%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG106+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 : n015.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 02:39:09 PM UTC 2026
% Result : Theorem 4.15s 1.19s
% Output : CNFRefutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 77 ( 7 unt; 0 def)
% Number of atoms : 352 ( 54 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 436 ( 161 ~; 169 |; 85 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-3 aty)
% Number of variables : 135 ( 0 sgn 110 !; 25 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
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(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(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1905) ).
fof(f39,conjecture,
( ! [X0,X1,X2] :
( ( aElement0(X2)
& aElementOf0(X1,slsdtgt0(xc))
& aElementOf0(X0,slsdtgt0(xc)) )
=> ? [X3] :
( ? [X4] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2))
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(xc,X4) = X1
& aElement0(X4) )
& sdtasdt0(xc,X3) = X0
& aElement0(X3) ) )
=> aIdeal0(slsdtgt0(xc)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ ( ! [X0,X1,X2] :
( ( aElement0(X2)
& aElementOf0(X1,slsdtgt0(xc))
& aElementOf0(X0,slsdtgt0(xc)) )
=> ? [X3] :
( ? [X4] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2))
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(xc,X4) = X1
& aElement0(X4) )
& sdtasdt0(xc,X3) = X0
& aElement0(X3) ) )
=> aIdeal0(slsdtgt0(xc)) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f42,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(f45,plain,
! [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(unused_predicate_definition_removal,[],[f42]) ).
fof(f46,plain,
( ! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ? [X3] :
( ? [X4] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2))
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(xc,X4) = X1
& aElement0(X4) )
& sdtasdt0(xc,X3) = X0
& aElement0(X3) ) )
& ~ aIdeal0(slsdtgt0(xc)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f47,plain,
( ! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ? [X3] :
( ? [X4] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2))
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
& sdtasdt0(xc,X4) = X1
& aElement0(X4) )
& sdtasdt0(xc,X3) = X0
& aElement0(X3) ) )
& ~ aIdeal0(slsdtgt0(xc)) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [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(ennf_transformation,[],[f45]) ).
fof(f49,plain,
! [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,[],[f48]) ).
fof(f68,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(f72,plain,
( ! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
& aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
& sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(sK0(X0,X1,X2),X2))
& sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(sK0(X0,X1,X2),sK1(X0,X1,X2)))
& sdtasdt0(xc,sK1(X0,X1,X2)) = X1
& aElement0(sK1(X0,X1,X2))
& sdtasdt0(xc,sK0(X0,X1,X2)) = X0
& aElement0(sK0(X0,X1,X2)) ) )
& ~ aIdeal0(slsdtgt0(xc)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X4,sK1(X0,X1,X2))],[f47]) ).
fof(f73,plain,
! [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))],[f49]) ).
fof(f75,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,[],[f68]) ).
fof(f76,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,[],[f75]) ).
fof(f77,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,[],[f76]) ).
fof(f78,plain,
! [X0] :
( ~ aElement0(X0)
| ! [X1] :
( ( slsdtgt0(X0) != X1
| ( ! [X5] :
( ( ~ aElementOf0(X5,X1)
| ( sdtasdt0(X0,sK9(X0,X5)) = X5
& aElement0(sK9(X0,X5)) ) )
& ( ! [X6] :
( sdtasdt0(X0,X6) != X5
| ~ aElement0(X6) )
| aElementOf0(X5,X1) ) )
& aSet0(X1) ) )
& ( ( ( aElementOf0(sK7(X0,X1),X1)
| ( sK7(X0,X1) = sdtasdt0(X0,sK8(X0,X1))
& aElement0(sK8(X0,X1)) ) )
& ( ~ aElementOf0(sK7(X0,X1),X1)
| ! [X3] :
( sdtasdt0(X0,X3) != sK7(X0,X1)
| ~ aElement0(X3) ) ) )
| ~ aSet0(X1)
| X1 = slsdtgt0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f77]) ).
fof(f79,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f88,plain,
~ aIdeal0(slsdtgt0(xc)),
inference(cnf_transformation,[],[f72]) ).
