%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG121+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 02:39:13 PM UTC 2026
% Result : Theorem 17.62s 4.16s
% Output : CNFRefutation 17.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 76 ( 20 unt; 2 def)
% Number of atoms : 344 ( 103 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 434 ( 166 ~; 170 |; 82 &)
% ( 13 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 184 ( 0 sgn 150 !; 34 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] :
( aElement0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(f22,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSSum) ).
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f39,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(f43,axiom,
( aElementOf0(xb,slsdtgt0(xb))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xa)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2203) ).
fof(f53,conjecture,
aElementOf0(xb,xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f54,negated_conjecture,
~ aElementOf0(xb,xI),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ aElementOf0(xb,xI),
inference(flattening,[],[f54]) ).
fof(f69,plain,
! [X0] :
( ~ aElement0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f118,plain,
! [X1,X0] :
( ~ sP1(X1,X0)
| ! [X2] :
( ( sdtpldt1(X0,X1) != X2
| sP0(X2,X0,X1) )
& ( ~ sP0(X2,X0,X1)
| X2 = sdtpldt1(X0,X1) ) ) ),
inference(nnf_transformation,[],[f106]) ).
fof(f119,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ! [X2] :
( ( sdtpldt1(X1,X0) != X2
| sP0(X2,X1,X0) )
& ( ~ sP0(X2,X1,X0)
| sdtpldt1(X1,X0) = X2 ) ) ),
inference(rectify,[],[f118]) ).
fof(f124,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& ( ~ aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f125,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& ( ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) )
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X2
& aElement0(X3) ) )
& ( ~ aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(flattening,[],[f124]) ).
fof(f126,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X5] :
( ( ~ aElementOf0(X5,X1)
| ? [X7] :
( sdtasdt0(X0,X7) = X5
& aElement0(X7) ) )
& ( ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ? [X4] :
( sdtasdt0(X0,X4) = X2
& aElement0(X4) ) )
& ( ~ aElementOf0(X2,X1)
| ! [X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(rectify,[],[f125]) ).
fof(f127,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X5] :
( ( ~ aElementOf0(X5,X1)
| ( sdtasdt0(X0,sK16(X0,X5)) = X5
& aElement0(sK16(X0,X5)) ) )
& ( ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,X1) ) )
& aSet0(X1) ) )
& ( ( ( aElementOf0(sK14(X0,X1),X1)
| ( sK14(X0,X1) = sdtasdt0(X0,sK15(X0,X1))
& aElement0(sK15(X0,X1)) ) )
& ( ~ aElementOf0(sK14(X0,X1),X1)
| ! [X3] :
( sdtasdt0(X0,X3) != sK14(X0,X1)
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X2,sK14(X0,X1)),skolemize(X4,sK15(X0,X1)),skolemize(X7,sK16(X0,X5))],[f126]) ).
fof(f135,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f136,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f139,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f42]) ).
fof(f141,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[],[f43]) ).
fof(f144,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[],[f43]) ).
fof(f162,plain,
~ aElementOf0(xb,xI),
inference(cnf_transformation,[],[f55]) ).
fof(f166,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f69]) ).
fof(f185,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1)
| sdtpldt1(X1,X0) != X2
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f196,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f200,plain,
! [X0,X1] :
( ~ aElement0(X0)
| slsdtgt0(X0) != X1
| aSet0(X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f236,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sP0(sdtpldt1(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f185]) ).
fof(f238,plain,
! [X0] :
( ~ aElement0(X0)
| aSet0(slsdtgt0(X0)) ),
inference(equality_resolution,[],[f200]) ).
tcf(c_49,plain,
aElement0(xa),
inference(cnf_transformation,[],[f136]) ).
tcf(c_50,plain,
aElement0(xb),
inference(cnf_transformation,[],[f135]) ).
tcf(c_54,plain,
sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
inference(cnf_transformation,[],[f139]) ).
tcf(c_55,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[],[f144]) ).
tcf(c_58,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[],[f141]) ).
tcf(c_76,negated_conjecture,
~ aElementOf0(xb,xI),
inference(cnf_transformation,[],[f162]) ).
tcf(c_81,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt1(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( sP1(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_114,plain,
! [X0: $i] :
( aSet0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f238]) ).
tcf(c_1320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(sdtpldt1(X2,X0),X2,X0)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_100,c_110]) ).
tcf(c_1321,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt1(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(unflattening,[status(thm)],[c_1320]) ).
tcf(c_4877,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_4879,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,X2)
| ~ aElementOf0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_6322,plain,
sdtpldt0(sz00,xb) = xb,
inference(superposition,[status(thm)],[c_50,c_81]) ).
