%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG112+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 02:39:11 PM UTC 2026
% Result : Theorem 0.89s 11.21s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 9 unt; 2 def)
% Number of atoms : 483 ( 150 equ)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 615 ( 193 ~; 157 |; 239 &)
% ( 13 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 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; 2 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 10 con; 0-2 aty)
% Number of variables : 224 ( 0 sgn 125 !; 99 ?; 8 :)
% 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] :
( X0 != sz00
& 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] :
( ( X0 != sz00
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) )
=> ? [X1] :
( ! [X2] :
( ( X2 != sz00
& ( aElementOf0(X2,xI)
| ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) )
& X1 != sz00
& 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] :
( ( X1 != sz00
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& X0 != sz00
& ( 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] :
( ( X1 != sz00
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
& X0 != sz00
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f56,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(f58,plain,
? [X0] :
( X0 != sz00
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X5,X6] :
( sdtpldt0(X5,X6) = X0
& aElementOf0(X6,slsdtgt0(xb))
& aElementOf0(X5,slsdtgt0(xa)) )
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( sdtasdt0(xb,X4) = X3
& aElement0(X4) ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( sdtasdt0(xa,X2) = X1
& aElement0(X2) ) ) ),
inference(rectify,[],[f44]) ).
fof(f59,plain,
! [X0] :
( ( X0 != sz00
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) )
=> ? [X3] :
( ! [X6] :
( ( sz00 != X6
& ( aElementOf0(X6,xI)
| ? [X7,X8] :
( sdtpldt0(X7,X8) = X6
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X6),sbrdtbr0(X3)) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f45]) ).
fof(f60,plain,
~ ? [X0] :
( ! [X3] :
( ( sz00 != X3
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X0)) )
& X0 != sz00
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f47]) ).
fof(f113,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,[],[f56]) ).
fof(f114,plain,
! [X0] :
( sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
| ? [X3] :
( ! [X6] :
( sz00 = X6
| ( ~ aElementOf0(X6,xI)
& ! [X7,X8] :
( sdtpldt0(X7,X8) != X6
| ~ aElementOf0(X8,slsdtgt0(xb))
| ~ aElementOf0(X7,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X6),sbrdtbr0(X3)) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(ennf_transformation,[],[f59]) ).
fof(f115,plain,
! [X0] :
( sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
| ? [X3] :
( ! [X6] :
( sz00 = X6
| ( ~ aElementOf0(X6,xI)
& ! [X7,X8] :
( sdtpldt0(X7,X8) != X6
| ~ aElementOf0(X8,slsdtgt0(xb))
| ~ aElementOf0(X7,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X6),sbrdtbr0(X3)) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(flattening,[],[f114]) ).
fof(f116,plain,
! [X0] :
( ? [X3] :
( sz00 != X3
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) )
& iLess0(sbrdtbr0(X3),sbrdtbr0(X0)) )
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(ennf_transformation,[],[f60]) ).
fof(f117,plain,
! [X0] :
( ? [X3] :
( sz00 != X3
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) )
& iLess0(sbrdtbr0(X3),sbrdtbr0(X0)) )
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(flattening,[],[f116]) ).
fof(f167,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,[],[f113]) ).
fof(f168,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,[],[f167]) ).
fof(f169,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X9] :
( ( ~ aElementOf0(X9,xI)
| ( sdtpldt0(sK31(X9),sK32(X9)) = X9
& aElementOf0(sK32(X9),slsdtgt0(xb))
& aElementOf0(sK31(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,sK30(X6)) = X6
& aElement0(sK30(X6)) ) )
& ( ! [X7] :
( sdtasdt0(xb,X7) != X6
| ~ aElement0(X7) )
| aElementOf0(X6,slsdtgt0(xb)) ) )
& ! [X3] :
( ( ~ aElementOf0(X3,slsdtgt0(xa))
| ( sdtasdt0(xa,sK29(X3)) = X3
& aElement0(sK29(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,[sK29,sK30,sK31,sK32]),skolemize(X5,sK29(X3)),skolemize(X8,sK30(X6)),skolemize(X12,sK31(X9)),skolemize(X13,sK32(X9))],[f168]) ).
