%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM535+2 : 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 : n013.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 02:25:53 PM UTC 2026
% Result : Theorem 4.05s 1.29s
% Output : CNFRefutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of formulae : 165 ( 22 unt; 11 def)
% Number of atoms : 857 ( 133 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 1005 ( 341 ~; 360 |; 240 &)
% ( 42 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 17 ( 15 usr; 8 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 223 ( 0 sgn 208 !; 15 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f15,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
fof(f16,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f17,axiom,
aSet0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617) ).
fof(f18,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617_02) ).
fof(f19,conjecture,
( ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx)) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(X0,xS) ) ) ) )
& ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx)) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f20,negated_conjecture,
~ ( ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx)) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(X0,xS) ) ) ) )
& ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx)) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f25,plain,
~ ( ( ( ! [X3] :
( aElementOf0(X3,sdtmndt0(xS,xx))
<=> ( xx != X3
& aElementOf0(X3,xS)
& aElement0(X3) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X4] :
( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( xx = X4
| aElementOf0(X4,sdtmndt0(xS,xx)) )
& aElement0(X4) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ! [X5] :
( aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx))
=> aElementOf0(X5,xS) ) ) ) )
& ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ) ) ),
inference(rectify,[],[f20]) ).
fof(f28,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f38,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f39,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f41,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
( ( ! [X3] :
( aElementOf0(X3,sdtmndt0(xS,xx))
<=> ( xx != X3
& aElementOf0(X3,xS)
& aElement0(X3) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X4] :
( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( xx = X4
| aElementOf0(X4,sdtmndt0(xS,xx)) )
& aElement0(X4) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ? [X5] :
( aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aElementOf0(X5,xS) ) )
| ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [X2] :
( aElementOf0(X2,xS)
& ~ aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f43,plain,
( ( ! [X3] :
( aElementOf0(X3,sdtmndt0(xS,xx))
<=> ( xx != X3
& aElementOf0(X3,xS)
& aElement0(X3) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X4] :
( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( xx = X4
| aElementOf0(X4,sdtmndt0(xS,xx)) )
& aElement0(X4) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ? [X5] :
( aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aElementOf0(X5,xS) ) )
| ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [X2] :
( aElementOf0(X2,xS)
& ~ aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ),
inference(flattening,[],[f42]) ).
fof(f64,plain,
! [X1,X0] :
( ~ sP1(X1,X0)
| ! [X2] :
( ( sdtpldt0(X0,X1) != X2
| sP0(X2,X0,X1) )
& ( ~ sP0(X2,X0,X1)
| X2 = sdtpldt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f65,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ! [X2] :
( ( sdtpldt0(X1,X0) != X2
| sP0(X2,X1,X0) )
& ( ~ sP0(X2,X1,X0)
| sdtpldt0(X1,X0) = X2 ) ) ),
inference(rectify,[],[f64]) ).
fof(f70,plain,
! [X1,X0] :
( ~ sP3(X1,X0)
| ! [X2] :
( ( sdtmndt0(X0,X1) != X2
| sP2(X2,X0,X1) )
& ( ~ sP2(X2,X0,X1)
| X2 = sdtmndt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f71,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| sP2(X2,X1,X0) )
& ( ~ sP2(X2,X1,X0)
| sdtmndt0(X1,X0) = X2 ) ) ),
inference(rectify,[],[f70]) ).
fof(f76,plain,
( ~ sP8
| ( sP4
& aSet0(sdtmndt0(xS,xx))
& sP5
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ? [X5] :
( aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aElementOf0(X5,xS) ) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f77,plain,
( ~ sP8
| ( sP4
& aSet0(sdtmndt0(xS,xx))
& sP5
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ? [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aElementOf0(X0,xS) ) ) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
( ~ sP8
| ( sP4
& aSet0(sdtmndt0(xS,xx))
& sP5
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aElementOf0(sK13,sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aElementOf0(sK13,xS) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f77]) ).