tcf(c_8492,plain,
xb = xb,
inference(instantiation,[status(thm)],[c_4877]) ).
tcf(c_8720,plain,
xI = xI,
inference(instantiation,[status(thm)],[c_4877]) ).
tcf(c_15200,plain,
( aSet0(slsdtgt0(xa))
| ~ aElement0(xa) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_15592,plain,
( aSet0(slsdtgt0(xb))
| ~ aElement0(xb) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_56618,plain,
! [X0: $i] :
( sP0(sdtpldt1(slsdtgt0(xa),X0),slsdtgt0(xa),X0)
| ~ aSet0(X0)
| ~ aSet0(slsdtgt0(xa)) ),
inference(instantiation,[status(thm)],[c_1321]) ).
tcf(c_74379,plain,
( sP0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),slsdtgt0(xa),slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa)) ),
inference(instantiation,[status(thm)],[c_56618]) ).
tcf(c_76764,plain,
! [X0: $i,X1: $i] :
( aElementOf0(xb,xI)
| ~ aElementOf0(X0,X1)
| ( xI != X1 )
| ( xb != X0 ) ),
inference(instantiation,[status(thm)],[c_4885]) ).
tcf(c_76834,plain,
! [X0: $i,X1: $i] :
( ( xb = X0 )
| ( xb != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_4879]) ).
tcf(c_77107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = sdtpldt1(X0,X1) )
| ( X3 != X2 )
| ( sdtpldt1(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_4879]) ).
tcf(c_77169,plain,
! [X0: $i] :
( ( xb = X0 )
| ( xb != xb )
| ( X0 != xb ) ),
inference(instantiation,[status(thm)],[c_76834]) ).
tcf(c_78041,plain,
! [X0: $i] :
( ( X0 = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) )
| ( X0 != xI )
| ( sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) != xI ) ),
inference(instantiation,[status(thm)],[c_77107]) ).
tcf(c_78163,plain,
( ( xb = sdtpldt0(sz00,xb) )
| ( xb != xb )
| ( sdtpldt0(sz00,xb) != xb ) ),
inference(instantiation,[status(thm)],[c_77169]) ).
tcf(c_79162,plain,
( ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) )
| ( xI != xI )
| ( sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) != xI ) ),
inference(instantiation,[status(thm)],[c_78041]) ).
tcf(c_79980,plain,
! [X0: $i] :
( aElementOf0(xb,xI)
| ~ aElementOf0(sdtpldt0(sz00,xb),X0)
| ( xI != X0 )
| ( xb != sdtpldt0(sz00,xb) ) ),
inference(instantiation,[status(thm)],[c_76764]) ).
tcf(c_85657,plain,
( aElementOf0(xb,xI)
| ~ aElementOf0(sdtpldt0(sz00,xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ( xI != sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) )
| ( xb != sdtpldt0(sz00,xb) ) ),
inference(instantiation,[status(thm)],[c_79980]) ).
fof(f105,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f106,definition,
! [X1,X0] :
( ~ sP1(X1,X0)
| ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> sP0(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f107,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(definition_folding,[],[f77,f106,f105]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& ( ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X0) )
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& ( ~ aElementOf0(X3,X2)
| ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X0) ) ) )
| ~ aSet0(X2)
| sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f105]) ).
fof(f121,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& ( ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X0) )
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& ( ~ aElementOf0(X3,X2)
| ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X1)
| ~ aElementOf0(X4,X0) ) ) )
| ~ aSet0(X2)
| sP0(X2,X0,X1) ) ),
inference(flattening,[],[f120]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X8] :
( ( ~ aElementOf0(X8,X0)
| ? [X11,X12] :
( sdtpldt0(X11,X12) = X8
& aElementOf0(X12,X2)
& aElementOf0(X11,X1) ) )
& ( ! [X9,X10] :
( sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X2)
| ~ aElementOf0(X9,X1) )
| aElementOf0(X8,X0) ) )
& aSet0(X0) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X0)
| ? [X6,X7] :
( sdtpldt0(X6,X7) = X3
& aElementOf0(X7,X2)
& aElementOf0(X6,X1) ) )
& ( ~ aElementOf0(X3,X0)
| ! [X4,X5] :
( sdtpldt0(X4,X5) != X3
| ~ aElementOf0(X5,X2)
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X0)
| sP0(X0,X1,X2) ) ),
inference(rectify,[],[f121]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X8] :
( ( ~ aElementOf0(X8,X0)
| ( sdtpldt0(sK12(X1,X2,X8),sK13(X1,X2,X8)) = X8
& aElementOf0(sK13(X1,X2,X8),X2)
& aElementOf0(sK12(X1,X2,X8),X1) ) )
& ( ! [X9,X10] :
( sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X2)
| ~ aElementOf0(X9,X1) )
| aElementOf0(X8,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK9(X0,X1,X2),X0)
| ( sK9(X0,X1,X2) = sdtpldt0(sK10(X0,X1,X2),sK11(X0,X1,X2))
& aElementOf0(sK11(X0,X1,X2),X2)
& aElementOf0(sK10(X0,X1,X2),X1) ) )
& ( ~ aElementOf0(sK9(X0,X1,X2),X0)
| ! [X4,X5] :
( sdtpldt0(X4,X5) != sK9(X0,X1,X2)
| ~ aElementOf0(X5,X2)
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X0)
| sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13]),skolemize(X3,sK9(X0,X1,X2)),skolemize(X6,sK10(X0,X1,X2)),skolemize(X7,sK11(X0,X1,X2)),skolemize(X11,sK12(X1,X2,X8)),skolemize(X12,sK13(X1,X2,X8))],[f122]) ).