fof(f171,plain,
? [X0] :
( X0 != sz00
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X5,X6] :
( sdtpldt0(X5,X6) = X0
& aElementOf0(X6,slsdtgt0(xb))
& aElementOf0(X5,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)) ) )
& ! [X1] :
( ( ~ aElementOf0(X1,slsdtgt0(xa))
| ? [X2] :
( sdtasdt0(xa,X2) = X1
& aElement0(X2) ) )
& ( ! [X2] :
( sdtasdt0(xa,X2) != X1
| ~ aElement0(X2) )
| aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f172,plain,
? [X0] :
( X0 != sz00
& aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X0
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) )
& ! [X4] :
( ( ~ aElementOf0(X4,slsdtgt0(xb))
| ? [X6] :
( sdtasdt0(xb,X6) = X4
& aElement0(X6) ) )
& ( ! [X5] :
( sdtasdt0(xb,X5) != X4
| ~ aElement0(X5) )
| aElementOf0(X4,slsdtgt0(xb)) ) )
& ! [X1] :
( ( ~ aElementOf0(X1,slsdtgt0(xa))
| ? [X3] :
( sdtasdt0(xa,X3) = X1
& aElement0(X3) ) )
& ( ! [X2] :
( sdtasdt0(xa,X2) != X1
| ~ aElement0(X2) )
| aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f171]) ).
fof(f173,plain,
( sz00 != sK37
& aElementOf0(sK37,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& sK37 = sdtpldt0(sK40,sK41)
& aElementOf0(sK41,slsdtgt0(xb))
& aElementOf0(sK40,slsdtgt0(xa))
& ! [X4] :
( ( ~ aElementOf0(X4,slsdtgt0(xb))
| ( sdtasdt0(xb,sK39(X4)) = X4
& aElement0(sK39(X4)) ) )
& ( ! [X5] :
( sdtasdt0(xb,X5) != X4
| ~ aElement0(X5) )
| aElementOf0(X4,slsdtgt0(xb)) ) )
& ! [X1] :
( ( ~ aElementOf0(X1,slsdtgt0(xa))
| ( sdtasdt0(xa,sK38(X1)) = X1
& aElement0(sK38(X1)) ) )
& ( ! [X2] :
( sdtasdt0(xa,X2) != X1
| ~ aElement0(X2) )
| aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37,sK38,sK39,sK40,sK41]),skolemize(X0,sK37),skolemize(X3,sK38(X1)),skolemize(X6,sK39(X4)),skolemize(X7,sK40),skolemize(X8,sK41)],[f172]) ).
fof(f294,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f169]) ).
fof(f321,plain,
sz00 != sK37,
inference(cnf_transformation,[],[f173]) ).
fof(f322,plain,
aElementOf0(sK37,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f173]) ).
fof(f339,plain,
! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| sP4 ),
inference(cnf_transformation,[],[f125]) ).
fof(f347,plain,
! [X0] :
( sP5(X0)
| sz00 = X0
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_177,plain,
sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
inference(cnf_transformation,[],[f294]) ).
tcf(c_199,plain,
aElementOf0(sK37,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[],[f322]) ).
tcf(c_200,plain,
sz00 != sK37,
inference(cnf_transformation,[],[f321]) ).
tcf(c_209,plain,
! [X0: $i] :
( sP4
| ( X0 = sz00 )
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f339]) ).
tcf(c_217,negated_conjecture,
! [X0: $i] :
( sP5(X0)
| ( X0 = sz00 )
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f347]) ).
tcf(c_5560,plain,
aElementOf0(sK37,xI),
inference(demodulation,[status(thm)],[c_199,c_177]) ).
tcf(c_5694,plain,
( sP4
| ( sz00 = sK37 ) ),
inference(superposition,[status(thm)],[c_5560,c_209]) ).
fof(f124,definition,
( ~ sP4
| ? [X3] :
( ! [X6] :
( sz00 = X6
| ( ~ aElementOf0(X6,xI)
& ! [X7,X8] :
( sdtpldt0(X7,X8) != X6
| ~ aElementOf0(X8,slsdtgt0(xb))
| ~ aElementOf0(X7,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X6),sbrdtbr0(X3)) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f125,plain,
! [X0] :
( sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) )
| sP4 ),
inference(definition_folding,[],[f115,f124]) ).