fof(f79,plain,
( ~ sP7
| ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& ( ( xx != X1
& ~ aElementOf0(X1,sdtmndt0(xS,xx)) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f80,plain,
( ~ sP7
| ! [X1] :
( ( ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) )
& ( ( xx != X1
& ~ aElementOf0(X1,sdtmndt0(xS,xx)) )
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
( ~ sP7
| ! [X0] :
( ( ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( ( xx = X0
| aElementOf0(X0,sdtmndt0(xS,xx)) )
& aElement0(X0) ) )
& ( ( xx != X0
& ~ aElementOf0(X0,sdtmndt0(xS,xx)) )
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ),
inference(rectify,[],[f80]) ).
fof(f82,plain,
( ~ sP6
| ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& ( xx = X0
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f83,plain,
( ~ sP6
| ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& ( xx = X0
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ) ) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
( ~ sP5
| ! [X4] :
( ( ~ aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( ( xx = X4
| aElementOf0(X4,sdtmndt0(xS,xx)) )
& aElement0(X4) ) )
& ( ( xx != X4
& ~ aElementOf0(X4,sdtmndt0(xS,xx)) )
| ~ aElement0(X4)
| aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f85,plain,
( ~ sP5
| ! [X4] :
( ( ~ aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( ( xx = X4
| aElementOf0(X4,sdtmndt0(xS,xx)) )
& aElement0(X4) ) )
& ( ( xx != X4
& ~ aElementOf0(X4,sdtmndt0(xS,xx)) )
| ~ aElement0(X4)
| aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
( ~ sP5
| ! [X0] :
( ( ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ( ( xx = X0
| aElementOf0(X0,sdtmndt0(xS,xx)) )
& aElement0(X0) ) )
& ( ( xx != X0
& ~ aElementOf0(X0,sdtmndt0(xS,xx)) )
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ),
inference(rectify,[],[f85]) ).
fof(f90,plain,
( sP8
| ( sP6
& aSet0(sdtmndt0(xS,xx))
& sP7
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [X0] :
( aElementOf0(X0,xS)
& ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ),
inference(rectify,[],[f55]) ).
fof(f91,plain,
( sP8
| ( sP6
& aSet0(sdtmndt0(xS,xx))
& sP7
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& aElementOf0(sK14,xS)
& ~ aElementOf0(sK14,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1)
| sdtpldt0(X1,X0) != X2
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f116,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1)
| sdtmndt0(X1,X0) != X2
| sP2(X2,X1,X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f128,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP3(X1,X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f129,plain,
aSet0(xS),
inference(cnf_transformation,[],[f17]) ).
fof(f130,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f18]) ).
fof(f131,plain,
( ~ sP8
| sP4 ),
inference(cnf_transformation,[],[f78]) ).
fof(f132,plain,
( ~ sP8
| aSet0(sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f133,plain,
( ~ sP8
| sP5 ),
inference(cnf_transformation,[],[f78]) ).
fof(f136,plain,
( ~ sP8
| aElementOf0(sK13,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f137,plain,
( ~ sP8
| ~ aElementOf0(sK13,xS) ),
inference(cnf_transformation,[],[f78]) ).
fof(f140,plain,
! [X0] :
( ~ sP7
| xx != X0
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f141,plain,
! [X0] :
( ~ sP7
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f143,plain,
! [X0] :
( ~ sP6
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f83]) ).
fof(f144,plain,
! [X0] :
( ~ sP6
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| aElement0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f148,plain,
! [X0] :
( ~ sP5
| xx != X0
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f149,plain,
! [X0] :
( ~ sP5
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f154,plain,
( sP8
| sP6 ),
inference(cnf_transformation,[],[f91]) ).
fof(f155,plain,
( sP8
| aSet0(sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f156,plain,
( sP8
| sP7 ),
inference(cnf_transformation,[],[f91]) ).
fof(f159,plain,
( sP8
| aElementOf0(sK14,xS) ),
inference(cnf_transformation,[],[f91]) ).
fof(f160,plain,
( sP8
| ~ aElementOf0(sK14,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f163,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sP0(sdtpldt0(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f105]) ).
