%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG118+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 : 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 02:39:13 PM UTC 2026
% Result : Theorem 72.45s 12.43s
% Output : CNFRefutation 72.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 98 ( 18 unt; 0 def)
% Number of atoms : 369 ( 131 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 454 ( 183 ~; 191 |; 63 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 135 ( 0 sgn 116 !; 19 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f16,axiom,
! [X0] :
( aElement0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(f17,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X1 = sz00
| X0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCancel) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f32,axiom,
! [X0,X1] :
( ( X1 != sz00
& aElement0(X1)
& aElement0(X0) )
=> ? [X2,X3] :
( ( X3 != sz00
=> iLess0(sbrdtbr0(X3),sbrdtbr0(X1)) )
& X0 = sdtpldt0(sdtasdt0(X2,X1),X3)
& aElement0(X3)
& aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivision) ).
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(f50,conjecture,
? [X0,X1] :
( ( iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
| X1 = sz00 )
& xb = sdtpldt0(sdtasdt0(X0,xu),X1)
& aElement0(X1)
& aElement0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f51,negated_conjecture,
~ ? [X0,X1] :
( ( iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
| X1 = sz00 )
& xb = sdtpldt0(sdtasdt0(X0,xu),X1)
& aElement0(X1)
& aElement0(X0) ),
inference(negated_conjecture,[status(cth)],[f50]) ).
fof(f55,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f79,plain,
! [X0] :
( ~ aElement0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f80,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(ennf_transformation,[],[f17]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f89,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( ~ aElementOf0(X1,X0)
| ( ! [X3] :
( ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f98,plain,
! [X0,X1] :
( sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0)
| ? [X2,X3] :
( ( sz00 = X3
| iLess0(sbrdtbr0(X3),sbrdtbr0(X1)) )
& X0 = sdtpldt0(sdtasdt0(X2,X1),X3)
& aElement0(X3)
& aElement0(X2) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f99,plain,
! [X0,X1] :
( sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0)
| ? [X2,X3] :
( ( sz00 = X3
| iLess0(sbrdtbr0(X3),sbrdtbr0(X1)) )
& X0 = sdtpldt0(sdtasdt0(X2,X1),X3)
& aElement0(X3)
& aElement0(X2) ) ),
inference(flattening,[],[f98]) ).
fof(f109,plain,
( ! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(ennf_transformation,[],[f45]) ).
fof(f110,plain,
( ! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
inference(flattening,[],[f109]) ).
fof(f112,plain,
! [X0,X1] :
( ( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
& sz00 != X1 )
| xb != sdtpldt0(sdtasdt0(X0,xu),X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f127,plain,
! [X0] :
( ( ~ aIdeal0(X0)
| ( ! [X1] :
( ~ aElementOf0(X1,X0)
| ( ! [X3] :
( ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ( ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) )
| ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f128,plain,
! [X0] :
( ( ~ aIdeal0(X0)
| ( ! [X1] :
( ~ aElementOf0(X1,X0)
| ( ! [X3] :
( ~ aElement0(X3)
| aElementOf0(sdtasdt0(X3,X1),X0) )
& ! [X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ( ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) )
| ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(flattening,[],[f127]) ).
fof(f129,plain,
! [X0] :
( ( ~ aIdeal0(X0)
| ( ! [X4] :
( ~ aElementOf0(X4,X0)
| ( ! [X6] :
( ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),X0) )
& ! [X5] :
( ~ aElementOf0(X5,X0)
| aElementOf0(sdtpldt0(X4,X5),X0) ) ) )
& aSet0(X0) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ( ? [X3] :
( aElement0(X3)
& ~ aElementOf0(sdtasdt0(X3,X1),X0) )
| ? [X2] :
( aElementOf0(X2,X0)
& ~ aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(rectify,[],[f128]) ).
fof(f130,plain,
! [X0] :
( ( ~ aIdeal0(X0)
| ( ! [X4] :
( ~ aElementOf0(X4,X0)
| ( ! [X6] :
( ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),X0) )
& ! [X5] :
( ~ aElementOf0(X5,X0)
| aElementOf0(sdtpldt0(X4,X5),X0) ) ) )
& aSet0(X0) ) )
& ( ( aElementOf0(sK10(X0),X0)
& ( ( aElement0(sK12(X0))
& ~ aElementOf0(sdtasdt0(sK12(X0),sK10(X0)),X0) )
| ( aElementOf0(sK11(X0),X0)
& ~ aElementOf0(sdtpldt0(sK10(X0),sK11(X0)),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X1,sK10(X0)),skolemize(X2,sK11(X0)),skolemize(X3,sK12(X0))],[f129]) ).