fof(f126,definition,
! [X0] :
( ~ sP5(X0)
| ? [X3] :
( sz00 != X3
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) )
& iLess0(sbrdtbr0(X3),sbrdtbr0(X0)) ) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f127,plain,
! [X0] :
( sP5(X0)
| sz00 = X0
| ( ~ aElementOf0(X0,xI)
& ! [X1,X2] :
( sdtpldt0(X1,X2) != X0
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(definition_folding,[],[f117,f126]) ).
fof(f174,plain,
( ~ sP4
| ? [X3] :
( ! [X6] :
( sz00 = X6
| ( ~ aElementOf0(X6,xI)
& ! [X7,X8] :
( sdtpldt0(X7,X8) != X6
| ~ aElementOf0(X8,slsdtgt0(xb))
| ~ aElementOf0(X7,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X6),sbrdtbr0(X3)) )
& sz00 != X3
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) ),
inference(nnf_transformation,[],[f124]) ).
fof(f175,plain,
( ~ sP4
| ? [X0] :
( ! [X3] :
( sz00 = X3
| ( ~ aElementOf0(X3,xI)
& ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,slsdtgt0(xb))
| ~ aElementOf0(X4,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X0)) )
& sz00 != X0
& aElementOf0(X0,xI)
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) ),
inference(rectify,[],[f174]) ).
fof(f176,plain,
( ~ sP4
| ( ! [X3] :
( sz00 = X3
| ( ~ aElementOf0(X3,xI)
& ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,slsdtgt0(xb))
| ~ aElementOf0(X4,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK42)) )
& sz00 != sK42
& aElementOf0(sK42,xI)
& sK42 = sdtpldt0(sK43,sK44)
& aElementOf0(sK44,slsdtgt0(xb))
& aElementOf0(sK43,slsdtgt0(xa)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42,sK43,sK44]),skolemize(X0,sK42),skolemize(X1,sK43),skolemize(X2,sK44)],[f175]) ).
fof(f177,plain,
! [X0] :
( ~ sP5(X0)
| ? [X3] :
( sz00 != X3
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) )
& iLess0(sbrdtbr0(X3),sbrdtbr0(X0)) ) ),
inference(nnf_transformation,[],[f126]) ).
fof(f178,plain,
! [X0] :
( ~ sP5(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)) ) ),
inference(rectify,[],[f177]) ).
fof(f179,plain,
! [X0] :
( ~ sP5(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))
& iLess0(sbrdtbr0(sK45(X0)),sbrdtbr0(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45,sK46,sK47]),skolemize(X1,sK45(X0)),skolemize(X2,sK46(X0)),skolemize(X3,sK47(X0))],[f178]) ).
fof(f332,plain,
! [X3] :
( ~ sP4
| sz00 = X3
| ~ aElementOf0(X3,xI)
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK42)) ),
inference(cnf_transformation,[],[f176]) ).
fof(f334,plain,
( ~ sP4
| sz00 != sK42 ),
inference(cnf_transformation,[],[f176]) ).
fof(f335,plain,
( ~ sP4
| aElementOf0(sK42,xI) ),
inference(cnf_transformation,[],[f176]) ).
fof(f341,plain,
! [X0] :
( ~ sP5(X0)
| sz00 != sK45(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f342,plain,
! [X0] :
( ~ sP5(X0)
| aElementOf0(sK45(X0),xI) ),
inference(cnf_transformation,[],[f179]) ).
fof(f346,plain,
! [X0] :
( ~ sP5(X0)
| iLess0(sbrdtbr0(sK45(X0)),sbrdtbr0(X0)) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_204,plain,
( aElementOf0(sK42,xI)
| ~ sP4 ),
inference(cnf_transformation,[],[f335]) ).
tcf(c_205,plain,
( ~ sP4
| ( sz00 != sK42 ) ),
inference(cnf_transformation,[],[f334]) ).
