%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG111+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 : n004.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 0.99s 1.76s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 46 ( 6 unt; 2 def)
% Number of atoms : 365 ( 120 equ)
% Maximal formula atoms : 33 ( 7 avg)
% Number of connectives : 485 ( 166 ~; 126 |; 175 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 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 : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 162 ( 0 sgn 78 !; 84 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f45,conjecture,
! [X0] :
( ( X0 != sz00
& aElementOf0(X0,xI)
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
=> ( ! [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))
=> ? [X2] :
( ! [X3] :
( ( X3 != sz00
& ( aElementOf0(X3,xI)
| ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) )
& X2 != sz00
& aElementOf0(X2,xI)
& ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,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__) ).
fof(f46,negated_conjecture,
~ ! [X0] :
( ( X0 != sz00
& aElementOf0(X0,xI)
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
=> ( ! [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))
=> ? [X2] :
( ! [X3] :
( ( X3 != sz00
& ( aElementOf0(X3,xI)
| ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) )
& X2 != sz00
& aElementOf0(X2,xI)
& ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,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)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f58,plain,
~ ! [X0] :
( ( X0 != sz00
& aElementOf0(X0,xI)
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
=> ( ! [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))
=> ? [X6] :
( ! [X9] :
( ( sz00 != X9
& ( aElementOf0(X9,xI)
| ? [X10,X11] :
( sdtpldt0(X10,X11) = X9
& aElementOf0(X11,slsdtgt0(xb))
& aElementOf0(X10,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X9),sbrdtbr0(X6)) )
& sz00 != X6
& aElementOf0(X6,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X6
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) ) ) )
=> ? [X12] :
( ! [X15] :
( ( sz00 != X15
& aElementOf0(X15,xI)
& ? [X16,X17] :
( sdtpldt0(X16,X17) = X15
& aElementOf0(X17,slsdtgt0(xb))
& aElementOf0(X16,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X15),sbrdtbr0(X12)) )
& sz00 != X12
& ( aElementOf0(X12,xI)
| ? [X13,X14] :
( sdtpldt0(X13,X14) = X12
& aElementOf0(X14,slsdtgt0(xb))
& aElementOf0(X13,slsdtgt0(xa)) ) ) ) ) ),
inference(rectify,[],[f46]) ).
fof(f112,plain,
? [X0] :
( X0 != sz00
& aElementOf0(X0,xI)
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [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))
| ? [X6] :
( ! [X9] :
( sz00 = X9
| ( ~ aElementOf0(X9,xI)
& ! [X10,X11] :
( sdtpldt0(X10,X11) != X9
| ~ aElementOf0(X11,slsdtgt0(xb))
| ~ aElementOf0(X10,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X9),sbrdtbr0(X6)) )
& sz00 != X6
& aElementOf0(X6,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X6
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) ) )
& ! [X12] :
( ? [X15] :
( sz00 != X15
& aElementOf0(X15,xI)
& ? [X16,X17] :
( sdtpldt0(X16,X17) = X15
& aElementOf0(X17,slsdtgt0(xb))
& aElementOf0(X16,slsdtgt0(xa)) )
& iLess0(sbrdtbr0(X15),sbrdtbr0(X12)) )
| sz00 = X12
| ( ~ aElementOf0(X12,xI)
& ! [X13,X14] :
( sdtpldt0(X13,X14) != X12
| ~ aElementOf0(X14,slsdtgt0(xb))
| ~ aElementOf0(X13,slsdtgt0(xa)) ) ) ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f113,plain,
? [X0] :
( X0 != sz00
& aElementOf0(X0,xI)
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [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))
| ? [X6] :
( ! [X9] :
( sz00 = X9
| ( ~ aElementOf0(X9,xI)
& ! [X10,X11] :
( sdtpldt0(X10,X11) != X9
| ~ aElementOf0(X11,slsdtgt0(xb))
| ~ aElementOf0(X10,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X9),sbrdtbr0(X6)) )
& sz00 != X6
& aElementOf0(X6,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X6
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) ) )
& ! [X12] :
( ? [X15] :
( sz00 != X15
& aElementOf0(X15,xI)
& ? [X16,X17] :
( sdtpldt0(X16,X17) = X15
& aElementOf0(X17,slsdtgt0(xb))
& aElementOf0(X16,slsdtgt0(xa)) )
& iLess0(sbrdtbr0(X15),sbrdtbr0(X12)) )
| sz00 = X12
| ( ~ aElementOf0(X12,xI)
& ! [X13,X14] :
( sdtpldt0(X13,X14) != X12
| ~ aElementOf0(X14,slsdtgt0(xb))
| ~ aElementOf0(X13,slsdtgt0(xa)) ) ) ) ),
inference(flattening,[],[f112]) ).
