%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG096+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:35:29 PM UTC 2026
% Result : Theorem 44.75s 7.18s
% Output : Refutation 45.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 36
% Syntax : Number of formulae : 285 ( 57 unt; 14 def)
% Number of atoms : 931 ( 158 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1146 ( 500 ~; 501 |; 101 &)
% ( 22 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 11 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 11 con; 0-3 aty)
% Number of variables : 322 ( 0 sgn 290 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f4,axiom,
! [X0] :
( aElement0(X0)
=> aElement0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).
fof(f5,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f7,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(f9,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(f10,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddInvr) ).
fof(f11,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2) )
=> ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(f15,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtasdt0(smndt0(sz10),X0) = smndt0(X0)
& smndt0(X0) = sdtasdt0(X0,smndt0(sz10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMnOne) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f22,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aSet0(X1) )
=> ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSSum) ).
fof(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f25,axiom,
! [X0,X1] :
( ( aIdeal0(X0)
& aIdeal0(X1) )
=> aIdeal0(sdtpldt1(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIdeSum) ).
fof(f28,axiom,
( aIdeal0(xI)
& aIdeal0(xJ) ),
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(f30,axiom,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1217) ).
fof(f31,axiom,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& sdtpldt0(xa,xb) = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1294) ).
fof(f32,axiom,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1319) ).
fof(f33,conjecture,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f34,negated_conjecture,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f38,plain,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) ) ) ) ) ),
inference(rectify,[],[f24]) ).
fof(f39,plain,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(flattening,[],[f34]) ).
fof(f40,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f42,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f44,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f46,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f8]) ).
fof(f48,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f50,plain,
! [X0] :
( ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f51,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f52,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f12]) ).
fof(f54,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f53]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0] :
( ( sdtasdt0(smndt0(sz10),X0) = smndt0(X0)
& smndt0(X0) = sdtasdt0(X0,smndt0(sz10)) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f65,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) )
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f66,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) )
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(flattening,[],[f65]) ).
fof(f69,plain,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f70,plain,
! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X0)
| ~ aIdeal0(X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f71,plain,
! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X0)
| ~ aIdeal0(X1) ),
inference(flattening,[],[f70]) ).
fof(f76,plain,
! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f77,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f78,definition,
! [X1,X0] :
( ! [X2] :
( X2 = sdtpldt1(X0,X1)
<=> sP0(X2,X0,X1) )
| ~ sP1(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f79,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(definition_folding,[],[f66,f78,f77]) ).
fof(f81,plain,
! [X1,X0] :
( ! [X2] :
( ( X2 = sdtpldt1(X0,X1)
| ~ sP0(X2,X0,X1) )
& ( sP0(X2,X0,X1)
| sdtpldt1(X0,X1) != X2 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f78]) ).
fof(f82,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X1,X0) = X2
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| sdtpldt1(X1,X0) != X2 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4,X5] :
( ~ aElementOf0(X4,X0)
| ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4,X5] :
( ~ aElementOf0(X4,X0)
| ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != X3 ) )
& ( ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f77]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4,X5] :
( ~ aElementOf0(X4,X0)
| ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4,X5] :
( ~ aElementOf0(X4,X0)
| ~ aElementOf0(X5,X1)
| sdtpldt0(X4,X5) != X3 ) )
& ( ? [X4,X5] :
( aElementOf0(X4,X0)
& aElementOf0(X5,X1)
& sdtpldt0(X4,X5) = X3 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ? [X3] :
( ( ! [X4,X5] :
( ~ aElementOf0(X4,X1)
| ~ aElementOf0(X5,X2)
| sdtpldt0(X4,X5) != X3 )
| ~ aElementOf0(X3,X0) )
& ( ? [X6,X7] :
( aElementOf0(X6,X1)
& aElementOf0(X7,X2)
& sdtpldt0(X6,X7) = X3 )
| aElementOf0(X3,X0) ) ) )
& ( ( aSet0(X0)
& ! [X8] :
( ( aElementOf0(X8,X0)
| ! [X9,X10] :
( ~ aElementOf0(X9,X1)
| ~ aElementOf0(X10,X2)
| sdtpldt0(X9,X10) != X8 ) )
& ( ? [X11,X12] :
( aElementOf0(X11,X1)
& aElementOf0(X12,X2)
& sdtpldt0(X11,X12) = X8 )
| ~ aElementOf0(X8,X0) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ! [X4,X5] :
( ~ aElementOf0(X4,X1)
| ~ aElementOf0(X5,X2)
| sdtpldt0(X4,X5) != sK4(X0,X1,X2) )
| ~ aElementOf0(sK4(X0,X1,X2),X0) )
& ( ( aElementOf0(sK5(X0,X1,X2),X1)
& aElementOf0(sK6(X0,X1,X2),X2)
& sK4(X0,X1,X2) = sdtpldt0(sK5(X0,X1,X2),sK6(X0,X1,X2)) )
| aElementOf0(sK4(X0,X1,X2),X0) ) ) )
& ( ( aSet0(X0)
& ! [X8] :
( ( aElementOf0(X8,X0)
| ! [X9,X10] :
( ~ aElementOf0(X9,X1)
| ~ aElementOf0(X10,X2)
| sdtpldt0(X9,X10) != X8 ) )
& ( ( aElementOf0(sK7(X1,X2,X8),X1)
& aElementOf0(sK8(X1,X2,X8),X2)
& sdtpldt0(sK7(X1,X2,X8),sK8(X1,X2,X8)) = X8 )
| ~ aElementOf0(X8,X0) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X6,sK5(X0,X1,X2)),skolemize(X7,sK6(X0,X1,X2)),skolemize(X11,sK7(X1,X2,X8)),skolemize(X12,sK8(X1,X2,X8))],[f85]) ).
fof(f91,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) )
& ( ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f92,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) )
& ( ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ? [X1] :
( ( ? [X2] :
( ~ aElementOf0(sdtpldt0(X1,X2),X0)
& aElementOf0(X2,X0) )
| ? [X3] :
( ~ aElementOf0(sdtasdt0(X3,X1),X0)
& aElement0(X3) ) )
& aElementOf0(X1,X0) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtpldt0(X4,X5),X0)
| ~ aElementOf0(X5,X0) )
& ! [X6] :
( aElementOf0(sdtasdt0(X6,X4),X0)
| ~ aElement0(X6) ) )
| ~ aElementOf0(X4,X0) ) )
| ~ aIdeal0(X0) ) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ( ( ( ~ aElementOf0(sdtpldt0(sK10(X0),sK11(X0)),X0)
& aElementOf0(sK11(X0),X0) )
| ( ~ aElementOf0(sdtasdt0(sK12(X0),sK10(X0)),X0)
& aElement0(sK12(X0)) ) )
& aElementOf0(sK10(X0),X0) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( ! [X5] :
( aElementOf0(sdtpldt0(X4,X5),X0)
| ~ aElementOf0(X5,X0) )
& ! [X6] :
( aElementOf0(sdtasdt0(X6,X4),X0)
| ~ aElement0(X6) ) )
| ~ aElementOf0(X4,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))],[f93]) ).
fof(f97,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f98,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f99,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f100,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f102,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aElement0(X0)
| ~ aElement0(X1)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f103,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f49]) ).
fof(f104,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f49]) ).
fof(f105,plain,
! [X0] :
( ~ aElement0(X0)
| sz00 = sdtpldt0(smndt0(X0),X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f106,plain,
! [X0] :
( ~ aElement0(X0)
| sz00 = sdtpldt0(X0,smndt0(X0)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f107,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aElement0(X0)
| ~ aElement0(X1)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aElement0(X0)
| ~ aElement0(X1)
| sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aElement0(X0)
| ~ aElement0(X1)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f113,plain,
! [X0] :
( ~ aElement0(X0)
| smndt0(X0) = sdtasdt0(X0,smndt0(sz10)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f114,plain,
! [X0] :
( ~ aElement0(X0)
| smndt0(X0) = sdtasdt0(smndt0(sz10),X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f119,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f124,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| sdtpldt1(X1,X0) != X2
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f129,plain,
! [X2,X10,X0,X1,X8,X9] :
( aElementOf0(X8,X0)
| ~ aElementOf0(X9,X1)
| ~ aElementOf0(X10,X2)
| sdtpldt0(X9,X10) != X8
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f135,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f143,plain,
! [X0,X6,X4] :
( aElementOf0(sdtasdt0(X6,X4),X0)
| ~ aElement0(X6)
| ~ aElementOf0(X4,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f145,plain,
! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f151,plain,
! [X0,X1] :
( aIdeal0(sdtpldt1(X0,X1))
| ~ aIdeal0(X0)
| ~ aIdeal0(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f155,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f28]) ).