tcf(c_207,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ sP4
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK42)) ),
inference(cnf_transformation,[],[f332]) ).
tcf(c_210,plain,
! [X0: $i] :
( iLess0(sbrdtbr0(sK45(X0)),sbrdtbr0(X0))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f346]) ).
tcf(c_214,plain,
! [X0: $i] :
( aElementOf0(sK45(X0),xI)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f342]) ).
tcf(c_215,plain,
! [X0: $i] :
( ~ sP5(X0)
| ( sK45(X0) != sz00 ) ),
inference(cnf_transformation,[],[f341]) ).
tcf(c_333,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK42))
| ~ aElementOf0(X0,xI) ),
inference(global_subsumption_just,[status(thm)],[c_207,c_209,c_207]) ).
tcf(c_334,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK42)) ),
inference(renaming,[status(thm)],[c_333]) ).
tcf(c_6086,plain,
( sP5(sK42)
| ( sz00 = sK42 )
| ~ sP4 ),
inference(superposition,[status(thm)],[c_204,c_217]) ).
tcf(c_6099,plain,
( sP5(sK42)
| ~ sP4 ),
inference(forward_subsumption_resolution,[status(thm)],[c_6086,c_205]) ).
tcf(c_7508,plain,
( ( sK45(sK42) = sz00 )
| ~ sP5(sK42)
| ~ aElementOf0(sK45(sK42),xI) ),
inference(superposition,[status(thm)],[c_210,c_334]) ).
tcf(c_7512,plain,
~ sP5(sK42),
inference(forward_subsumption_resolution,[status(thm)],[c_7508,c_215,c_214]) ).
tcf(c_7513,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7512,c_6099,c_5694,c_200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG112+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/10.38 % Computer : n008.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Thu Sep 24 08:19:08 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/10.42 Running first-order theorem proving
% 0.14/10.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/10.43
% 0.14/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.43
% 0.14/10.43 % Detected problem language: tptp
% 0.14/10.45 % Proving...
% 0.89/11.21 % SZS status Started for theBenchmark.p
% 0.89/11.21 % SZS status Theorem for theBenchmark.p
% 0.89/11.21
% 0.89/11.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.89/11.21
% 0.89/11.21 % ------ iProver source info
% 0.89/11.21
% 0.89/11.21 % git: date: 2026-07-19 20:42:38 +0200
% 0.89/11.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.89/11.21 % git: non_committed_changes: false
% 0.89/11.21
% 0.89/11.21 % ------ Parsing...
% 0.89/11.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.89/11.21
% 0.89/11.21 % ------ Preprocessing... sup_sim: 0 pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 pe_s pe_e %
% 0.89/11.21
% 0.89/11.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 1 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 0.89/11.21
% 0.89/11.21 % ------ Preprocessing...
% 0.89/11.21 % ------ Proving...
% 0.89/11.21 % ------ Problem Properties
% 0.89/11.21
% 0.89/11.21 %
% 0.89/11.21 % clauses 162
% 0.89/11.21 % conjectures 2
% 0.89/11.21 % EPR 40
% 0.89/11.21 % Horn 130
% 0.89/11.21 % unary 35
% 0.89/11.21 % binary 43
% 0.89/11.21 % lits 465
% 0.89/11.21 % lits eq 73
% 0.89/11.21 % fd_pure 0
% 0.89/11.21 % fd_pseudo 0
% 0.89/11.21 % fd_cond 7
% 0.89/11.21 % fd_pseudo_cond 11
% 0.89/11.21 % AC symbols 0
% 0.89/11.21
% 0.89/11.21 % ------ Input Options Time Limit: Unbounded
% 0.89/11.21
% 0.89/11.21
% 0.89/11.21 % ------
% 0.89/11.21 % Current options:
% 0.89/11.21 % ------
% 0.89/11.21
% 0.89/11.21
% 0.89/11.21 %
% 0.89/11.21
% 0.89/11.21 % ------ Proving...
% 0.89/11.21 %
% 0.89/11.21
% 0.89/11.21 % SZS status Theorem for theBenchmark.p
% 0.89/11.21
% 0.89/11.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.89/11.21
%------------------------------------------------------------------------------