fof(f89,plain,
! [X0] :
( aElementOf0(sK2(X0),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f90,plain,
! [X0] :
( aElement0(sK4(X0))
| aElementOf0(sK3(X0),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f91,plain,
! [X0] :
( ~ aElementOf0(sdtasdt0(sK4(X0),sK2(X0)),X0)
| aElementOf0(sK3(X0),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f92,plain,
! [X0] :
( aElement0(sK4(X0))
| ~ aElementOf0(sdtpldt0(sK2(X0),sK3(X0)),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f93,plain,
! [X0] :
( ~ aElementOf0(sdtasdt0(sK4(X0),sK2(X0)),X0)
| ~ aElementOf0(sdtpldt0(sK2(X0),sK3(X0)),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f112,plain,
! [X0,X1] :
( ~ aElement0(X0)
| slsdtgt0(X0) != X1
| aSet0(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f120,plain,
! [X0] :
( ~ aElement0(X0)
| aSet0(slsdtgt0(X0)) ),
inference(equality_resolution,[],[f112]) ).
tcf(c_49,plain,
aElement0(xc),
inference(cnf_transformation,[],[f79]) ).
tcf(c_50,negated_conjecture,
~ aIdeal0(slsdtgt0(xc)),
inference(cnf_transformation,[],[f88]) ).
tcf(c_57,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
| ~ aElement0(X2)
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_58,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
| ~ aElement0(X2)
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_59,plain,
! [X0: $i] :
( aIdeal0(X0)
| ~ aSet0(X0)
| ~ aElementOf0(sdtpldt0(sK2(X0),sK3(X0)),X0)
| ~ aElementOf0(sdtasdt0(sK4(X0),sK2(X0)),X0) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_60,plain,
! [X0: $i] :
( aIdeal0(X0)
| aElement0(sK4(X0))
| ~ aSet0(X0)
| ~ aElementOf0(sdtpldt0(sK2(X0),sK3(X0)),X0) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_61,plain,
! [X0: $i] :
( aIdeal0(X0)
| aElementOf0(sK3(X0),X0)
| ~ aSet0(X0)
| ~ aElementOf0(sdtasdt0(sK4(X0),sK2(X0)),X0) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_62,plain,
! [X0: $i] :
( aIdeal0(X0)
| aElement0(sK4(X0))
| aElementOf0(sK3(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_63,plain,
! [X0: $i] :
( aIdeal0(X0)
| aElementOf0(sK2(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_82,plain,
! [X0: $i] :
( aSet0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_90,plain,
( aSet0(slsdtgt0(xc))
| ~ aElement0(xc) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_709,plain,
! [X0: $i] :
( aElementOf0(sK2(X0),X0)
| ~ aSet0(X0)
| ( slsdtgt0(xc) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_63]) ).
tcf(c_710,plain,
( aElementOf0(sK2(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aSet0(slsdtgt0(xc)) ),
inference(unflattening,[status(thm)],[c_709]) ).
tcf(c_711,plain,
aElementOf0(sK2(slsdtgt0(xc)),slsdtgt0(xc)),
inference(global_subsumption_just,[status(thm)],[c_710,c_49,c_90,c_710]) ).
tcf(c_716,plain,
! [X0: $i] :
( aElement0(sK4(X0))
| aElementOf0(sK3(X0),X0)
| ~ aSet0(X0)
| ( slsdtgt0(xc) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_62]) ).
tcf(c_717,plain,
( aElement0(sK4(slsdtgt0(xc)))
| aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aSet0(slsdtgt0(xc)) ),
inference(unflattening,[status(thm)],[c_716]) ).
tcf(c_718,plain,
( aElement0(sK4(slsdtgt0(xc)))
| aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(global_subsumption_just,[status(thm)],[c_717,c_49,c_90,c_717]) ).
tcf(c_726,plain,
! [X0: $i] :
( aElementOf0(sK3(X0),X0)
| ~ aSet0(X0)
| ~ aElementOf0(sdtasdt0(sK4(X0),sK2(X0)),X0)
| ( slsdtgt0(xc) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_61]) ).
tcf(c_727,plain,
( aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(sK4(slsdtgt0(xc)),sK2(slsdtgt0(xc))),slsdtgt0(xc)) ),
inference(unflattening,[status(thm)],[c_726]) ).