fof(f156,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f28]) ).
fof(f157,plain,
! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f158,plain,
aElement0(xy),
inference(cnf_transformation,[],[f30]) ).
fof(f159,plain,
aElement0(xx),
inference(cnf_transformation,[],[f30]) ).
fof(f160,plain,
sz10 = sdtpldt0(xa,xb),
inference(cnf_transformation,[],[f31]) ).
fof(f161,plain,
aElementOf0(xb,xJ),
inference(cnf_transformation,[],[f31]) ).
fof(f162,plain,
aElementOf0(xa,xI),
inference(cnf_transformation,[],[f31]) ).
fof(f163,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(cnf_transformation,[],[f32]) ).
fof(f164,plain,
~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(cnf_transformation,[],[f39]) ).
fof(f165,plain,
! [X0,X1] :
( sP0(sdtpldt1(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f124]) ).
fof(f166,plain,
! [X2,X10,X0,X1,X9] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X9,X1)
| ~ aElementOf0(X10,X2)
| aElementOf0(sdtpldt0(X9,X10),X0) ),
inference(equality_resolution,[],[f129]) ).
fof(f171,definition,
sF13 = smndt0(xx),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f172,plain,
smndt0(xx) = sF13,
inference(reorient_equations,[],[f171]) ).
fof(f173,definition,
sF14 = sdtpldt0(xw,sF13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f174,plain,
sdtpldt0(xw,sF13) = sF14,
inference(reorient_equations,[],[f173]) ).
fof(f175,plain,
~ aElementOf0(sF14,xI),
inference(definition_folding,[],[f164,f174,f172]) ).
fof(f176,plain,
( aElement0(sF13)
| ~ aElement0(xx) ),
inference(superposition,[],[f98,f172]) ).
fof(f177,plain,
aElement0(sF13),
inference(forward_subsumption_resolution,[],[f176,f159]) ).
fof(f180,plain,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(superposition,[],[f99,f163]) ).
fof(f182,definition,
( spl15_1
<=> aElement0(sdtasdt0(xx,xb)) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f183,plain,
( aElement0(sdtasdt0(xx,xb))
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f184,plain,
( ~ aElement0(sdtasdt0(xx,xb))
| spl15_1 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f186,definition,
( spl15_2
<=> aElement0(sdtasdt0(xy,xa)) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f187,plain,
( aElement0(sdtasdt0(xy,xa))
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f188,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| spl15_2 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f190,definition,
( spl15_3
<=> aElement0(xw) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f192,plain,
( aElement0(xw)
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f193,plain,
( ~ spl15_1
| ~ spl15_2
| spl15_3 ),
inference(avatar_split_clause,[],[f180,f190,f186,f182]) ).
fof(f214,plain,
aSet0(xI),
inference(resolution,[],[f156,f145]) ).
fof(f225,plain,
( ~ aElement0(xx)
| ~ aElement0(xb)
| spl15_1 ),
inference(resolution,[],[f100,f184]) ).
fof(f229,plain,
( ~ aElement0(xb)
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f225,f159]) ).
fof(f233,definition,
( spl15_5
<=> aIdeal0(sdtpldt1(xI,xJ)) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
fof(f234,plain,
( aIdeal0(sdtpldt1(xI,xJ))
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f235,plain,
( ~ aIdeal0(sdtpldt1(xI,xJ))
| spl15_5 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f248,plain,
smndt0(xx) = sdtasdt0(xx,smndt0(sz10)),
inference(resolution,[],[f113,f159]) ).
fof(f251,plain,
sF13 = sdtasdt0(xx,smndt0(sz10)),
inference(forward_demodulation,[],[f248,f172]) ).
fof(f264,plain,
! [X2,X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aSet0(X2)
| ~ aElement0(X0)
| ~ aElementOf0(X1,X2)
| ~ aIdeal0(X2) ),
inference(resolution,[],[f119,f143]) ).
fof(f265,plain,
( aElement0(xa)
| ~ aSet0(xI) ),
inference(resolution,[],[f119,f162]) ).
fof(f266,plain,
( aElement0(xb)
| ~ aSet0(xJ) ),
inference(resolution,[],[f119,f161]) ).
fof(f267,plain,
( ~ aSet0(xJ)
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f266,f229]) ).
fof(f268,plain,
aElement0(xa),
inference(forward_subsumption_resolution,[],[f265,f214]) ).
