TSTP Solution File: RNG112+4 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : RNG112+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n019.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 13:55:22 EDT 2023
% Result : Theorem 3.56s 1.16s
% Output : CNFRefutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 72 ( 9 unt; 0 def)
% Number of atoms : 590 ( 190 equ)
% Maximal formula atoms : 34 ( 8 avg)
% Number of connectives : 741 ( 223 ~; 180 |; 301 &)
% ( 13 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 10 con; 0-2 aty)
% Number of variables : 275 ( 0 sgn; 140 !; 127 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f44,axiom,
? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( sdtasdt0(xb,X2) = X1
& aElement0(X2) ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( sdtasdt0(xa,X2) = X1
& aElement0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2228) ).
fof(f45,axiom,
! [X0] :
( ( sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) )
=> ? [X1] :
( ! [X2] :
( ( sz00 != X2
& ( aElementOf0(X2,xI)
| ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) )
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2351) ).
fof(f46,conjecture,
? [X0] :
( ! [X1] :
( ( sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ? [X0] :
( ! [X1] :
( ( sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(negated_conjecture,[],[f46]) ).
fof(f56,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xa))
<=> ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) ) )
& aIdeal0(xI)
& ! [X7] :
( aElementOf0(X7,xI)
=> ( ! [X8] :
( aElement0(X8)
=> aElementOf0(sdtasdt0(X8,X7),xI) )
& ! [X9] :
( aElementOf0(X9,xI)
=> aElementOf0(sdtpldt0(X7,X9),xI) ) ) )
& aSet0(xI) ),
inference(rectify,[],[f42]) ).
fof(f58,plain,
? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xa))
<=> ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) ) ) ),
inference(rectify,[],[f44]) ).
fof(f59,plain,
! [X0] :
( ( sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) )
=> ? [X3] :
( ! [X4] :
( ( sz00 != X4
& ( aElementOf0(X4,xI)
| ? [X5,X6] :
( sdtpldt0(X5,X6) = X4
& aElementOf0(X6,slsdtgt0(xb))
& aElementOf0(X5,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3)) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f45]) ).
fof(f60,plain,
~ ? [X0] :
( ! [X1] :
( ( sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& sz00 != X0
& ( aElementOf0(X0,xI)
| ? [X4,X5] :
( sdtpldt0(X4,X5) = X0
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f47]) ).
fof(f113,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ! [X5] :
( aElementOf0(X5,slsdtgt0(xa))
<=> ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) ) )
& aIdeal0(xI)
& ! [X7] :
( ( ! [X8] :
( aElementOf0(sdtasdt0(X8,X7),xI)
| ~ aElement0(X8) )
& ! [X9] :
( aElementOf0(sdtpldt0(X7,X9),xI)
| ~ aElementOf0(X9,xI) ) )
| ~ aElementOf0(X7,xI) )
& aSet0(xI) ),
inference(ennf_transformation,[],[f56]) ).
fof(f114,plain,
! [X0] :
( ? [X3] :
( ! [X4] :
( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3))
| sz00 = X4
| ( ~ aElementOf0(X4,xI)
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) )
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(ennf_transformation,[],[f59]) ).
fof(f115,plain,
! [X0] :
( ? [X3] :
( ! [X4] :
( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3))
| sz00 = X4
| ( ~ aElementOf0(X4,xI)
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) )
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(flattening,[],[f114]) ).
fof(f116,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X4,X5] :
( sdtpldt0(X4,X5) != X0
| ~ aElementOf0(X5,slsdtgt0(xb))
| ~ aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(ennf_transformation,[],[f60]) ).
fof(f117,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X4,X5] :
( sdtpldt0(X4,X5) != X0
| ~ aElementOf0(X5,slsdtgt0(xb))
| ~ aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(flattening,[],[f116]) ).
fof(f124,plain,
( ? [X3] :
( ! [X4] :
( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3))
| sz00 = X4
| ( ~ aElementOf0(X4,xI)
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) )
| ~ sP4 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f125,plain,
! [X0] :
( sP4
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(definition_folding,[],[f115,f124]) ).
