%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG093+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 : 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 02:38:50 PM UTC 2026
% Result : Theorem 10.61s 13.94s
% Output : CNFRefutation 10.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 86 ( 12 unt; 0 def)
% Number of atoms : 421 ( 15 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 577 ( 242 ~; 257 |; 62 &)
% ( 9 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 153 ( 0 sgn 141 !; 12 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f23,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ! [X2] :
( X2 = sdtasasdt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSInt) ).
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/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f26,axiom,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1150) ).
fof(f27,conjecture,
aIdeal0(sdtasasdt0(xI,xJ)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f28,negated_conjecture,
~ aIdeal0(sdtasasdt0(xI,xJ)),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f32,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(f33,plain,
~ aIdeal0(sdtasasdt0(xI,xJ)),
inference(flattening,[],[f28]) ).
fof(f61,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtasasdt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f62,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtasasdt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f61]) ).
fof(f63,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,[],[f32]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ! [X2] :
( ( sdtasasdt0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = sdtasasdt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ! [X2] :
( ( sdtasasdt0(X0,X1) != X2
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = sdtasasdt0(X0,X1) ) ) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ! [X2] :
( ( sdtasasdt0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( aElementOf0(X4,X1)
& aElementOf0(X4,X0) ) )
& ( ~ aElementOf0(X4,X1)
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& ( ~ aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0) ) )
| ~ aSet0(X2)
| X2 = sdtasasdt0(X0,X1) ) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ! [X2] :
( ( sdtasasdt0(X0,X1) != X2
| ( ! [X4] :
( ( ~ aElementOf0(X4,X2)
| ( aElementOf0(X4,X1)
& aElementOf0(X4,X0) ) )
& ( ~ aElementOf0(X4,X1)
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X2) ) )
& aSet0(X2) ) )
& ( ( ( aElementOf0(sK9(X0,X1,X2),X2)
| ( aElementOf0(sK9(X0,X1,X2),X1)
& aElementOf0(sK9(X0,X1,X2),X0) ) )
& ( ~ aElementOf0(sK9(X0,X1,X2),X2)
| ~ aElementOf0(sK9(X0,X1,X2),X1)
| ~ aElementOf0(sK9(X0,X1,X2),X0) ) )
| ~ aSet0(X2)
| X2 = sdtasasdt0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X1,X2))],[f78]) ).
fof(f80,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,[],[f63]) ).
fof(f81,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,[],[f80]) ).
fof(f82,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,[],[f81]) ).
fof(f83,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))],[f82]) ).
fof(f124,plain,
! [X2,X0,X1,X4] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| sdtasasdt0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f125,plain,
! [X2,X0,X1,X4] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| sdtasasdt0(X0,X1) != X2
| ~ aElementOf0(X4,X2)
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f126,plain,
! [X2,X0,X1,X4] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| sdtasasdt0(X0,X1) != X2
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| sdtasasdt0(X0,X1) != X2
| aSet0(X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f131,plain,
! [X0,X6,X4] :
( ~ aIdeal0(X0)
| ~ aElementOf0(X4,X0)
| ~ aElement0(X6)
| aElementOf0(sdtasdt0(X6,X4),X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f132,plain,
! [X0,X4,X5] :
( ~ aIdeal0(X0)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X5,X0)
| aElementOf0(sdtpldt0(X4,X5),X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f133,plain,
! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f134,plain,
! [X0] :
( aElementOf0(sK10(X0),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f135,plain,
! [X0] :
( aElement0(sK12(X0))
| aElementOf0(sK11(X0),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f136,plain,
! [X0] :
( ~ aElementOf0(sdtasdt0(sK12(X0),sK10(X0)),X0)
| aElementOf0(sK11(X0),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f137,plain,
! [X0] :
( aElement0(sK12(X0))
| ~ aElementOf0(sdtpldt0(sK10(X0),sK11(X0)),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f138,plain,
! [X0] :
( ~ aElementOf0(sdtasdt0(sK12(X0),sK10(X0)),X0)
| ~ aElementOf0(sdtpldt0(sK10(X0),sK11(X0)),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f140,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f26]) ).
fof(f141,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f26]) ).
fof(f142,plain,
~ aIdeal0(sdtasasdt0(xI,xJ)),
inference(cnf_transformation,[],[f33]) ).
fof(f145,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| aSet0(sdtasasdt0(X0,X1)) ),
inference(equality_resolution,[],[f127]) ).
fof(f146,plain,
! [X0,X1,X4] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(X4,X1)
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,sdtasasdt0(X0,X1)) ),
inference(equality_resolution,[],[f126]) ).
fof(f147,plain,
! [X0,X1,X4] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(X4,sdtasasdt0(X0,X1))
| aElementOf0(X4,X0) ),
inference(equality_resolution,[],[f125]) ).