fof(f165,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| sP2(sdtmndt0(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f117]) ).
fof(f167,plain,
( ~ sP7
| ~ aElement0(xx)
| aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(equality_resolution,[],[f140]) ).
fof(f169,plain,
( ~ sP5
| ~ aElement0(xx)
| aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(equality_resolution,[],[f148]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt0(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( sP3(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_86,plain,
aSet0(xS),
inference(cnf_transformation,[],[f129]) ).
tcf(c_87,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f130]) ).
tcf(c_88,plain,
( ~ sP8
| ~ aElementOf0(sK13,xS) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_89,plain,
( aElementOf0(sK13,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP8 ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_92,plain,
( sP5
| ~ sP8 ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_93,plain,
( aSet0(sdtmndt0(xS,xx))
| ~ sP8 ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_94,plain,
( sP4
| ~ sP8 ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_95,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP7
| ~ aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_96,plain,
( aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP7
| ~ aElement0(xx) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_100,plain,
! [X0: $i] :
( aElement0(X0)
| ~ sP6
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_101,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ sP6
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_103,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP5
| ~ aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_104,plain,
( aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ sP5
| ~ aElement0(xx) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_111,negated_conjecture,
( sP8
| ~ aElementOf0(sK14,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_112,negated_conjecture,
( sP8
| aElementOf0(sK14,xS) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_115,negated_conjecture,
( sP7
| sP8 ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_116,negated_conjecture,
( sP8
| aSet0(sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_117,negated_conjecture,
( sP6
| sP8 ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_147,negated_conjecture,
aSet0(sdtmndt0(xS,xx)),
inference(global_subsumption_just,[status(thm)],[c_116,c_116,c_93]) ).
tcf(c_149,plain,
aSet0(sdtmndt0(xS,xx)),
inference(global_subsumption_just,[status(thm)],[c_93,c_147]) ).
tcf(c_170,plain,
( aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(xx) ),
inference(global_subsumption_just,[status(thm)],[c_104,c_115,c_92,c_104,c_96]) ).
tcf(c_174,plain,
( aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(xx) ),
inference(global_subsumption_just,[status(thm)],[c_96,c_170]) ).
tcf(c_838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(sdtpldt0(X3,X1),X3,X1)
| ~ aSet0(X2)
| ~ aElement0(X0)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_63]) ).
tcf(c_839,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt0(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_838]) ).
tcf(c_872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP2(sdtmndt0(X3,X1),X3,X1)
| ~ aSet0(X2)
| ~ aElement0(X0)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_85,c_75]) ).
tcf(c_873,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_872]) ).
tcf(c_6028,definition,
iPr_def_10 = sdtmndt0(xS,xx),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_6029,definition,
iPr_def_11 = sdtpldt0(iPr_def_10,xx),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_6031,negated_conjecture,
( sP8
| aElementOf0(sK14,xS) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_6032,negated_conjecture,
( sP8
| ~ aElementOf0(sK14,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_6768,plain,
aSet0(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_149,c_6028]) ).
tcf(c_6800,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_87,c_49]) ).
tcf(c_6801,plain,
( sP8
| aElement0(sK14)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_6031,c_49]) ).
tcf(c_6802,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[status(thm)],[c_6800,c_86]) ).
tcf(c_6803,plain,
( sP8
| aElement0(sK14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6801,c_86]) ).
tcf(c_6821,plain,
( aElementOf0(sK13,iPr_def_11)
| ~ sP8 ),
inference(light_normalisation,[status(thm)],[c_89,c_6028,c_6029]) ).
tcf(c_6865,plain,
aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(global_subsumption_just,[status(thm)],[c_174,c_170,c_6802]) ).
tcf(c_6867,plain,
aElementOf0(xx,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_6865,c_6028,c_6029]) ).
tcf(c_6965,plain,
( sP0(iPr_def_11,iPr_def_10,xx)
| ~ aSet0(iPr_def_10)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_6029,c_839]) ).