tcf(c_728,plain,
( aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(sK4(slsdtgt0(xc)),sK2(slsdtgt0(xc))),slsdtgt0(xc)) ),
inference(global_subsumption_just,[status(thm)],[c_727,c_49,c_90,c_727]) ).
tcf(c_736,plain,
! [X0: $i] :
( aElement0(sK4(X0))
| ~ aSet0(X0)
| ~ aElementOf0(sdtpldt0(sK2(X0),sK3(X0)),X0)
| ( slsdtgt0(xc) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_60]) ).
tcf(c_737,plain,
( aElement0(sK4(slsdtgt0(xc)))
| ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sK2(slsdtgt0(xc)),sK3(slsdtgt0(xc))),slsdtgt0(xc)) ),
inference(unflattening,[status(thm)],[c_736]) ).
tcf(c_738,plain,
( aElement0(sK4(slsdtgt0(xc)))
| ~ aElementOf0(sdtpldt0(sK2(slsdtgt0(xc)),sK3(slsdtgt0(xc))),slsdtgt0(xc)) ),
inference(global_subsumption_just,[status(thm)],[c_737,c_49,c_90,c_737]) ).
tcf(c_746,plain,
! [X0: $i] :
( ~ aSet0(X0)
| ~ aElementOf0(sdtpldt0(sK2(X0),sK3(X0)),X0)
| ~ aElementOf0(sdtasdt0(sK4(X0),sK2(X0)),X0)
| ( slsdtgt0(xc) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_59]) ).
tcf(c_747,plain,
( ~ aSet0(slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sK2(slsdtgt0(xc)),sK3(slsdtgt0(xc))),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(sK4(slsdtgt0(xc)),sK2(slsdtgt0(xc))),slsdtgt0(xc)) ),
inference(unflattening,[status(thm)],[c_746]) ).
tcf(c_1305,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_58]) ).
tcf(c_1306,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_11
| ~ aElement0(X1)
| aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_58]) ).
tcf(c_1307,negated_conjecture,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_58]) ).
tcf(c_1308,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ~ aElement0(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_57]) ).
tcf(c_1309,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_13
| aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_57]) ).
tcf(c_1310,negated_conjecture,
( iPr_def_13
| iPr_def_12 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_57]) ).
tcf(c_1332,plain,
( ~ iPr_def_12
| ~ aElement0(xc) ),
inference(instantiation,[status(thm)],[c_1308]) ).
tcf(c_1334,plain,
! [X0: $i,X1: $i] :
( ~ aElementOf0(X0,slsdtgt0(xc))
| aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
| ~ aElement0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_1306,c_1305,c_1306,c_1307]) ).
tcf(c_1335,negated_conjecture,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
| ~ aElement0(X1)
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(renaming,[status(thm)],[c_1334]) ).
tcf(c_1338,plain,
! [X0: $i,X1: $i] :
( ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc)) ),
inference(global_subsumption_just,[status(thm)],[c_1309,c_49,c_1332,c_1309,c_1310]) ).
tcf(c_1339,negated_conjecture,
! [X0: $i,X1: $i] :
( aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(renaming,[status(thm)],[c_1338]) ).
tcf(c_2007,plain,
! [X0: $i,X1: $i] :
( ~ aElementOf0(X0,slsdtgt0(xc))
| aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
| ~ aElement0(X1) ),
inference(global_subsumption_just,[status(thm)],[c_1306,c_1305,c_1306,c_1307]) ).
tcf(c_2008,negated_conjecture,
! [X0: $i,X1: $i] :
( aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
| ~ aElement0(X1)
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(renaming,[status(thm)],[c_2007]) ).
tcf(c_2035,plain,
! [X0: $i,X1: $i] :
( ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc)) ),
inference(global_subsumption_just,[status(thm)],[c_1309,c_49,c_1332,c_1309,c_1310]) ).
tcf(c_2036,negated_conjecture,
! [X0: $i,X1: $i] :
( aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
| ~ aElementOf0(X1,slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc)) ),
inference(renaming,[status(thm)],[c_2035]) ).