fof(f148,plain,
! [X0,X1,X4] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(X4,sdtasasdt0(X0,X1))
| aElementOf0(X4,X1) ),
inference(equality_resolution,[],[f124]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( aSet0(sdtasasdt0(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtasasdt0(X1,X2))
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X0,sdtasasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X0,sdtasasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_96,plain,
! [X0: $i] :
( aIdeal0(X0)
| ~ aSet0(X0)
| ~ aElementOf0(sdtasdt0(sK12(X0),sK10(X0)),X0)
| ~ aElementOf0(sdtpldt0(sK10(X0),sK11(X0)),X0) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_97,plain,
! [X0: $i] :
( aIdeal0(X0)
| aElement0(sK12(X0))
| ~ aSet0(X0)
| ~ aElementOf0(sdtpldt0(sK10(X0),sK11(X0)),X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_98,plain,
! [X0: $i] :
( aIdeal0(X0)
| aElementOf0(sK11(X0),X0)
| ~ aSet0(X0)
| ~ aElementOf0(sdtasdt0(sK12(X0),sK10(X0)),X0) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_99,plain,
! [X0: $i] :
( aIdeal0(X0)
| aElement0(sK12(X0))
| aElementOf0(sK11(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_100,plain,
! [X0: $i] :
( aIdeal0(X0)
| aElementOf0(sK10(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_101,plain,
! [X0: $i] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtpldt0(X0,X2),X1)
| ~ aIdeal0(X1)
| ~ aElementOf0(X2,X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtasdt0(X2,X0),X1)
| ~ aIdeal0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_105,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f141]) ).
tcf(c_106,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_107,negated_conjecture,
~ aIdeal0(sdtasasdt0(xI,xJ)),
inference(cnf_transformation,[],[f142]) ).
tcf(c_3883,plain,
aSet0(xI),
inference(superposition,[status(thm)],[c_105,c_101]) ).
tcf(c_3884,plain,
aSet0(xJ),
inference(superposition,[status(thm)],[c_106,c_101]) ).
tcf(c_4338,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aIdeal0(xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_4340,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtpldt0(X0,X1),xJ)
| ~ aIdeal0(xJ)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xJ) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_4423,plain,
! [X0: $i] :
( aSet0(sdtasasdt0(xI,X0))
| ~ aSet0(xI)
| ~ aSet0(X0) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_4435,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtasasdt0(xI,X1))
| ~ aSet0(xI)
| ~ aSet0(X1)
| ~ aElementOf0(X0,xI)
| ~ aElementOf0(X0,X1) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_4437,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,xI)
| ~ aSet0(xI)
| ~ aSet0(X1)
| ~ aElementOf0(X0,sdtasasdt0(xI,X1)) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_5325,plain,
( aSet0(sdtasasdt0(xI,xJ))
| ~ aSet0(xJ)
| ~ aSet0(xI) ),
inference(instantiation,[status(thm)],[c_4423]) ).
tcf(c_5545,plain,
! [X0: $i] :
( aElementOf0(X0,xI)
| ~ aSet0(xJ)
| ~ aSet0(xI)
| ~ aElementOf0(X0,sdtasasdt0(xI,xJ)) ),
inference(instantiation,[status(thm)],[c_4437]) ).
tcf(c_6167,plain,
! [X0: $i] :
( aElementOf0(X0,sdtasasdt0(xI,xJ))
| ~ aSet0(xJ)
| ~ aSet0(xI)
| ~ aElementOf0(X0,xJ)
| ~ aElementOf0(X0,xI) ),
inference(instantiation,[status(thm)],[c_4435]) ).
tcf(c_7271,plain,
( aIdeal0(sdtasasdt0(xI,xJ))
| ~ aSet0(sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtasdt0(sK12(sdtasasdt0(xI,xJ)),sK10(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtpldt0(sK10(sdtasasdt0(xI,xJ)),sK11(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ)) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_7272,plain,
( aIdeal0(sdtasasdt0(xI,xJ))
| aElementOf0(sK11(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ))
| ~ aSet0(sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtasdt0(sK12(sdtasasdt0(xI,xJ)),sK10(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ)) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_7273,plain,
( aIdeal0(sdtasasdt0(xI,xJ))
| aElement0(sK12(sdtasasdt0(xI,xJ)))
| ~ aSet0(sdtasasdt0(xI,xJ))
| ~ aElementOf0(sdtpldt0(sK10(sdtasasdt0(xI,xJ)),sK11(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ)) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_7274,plain,
( aIdeal0(sdtasasdt0(xI,xJ))
| aElement0(sK12(sdtasasdt0(xI,xJ)))
| aElementOf0(sK11(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ))
| ~ aSet0(sdtasasdt0(xI,xJ)) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_7275,plain,
( aIdeal0(sdtasasdt0(xI,xJ))
| aElementOf0(sK10(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ))
| ~ aSet0(sdtasasdt0(xI,xJ)) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_21696,plain,
( aElementOf0(sdtpldt0(sK10(sdtasasdt0(xI,xJ)),sK11(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ))
| ~ aSet0(xJ)
| ~ aSet0(xI)
| ~ aElementOf0(sdtpldt0(sK10(sdtasasdt0(xI,xJ)),sK11(sdtasasdt0(xI,xJ))),xJ)
| ~ aElementOf0(sdtpldt0(sK10(sdtasasdt0(xI,xJ)),sK11(sdtasasdt0(xI,xJ))),xI) ),
inference(instantiation,[status(thm)],[c_6167]) ).
