%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG115+1 : 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 : n014.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 02:39:12 PM UTC 2026
% Result : Theorem 103.85s 21.84s
% Output : CNFRefutation 103.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 67 ( 12 unt; 2 def)
% Number of atoms : 330 ( 85 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 428 ( 165 ~; 159 |; 88 &)
% ( 13 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 191 ( 0 sgn 153 !; 38 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f39,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(f42,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(f45,axiom,
( ! [X0] :
( ( X0 != sz00
& aElementOf0(X0,xI) )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).
fof(f47,conjecture,
? [X0,X1] :
( xu = sdtpldt0(X0,X1)
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f48,negated_conjecture,
~ ? [X0,X1] :
( xu = sdtpldt0(X0,X1)
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f82,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(f83,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,[],[f82]) ).
fof(f104,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(f106,plain,
( ! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(ennf_transformation,[],[f45]) ).
fof(f107,plain,
( ! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(flattening,[],[f106]) ).
fof(f109,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) != xu
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(ennf_transformation,[],[f48]) ).
fof(f114,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,[],[f111]) ).
fof(f115,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,[],[f114]) ).
fof(f142,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,[],[f104]) ).
fof(f143,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,[],[f142]) ).
fof(f144,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,[],[f143]) ).
fof(f145,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X5] :
( ( ~ aElementOf0(X5,X1)
| ( sdtasdt0(X0,sK21(X0,X5)) = X5
& aElement0(sK21(X0,X5)) ) )
& ( ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,X1) ) )
& aSet0(X1) ) )
& ( ( ( aElementOf0(sK19(X0,X1),X1)
| ( sK19(X0,X1) = sdtasdt0(X0,sK20(X0,X1))
& aElement0(sK20(X0,X1)) ) )
& ( ~ aElementOf0(sK19(X0,X1),X1)
| ! [X3] :
( sdtasdt0(X0,X3) != sK19(X0,X1)
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21]),skolemize(X2,sK19(X0,X1)),skolemize(X4,sK20(X0,X1)),skolemize(X7,sK21(X0,X5))],[f144]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1)
| sdtpldt1(X1,X0) != X2
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f186,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f233,plain,
! [X0,X1] :
( ~ aElement0(X0)
| slsdtgt0(X0) != X1
| aSet0(X1) ),
inference(cnf_transformation,[],[f145]) ).
fof(f238,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f239,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f242,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[],[f42]) ).
fof(f252,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f107]) ).
fof(f254,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) != xu
| ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(cnf_transformation,[],[f109]) ).
fof(f255,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sP0(sdtpldt1(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f175]) ).
fof(f262,plain,
! [X0] :
( ~ aElement0(X0)
| aSet0(slsdtgt0(X0)) ),
inference(equality_resolution,[],[f233]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt1(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( sP1(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_135,plain,
! [X0: $i] :
( aSet0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f262]) ).
tcf(c_140,plain,
aElement0(xa),
inference(cnf_transformation,[],[f239]) ).
tcf(c_141,plain,
aElement0(xb),
inference(cnf_transformation,[],[f238]) ).
tcf(c_145,plain,
sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
inference(cnf_transformation,[],[f242]) ).
tcf(c_152,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f252]) ).
tcf(c_156,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ aElementOf0(X1,slsdtgt0(xb))
| ~ aElementOf0(X0,slsdtgt0(xa))
| ( sdtpldt0(X0,X1) != xu ) ),
inference(cnf_transformation,[],[f254]) ).
tcf(c_258,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,X2)
| ~ aElementOf0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_427,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,X1)
| ~ aElementOf0(xu,xI)
| ( X1 != xI )
| ( X0 != xu ) ),
inference(instantiation,[status(thm)],[c_265]) ).
tcf(c_1021,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ aElementOf0(xu,xI)
| ( X0 != xu )
| ( sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) != xI ) ),
inference(instantiation,[status(thm)],[c_427]) ).
tcf(c_1543,plain,
xu = xu,
inference(instantiation,[status(thm)],[c_258]) ).
tcf(c_3628,plain,
( aSet0(slsdtgt0(xa))
| ~ aElement0(xa) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_3641,plain,
( aSet0(slsdtgt0(xb))
| ~ aElement0(xb) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_4966,plain,
( aElementOf0(xu,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ aElementOf0(xu,xI)
| ( xu != xu )
| ( sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) != xI ) ),
inference(instantiation,[status(thm)],[c_1021]) ).
fof(f110,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(f111,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(f112,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(definition_folding,[],[f83,f111,f110]) ).
fof(f116,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,[],[f110]) ).
fof(f117,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,[],[f116]) ).
fof(f118,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,[],[f117]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X8] :
( ( ~ aElementOf0(X8,X0)
| ( sdtpldt0(sK7(X1,X2,X8),sK8(X1,X2,X8)) = X8
& aElementOf0(sK8(X1,X2,X8),X2)
& aElementOf0(sK7(X1,X2,X8),X1) ) )
& ( ! [X9,X10] :
( sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X2)
| ~ aElementOf0(X9,X1) )
| aElementOf0(X8,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK4(X0,X1,X2),X0)
| ( sK4(X0,X1,X2) = sdtpldt0(sK5(X0,X1,X2),sK6(X0,X1,X2))
& aElementOf0(sK6(X0,X1,X2),X2)
& aElementOf0(sK5(X0,X1,X2),X1) ) )
& ( ~ aElementOf0(sK4(X0,X1,X2),X0)
| ! [X4,X5] :
( sdtpldt0(X4,X5) != sK4(X0,X1,X2)
| ~ aElementOf0(X5,X2)
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X0)
| sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X6,sK5(X0,X1,X2)),skolemize(X7,sK6(X0,X1,X2)),skolemize(X11,sK7(X1,X2,X8)),skolemize(X12,sK8(X1,X2,X8))],[f118]) ).