fof(f134,plain,
! [X0,X1] :
( sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0)
| ( ( sz00 = sK16(X0,X1)
| iLess0(sbrdtbr0(sK16(X0,X1)),sbrdtbr0(X1)) )
& sdtpldt0(sdtasdt0(sK15(X0,X1),X1),sK16(X0,X1)) = X0
& aElement0(sK16(X0,X1))
& aElement0(sK15(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X2,sK15(X0,X1)),skolemize(X3,sK16(X0,X1))],[f99]) ).
fof(f151,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f170,plain,
! [X0] :
( ~ aElement0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f172,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f81]) ).
fof(f174,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f200,plain,
! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f216,plain,
! [X0,X1] :
( sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0)
| sz00 = sK16(X0,X1)
| iLess0(sbrdtbr0(sK16(X0,X1)),sbrdtbr0(X1)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f217,plain,
! [X0,X1] :
( sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0)
| sdtpldt0(sdtasdt0(sK15(X0,X1),X1),sK16(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f218,plain,
! [X0,X1] :
( sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sK16(X0,X1)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f219,plain,
! [X0,X1] :
( sz00 = X1
| ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sK15(X0,X1)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f242,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f247,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f42]) ).
fof(f255,plain,
sz00 != xu,
inference(cnf_transformation,[],[f110]) ).
fof(f256,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f110]) ).
fof(f263,plain,
! [X0,X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
| xb != sdtpldt0(sdtasdt0(X0,xu),X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f264,plain,
! [X0,X1] :
( sz00 != X1
| xb != sdtpldt0(sdtasdt0(X0,xu),X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f277,plain,
! [X0] :
( xb != sdtpldt0(sdtasdt0(X0,xu),sz00)
| ~ aElement0(sz00)
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f264]) ).
tcf(c_49,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f151]) ).
tcf(c_69,plain,
! [X0: $i] :
( ( sdtasdt0(sz00,X0) = sz00 )
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( X0 = sz00 )
| ~ aElement0(X1)
| ~ aElement0(X0)
| ( sdtasdt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_101,plain,
! [X0: $i] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( aElement0(sK15(X0,X1))
| ( X1 = sz00 )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( aElement0(sK16(X0,X1))
| ( X1 = sz00 )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( sdtpldt0(sdtasdt0(sK15(X0,X1),X1),sK16(X0,X1)) = X0 )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( iLess0(sbrdtbr0(sK16(X0,X1)),sbrdtbr0(X1))
| ( X1 = sz00 )
| ( sK16(X0,X1) = sz00 )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_141,plain,
aElement0(xb),
inference(cnf_transformation,[],[f242]) ).
tcf(c_144,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f247]) ).
tcf(c_152,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[],[f256]) ).
tcf(c_153,plain,
sz00 != xu,
inference(cnf_transformation,[],[f255]) ).
tcf(c_161,negated_conjecture,
! [X0: $i] :
( ~ aElement0(sz00)
| ~ aElement0(X0)
| ( sdtpldt0(sdtasdt0(X0,xu),sz00) != xb ) ),
inference(cnf_transformation,[],[f277]) ).
tcf(c_162,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
| ( sdtpldt0(sdtasdt0(X0,xu),X1) != xb ) ),
inference(cnf_transformation,[],[f263]) ).
tcf(c_170,plain,
( ( sdtasdt0(sz00,sz00) = sz00 )
| ~ aElement0(sz00) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_223,plain,
( ( sz00 = sz00 )
| ~ aElement0(sz00)
| ( sdtasdt0(sz00,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_243,plain,
! [X0: $i] :
( ( sdtpldt0(sdtasdt0(X0,xu),sz00) != xb )
| ~ aElement0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_161,c_49,c_161]) ).
tcf(c_244,negated_conjecture,
! [X0: $i] :
( ~ aElement0(X0)
| ( sdtpldt0(sdtasdt0(X0,xu),sz00) != xb ) ),
inference(renaming,[status(thm)],[c_243]) ).
tcf(c_5754,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_5756,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_5759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(X0,X2) = sdtpldt0(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_7443,plain,
! [X0: $i] :
( ( sz00 = xu )
| ( xu != X0 )
| ( sz00 != X0 ) ),
inference(instantiation,[status(thm)],[c_5756]) ).
tcf(c_7444,plain,
( ( sz00 = xu )
| ( xu != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_7443]) ).
tcf(c_7509,plain,
aSet0(xI),
inference(superposition,[status(thm)],[c_144,c_101]) ).
