%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG095+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 : n001.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 22.13s 3.81s
% Output : CNFRefutation 22.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 10 unt; 2 def)
% Number of atoms : 353 ( 44 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 413 ( 157 ~; 154 |; 82 &)
% ( 12 <=>; 8 =>; 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 : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 193 ( 0 sgn 157 !; 36 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
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(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(f28,axiom,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205) ).
fof(f29,axiom,
! [X0] :
( aElement0(X0)
=> aElementOf0(X0,sdtpldt1(xI,xJ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205_03) ).
fof(f31,conjecture,
? [X0,X1] :
( sdtpldt0(X0,X1) = sz10
& aElementOf0(X1,xJ)
& aElementOf0(X0,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f32,negated_conjecture,
~ ? [X0,X1] :
( sdtpldt0(X0,X1) = sz10
& aElementOf0(X1,xJ)
& aElementOf0(X0,xI) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,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(f37,plain,
! [X0] :
( ~ aElement0(X0)
| aElementOf0(X0,sdtpldt1(xI,xJ)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f38,plain,
! [X0,X1] :
( sz10 != sdtpldt0(X0,X1)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xI) ),
inference(ennf_transformation,[],[f32]) ).
fof(f39,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,[],[f33]) ).
fof(f45,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(f46,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,[],[f45]) ).
fof(f72,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,[],[f39]) ).
fof(f73,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,[],[f72]) ).
fof(f74,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,[],[f73]) ).
fof(f75,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(sK2(X0),X0)
& ( ( aElement0(sK4(X0))
& ~ aElementOf0(sdtasdt0(sK4(X0),sK2(X0)),X0) )
| ( aElementOf0(sK3(X0),X0)
& ~ aElementOf0(sdtpldt0(sK2(X0),sK3(X0)),X0) ) ) )
| ~ aSet0(X0)
| aIdeal0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X1,sK2(X0)),skolemize(X2,sK3(X0)),skolemize(X3,sK4(X0))],[f74]) ).
fof(f77,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,[],[f70]) ).
fof(f78,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,[],[f77]) ).
fof(f83,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f28]) ).
fof(f84,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f28]) ).
fof(f85,plain,
! [X0] :
( ~ aElement0(X0)
| aElementOf0(X0,sdtpldt1(xI,xJ)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f88,plain,
! [X0,X1] :
( sz10 != sdtpldt0(X0,X1)
| ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f38]) ).
fof(f91,plain,
! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f103,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1)
| sdtpldt1(X1,X0) != X2
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f114,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f120,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f138,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sP0(sdtpldt1(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f103]) ).
tcf(c_49,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f84]) ).
tcf(c_50,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_51,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ aElementOf0(X1,xJ)
| ~ aElementOf0(X0,xI)
| ( sdtpldt0(X0,X1) != sz10 ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_60,plain,
! [X0: $i] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt1(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( sP1(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_86,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f120]) ).
tcf(c_796,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_70,c_80]) ).
tcf(c_797,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt1(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(unflattening,[status(thm)],[c_796]) ).
tcf(c_3508,plain,
aSet0(xI),
inference(superposition,[status(thm)],[c_49,c_60]) ).
tcf(c_3509,plain,
aSet0(xJ),
inference(superposition,[status(thm)],[c_50,c_60]) ).
tcf(c_4112,plain,
! [X0: $i] :
( sP0(sdtpldt1(X0,xJ),X0,xJ)
| ~ aSet0(xJ)
| ~ aSet0(X0) ),
inference(instantiation,[status(thm)],[c_797]) ).
tcf(c_5707,plain,
( sP0(sdtpldt1(xI,xJ),xI,xJ)
| ~ aSet0(xJ)
| ~ aSet0(xI) ),
inference(instantiation,[status(thm)],[c_4112]) ).