tcf(c_35057,plain,
( aElementOf0(sdtpldt0(sK10(sdtasasdt0(xI,xJ)),sK11(sdtasasdt0(xI,xJ))),xI)
| ~ aIdeal0(xI)
| ~ aElementOf0(sK11(sdtasasdt0(xI,xJ)),xI)
| ~ aElementOf0(sK10(sdtasasdt0(xI,xJ)),xI) ),
inference(instantiation,[status(thm)],[c_4338]) ).
tcf(c_46154,plain,
( aElementOf0(sdtpldt0(sK10(sdtasasdt0(xI,xJ)),sK11(sdtasasdt0(xI,xJ))),xJ)
| ~ aIdeal0(xJ)
| ~ aElementOf0(sK11(sdtasasdt0(xI,xJ)),xJ)
| ~ aElementOf0(sK10(sdtasasdt0(xI,xJ)),xJ) ),
inference(instantiation,[status(thm)],[c_4340]) ).
tcf(c_59295,plain,
( aElementOf0(sK10(sdtasasdt0(xI,xJ)),xI)
| ~ aSet0(xJ)
| ~ aSet0(xI)
| ~ aElementOf0(sK10(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)) ),
inference(instantiation,[status(thm)],[c_5545]) ).
tcf(c_110721,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X1,X0),xI)
| ~ aIdeal0(xI)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xI) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_110722,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aIdeal0(xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xJ) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_110764,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtasasdt0(xI,X1))
| ~ aSet0(xI)
| ~ aSet0(X1)
| ~ aElementOf0(X0,xI)
| ~ aElementOf0(X0,X1) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_110765,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,X1)
| ~ aSet0(xI)
| ~ aSet0(X1)
| ~ aElementOf0(X0,sdtasasdt0(xI,X1)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_111656,plain,
! [X0: $i] :
( aElementOf0(X0,xJ)
| ~ aSet0(xJ)
| ~ aSet0(xI)
| ~ aElementOf0(X0,sdtasasdt0(xI,xJ)) ),
inference(instantiation,[status(thm)],[c_110765]) ).
tcf(c_111732,plain,
! [X0: $i] :
( aElementOf0(X0,sdtasasdt0(xI,xJ))
| ~ aSet0(xJ)
| ~ aSet0(xI)
| ~ aElementOf0(X0,xJ)
| ~ aElementOf0(X0,xI) ),
inference(instantiation,[status(thm)],[c_110764]) ).
tcf(c_115938,plain,
( aElementOf0(sdtasdt0(sK12(sdtasasdt0(xI,xJ)),sK10(sdtasasdt0(xI,xJ))),sdtasasdt0(xI,xJ))
| ~ aSet0(xJ)
| ~ aSet0(xI)
| ~ aElementOf0(sdtasdt0(sK12(sdtasasdt0(xI,xJ)),sK10(sdtasasdt0(xI,xJ))),xJ)
| ~ aElementOf0(sdtasdt0(sK12(sdtasasdt0(xI,xJ)),sK10(sdtasasdt0(xI,xJ))),xI) ),
inference(instantiation,[status(thm)],[c_111732]) ).
tcf(c_118693,plain,
( aElementOf0(sdtasdt0(sK12(sdtasasdt0(xI,xJ)),sK10(sdtasasdt0(xI,xJ))),xI)
| ~ aIdeal0(xI)
| ~ aElement0(sK12(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(sK10(sdtasasdt0(xI,xJ)),xI) ),
inference(instantiation,[status(thm)],[c_110721]) ).
tcf(c_120078,plain,
! [X0: $i] :
( aElementOf0(sK10(X0),xJ)
| ~ aSet0(xJ)
| ~ aSet0(xI)
| ~ aElementOf0(sK10(X0),sdtasasdt0(xI,xJ)) ),
inference(instantiation,[status(thm)],[c_111656]) ).