fof(f169,plain,
! [X12] :
( ~ sP5(X12)
| ? [X15] :
( sz00 != X15
& aElementOf0(X15,xI)
& ? [X16,X17] :
( sdtpldt0(X16,X17) = X15
& aElementOf0(X17,slsdtgt0(xb))
& aElementOf0(X16,slsdtgt0(xa)) )
& iLess0(sbrdtbr0(X15),sbrdtbr0(X12)) ) ),
inference(nnf_transformation,[],[f121]) ).
fof(f170,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,[],[f169]) ).
fof(f171,plain,
! [X0] :
( ~ sP5(X0)
| ( sz00 != sK42(X0)
& aElementOf0(sK42(X0),xI)
& sK42(X0) = sdtpldt0(sK43(X0),sK44(X0))
& aElementOf0(sK44(X0),slsdtgt0(xb))
& aElementOf0(sK43(X0),slsdtgt0(xa))
& iLess0(sbrdtbr0(sK42(X0)),sbrdtbr0(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42,sK43,sK44]),skolemize(X1,sK42(X0)),skolemize(X2,sK43(X0)),skolemize(X3,sK44(X0))],[f170]) ).
fof(f175,plain,
? [X0] :
( X0 != sz00
& aElementOf0(X0,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X0
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) )
& ! [X4] :
( sz00 = X4
| ( ~ aElementOf0(X4,xI)
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X0))
| sP4 )
& ! [X1] :
( sP5(X1)
| sz00 = X1
| ( ~ aElementOf0(X1,xI)
& ! [X2,X3] :
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa)) ) ) ) ),
inference(rectify,[],[f122]) ).
fof(f176,plain,
( sz00 != sK48
& aElementOf0(sK48,xI)
& sK48 = sdtpldt0(sK49,sK50)
& aElementOf0(sK50,slsdtgt0(xb))
& aElementOf0(sK49,slsdtgt0(xa))
& ! [X4] :
( sz00 = X4
| ( ~ aElementOf0(X4,xI)
& ! [X5,X6] :
( sdtpldt0(X5,X6) != X4
| ~ aElementOf0(X6,slsdtgt0(xb))
| ~ aElementOf0(X5,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X4),sbrdtbr0(sK48))
| sP4 )
& ! [X1] :
( sP5(X1)
| sz00 = X1
| ( ~ aElementOf0(X1,xI)
& ! [X2,X3] :
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48,sK49,sK50]),skolemize(X0,sK48),skolemize(X7,sK49),skolemize(X8,sK50)],[f175]) ).
fof(f329,plain,
! [X0] :
( ~ sP5(X0)
| sz00 != sK42(X0) ),
inference(cnf_transformation,[],[f171]) ).
fof(f330,plain,
! [X0] :
( ~ sP5(X0)
| aElementOf0(sK42(X0),xI) ),
inference(cnf_transformation,[],[f171]) ).
fof(f334,plain,
! [X0] :
( ~ sP5(X0)
| iLess0(sbrdtbr0(sK42(X0)),sbrdtbr0(X0)) ),
inference(cnf_transformation,[],[f171]) ).
fof(f342,plain,
sz00 != sK48,
inference(cnf_transformation,[],[f176]) ).
fof(f343,plain,
aElementOf0(sK48,xI),
inference(cnf_transformation,[],[f176]) ).
fof(f347,plain,
! [X4] :
( sz00 = X4
| ~ aElementOf0(X4,xI)
| ~ iLess0(sbrdtbr0(X4),sbrdtbr0(sK48))
| sP4 ),
inference(cnf_transformation,[],[f176]) ).
fof(f349,plain,
! [X1] :
( sP5(X1)
| sz00 = X1
| ~ aElementOf0(X1,xI) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_201,plain,
! [X0: $i] :
( iLess0(sbrdtbr0(sK42(X0)),sbrdtbr0(X0))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f334]) ).