tcf(c_28400,plain,
! [X0: $i,X1: $i] :
( ~ aElementOf0(sK11(X0,X1,sz10),xJ)
| ~ aElementOf0(sK10(X0,X1,sz10),xI)
| ( sdtpldt0(sK10(X0,X1,sz10),sK11(X0,X1,sz10)) != sz10 ) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_37233,plain,
( aElementOf0(sz10,sdtpldt1(xI,xJ))
| ~ aElement0(sz10) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_37245,plain,
! [X0: $i] :
( ~ aElementOf0(sK11(xI,X0,sz10),xJ)
| ~ aElementOf0(sK10(xI,X0,sz10),xI)
| ( sdtpldt0(sK10(xI,X0,sz10),sK11(xI,X0,sz10)) != sz10 ) ),
inference(instantiation,[status(thm)],[c_28400]) ).
tcf(c_65901,plain,
( ~ aElementOf0(sK11(xI,xJ,sz10),xJ)
| ~ aElementOf0(sK10(xI,xJ,sz10),xI)
| ( sdtpldt0(sK10(xI,xJ,sz10),sK11(xI,xJ,sz10)) != sz10 ) ),
inference(instantiation,[status(thm)],[c_37245]) ).
fof(f69,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(f70,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(f71,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(definition_folding,[],[f46,f70,f69]) ).
fof(f79,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,[],[f69]) ).
fof(f80,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,[],[f79]) ).
fof(f81,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,[],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X8] :
( ( ~ aElementOf0(X8,X0)
| ( sdtpldt0(sK10(X1,X2,X8),sK11(X1,X2,X8)) = X8
& aElementOf0(sK11(X1,X2,X8),X2)
& aElementOf0(sK10(X1,X2,X8),X1) ) )
& ( ! [X9,X10] :
( sdtpldt0(X9,X10) != X8
| ~ aElementOf0(X10,X2)
| ~ aElementOf0(X9,X1) )
| aElementOf0(X8,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK7(X0,X1,X2),X0)
| ( sK7(X0,X1,X2) = sdtpldt0(sK8(X0,X1,X2),sK9(X0,X1,X2))
& aElementOf0(sK9(X0,X1,X2),X2)
& aElementOf0(sK8(X0,X1,X2),X1) ) )
& ( ~ aElementOf0(sK7(X0,X1,X2),X0)
| ! [X4,X5] :
( sdtpldt0(X4,X5) != sK7(X0,X1,X2)
| ~ aElementOf0(X5,X2)
| ~ aElementOf0(X4,X1) ) ) )
| ~ aSet0(X0)
| sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11]),skolemize(X3,sK7(X0,X1,X2)),skolemize(X6,sK8(X0,X1,X2)),skolemize(X7,sK9(X0,X1,X2)),skolemize(X11,sK10(X1,X2,X8)),skolemize(X12,sK11(X1,X2,X8))],[f81]) ).
fof(f105,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X8,X0)
| sdtpldt0(sK10(X1,X2,X8),sK11(X1,X2,X8)) = X8 ),
inference(cnf_transformation,[],[f82]) ).
fof(f106,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X8,X0)
| aElementOf0(sK11(X1,X2,X8),X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f107,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X8,X0)
| aElementOf0(sK10(X1,X2,X8),X1) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(sK10(X1,X2,X3),X1)
| ~ aElementOf0(X3,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(sK11(X1,X2,X3),X2)
| ~ aElementOf0(X3,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sK10(X1,X2,X3),sK11(X1,X2,X3)) = X3 )
| ~ aElementOf0(X3,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_3916,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sK10(X0,X1,X2),X0)
| ~ aElementOf0(X2,sdtpldt1(xI,xJ))
| ~ sP0(sdtpldt1(xI,xJ),X0,X1) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_3918,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sK11(X0,X1,X2),X1)
| ~ aElementOf0(X2,sdtpldt1(xI,xJ))
| ~ sP0(sdtpldt1(xI,xJ),X0,X1) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_3955,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sK10(X0,X1,X2),sK11(X0,X1,X2)) = X2 )
| ~ aElementOf0(X2,sdtpldt1(xI,xJ))
| ~ sP0(sdtpldt1(xI,xJ),X0,X1) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_8064,plain,
! [X0: $i] :
( aElementOf0(sK11(xI,xJ,X0),xJ)
| ~ aElementOf0(X0,sdtpldt1(xI,xJ))
| ~ sP0(sdtpldt1(xI,xJ),xI,xJ) ),
inference(instantiation,[status(thm)],[c_3918]) ).