tcf(c_132590,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sK11(sdtasasdt0(X0,X1)),X0)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(sK11(sdtasasdt0(X0,X1)),sdtasasdt0(X0,X1)) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_145034,plain,
( aElementOf0(sK11(sdtasasdt0(xI,xJ)),xI)
| ~ aSet0(xJ)
| ~ aSet0(xI)
| ~ aElementOf0(sK11(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)) ),
inference(instantiation,[status(thm)],[c_132590]) ).
tcf(c_150304,plain,
( aElementOf0(sdtasdt0(sK12(sdtasasdt0(xI,xJ)),sK10(sdtasasdt0(xI,xJ))),xJ)
| ~ aIdeal0(xJ)
| ~ aElement0(sK12(sdtasasdt0(xI,xJ)))
| ~ aElementOf0(sK10(sdtasasdt0(xI,xJ)),xJ) ),
inference(instantiation,[status(thm)],[c_110722]) ).
tcf(c_152214,plain,
( aElementOf0(sK10(sdtasasdt0(xI,xJ)),xJ)
| ~ aSet0(xJ)
| ~ aSet0(xI)
| ~ aElementOf0(sK10(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)) ),
inference(instantiation,[status(thm)],[c_120078]) ).
tcf(c_191405,plain,
( aElementOf0(sK11(sdtasasdt0(xI,xJ)),xJ)
| ~ aSet0(xJ)
| ~ aSet0(xI)
| ~ aElementOf0(sK11(sdtasasdt0(xI,xJ)),sdtasasdt0(xI,xJ)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_191407,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_191405,c_152214,c_150304,c_145034,c_118693,c_115938,c_59295,c_46154,c_35057,c_21696,c_7271,c_7272,c_7273,c_7274,c_7275,c_5325,c_3883,c_3884,c_107,c_105,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG093+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 08:11:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 0.15/0.41
% 0.15/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.41
% 0.15/0.41 % Detected problem language: tptp
% 0.15/0.42 % Proving...
% 10.61/13.94 % SZS status Started for theBenchmark.p
% 10.61/13.94 % SZS status Theorem for theBenchmark.p
% 10.61/13.94
% 10.61/13.94 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.61/13.94
% 10.61/13.94 % ------ iProver source info
% 10.61/13.94
% 10.61/13.94 % git: date: 2026-07-19 20:42:38 +0200
% 10.61/13.94 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.61/13.94 % git: non_committed_changes: false
% 10.61/13.94
% 10.61/13.94 % ------ Parsing...
% 10.61/13.94 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.61/13.94
% 10.61/13.94 % ------ Preprocessing... sup_sim: 0 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 %
% 10.61/13.94
% 10.61/13.94 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.61/13.94
% 10.61/13.94 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.61/13.94 % ------ Proving...
% 10.61/13.94 % ------ Problem Properties
% 10.61/13.94
% 10.61/13.94 %
% 10.61/13.94 % clauses 59
% 10.61/13.94 % conjectures 1
% 10.61/13.94 % EPR 9
% 10.61/13.94 % Horn 46
% 10.61/13.94 % unary 7
% 10.61/13.94 % binary 13
% 10.61/13.94 % lits 192
% 10.61/13.94 % lits eq 32
% 10.61/13.94 % fd_pure 0
% 10.61/13.94 % fd_pseudo 0
% 10.61/13.94 % fd_cond 1
% 10.61/13.94 % fd_pseudo_cond 8
% 10.61/13.94 % AC symbols 0
% 10.61/13.94
% 10.61/13.94 % ------ Schedule dynamic 5 is on
% 10.61/13.94
% 10.61/13.94 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.61/13.94
% 10.61/13.94
% 10.61/13.94 % ------
% 10.61/13.94 % Current options:
% 10.61/13.94 % ------
% 10.61/13.94
% 10.61/13.94
% 10.61/13.94 %
% 10.61/13.94
% 10.61/13.94 % ------ Proving...
% 10.61/13.94 % Proof_search_loop: time out after: 7741 full_loop iterations
% 10.61/13.94
% 10.61/13.94 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 10.61/13.94
% 10.61/13.94
% 10.61/13.94 % ------
% 10.61/13.94 % Current options:
% 10.61/13.94 % ------
% 10.61/13.94
% 10.61/13.94
% 10.61/13.94 %
% 10.61/13.94
% 10.61/13.94 % ------ Proving...
% 10.61/13.94 %
% 10.61/13.94
% 10.61/13.94 % SZS status Theorem for theBenchmark.p
% 10.61/13.94
% 10.61/13.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.61/13.94
% 10.61/13.94
%------------------------------------------------------------------------------