fof(f126,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f127,plain,
! [X0] :
( sP5(X0)
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X4,X5] :
( sdtpldt0(X4,X5) != X0
| ~ aElementOf0(X5,slsdtgt0(xb))
| ~ aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(definition_folding,[],[f117,f126]) ).
fof(f185,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( ( aElementOf0(X0,xI)
| ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ( ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
| ~ aElementOf0(X0,xI) ) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xa))
| ! [X6] :
( sdtasdt0(xa,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) )
| ~ aElementOf0(X5,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X7] :
( ( ! [X8] :
( aElementOf0(sdtasdt0(X8,X7),xI)
| ~ aElement0(X8) )
& ! [X9] :
( aElementOf0(sdtpldt0(X7,X9),xI)
| ~ aElementOf0(X9,xI) ) )
| ~ aElementOf0(X7,xI) )
& aSet0(xI) ),
inference(nnf_transformation,[],[f113]) ).
fof(f186,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( ( aElementOf0(X0,xI)
| ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ( ? [X3,X4] :
( sdtpldt0(X3,X4) = X0
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) )
| ~ aElementOf0(X0,xI) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xb))
| ! [X6] :
( sdtasdt0(xb,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X7] :
( sdtasdt0(xb,X7) = X5
& aElement0(X7) )
| ~ aElementOf0(X5,slsdtgt0(xb)) ) )
& ! [X8] :
( ( aElementOf0(X8,slsdtgt0(xa))
| ! [X9] :
( sdtasdt0(xa,X9) != X8
| ~ aElement0(X9) ) )
& ( ? [X10] :
( sdtasdt0(xa,X10) = X8
& aElement0(X10) )
| ~ aElementOf0(X8,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X11] :
( ( ! [X12] :
( aElementOf0(sdtasdt0(X12,X11),xI)
| ~ aElement0(X12) )
& ! [X13] :
( aElementOf0(sdtpldt0(X11,X13),xI)
| ~ aElementOf0(X13,xI) ) )
| ~ aElementOf0(X11,xI) )
& aSet0(xI) ),
inference(rectify,[],[f185]) ).
fof(f187,plain,
! [X0] :
( ? [X3,X4] :
( sdtpldt0(X3,X4) = X0
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) )
=> ( sdtpldt0(sK29(X0),sK30(X0)) = X0
& aElementOf0(sK30(X0),slsdtgt0(xb))
& aElementOf0(sK29(X0),slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f188,plain,
! [X5] :
( ? [X7] :
( sdtasdt0(xb,X7) = X5
& aElement0(X7) )
=> ( sdtasdt0(xb,sK31(X5)) = X5
& aElement0(sK31(X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f189,plain,
! [X8] :
( ? [X10] :
( sdtasdt0(xa,X10) = X8
& aElement0(X10) )
=> ( sdtasdt0(xa,sK32(X8)) = X8
& aElement0(sK32(X8)) ) ),
introduced(choice_axiom,[]) ).
fof(f190,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( ( aElementOf0(X0,xI)
| ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
& ( ( sdtpldt0(sK29(X0),sK30(X0)) = X0
& aElementOf0(sK30(X0),slsdtgt0(xb))
& aElementOf0(sK29(X0),slsdtgt0(xa)) )
| ~ aElementOf0(X0,xI) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xb))
| ! [X6] :
( sdtasdt0(xb,X6) != X5
| ~ aElement0(X6) ) )
& ( ( sdtasdt0(xb,sK31(X5)) = X5
& aElement0(sK31(X5)) )
| ~ aElementOf0(X5,slsdtgt0(xb)) ) )
& ! [X8] :
( ( aElementOf0(X8,slsdtgt0(xa))
| ! [X9] :
( sdtasdt0(xa,X9) != X8
| ~ aElement0(X9) ) )
& ( ( sdtasdt0(xa,sK32(X8)) = X8
& aElement0(sK32(X8)) )
| ~ aElementOf0(X8,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [X11] :
( ( ! [X12] :
( aElementOf0(sdtasdt0(X12,X11),xI)
| ~ aElement0(X12) )
& ! [X13] :
( aElementOf0(sdtpldt0(X11,X13),xI)
| ~ aElementOf0(X13,xI) ) )
| ~ aElementOf0(X11,xI) )
& aSet0(xI) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31,sK32])],[f186,f189,f188,f187]) ).