tcf(c_6972,plain,
sP0(iPr_def_11,iPr_def_10,xx),
inference(forward_subsumption_resolution,[status(thm)],[c_6965,c_6768,c_6802]) ).
tcf(c_7871,plain,
( sP2(iPr_def_10,xS,xx)
| ~ aSet0(xS)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_6028,c_873]) ).
tcf(c_7880,plain,
sP2(iPr_def_10,xS,xx),
inference(forward_subsumption_resolution,[status(thm)],[c_7871,c_86,c_6802]) ).
fof(f44,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f45,definition,
! [X1,X0] :
( ~ sP1(X1,X0)
| ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> sP0(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f46,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(definition_folding,[],[f39,f45,f44]) ).
fof(f47,definition,
! [X2,X0,X1] :
( sP2(X2,X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f48,definition,
! [X1,X0] :
( ~ sP3(X1,X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> sP2(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f49,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP3(X1,X0) ),
inference(definition_folding,[],[f41,f48,f47]) ).
fof(f50,definition,
( ~ sP4
| ! [X3] :
( aElementOf0(X3,sdtmndt0(xS,xx))
<=> ( xx != X3
& aElementOf0(X3,xS)
& aElement0(X3) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f51,definition,
( ~ sP5
| ! [X4] :
( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( xx = X4
| aElementOf0(X4,sdtmndt0(xS,xx)) )
& aElement0(X4) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f52,definition,
( ~ sP6
| ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f53,definition,
( ~ sP7
| ! [X1] :
( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( xx = X1
| aElementOf0(X1,sdtmndt0(xS,xx)) )
& aElement0(X1) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f54,definition,
( ~ sP8
| ( sP4
& aSet0(sdtmndt0(xS,xx))
& sP5
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& ? [X5] :
( aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aElementOf0(X5,xS) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f55,plain,
( sP8
| ( sP6
& aSet0(sdtmndt0(xS,xx))
& sP7
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
& ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
& ? [X2] :
( aElementOf0(X2,xS)
& ~ aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ),
inference(definition_folding,[],[f43,f54,f53,f52,f51,f50]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& ( ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& ( ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP0(X2,X0,X1) ) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( ( X2 = X4
| aElementOf0(X4,X1) )
& aElement0(X4) ) )
& ( ( X2 != X4
& ~ aElementOf0(X4,X1) )
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X0)
| ( ( X2 = X3
| aElementOf0(X3,X1) )
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X0)
| ( X2 != X3
& ~ aElementOf0(X3,X1) )
| ~ aElement0(X3) ) )
| ~ aSet0(X0)
| sP0(X0,X1,X2) ) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( ( X2 = X4
| aElementOf0(X4,X1) )
& aElement0(X4) ) )
& ( ( X2 != X4
& ~ aElementOf0(X4,X1) )
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK11(X0,X1,X2),X0)
| ( ( sK11(X0,X1,X2) = X2
| aElementOf0(sK11(X0,X1,X2),X1) )
& aElement0(sK11(X0,X1,X2)) ) )
& ( ~ aElementOf0(sK11(X0,X1,X2),X0)
| ( sK11(X0,X1,X2) != X2
& ~ aElementOf0(sK11(X0,X1,X2),X1) )
| ~ aElement0(sK11(X0,X1,X2)) ) )
| ~ aSet0(X0)
| sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1,X2))],[f68]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ( ~ sP2(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ( ~ sP2(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP2(X2,X0,X1) ) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( ~ sP2(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( X2 != X4
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& ( X2 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X0)
| ( X2 != X3
& aElementOf0(X3,X1)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X0)
| X2 = X3
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3) ) )
| ~ aSet0(X0)
| sP2(X0,X1,X2) ) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( ~ sP2(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( X2 != X4
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& ( X2 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK12(X0,X1,X2),X0)
| ( sK12(X0,X1,X2) != X2
& aElementOf0(sK12(X0,X1,X2),X1)
& aElement0(sK12(X0,X1,X2)) ) )
& ( ~ aElementOf0(sK12(X0,X1,X2),X0)
| sK12(X0,X1,X2) = X2
| ~ aElementOf0(sK12(X0,X1,X2),X1)
| ~ aElement0(sK12(X0,X1,X2)) ) )
| ~ aSet0(X0)
| sP2(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X3,sK12(X0,X1,X2))],[f74]) ).