fof(f269,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X1,X2)
| ~ aElement0(X0)
| aElement0(sdtasdt0(X0,X1))
| ~ aIdeal0(X2) ),
inference(forward_subsumption_resolution,[],[f264,f145]) ).
fof(f272,plain,
smndt0(xa) = sdtasdt0(xa,smndt0(sz10)),
inference(resolution,[],[f268,f113]) ).
fof(f274,plain,
sz00 = sdtpldt0(smndt0(xa),xa),
inference(resolution,[],[f268,f105]) ).
fof(f276,plain,
aSet0(xJ),
inference(resolution,[],[f155,f145]) ).
fof(f277,plain,
( $false
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f276,f267]) ).
fof(f278,plain,
spl15_1,
inference(avatar_contradiction_clause,[],[f277]) ).
fof(f280,definition,
( spl15_8
<=> aSet0(xJ) ),
introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition]) ).
fof(f284,definition,
( spl15_9
<=> aElement0(xb) ),
introduced(definition,[new_symbols(definition,[spl15_9])],[avatar_definition]) ).
fof(f286,plain,
( aElement0(xb)
| ~ spl15_9 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f287,plain,
( ~ spl15_8
| spl15_9 ),
inference(avatar_split_clause,[],[f266,f284,f280]) ).
fof(f288,plain,
spl15_8,
inference(avatar_split_clause,[],[f276,f280]) ).
fof(f289,plain,
( ~ aElement0(xy)
| ~ aElement0(xa)
| spl15_2 ),
inference(resolution,[],[f188,f100]) ).
fof(f290,plain,
( ~ aElement0(xa)
| spl15_2 ),
inference(forward_subsumption_resolution,[],[f289,f158]) ).
fof(f291,plain,
( $false
| spl15_2 ),
inference(forward_subsumption_resolution,[],[f290,f268]) ).
fof(f292,plain,
spl15_2,
inference(avatar_contradiction_clause,[],[f291]) ).
fof(f307,plain,
( ! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtpldt0(sdtpldt0(X0,X1),sdtasdt0(xx,xb)) = sdtpldt0(X0,sdtpldt0(X1,sdtasdt0(xx,xb))) )
| ~ spl15_1 ),
inference(resolution,[],[f183,f102]) ).
fof(f317,plain,
( ! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtpldt0(sdtpldt0(X0,X1),xb) = sdtpldt0(X0,sdtpldt0(X1,xb)) )
| ~ spl15_9 ),
inference(resolution,[],[f286,f102]) ).
fof(f356,plain,
sz00 = sdtpldt0(sz10,smndt0(sz10)),
inference(resolution,[],[f97,f106]) ).
fof(f366,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,sdtasdt0(xy,xa)) = sdtpldt0(sdtasdt0(xy,xa),X0) )
| ~ spl15_2 ),
inference(resolution,[],[f101,f187]) ).
fof(f369,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,xy) = sdtpldt0(xy,X0) ),
inference(resolution,[],[f101,f158]) ).
fof(f372,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,xw) = sdtpldt0(xw,X0) )
| ~ spl15_3 ),
inference(resolution,[],[f101,f192]) ).
fof(f373,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,sF13) = sdtpldt0(sF13,X0) ),
inference(resolution,[],[f101,f177]) ).
fof(f394,plain,
smndt0(xx) = sdtasdt0(smndt0(sz10),xx),
inference(resolution,[],[f114,f159]) ).
fof(f396,plain,
smndt0(xa) = sdtasdt0(smndt0(sz10),xa),
inference(resolution,[],[f114,f268]) ).
fof(f401,plain,
sF13 = sdtasdt0(smndt0(sz10),xx),
inference(forward_demodulation,[],[f394,f172]) ).
fof(f402,plain,
! [X0] :
( aElementOf0(sF13,X0)
| ~ aElement0(smndt0(sz10))
| ~ aElementOf0(xx,X0)
| ~ aIdeal0(X0) ),
inference(superposition,[],[f143,f401]) ).
fof(f405,definition,
( spl15_10
<=> aElement0(smndt0(sz10)) ),
introduced(definition,[new_symbols(definition,[spl15_10])],[avatar_definition]) ).
