(superposition,[status(thm)],[c_8345,c_123]) ).
cnf(c_8370,plain,
aElement0(xc),
inference(forward_subsumption_resolution,[status(thm)],[c_8369,c_140]) ).
cnf(c_9792,plain,
( ~ aElement0(xc)
| ~ aElement0(xu)
| sdtasdt0(xu,sK17(xu,xc)) = xc ),
inference(superposition,[status(thm)],[c_157,c_119]) ).
cnf(c_9835,plain,
sdtasdt0(xu,sK17(xu,xc)) = xc,
inference(forward_subsumption_resolution,[status(thm)],[c_9792,c_7257,c_8370]) ).
cnf(c_16813,plain,
( ~ aElement0(sK17(xu,xc))
| ~ aElement0(xu)
| aElementOf0(xc,slsdtgt0(xu)) ),
inference(superposition,[status(thm)],[c_9835,c_135]) ).
cnf(c_16817,plain,
( ~ aElement0(sK17(xu,xc))
| aElementOf0(xc,slsdtgt0(xu)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16813,c_7257]) ).
cnf(c_21490,plain,
aElementOf0(xc,slsdtgt0(xu)),
inference(global_subsumption_just,[status(thm)],[c_16817,c_2240,c_7257,c_8370,c_16817]) ).
cnf(c_21493,plain,
( ~ aElement0(xu)
| sdtasdt0(xu,sK21(xu,xc)) = xc ),
inference(superposition,[status(thm)],[c_21490,c_136]) ).
cnf(c_21494,plain,
( ~ aElement0(xu)
| aElement0(sK21(xu,xc)) ),
inference(superposition,[status(thm)],[c_21490,c_137]) ).
cnf(c_21495,plain,
aElement0(sK21(xu,xc)),
inference(forward_subsumption_resolution,[status(thm)],[c_21494,c_7257]) ).
cnf(c_21496,plain,
sdtasdt0(xu,sK21(xu,xc)) = xc,
inference(forward_subsumption_resolution,[status(thm)],[c_21493,c_7257]) ).
cnf(c_110324,plain,
sdtasdt0(sK21(xu,xc),xu) = sdtasdt0(xu,sK21(xu,xc)),
inference(superposition,[status(thm)],[c_21495,c_7966]) ).
cnf(c_110549,plain,
sdtasdt0(sK21(xu,xc),xu) = xc,
inference(light_normalisation,[status(thm)],[c_110324,c_21496]) ).
cnf(c_112205,plain,
( ~ aElement0(sK21(xu,xc))
| ~ aElementOf0(xu,X0)
| ~ aIdeal0(X0)
| aElementOf0(xc,X0) ),
inference(superposition,[status(thm)],[c_110549,c_101]) ).
cnf(c_112208,plain,
( ~ aElementOf0(xu,X0)
| ~ aIdeal0(X0)
| aElementOf0(xc,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112205,c_21495]) ).
cnf(c_117942,plain,
( ~ aIdeal0(xI)
| aElementOf0(xc,xI) ),
inference(superposition,[status(thm)],[c_154,c_112208]) ).
cnf(c_117946,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_117942,c_992,c_145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : RNG126+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : run_iprover %s %d THM
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sun Aug 27 01:32:44 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.40 Running first-order theorem proving
% 0.16/0.40 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 35.16/5.63 % SZS status Started for theBenchmark.p
% 35.16/5.63 % SZS status Theorem for theBenchmark.p
% 35.16/5.63
% 35.16/5.63 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 35.16/5.63
% 35.16/5.63 ------ iProver source info
% 35.16/5.63
% 35.16/5.63 git: date: 2023-05-31 18:12:56 +0000
% 35.16/5.63 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 35.16/5.63 git: non_committed_changes: false
% 35.16/5.63 git: last_make_outside_of_git: false
% 35.16/5.63
% 35.16/5.63 ------ Parsing...
% 35.16/5.63 ------ Clausification by vclausify_rel & Parsing by iProver...
% 35.16/5.63
% 35.16/5.63 ------ 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
% 35.16/5.63
% 35.16/5.63 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 35.16/5.63
% 35.16/5.63 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 35.16/5.63 ------ Proving...
% 35.16/5.63 ------ Problem Properties
% 35.16/5.63
% 35.16/5.63
% 35.16/5.63 clauses 105
% 35.16/5.63 conjectures 0
% 35.16/5.63 EPR 25
% 35.16/5.63 Horn 81
% 35.16/5.63 unary 20
% 35.16/5.63 binary 16
% 35.16/5.63 lits 348
% 35.16/5.63 lits eq 50
% 35.16/5.63 fd_pure 0
% 35.16/5.63 fd_pseudo 0
% 35.16/5.63 fd_cond 5
% 35.16/5.63 fd_pseudo_cond 11
% 35.16/5.63 AC symbols 0
% 35.16/5.63
% 35.16/5.63 ------ Schedule dynamic 5 is on
% 35.16/5.63
% 35.16/5.63 ------ no conjectures: strip conj schedule
% 35.16/5.63
% 35.16/5.63 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 35.16/5.63
% 35.16/5.63
% 35.16/5.63 ------
% 35.16/5.63 Current options:
% 35.16/5.63 ------
% 35.16/5.63
% 35.16/5.63
% 35.16/5.63
% 35.16/5.63
% 35.16/5.63 ------ Proving...
% 35.16/5.63
% 35.16/5.63
% 35.16/5.63 % SZS status Theorem for theBenchmark.p
% 35.16/5.63
% 35.16/5.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 35.16/5.63
% 35.16/5.63
%------------------------------------------------------------------------------