fof(f87,plain,
( ~ sP4
| ! [X3] :
( ( ~ aElementOf0(X3,sdtmndt0(xS,xx))
| ( xx != X3
& aElementOf0(X3,xS)
& aElement0(X3) ) )
& ( xx = X3
| ~ aElementOf0(X3,xS)
| ~ aElement0(X3)
| aElementOf0(X3,sdtmndt0(xS,xx)) ) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f88,plain,
( ~ sP4
| ! [X3] :
( ( ~ aElementOf0(X3,sdtmndt0(xS,xx))
| ( xx != X3
& aElementOf0(X3,xS)
& aElement0(X3) ) )
& ( xx = X3
| ~ aElementOf0(X3,xS)
| ~ aElement0(X3)
| aElementOf0(X3,sdtmndt0(xS,xx)) ) ) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
( ~ sP4
| ! [X0] :
( ( ~ aElementOf0(X0,sdtmndt0(xS,xx))
| ( xx != X0
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& ( xx = X0
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ) ) ),
inference(rectify,[],[f88]) ).
fof(f107,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| X2 = X4
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f122,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| X2 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f151,plain,
! [X0] :
( ~ sP4
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f89]) ).
fof(f152,plain,
! [X0] :
( ~ sP4
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| aElement0(X0) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X1)
| ( X2 = X3 )
| ~ aElementOf0(X3,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X0)
| ( X2 = X3 )
| ~ aElement0(X3)
| ~ aElementOf0(X3,X1)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_108,plain,
! [X0: $i] :
( aElement0(X0)
| ~ sP4
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_109,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ sP4
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_159,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(global_subsumption_just,[status(thm)],[c_108,c_117,c_94,c_108,c_100]) ).
tcf(c_163,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(global_subsumption_just,[status(thm)],[c_109,c_117,c_94,c_109,c_101]) ).
tcf(c_165,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(global_subsumption_just,[status(thm)],[c_101,c_163]) ).
tcf(c_179,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(global_subsumption_just,[status(thm)],[c_103,c_115,c_92,c_103,c_95,c_159]) ).
tcf(c_183,plain,
! [X0: $i] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_179]) ).
tcf(c_6836,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_165,c_6028]) ).
tcf(c_6843,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_11)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_183,c_6028,c_6029]) ).
tcf(c_7238,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ( X0 = xx )
| ~ aElementOf0(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_6972,c_72]) ).
tcf(c_7748,plain,
( aElementOf0(sK13,iPr_def_10)
| ( xx = sK13 )
| ~ sP8 ),
inference(superposition,[status(thm)],[c_6821,c_7238]) ).
tcf(c_7832,plain,
( aElementOf0(sK13,iPr_def_11)
| ( xx = sK13 )
| ~ sP8 ),
inference(superposition,[status(thm)],[c_7748,c_6843]) ).
tcf(c_7833,plain,
( aElementOf0(sK13,xS)
| ( xx = sK13 )
| ~ sP8 ),
inference(superposition,[status(thm)],[c_7748,c_6836]) ).
tcf(c_7859,plain,
( ~ sP8
| ( xx = sK13 ) ),
inference(global_subsumption_just,[status(thm)],[c_7832,c_88,c_7833]) ).
tcf(c_7860,plain,
( ( xx = sK13 )
| ~ sP8 ),
inference(renaming,[status(thm)],[c_7859]) ).
tcf(c_7904,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ( X0 = xx )
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(superposition,[status(thm)],[c_7880,c_81]) ).
tcf(c_8730,plain,
( sP8
| aElementOf0(sK14,iPr_def_10)
| ( xx = sK14 )
| ~ aElement0(sK14) ),
inference(superposition,[status(thm)],[c_6031,c_7904]) ).