fof(f406,plain,
( aElement0(smndt0(sz10))
| ~ spl15_10 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f407,plain,
( ~ aElement0(smndt0(sz10))
| spl15_10 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f409,definition,
( spl15_11
<=> ! [X0] :
( aElementOf0(sF13,X0)
| ~ aIdeal0(X0)
| ~ aElementOf0(xx,X0) ) ),
introduced(definition,[new_symbols(definition,[spl15_11])],[avatar_definition]) ).
fof(f410,plain,
( ! [X0] :
( ~ aElementOf0(xx,X0)
| ~ aIdeal0(X0)
| aElementOf0(sF13,X0) )
| ~ spl15_11 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f411,plain,
( ~ spl15_10
| spl15_11 ),
inference(avatar_split_clause,[],[f402,f409,f405]) ).
fof(f412,plain,
( ~ aElement0(sz10)
| spl15_10 ),
inference(resolution,[],[f407,f98]) ).
fof(f413,plain,
( $false
| spl15_10 ),
inference(forward_subsumption_resolution,[],[f412,f97]) ).
fof(f414,plain,
spl15_10,
inference(avatar_contradiction_clause,[],[f413]) ).
fof(f416,plain,
( ! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtpldt0(sdtpldt0(X0,X1),smndt0(sz10)) = sdtpldt0(X0,sdtpldt0(X1,smndt0(sz10))) )
| ~ spl15_10 ),
inference(resolution,[],[f406,f102]) ).
fof(f420,plain,
( ! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(X0,sdtpldt0(X1,smndt0(sz10))) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,smndt0(sz10))) )
| ~ spl15_10 ),
inference(resolution,[],[f406,f112]) ).
fof(f453,plain,
sdtpldt0(sF13,xy) = sdtpldt0(xy,sF13),
inference(resolution,[],[f369,f177]) ).
fof(f460,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sdtpldt0(X0,sdtasdt0(xy,xa)),sdtasdt0(xx,xb)) = sdtpldt0(X0,sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))) )
| ~ spl15_1
| ~ spl15_2 ),
inference(resolution,[],[f307,f187]) ).
fof(f467,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sdtpldt0(X0,sF13),sdtasdt0(xx,xb)) = sdtpldt0(X0,sdtpldt0(sF13,sdtasdt0(xx,xb))) )
| ~ spl15_1 ),
inference(resolution,[],[f307,f177]) ).
fof(f469,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,xw) = sdtpldt0(sdtpldt0(X0,sdtasdt0(xy,xa)),sdtasdt0(xx,xb)) )
| ~ spl15_1
| ~ spl15_2 ),
inference(forward_demodulation,[],[f460,f163]) ).
fof(f501,plain,
( xb = sdtpldt0(sz00,xb)
| ~ spl15_9 ),
inference(resolution,[],[f103,f286]) ).
fof(f526,plain,
( ~ aIdeal0(sdtpldt1(xI,xJ))
| aElementOf0(sF13,sdtpldt1(xI,xJ))
| ~ aElement0(xx)
| ~ spl15_11 ),
inference(resolution,[],[f410,f157]) ).
fof(f529,plain,
! [X0,X1] :
( aSet0(sdtpldt1(X1,X0))
| ~ sP1(X0,X1) ),
inference(resolution,[],[f165,f130]) ).
fof(f542,plain,
( sdtpldt0(xw,sF13) = sdtpldt0(sF13,xw)
| ~ spl15_3 ),
inference(resolution,[],[f372,f177]) ).
fof(f544,plain,
( sF14 = sdtpldt0(sF13,xw)
| ~ spl15_3 ),
inference(forward_demodulation,[],[f542,f174]) ).
fof(f554,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,xx) = sdtasdt0(xx,X0) ),
inference(resolution,[],[f107,f159]) ).
fof(f555,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,xy) = sdtasdt0(xy,X0) ),
inference(resolution,[],[f107,f158]) ).
fof(f559,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sF13) = sdtasdt0(sF13,X0) ),
inference(resolution,[],[f107,f177]) ).
fof(f570,plain,
sdtasdt0(xy,xa) = sdtasdt0(xa,xy),
inference(resolution,[],[f555,f268]) ).
fof(f588,plain,
( sdtasdt0(xx,xb) = sdtasdt0(xb,xx)
| ~ spl15_9 ),
inference(resolution,[],[f554,f286]) ).
fof(f596,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sdtpldt0(X0,sz10),smndt0(sz10)) = sdtpldt0(X0,sdtpldt0(sz10,smndt0(sz10))) )
| ~ spl15_10 ),
inference(resolution,[],[f416,f97]) ).