tcf(c_205,plain,
! [X0: $i] :
( aElementOf0(sK42(X0),xI)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f330]) ).
tcf(c_206,plain,
! [X0: $i] :
( ~ sP5(X0)
| ( sK42(X0) != sz00 ) ),
inference(cnf_transformation,[],[f329]) ).
tcf(c_215,negated_conjecture,
! [X0: $i] :
( sP5(X0)
| ( X0 = sz00 )
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f349]) ).
tcf(c_217,negated_conjecture,
! [X0: $i] :
( sP4
| ( X0 = sz00 )
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK48)) ),
inference(cnf_transformation,[],[f347]) ).
tcf(c_221,negated_conjecture,
aElementOf0(sK48,xI),
inference(cnf_transformation,[],[f343]) ).
tcf(c_222,negated_conjecture,
sz00 != sK48,
inference(cnf_transformation,[],[f342]) ).
tcf(c_6736,plain,
( sP5(sK48)
| ( sz00 = sK48 ) ),
inference(superposition,[status(thm)],[c_221,c_215]) ).
tcf(c_9187,plain,
( sP4
| ( sK42(sK48) = sz00 )
| ~ sP5(sK48)
| ~ aElementOf0(sK42(sK48),xI) ),
inference(superposition,[status(thm)],[c_201,c_217]) ).
tcf(c_9192,plain,
( sP4
| ~ sP5(sK48) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9187,c_206,c_205]) ).
fof(f120,definition,
( ~ sP4
| ? [X6] :
( ! [X9] :
( sz00 = X9
| ( ~ aElementOf0(X9,xI)
& ! [X10,X11] :
( sdtpldt0(X10,X11) != X9
| ~ aElementOf0(X11,slsdtgt0(xb))
| ~ aElementOf0(X10,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X9),sbrdtbr0(X6)) )
& sz00 != X6
& aElementOf0(X6,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X6
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f121,definition,
! [X12] :
( ~ sP5(X12)
| ? [X15] :
( sz00 != X15
& aElementOf0(X15,xI)
& ? [X16,X17] :
( sdtpldt0(X16,X17) = X15
& aElementOf0(X17,slsdtgt0(xb))
& aElementOf0(X16,slsdtgt0(xa)) )
& iLess0(sbrdtbr0(X15),sbrdtbr0(X12)) ) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f122,plain,
? [X0] :
( X0 != sz00
& aElementOf0(X0,xI)
& ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) )
& ! [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))
| sP4 )
& ! [X12] :
( sP5(X12)
| sz00 = X12
| ( ~ aElementOf0(X12,xI)
& ! [X13,X14] :
( sdtpldt0(X13,X14) != X12
| ~ aElementOf0(X14,slsdtgt0(xb))
| ~ aElementOf0(X13,slsdtgt0(xa)) ) ) ) ),
inference(definition_folding,[],[f113,f121,f120]) ).
fof(f172,plain,
( ~ sP4
| ? [X6] :
( ! [X9] :
( sz00 = X9
| ( ~ aElementOf0(X9,xI)
& ! [X10,X11] :
( sdtpldt0(X10,X11) != X9
| ~ aElementOf0(X11,slsdtgt0(xb))
| ~ aElementOf0(X10,slsdtgt0(xa)) ) )
| ~ iLess0(sbrdtbr0(X9),sbrdtbr0(X6)) )
& sz00 != X6
& aElementOf0(X6,xI)
& ? [X7,X8] :
( sdtpldt0(X7,X8) = X6
& aElementOf0(X8,slsdtgt0(xb))
& aElementOf0(X7,slsdtgt0(xa)) ) ) ),
inference(nnf_transformation,[],[f120]) ).
fof(f173,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,[],[f172]) ).
fof(f174,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(sK45)) )
& sz00 != sK45
& aElementOf0(sK45,xI)
& sK45 = sdtpldt0(sK46,sK47)
& aElementOf0(sK47,slsdtgt0(xb))
& aElementOf0(sK46,slsdtgt0(xa)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45,sK46,sK47]),skolemize(X0,sK45),skolemize(X1,sK46),skolemize(X2,sK47)],[f173]) ).