tcf(c_2225,plain,
( aElement0(sK4(slsdtgt0(xc)))
| ~ aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(sK2(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(superposition,[status(thm)],[c_2036,c_738]) ).
tcf(c_2226,plain,
( aElement0(sK4(slsdtgt0(xc)))
| ~ aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2225,c_711]) ).
tcf(c_2387,plain,
( aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElement0(sK4(slsdtgt0(xc)))
| ~ aElementOf0(sK2(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(superposition,[status(thm)],[c_2008,c_728]) ).
tcf(c_2388,plain,
( aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElement0(sK4(slsdtgt0(xc))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2387,c_711]) ).
tcf(c_2439,plain,
! [X0: $i] :
( aElementOf0(sdtpldt0(sK2(slsdtgt0(xc)),X0),slsdtgt0(xc))
| ~ aElementOf0(X0,slsdtgt0(xc))
| ~ aElementOf0(sK2(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(instantiation,[status(thm)],[c_1339]) ).
tcf(c_2622,plain,
( aElementOf0(sdtasdt0(sK4(slsdtgt0(xc)),sK2(slsdtgt0(xc))),slsdtgt0(xc))
| ~ aElement0(sK4(slsdtgt0(xc)))
| ~ aElementOf0(sK2(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(instantiation,[status(thm)],[c_1335]) ).
tcf(c_2992,plain,
( aElementOf0(sdtpldt0(sK2(slsdtgt0(xc)),sK3(slsdtgt0(xc))),slsdtgt0(xc))
| ~ aElementOf0(sK3(slsdtgt0(xc)),slsdtgt0(xc))
| ~ aElementOf0(sK2(slsdtgt0(xc)),slsdtgt0(xc)) ),
inference(instantiation,[status(thm)],[c_2439]) ).
tcf(c_2993,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2992,c_2622,c_2388,c_2226,c_747,c_718,c_710,c_90,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG106+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 08:19:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 4.15/1.19 % SZS status Started for theBenchmark.p
% 4.15/1.19 % SZS status Theorem for theBenchmark.p
% 4.15/1.19
% 4.15/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.15/1.19
% 4.15/1.19 % ------ iProver source info
% 4.15/1.19
% 4.15/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 4.15/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.15/1.19 % git: non_committed_changes: false
% 4.15/1.19
% 4.15/1.19 % ------ Parsing...
% 4.15/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.15/1.19
% 4.15/1.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 4.15/1.19
% 4.15/1.19 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.15/1.19
% 4.15/1.19 % ------ Preprocessing... sf_s rm: 5 0s sf_e sf_s rm: 0 0s sf_e
% 4.15/1.19 % ------ Proving...
% 4.15/1.19 % ------ Problem Properties
% 4.15/1.19
% 4.15/1.19 %
% 4.15/1.19 % clauses 44
% 4.15/1.19 % conjectures 12
% 4.15/1.19 % EPR 6
% 4.15/1.19 % Horn 35
% 4.15/1.19 % unary 3
% 4.15/1.19 % binary 13
% 4.15/1.19 % lits 142
% 4.15/1.19 % lits eq 27
% 4.15/1.19 % fd_pure 0
% 4.15/1.19 % fd_pseudo 0
% 4.15/1.19 % fd_cond 1
% 4.15/1.19 % fd_pseudo_cond 7
% 4.15/1.19 % AC symbols 0
% 4.15/1.19
% 4.15/1.19 % ------ Schedule dynamic 5 is on
% 4.15/1.19
% 4.15/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.15/1.19
% 4.15/1.19
% 4.15/1.19 % ------
% 4.15/1.19 % Current options:
% 4.15/1.19 % ------
% 4.15/1.19
% 4.15/1.19
% 4.15/1.19 %
% 4.15/1.19
% 4.15/1.19 % ------ Proving...
% 4.15/1.19 %
% 4.15/1.19
% 4.15/1.19 % SZS status Theorem for theBenchmark.p
% 4.15/1.19
% 4.15/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.15/1.19
% 4.15/1.19
%------------------------------------------------------------------------------