tcf(c_7567,plain,
! [X0: $i,X1: $i] :
( ( xb = X0 )
| ( xb != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_5756]) ).
tcf(c_7702,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(superposition,[status(thm)],[c_152,c_72]) ).
tcf(c_7705,plain,
aElement0(xu),
inference(forward_subsumption_resolution,[status(thm)],[c_7702,c_7509]) ).
tcf(c_8215,plain,
! [X0: $i,X1: $i] : sdtasdt0(X0,X1) = sdtasdt0(X0,X1),
inference(instantiation,[status(thm)],[c_5754]) ).
tcf(c_9131,plain,
! [X0: $i] :
( ( xu = sz00 )
| ( sdtpldt0(sdtasdt0(sK15(X0,xu),xu),sK16(X0,xu)) = X0 )
| ~ aElement0(xu)
| ~ aElement0(X0) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_9134,plain,
! [X0: $i] :
( aElement0(sK16(X0,xu))
| ( xu = sz00 )
| ~ aElement0(xu)
| ~ aElement0(X0) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_9135,plain,
! [X0: $i] :
( aElement0(sK15(X0,xu))
| ( xu = sz00 )
| ~ aElement0(xu)
| ~ aElement0(X0) ),
inference(instantiation,[status(thm)],[c_114]) ).
tcf(c_9203,plain,
! [X0: $i] :
( ( xb = X0 )
| ( xb != xb )
| ( X0 != xb ) ),
inference(instantiation,[status(thm)],[c_7567]) ).
tcf(c_9204,plain,
xb = xb,
inference(instantiation,[status(thm)],[c_5754]) ).
tcf(c_10386,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_5756,c_5754]) ).
tcf(c_20051,plain,
( ( xu = sz00 )
| ( sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu)) = xb )
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(instantiation,[status(thm)],[c_9131]) ).
tcf(c_22721,plain,
( ( xu = sz00 )
| ~ aElement0(xu)
| ~ aElement0(xb)
| ~ aElement0(sK16(xb,xu))
| ~ aElement0(sK15(xb,xu))
| ~ iLess0(sbrdtbr0(sK16(xb,xu)),sbrdtbr0(xu)) ),
inference(resolution,[status(thm)],[c_162,c_116]) ).
tcf(c_22722,plain,
( ~ iLess0(sbrdtbr0(sK16(xb,xu)),sbrdtbr0(xu))
| ~ aElement0(sK15(xb,xu))
| ~ aElement0(sK16(xb,xu)) ),
inference(global_subsumption_just,[status(thm)],[c_22721,c_141,c_49,c_153,c_170,c_223,c_7444,c_7705,c_22721]) ).
tcf(c_22723,plain,
( ~ aElement0(sK16(xb,xu))
| ~ aElement0(sK15(xb,xu))
| ~ iLess0(sbrdtbr0(sK16(xb,xu)),sbrdtbr0(xu)) ),
inference(renaming,[status(thm)],[c_22722]) ).
tcf(c_22736,plain,
( ( xu = sz00 )
| ( sK16(xb,xu) = sz00 )
| ~ aElement0(xu)
| ~ aElement0(xb)
| ~ aElement0(sK16(xb,xu))
| ~ aElement0(sK15(xb,xu)) ),
inference(resolution,[status(thm)],[c_22723,c_117]) ).
tcf(c_22744,plain,
( ~ aElement0(sK15(xb,xu))
| ~ aElement0(sK16(xb,xu))
| ( sK16(xb,xu) = sz00 ) ),
inference(global_subsumption_just,[status(thm)],[c_22736,c_141,c_49,c_153,c_170,c_223,c_7444,c_7705,c_22736]) ).
tcf(c_22745,plain,
( ( sK16(xb,xu) = sz00 )
| ~ aElement0(sK16(xb,xu))
| ~ aElement0(sK15(xb,xu)) ),
inference(renaming,[status(thm)],[c_22744]) ).
tcf(c_22761,plain,
( ( sz00 = sK16(xb,xu) )
| ~ aElement0(sK16(xb,xu))
| ~ aElement0(sK15(xb,xu)) ),
inference(resolution,[status(thm)],[c_22745,c_10386]) ).
tcf(c_33782,plain,
( ( xb = sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu)) )
| ( xb != xb )
| ( sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu)) != xb ) ),
inference(instantiation,[status(thm)],[c_9203]) ).
tcf(c_48484,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu)) )
| ( X1 != sK16(xb,xu) )
| ( X0 != sdtasdt0(sK15(xb,xu),xu) ) ),
inference(instantiation,[status(thm)],[c_5759]) ).