fof(f335,plain,
! [X3] :
( ~ sP4
| sz00 = X3
| ~ aElementOf0(X3,xI)
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(sK45)) ),
inference(cnf_transformation,[],[f174]) ).
fof(f337,plain,
( ~ sP4
| sz00 != sK45 ),
inference(cnf_transformation,[],[f174]) ).
fof(f338,plain,
( ~ sP4
| aElementOf0(sK45,xI) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_210,plain,
( aElementOf0(sK45,xI)
| ~ sP4 ),
inference(cnf_transformation,[],[f338]) ).
tcf(c_211,plain,
( ~ sP4
| ( sz00 != sK45 ) ),
inference(cnf_transformation,[],[f337]) ).
tcf(c_213,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ sP4
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK45)) ),
inference(cnf_transformation,[],[f335]) ).
tcf(c_6735,plain,
( sP5(sK45)
| ( sz00 = sK45 )
| ~ sP4 ),
inference(superposition,[status(thm)],[c_210,c_215]) ).
tcf(c_6752,plain,
( sP5(sK45)
| ~ sP4 ),
inference(forward_subsumption_resolution,[status(thm)],[c_6735,c_211]) ).
tcf(c_9722,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK45))
| ~ aElementOf0(X0,xI) ),
inference(global_subsumption_just,[status(thm)],[c_213,c_222,c_213,c_6736,c_9192]) ).
tcf(c_9723,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK45)) ),
inference(renaming,[status(thm)],[c_9722]) ).
tcf(c_9728,plain,
( ( sK42(sK45) = sz00 )
| ~ sP5(sK45)
| ~ aElementOf0(sK42(sK45),xI) ),
inference(superposition,[status(thm)],[c_201,c_9723]) ).
tcf(c_9732,plain,
~ sP5(sK45),
inference(forward_subsumption_resolution,[status(thm)],[c_9728,c_206,c_205]) ).
tcf(c_9733,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9732,c_9192,c_6736,c_6752,c_222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG111+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 08:17:05 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.42 % Proving...
% 0.99/1.76 % SZS status Started for theBenchmark.p
% 0.99/1.76 % SZS status Theorem for theBenchmark.p
% 0.99/1.76
% 0.99/1.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.99/1.76
% 0.99/1.76 % ------ iProver source info
% 0.99/1.76
% 0.99/1.76 % git: date: 2026-07-19 20:42:38 +0200
% 0.99/1.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.99/1.76 % git: non_committed_changes: false
% 0.99/1.76
% 0.99/1.76 % ------ Parsing...
% 0.99/1.76 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.99/1.76
% 0.99/1.76 % ------ Preprocessing... sup_sim: 0 pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 pe_s pe_e %
% 0.99/1.76
% 0.99/1.76 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 1 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 0.99/1.76
% 0.99/1.76 % ------ Preprocessing...
% 0.99/1.76 % ------ Proving...
% 0.99/1.76 % ------ Problem Properties
% 0.99/1.76
% 0.99/1.76 %
% 0.99/1.76 % clauses 167
% 0.99/1.76 % conjectures 9
% 0.99/1.76 % EPR 41
% 0.99/1.76 % Horn 135
% 0.99/1.76 % unary 40
% 0.99/1.76 % binary 43
% 0.99/1.76 % lits 474
% 0.99/1.76 % lits eq 75
% 0.99/1.76 % fd_pure 0
% 0.99/1.76 % fd_pseudo 0
% 0.99/1.76 % fd_cond 7
% 0.99/1.76 % fd_pseudo_cond 11
% 0.99/1.76 % AC symbols 0
% 0.99/1.76
% 0.99/1.76 % ------ Input Options Time Limit: Unbounded
% 0.99/1.76
% 0.99/1.76
% 0.99/1.76 % ------
% 0.99/1.76 % Current options:
% 0.99/1.76 % ------
% 0.99/1.76
% 0.99/1.76
% 0.99/1.76 %
% 0.99/1.76
% 0.99/1.76 % ------ Proving...
% 0.99/1.76 %
% 0.99/1.76
% 0.99/1.76 % SZS status Theorem for theBenchmark.p
% 0.99/1.76
% 0.99/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.99/1.77
% 0.99/1.77
%------------------------------------------------------------------------------