fof(f612,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,sz10),smndt0(sz10)) )
| ~ spl15_10 ),
inference(forward_demodulation,[],[f596,f356]) ).
fof(f643,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sdtpldt0(xb,smndt0(sz10))) = sdtpldt0(sdtasdt0(X0,xb),sdtasdt0(X0,smndt0(sz10))) )
| ~ spl15_9
| ~ spl15_10 ),
inference(resolution,[],[f420,f286]) ).
fof(f707,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sdtpldt0(X0,xa),xb) = sdtpldt0(X0,sdtpldt0(xa,xb)) )
| ~ spl15_9 ),
inference(resolution,[],[f317,f268]) ).
fof(f713,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,xa),xb) )
| ~ spl15_9 ),
inference(forward_demodulation,[],[f707,f160]) ).
fof(f924,plain,
( sdtpldt0(sF13,xw) = sdtpldt0(sdtpldt0(sF13,sdtasdt0(xy,xa)),sdtasdt0(xx,xb))
| ~ spl15_1
| ~ spl15_2 ),
inference(resolution,[],[f469,f177]) ).
fof(f927,plain,
( sdtpldt0(sF13,xw) = sdtpldt0(sdtpldt0(sF13,sdtasdt0(xy,xa)),sdtasdt0(xb,xx))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_9 ),
inference(forward_demodulation,[],[f924,f588]) ).
fof(f942,plain,
( sdtpldt0(sF13,xw) = sdtpldt0(sdtpldt0(sF13,sdtasdt0(xa,xy)),sdtasdt0(xb,xx))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_9 ),
inference(forward_demodulation,[],[f927,f570]) ).
fof(f957,plain,
( sF14 = sdtpldt0(sdtpldt0(sF13,sdtasdt0(xa,xy)),sdtasdt0(xb,xx))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_9 ),
inference(forward_demodulation,[],[f942,f544]) ).
fof(f961,plain,
! [X2,X3,X0,X1] :
( aElementOf0(sdtpldt0(X0,X2),sdtpldt1(X1,X3))
| ~ aElementOf0(X2,X3)
| ~ aElementOf0(X0,X1)
| ~ sP1(X3,X1) ),
inference(resolution,[],[f166,f165]) ).
fof(f1044,plain,
( sdtpldt0(sF13,sdtasdt0(xy,xa)) = sdtpldt0(sdtasdt0(xy,xa),sF13)
| ~ spl15_2 ),
inference(resolution,[],[f373,f187]) ).
fof(f1045,plain,
( sdtpldt0(sF13,sdtasdt0(xx,xb)) = sdtpldt0(sdtasdt0(xx,xb),sF13)
| ~ spl15_1 ),
inference(resolution,[],[f373,f183]) ).
fof(f1055,plain,
( sdtpldt0(sdtasdt0(xb,xx),sF13) = sdtpldt0(sF13,sdtasdt0(xb,xx))
| ~ spl15_1
| ~ spl15_9 ),
inference(forward_demodulation,[],[f1045,f588]) ).
fof(f1056,plain,
( sdtpldt0(sdtasdt0(xa,xy),sF13) = sdtpldt0(sF13,sdtasdt0(xa,xy))
| ~ spl15_2 ),
inference(forward_demodulation,[],[f1044,f570]) ).
fof(f1067,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(sdtpldt0(X1,xy),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(xy,X0)) ),
inference(resolution,[],[f111,f158]) ).
fof(f1202,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(sdtpldt0(sF13,xy),X0) = sdtpldt0(sdtasdt0(sF13,X0),sdtasdt0(xy,X0)) ),
inference(resolution,[],[f1067,f177]) ).
fof(f1205,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sdtasdt0(sF13,X0),sdtasdt0(xy,X0)) = sdtasdt0(sdtpldt0(xy,sF13),X0) ),
inference(forward_demodulation,[],[f1202,f453]) ).
fof(f1266,plain,
! [X2,X3,X0,X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X2,X3)
| ~ sP1(X1,X3)
| aElement0(sdtpldt0(X2,X0))
| ~ aSet0(sdtpldt1(X3,X1)) ),
inference(resolution,[],[f961,f119]) ).
fof(f1294,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X1,X3)
| ~ aElementOf0(X2,X3)
| ~ aElementOf0(X0,X1)
| aElement0(sdtpldt0(X2,X0)) ),
inference(forward_subsumption_resolution,[],[f1266,f529]) ).