tcf(c_8896,plain,
( sP8
| aElementOf0(sK14,iPr_def_10)
| ( xx = sK14 ) ),
inference(global_subsumption_just,[status(thm)],[c_8730,c_6803,c_8730]) ).
tcf(c_8906,plain,
( sP8
| aElementOf0(sK14,iPr_def_11)
| ( xx = sK14 ) ),
inference(superposition,[status(thm)],[c_8896,c_6843]) ).
tcf(c_8918,plain,
( sP8
| ( xx = sK14 ) ),
inference(global_subsumption_just,[status(thm)],[c_8906,c_6032,c_8906]) ).
tcf(c_8924,plain,
( ( xx = sK14 )
| ( xx = sK13 ) ),
inference(superposition,[status(thm)],[c_8918,c_7860]) ).
tcf(c_9190,plain,
( sP8
| ( xx = sK13 )
| ~ aElementOf0(xx,iPr_def_11) ),
inference(superposition,[status(thm)],[c_8924,c_6032]) ).
tcf(c_9192,plain,
( sP8
| ( xx = sK13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9190,c_6867]) ).
tcf(c_9197,plain,
xx = sK13,
inference(global_subsumption_just,[status(thm)],[c_9192,c_7860,c_9192]) ).
tcf(c_9203,plain,
( ~ sP8
| ~ aElementOf0(xx,xS) ),
inference(demodulation,[status(thm)],[c_88,c_9197]) ).
tcf(c_9204,plain,
~ sP8,
inference(forward_subsumption_resolution,[status(thm)],[c_9203,c_87]) ).
tcf(c_9205,plain,
xx = sK14,
inference(backward_subsumption_resolution,[status(thm)],[c_8918,c_9204]) ).
tcf(c_9208,plain,
~ aElementOf0(sK14,iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_6032,c_9204]) ).
tcf(c_9217,plain,
~ aElementOf0(xx,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_9208,c_9205]) ).
tcf(c_9218,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9217,c_6867]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM535+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n013.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
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 04:29:36 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 4.05/1.29 % SZS status Started for theBenchmark.p
% 4.05/1.29 % SZS status Theorem for theBenchmark.p
% 4.05/1.29
% 4.05/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.05/1.29
% 4.05/1.29 % ------ iProver source info
% 4.05/1.29
% 4.05/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 4.05/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.05/1.29 % git: non_committed_changes: false
% 4.05/1.29
% 4.05/1.29 % ------ Parsing...
% 4.05/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.05/1.29
% 4.05/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 8 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 %
% 4.05/1.29
% 4.05/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.05/1.29
% 4.05/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.05/1.29 % ------ Proving...
% 4.05/1.29 % ------ Problem Properties
% 4.05/1.29
% 4.05/1.29 %
% 4.05/1.29 % clauses 53
% 4.05/1.29 % conjectures 3
% 4.05/1.29 % EPR 24
% 4.05/1.29 % Horn 40
% 4.05/1.29 % unary 9
% 4.05/1.29 % binary 15
% 4.05/1.29 % lits 147
% 4.05/1.29 % lits eq 14
% 4.05/1.29 % fd_pure 0
% 4.05/1.29 % fd_pseudo 0
% 4.05/1.29 % fd_cond 3
% 4.05/1.29 % fd_pseudo_cond 5
% 4.05/1.29 % AC symbols 0
% 4.05/1.29
% 4.05/1.29 % ------ Schedule dynamic 5 is on
% 4.05/1.29
% 4.05/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.05/1.29
% 4.05/1.29
% 4.05/1.29 % ------
% 4.05/1.29 % Current options:
% 4.05/1.29 % ------
% 4.05/1.29
% 4.05/1.29
% 4.05/1.29 %
% 4.05/1.29
% 4.05/1.29 % ------ Proving...
% 4.05/1.29 %
% 4.05/1.29
% 4.05/1.29 % SZS status Theorem for theBenchmark.p
% 4.05/1.29
% 4.05/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.05/1.29
% 4.05/1.29
%------------------------------------------------------------------------------