fof(f177,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X8,X0)
| sdtpldt0(sK7(X1,X2,X8),sK8(X1,X2,X8)) = X8 ),
inference(cnf_transformation,[],[f119]) ).
fof(f178,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X8,X0)
| aElementOf0(sK8(X1,X2,X8),X2) ),
inference(cnf_transformation,[],[f119]) ).
fof(f179,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X8,X0)
| aElementOf0(sK7(X1,X2,X8),X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(sK7(X1,X2,X3),X1)
| ~ aElementOf0(X3,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(sK8(X1,X2,X3),X2)
| ~ aElementOf0(X3,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sK7(X1,X2,X3),sK8(X1,X2,X3)) = X3 )
| ~ aElementOf0(X3,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_4099,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sK7(X1,X2,X0),X1)
| ~ sP1(X2,X1)
| ~ aElementOf0(X0,sdtpldt1(X1,X2)) ),
inference(resolution,[status(thm)],[c_85,c_78]) ).
tcf(c_4107,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sK8(X1,X2,X0),X2)
| ~ sP1(X2,X1)
| ~ aElementOf0(X0,sdtpldt1(X1,X2)) ),
inference(resolution,[status(thm)],[c_86,c_78]) ).
tcf(c_11457,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sK7(X1,X2,X0),sK8(X1,X2,X0)) = X0 )
| ~ sP1(X2,X1)
| ~ aElementOf0(X0,sdtpldt1(X1,X2)) ),
inference(resolution,[status(thm)],[c_87,c_78]) ).
tcf(c_121004,plain,
! [X0: $i,X1: $i] :
( ~ sP1(X1,X0)
| ~ aElementOf0(xu,sdtpldt1(X0,X1))
| ~ aElementOf0(sK8(X0,X1,xu),slsdtgt0(xb))
| ~ aElementOf0(sK7(X0,X1,xu),slsdtgt0(xa)) ),
inference(resolution,[status(thm)],[c_11457,c_156]) ).
tcf(c_122335,plain,
! [X0: $i] :
( ~ sP1(slsdtgt0(xb),X0)
| ~ aElementOf0(xu,sdtpldt1(X0,slsdtgt0(xb)))
| ~ aElementOf0(sK7(X0,slsdtgt0(xb),xu),slsdtgt0(xa)) ),
inference(resolution,[status(thm)],[c_121004,c_4107]) ).
tcf(c_122791,plain,
( ~ sP1(slsdtgt0(xb),slsdtgt0(xa))
| ~ aElementOf0(xu,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(resolution,[status(thm)],[c_122335,c_4099]) ).
tcf(c_122805,plain,
~ sP1(slsdtgt0(xb),slsdtgt0(xa)),
inference(global_subsumption_just,[status(thm)],[c_122791,c_152,c_145,c_1543,c_4966,c_122791]) ).
tcf(c_122811,plain,
( ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa)) ),
inference(resolution,[status(thm)],[c_122805,c_88]) ).
tcf(c_122812,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_122811,c_3641,c_3628,c_140,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG115+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n014.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Thu Sep 24 08:18:24 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 103.85/21.84 % SZS status Started for theBenchmark.p
% 103.85/21.84 % SZS status Theorem for theBenchmark.p
% 103.85/21.84
% 103.85/21.84 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 103.85/21.84
% 103.85/21.84 % ------ iProver source info
% 103.85/21.84
% 103.85/21.84 % git: date: 2026-07-19 20:42:38 +0200
% 103.85/21.84 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 103.85/21.84 % git: non_committed_changes: false
% 103.85/21.84
% 103.85/21.84 % ------ Parsing...
% 103.85/21.84 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 103.85/21.84
% 103.85/21.84 % ------ Preprocessing... sf_s rm: 1 0s sf_e %
% 103.85/21.84
% 103.85/21.84 % ------ Preprocessing...%
% 103.85/21.84
% 103.85/21.84 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 103.85/21.84 % ------ Proving...
% 103.85/21.84 % ------ Problem Properties
% 103.85/21.84
% 103.85/21.84 %
% 103.85/21.84 % clauses 108
% 103.85/21.84 % conjectures 1
% 103.85/21.84 % EPR 24
% 103.85/21.84 % Horn 84
% 103.85/21.84 % unary 16
% 103.85/21.84 % binary 18
% 103.85/21.84 % lits 368
% 103.85/21.84 % lits eq 51
% 103.85/21.84 % fd_pure 0
% 103.85/21.84 % fd_pseudo 0
% 103.85/21.84 % fd_cond 5
% 103.85/21.84 % fd_pseudo_cond 11
% 103.85/21.84 % AC symbols 0
% 103.85/21.84
% 103.85/21.84 % ------ Input Options Time Limit: Unbounded
% 103.85/21.84
% 103.85/21.84
% 103.85/21.84 % ------
% 103.85/21.84 % Current options:
% 103.85/21.84 % ------
% 103.85/21.84
% 103.85/21.84
% 103.85/21.84 %
% 103.85/21.84
% 103.85/21.84 % ------ Proving...
% 103.85/21.84 %
% 103.85/21.84
% 103.85/21.84 % SZS status Theorem for theBenchmark.p
% 103.85/21.84
% 103.85/21.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 103.85/21.84
% 103.85/21.84
%------------------------------------------------------------------------------