tcf(c_53619,plain,
( aElement0(sK16(xb,xu))
| ( xu = sz00 )
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(instantiation,[status(thm)],[c_9134]) ).
tcf(c_65542,plain,
( aElement0(sK15(xb,xu))
| ( xu = sz00 )
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(instantiation,[status(thm)],[c_9135]) ).
tcf(c_66552,plain,
! [X0: $i] :
( ( sdtpldt0(sdtasdt0(sK15(xb,xu),xu),X0) = sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu)) )
| ( X0 != sK16(xb,xu) )
| ( sdtasdt0(sK15(xb,xu),xu) != sdtasdt0(sK15(xb,xu),xu) ) ),
inference(instantiation,[status(thm)],[c_48484]) ).
tcf(c_66553,plain,
sdtasdt0(sK15(xb,xu),xu) = sdtasdt0(sK15(xb,xu),xu),
inference(instantiation,[status(thm)],[c_8215]) ).
tcf(c_66554,plain,
( ( sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sz00) = sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu)) )
| ( sz00 != sK16(xb,xu) )
| ( sdtasdt0(sK15(xb,xu),xu) != sdtasdt0(sK15(xb,xu),xu) ) ),
inference(instantiation,[status(thm)],[c_66552]) ).
tcf(c_71607,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,xu),sz00) = xb )
| ( xb != X1 )
| ( sdtpldt0(sdtasdt0(X0,xu),sz00) != X1 ) ),
inference(instantiation,[status(thm)],[c_5756]) ).
tcf(c_76053,plain,
! [X0: $i] :
( ( sdtpldt0(sdtasdt0(X0,xu),sz00) = xb )
| ( xb != sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu)) )
| ( sdtpldt0(sdtasdt0(X0,xu),sz00) != sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu)) ) ),
inference(instantiation,[status(thm)],[c_71607]) ).
tcf(c_85836,plain,
( ( sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sz00) = xb )
| ( xb != sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu)) )
| ( sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sz00) != sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu)) ) ),
inference(instantiation,[status(thm)],[c_76053]) ).
tcf(c_85903,plain,
( ~ aElement0(sK15(xb,xu))
| ( sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sz00) != xb ) ),
inference(instantiation,[status(thm)],[c_244]) ).
tcf(c_85904,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_85903,c_85836,c_66553,c_66554,c_65542,c_53619,c_33782,c_22761,c_20051,c_9204,c_7705,c_7444,c_223,c_170,c_153,c_49,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG118+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 08:20:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 72.45/12.43 % SZS status Started for theBenchmark.p
% 72.45/12.43 % SZS status Theorem for theBenchmark.p
% 72.45/12.43
% 72.45/12.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 72.45/12.43
% 72.45/12.43 % ------ iProver source info
% 72.45/12.43
% 72.45/12.43 % git: date: 2026-07-19 20:42:38 +0200
% 72.45/12.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 72.45/12.43 % git: non_committed_changes: false
% 72.45/12.43
% 72.45/12.43 % ------ Parsing...
% 72.45/12.43 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 72.45/12.43
% 72.45/12.43 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 72.45/12.43
% 72.45/12.43 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 72.45/12.43
% 72.45/12.43 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 72.45/12.43 % ------ Proving...
% 72.45/12.43 % ------ Problem Properties
% 72.45/12.43
% 72.45/12.43 %
% 72.45/12.43 % clauses 109
% 72.45/12.43 % conjectures 2
% 72.45/12.43 % EPR 26
% 72.45/12.43 % Horn 85
% 72.45/12.43 % unary 22
% 72.45/12.43 % binary 17
% 72.45/12.43 % lits 356
% 72.45/12.43 % lits eq 53
% 72.45/12.43 % fd_pure 0
% 72.45/12.43 % fd_pseudo 0
% 72.45/12.43 % fd_cond 5
% 72.45/12.43 % fd_pseudo_cond 11
% 72.45/12.43 % AC symbols 0
% 72.45/12.43
% 72.45/12.43 % ------ Input Options Time Limit: Unbounded
% 72.45/12.43
% 72.45/12.43
% 72.45/12.43 % ------
% 72.45/12.43 % Current options:
% 72.45/12.43 % ------
% 72.45/12.43
% 72.45/12.43
% 72.45/12.43 %
% 72.45/12.43
% 72.45/12.43 % ------ Proving...
% 72.45/12.43 %
% 72.45/12.43
% 72.45/12.43 % SZS status Theorem for theBenchmark.p
% 72.45/12.43
% 72.45/12.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 72.45/12.43
% 72.45/12.43
%------------------------------------------------------------------------------