tcf(c_28399,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sK10(X0,X1,sz10),sK11(X0,X1,sz10)) = sz10 )
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
| ~ sP0(sdtpldt1(xI,xJ),X0,X1) ),
inference(instantiation,[status(thm)],[c_3955]) ).
tcf(c_37246,plain,
! [X0: $i] :
( aElementOf0(sK10(xI,X0,sz10),xI)
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
| ~ sP0(sdtpldt1(xI,xJ),xI,X0) ),
inference(instantiation,[status(thm)],[c_3916]) ).
tcf(c_43534,plain,
( ( sdtpldt0(sK10(xI,xJ,sz10),sK11(xI,xJ,sz10)) = sz10 )
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
| ~ sP0(sdtpldt1(xI,xJ),xI,xJ) ),
inference(instantiation,[status(thm)],[c_28399]) ).
tcf(c_49201,plain,
( aElementOf0(sK10(xI,xJ,sz10),xI)
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
| ~ sP0(sdtpldt1(xI,xJ),xI,xJ) ),
inference(instantiation,[status(thm)],[c_37246]) ).
tcf(c_72300,plain,
( aElementOf0(sK11(xI,xJ,sz10),xJ)
| ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
| ~ sP0(sdtpldt1(xI,xJ),xI,xJ) ),
inference(instantiation,[status(thm)],[c_8064]) ).
tcf(c_72301,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_72300,c_65901,c_49201,c_43534,c_37233,c_5707,c_3508,c_3509,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG095+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 08:17:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.42
% 0.15/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.42
% 0.15/0.42 % Detected problem language: tptp
% 0.15/0.43 % Proving...
% 22.13/3.81 % SZS status Started for theBenchmark.p
% 22.13/3.81 % SZS status Theorem for theBenchmark.p
% 22.13/3.81
% 22.13/3.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.13/3.81
% 22.13/3.81 % ------ iProver source info
% 22.13/3.81
% 22.13/3.81 % git: date: 2026-07-19 20:42:38 +0200
% 22.13/3.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.13/3.81 % git: non_committed_changes: false
% 22.13/3.81
% 22.13/3.81 % ------ Parsing...
% 22.13/3.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.13/3.81
% 22.13/3.81 % ------ 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 %
% 22.13/3.81
% 22.13/3.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 22.13/3.81
% 22.13/3.81 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 22.13/3.81 % ------ Proving...
% 22.13/3.81 % ------ Problem Properties
% 22.13/3.81
% 22.13/3.81 %
% 22.13/3.81 % clauses 54
% 22.13/3.81 % conjectures 1
% 22.13/3.81 % EPR 10
% 22.13/3.81 % Horn 43
% 22.13/3.81 % unary 7
% 22.13/3.81 % binary 14
% 22.13/3.81 % lits 162
% 22.13/3.81 % lits eq 29
% 22.13/3.81 % fd_pure 0
% 22.13/3.81 % fd_pseudo 0
% 22.13/3.81 % fd_cond 1
% 22.13/3.81 % fd_pseudo_cond 5
% 22.13/3.81 % AC symbols 0
% 22.13/3.81
% 22.13/3.81 % ------ Schedule dynamic 5 is on
% 22.13/3.81
% 22.13/3.81 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 22.13/3.81
% 22.13/3.81
% 22.13/3.81 % ------
% 22.13/3.81 % Current options:
% 22.13/3.81 % ------
% 22.13/3.81
% 22.13/3.81
% 22.13/3.81 %
% 22.13/3.81
% 22.13/3.81 % ------ Proving...
% 22.13/3.81 %
% 22.13/3.81
% 22.13/3.81 % SZS status Theorem for theBenchmark.p
% 22.13/3.81
% 22.13/3.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.13/3.81
% 22.13/3.81
%------------------------------------------------------------------------------