fof(f196,plain,
? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X5] :
( ( aElementOf0(X5,slsdtgt0(xa))
| ! [X6] :
( sdtasdt0(xa,X6) != X5
| ~ aElement0(X6) ) )
& ( ? [X6] :
( sdtasdt0(xa,X6) = X5
& aElement0(X6) )
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f197,plain,
? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X5] :
( sdtasdt0(xb,X5) = X3
& aElement0(X5) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) ) )
& ( ? [X8] :
( sdtasdt0(xa,X8) = X6
& aElement0(X8) )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f196]) ).
fof(f198,plain,
( ? [X0] :
( sz00 != X0
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X5] :
( sdtasdt0(xb,X5) = X3
& aElement0(X5) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) ) )
& ( ? [X8] :
( sdtasdt0(xa,X8) = X6
& aElement0(X8) )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) )
=> ( sz00 != sK37
& aElementOf0(sK37,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X2,X1] :
( sdtpldt0(X1,X2) = sK37
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ? [X5] :
( sdtasdt0(xb,X5) = X3
& aElement0(X5) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) ) )
& ( ? [X8] :
( sdtasdt0(xa,X8) = X6
& aElement0(X8) )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f199,plain,
( ? [X2,X1] :
( sdtpldt0(X1,X2) = sK37
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
=> ( sK37 = sdtpldt0(sK38,sK39)
& aElementOf0(sK39,slsdtgt0(xb))
& aElementOf0(sK38,slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f200,plain,
! [X3] :
( ? [X5] :
( sdtasdt0(xb,X5) = X3
& aElement0(X5) )
=> ( sdtasdt0(xb,sK40(X3)) = X3
& aElement0(sK40(X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f201,plain,
! [X6] :
( ? [X8] :
( sdtasdt0(xa,X8) = X6
& aElement0(X8) )
=> ( sdtasdt0(xa,sK41(X6)) = X6
& aElement0(sK41(X6)) ) ),
introduced(choice_axiom,[]) ).
fof(f202,plain,
( sz00 != sK37
& aElementOf0(sK37,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& sK37 = sdtpldt0(sK38,sK39)
& aElementOf0(sK39,slsdtgt0(xb))
& aElementOf0(sK38,slsdtgt0(xa))
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( sdtasdt0(xb,X4) != X3
| ~ aElement0(X4) ) )
& ( ( sdtasdt0(xb,sK40(X3)) = X3
& aElement0(sK40(X3)) )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( sdtasdt0(xa,X7) != X6
| ~ aElement0(X7) ) )
& ( ( sdtasdt0(xa,sK41(X6)) = X6
& aElement0(sK41(X6)) )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38,sK39,sK40,sK41])],[f197,f201,f200,f199,f198]) ).
fof(f203,plain,
( ? [X3] :
( ! [X4] :
( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3))
| sz00 = X4
| ( ~ aElementOf0(X4,xI)
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) ) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X3
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) )
| ~ sP4 ),
inference(nnf_transformation,[],[f124]) ).
fof(f204,plain,
( ? [X0] :
( ! [X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
| sz00 = X1
| ( ~ aElementOf0(X1,xI)
& ! [X2,X3] :
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa)) ) ) )
& sz00 != X0
& aElementOf0(X0,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X0
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) )
| ~ sP4 ),
inference(rectify,[],[f203]) ).
fof(f205,plain,
( ? [X0] :
( ! [X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
| sz00 = X1
| ( ~ aElementOf0(X1,xI)
& ! [X2,X3] :
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa)) ) ) )
& sz00 != X0
& aElementOf0(X0,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X0
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) )
=> ( ! [X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK42))
| sz00 = X1
| ( ~ aElementOf0(X1,xI)
& ! [X2,X3] :
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa)) ) ) )
& sz00 != sK42
& aElementOf0(sK42,xI)
& ? [X5,X4] :
( sdtpldt0(X4,X5) = sK42
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f206,plain,
( ? [X5,X4] :
( sdtpldt0(X4,X5) = sK42
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) )
=> ( sK42 = sdtpldt0(sK43,sK44)
& aElementOf0(sK44,slsdtgt0(xb))
& aElementOf0(sK43,slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f207,plain,
( ( ! [X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK42))
| sz00 = X1
| ( ~ aElementOf0(X1,xI)
& ! [X2,X3] :
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa)) ) ) )
& sz00 != sK42
& aElementOf0(sK42,xI)
& sK42 = sdtpldt0(sK43,sK44)
& aElementOf0(sK44,slsdtgt0(xb))
& aElementOf0(sK43,slsdtgt0(xa)) )
| ~ sP4 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43,sK44])],[f204,f206,f205]) ).