fof(f190,plain,
! [X2,X10,X0,X1,X8,X9] :
( ~ sP0(X0,X1,X2)
| sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X2)
| ~ aElementOf0(X9,X1)
| aElementOf0(X8,X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f237,plain,
! [X2,X10,X0,X1,X9] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X10,X2)
| ~ aElementOf0(X9,X1)
| aElementOf0(sdtpldt0(X9,X10),X0) ),
inference(equality_resolution,[],[f190]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( aElementOf0(sdtpldt0(X3,X4),X0)
| ~ aElementOf0(X4,X2)
| ~ aElementOf0(X3,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_6809,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtpldt0(sz00,X2),X0)
| ~ aElementOf0(X2,X1)
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ sP0(X0,slsdtgt0(xa),X1) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_8832,plain,
! [X0: $i] :
( aElementOf0(sdtpldt0(sz00,xb),X0)
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb))
| ~ sP0(X0,slsdtgt0(xa),slsdtgt0(xb)) ),
inference(instantiation,[status(thm)],[c_6809]) ).
tcf(c_74382,plain,
( aElementOf0(sdtpldt0(sz00,xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb))
| ~ sP0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),slsdtgt0(xa),slsdtgt0(xb)) ),
inference(instantiation,[status(thm)],[c_8832]) ).
tcf(c_85665,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_85657,c_79162,c_78163,c_74382,c_74379,c_15592,c_15200,c_8720,c_8492,c_6322,c_54,c_55,c_58,c_76,c_49,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG121+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 08:23:03 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 17.62/4.16 % SZS status Started for theBenchmark.p
% 17.62/4.16 % SZS status Theorem for theBenchmark.p
% 17.62/4.16
% 17.62/4.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.62/4.16
% 17.62/4.16 % ------ iProver source info
% 17.62/4.16
% 17.62/4.16 % git: date: 2026-07-19 20:42:38 +0200
% 17.62/4.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.62/4.16 % git: non_committed_changes: false
% 17.62/4.16
% 17.62/4.16 % ------ Parsing...
% 17.62/4.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.62/4.16
% 17.62/4.16 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 17.62/4.16
% 17.62/4.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 17.62/4.16
% 17.62/4.16 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.62/4.16 % ------ Proving...
% 17.62/4.16 % ------ Problem Properties
% 17.62/4.16
% 17.62/4.16 %
% 17.62/4.16 % clauses 100
% 17.62/4.16 % conjectures 1
% 17.62/4.16 % EPR 30
% 17.62/4.16 % Horn 81
% 17.62/4.16 % unary 29
% 17.62/4.16 % binary 16
% 17.62/4.16 % lits 283
% 17.62/4.16 % lits eq 50
% 17.62/4.16 % fd_pure 0
% 17.62/4.16 % fd_pseudo 0
% 17.62/4.16 % fd_cond 5
% 17.62/4.16 % fd_pseudo_cond 8
% 17.62/4.16 % AC symbols 0
% 17.62/4.16
% 17.62/4.16 % ------ Schedule dynamic 5 is on
% 17.62/4.16
% 17.62/4.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.62/4.16
% 17.62/4.16
% 17.62/4.16 % ------
% 17.62/4.16 % Current options:
% 17.62/4.16 % ------
% 17.62/4.16
% 17.62/4.16
% 17.62/4.16 %
% 17.62/4.16
% 17.62/4.16 % ------ Proving...
% 17.62/4.16 %
% 17.62/4.16
% 17.62/4.16 % SZS status Theorem for theBenchmark.p
% 17.62/4.16
% 17.62/4.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.62/4.16
% 17.62/4.16
%------------------------------------------------------------------------------