fof(f208,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f126]) ).
fof(f209,plain,
! [X0] :
( ? [X1] :
( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
& sz00 != X1
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ( iLess0(sbrdtbr0(sK45(X0)),sbrdtbr0(X0))
& sz00 != sK45(X0)
& aElementOf0(sK45(X0),xI)
& ? [X3,X2] :
( sdtpldt0(X2,X3) = sK45(X0)
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f210,plain,
! [X0] :
( ? [X3,X2] :
( sdtpldt0(X2,X3) = sK45(X0)
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) )
=> ( sK45(X0) = sdtpldt0(sK46(X0),sK47(X0))
& aElementOf0(sK47(X0),slsdtgt0(xb))
& aElementOf0(sK46(X0),slsdtgt0(xa)) ) ),
introduced(choice_axiom,[]) ).
fof(f211,plain,
! [X0] :
( ( iLess0(sbrdtbr0(sK45(X0)),sbrdtbr0(X0))
& sz00 != sK45(X0)
& aElementOf0(sK45(X0),xI)
& sK45(X0) = sdtpldt0(sK46(X0),sK47(X0))
& aElementOf0(sK47(X0),slsdtgt0(xb))
& aElementOf0(sK46(X0),slsdtgt0(xa)) )
| ~ sP5(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45,sK46,sK47])],[f208,f210,f209]) ).
fof(f212,plain,
! [X0] :
( sP5(X0)
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f127]) ).
fof(f341,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f190]) ).
fof(f363,plain,
aElementOf0(sK37,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f202]) ).
fof(f364,plain,
sz00 != sK37,
inference(cnf_transformation,[],[f202]) ).
fof(f368,plain,
( aElementOf0(sK42,xI)
| ~ sP4 ),
inference(cnf_transformation,[],[f207]) ).
fof(f369,plain,
( sz00 != sK42
| ~ sP4 ),
inference(cnf_transformation,[],[f207]) ).
fof(f371,plain,
! [X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK42))
| sz00 = X1
| ~ aElementOf0(X1,xI)
| ~ sP4 ),
inference(cnf_transformation,[],[f207]) ).
fof(f373,plain,
! [X0] :
( sP4
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f125]) ).
fof(f377,plain,
! [X0] :
( aElementOf0(sK45(X0),xI)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f378,plain,
! [X0] :
( sz00 != sK45(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f379,plain,
! [X0] :
( iLess0(sbrdtbr0(sK45(X0)),sbrdtbr0(X0))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f381,plain,
! [X0] :
( sP5(X0)
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f212]) ).
cnf(c_163,plain,
sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
inference(cnf_transformation,[],[f341]) ).
cnf(c_190,plain,
sz00 != sK37,
inference(cnf_transformation,[],[f364]) ).
cnf(c_191,plain,
aElementOf0(sK37,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f363]) ).
cnf(c_201,plain,
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK42))
| ~ aElementOf0(X0,xI)
| ~ sP4
| X0 = sz00 ),
inference(cnf_transformation,[],[f371]) ).
cnf(c_203,plain,
( sz00 != sK42
| ~ sP4 ),
inference(cnf_transformation,[],[f369]) ).
cnf(c_204,plain,
( ~ sP4
| aElementOf0(sK42,xI) ),
inference(cnf_transformation,[],[f368]) ).
cnf(c_208,plain,
( ~ aElementOf0(X0,xI)
| X0 = sz00
| sP4 ),
inference(cnf_transformation,[],[f373]) ).
cnf(c_210,plain,
( ~ sP5(X0)
| iLess0(sbrdtbr0(sK45(X0)),sbrdtbr0(X0)) ),
inference(cnf_transformation,[],[f379]) ).
cnf(c_211,plain,
( sK45(X0) != sz00
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f378]) ).
cnf(c_212,plain,
( ~ sP5(X0)
| aElementOf0(sK45(X0),xI) ),
inference(cnf_transformation,[],[f377]) ).
cnf(c_216,negated_conjecture,
( ~ aElementOf0(X0,xI)
| X0 = sz00
| sP5(X0) ),
inference(cnf_transformation,[],[f381]) ).
cnf(c_333,plain,
( ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK42))
| X0 = sz00 ),
inference(global_subsumption_just,[status(thm)],[c_201,c_208,c_201]) ).
cnf(c_334,plain,
( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK42))
| ~ aElementOf0(X0,xI)
| X0 = sz00 ),
inference(renaming,[status(thm)],[c_333]) ).
cnf(c_5557,plain,
aElementOf0(sK37,xI),
inference(demodulation,[status(thm)],[c_191,c_163]) ).
cnf(c_5655,plain,
( sz00 = sK37
| sP4 ),
inference(superposition,[status(thm)],[c_5557,c_208]) ).
cnf(c_6038,plain,
( ~ sP4
| sz00 = sK42
| sP5(sK42) ),
inference(superposition,[status(thm)],[c_204,c_216]) ).
cnf(c_6051,plain,
( ~ sP4
| sP5(sK42) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6038,c_203]) ).
cnf(c_7418,plain,
( ~ aElementOf0(sK45(sK42),xI)
| ~ sP5(sK42)
| sK45(sK42) = sz00 ),
inference(superposition,[status(thm)],[c_210,c_334]) ).
cnf(c_7422,plain,
~ sP5(sK42),
inference(forward_subsumption_resolution,[status(thm)],[c_7418,c_211,c_212]) ).
cnf(c_7423,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7422,c_6051,c_5655,c_190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG112+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 01:32:13 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.56/1.16 % SZS status Started for theBenchmark.p
% 3.56/1.16 % SZS status Theorem for theBenchmark.p
% 3.56/1.16
% 3.56/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.56/1.16
% 3.56/1.16 ------ iProver source info
% 3.56/1.16
% 3.56/1.16 git: date: 2023-05-31 18:12:56 +0000
% 3.56/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.56/1.16 git: non_committed_changes: false
% 3.56/1.16 git: last_make_outside_of_git: false
% 3.56/1.16
% 3.56/1.16 ------ Parsing...
% 3.56/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.56/1.16
% 3.56/1.16 ------ Preprocessing... sup_sim: 0 pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 pe_s pe_e
% 3.56/1.16
% 3.56/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 1 0s scvd_e snvd_s sp: 0 0s snvd_e
% 3.56/1.16
% 3.56/1.16 ------ Preprocessing...
% 3.56/1.16 ------ Proving...
% 3.56/1.16 ------ Problem Properties
% 3.56/1.16
% 3.56/1.16
% 3.56/1.16 clauses 162
% 3.56/1.16 conjectures 2
% 3.56/1.16 EPR 40
% 3.56/1.16 Horn 130
% 3.56/1.16 unary 35
% 3.56/1.16 binary 43
% 3.56/1.16 lits 465
% 3.56/1.16 lits eq 73
% 3.56/1.16 fd_pure 0
% 3.56/1.16 fd_pseudo 0
% 3.56/1.16 fd_cond 7
% 3.56/1.16 fd_pseudo_cond 11
% 3.56/1.16 AC symbols 0
% 3.56/1.16
% 3.56/1.16 ------ Input Options Time Limit: Unbounded
% 3.56/1.16
% 3.56/1.16
% 3.56/1.16 ------
% 3.56/1.16 Current options:
% 3.56/1.16 ------
% 3.56/1.16
% 3.56/1.16
% 3.56/1.16
% 3.56/1.16
% 3.56/1.16 ------ Proving...
% 3.56/1.16
% 3.56/1.16
% 3.56/1.16 % SZS status Theorem for theBenchmark.p
% 3.56/1.16
% 3.56/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.56/1.16
% 3.56/1.17
%------------------------------------------------------------------------------