fof(f1477,plain,
sdtasdt0(xa,sF13) = sdtasdt0(sF13,xa),
inference(resolution,[],[f559,f268]) ).
fof(f1527,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(sdtasdt0(X0,X1),xx) = sdtasdt0(X0,sdtasdt0(X1,xx)) ),
inference(resolution,[],[f108,f159]) ).
fof(f1565,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtasdt0(sdtasdt0(X0,smndt0(sz10)),xx) = sdtasdt0(X0,sdtasdt0(smndt0(sz10),xx)) )
| ~ spl15_10 ),
inference(resolution,[],[f1527,f406]) ).
fof(f1581,plain,
( ! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sF13) = sdtasdt0(sdtasdt0(X0,smndt0(sz10)),xx) )
| ~ spl15_10 ),
inference(forward_demodulation,[],[f1565,f401]) ).
fof(f1611,plain,
! [X0,X1] :
( aSet0(sdtpldt1(X0,X1))
| ~ aIdeal0(X1)
| ~ aIdeal0(X0) ),
inference(resolution,[],[f151,f145]) ).
fof(f2703,plain,
! [X2,X3,X0,X1] :
( ~ aElementOf0(X2,X3)
| ~ aElementOf0(X0,X1)
| aElement0(sdtpldt0(X0,X2))
| ~ aSet0(X1)
| ~ aSet0(X3) ),
inference(resolution,[],[f1294,f135]) ).
fof(f4757,plain,
( sdtasdt0(xa,sF13) = sdtasdt0(sdtasdt0(xa,smndt0(sz10)),xx)
| ~ spl15_10 ),
inference(resolution,[],[f1581,f268]) ).
fof(f4766,plain,
( sdtasdt0(xa,sF13) = sdtasdt0(smndt0(xa),xx)
| ~ spl15_10 ),
inference(forward_demodulation,[],[f4757,f272]) ).
fof(f4854,plain,
! [X0] :
( ~ aElement0(X0)
| aElement0(sdtasdt0(X0,xa))
| ~ aIdeal0(xI) ),
inference(resolution,[],[f269,f162]) ).
fof(f4861,plain,
! [X0] :
( aElement0(sdtasdt0(X0,xa))
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f4854,f156]) ).
fof(f5391,plain,
( aElement0(smndt0(xa))
| ~ aElement0(smndt0(sz10)) ),
inference(superposition,[],[f4861,f396]) ).
fof(f5397,plain,
( aElement0(smndt0(xa))
| ~ spl15_10 ),
inference(forward_subsumption_resolution,[],[f5391,f406]) ).
fof(f5411,plain,
( smndt0(xa) = sdtpldt0(smndt0(xa),sz00)
| ~ spl15_10 ),
inference(resolution,[],[f5397,f104]) ).
fof(f5457,plain,
( sdtasdt0(smndt0(xa),xx) = sdtasdt0(xx,smndt0(xa))
| ~ spl15_10 ),
inference(resolution,[],[f5397,f554]) ).
fof(f5470,plain,
( sdtpldt0(smndt0(xa),sz10) = sdtpldt0(sdtpldt0(smndt0(xa),xa),xb)
| ~ spl15_9
| ~ spl15_10 ),
inference(resolution,[],[f5397,f713]) ).
fof(f5499,plain,
( sdtpldt0(sz00,xb) = sdtpldt0(smndt0(xa),sz10)
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f5470,f274]) ).
fof(f5503,plain,
( sdtasdt0(xa,sF13) = sdtasdt0(xx,smndt0(xa))
| ~ spl15_10 ),
inference(forward_demodulation,[],[f5457,f4766]) ).
fof(f5525,plain,
( xb = sdtpldt0(smndt0(xa),sz10)
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f5499,f501]) ).
fof(f6130,plain,
( aElement0(sdtasdt0(xa,sF13))
| ~ aElement0(sF13) ),
inference(superposition,[],[f4861,f1477]) ).
fof(f6135,plain,
aElement0(sdtasdt0(xa,sF13)),
inference(forward_subsumption_resolution,[],[f6130,f177]) ).
fof(f6718,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X0,X1)
| aElement0(sdtpldt0(X0,X2))
| ~ aSet0(X1)
| ~ aSet0(sdtpldt1(xI,xJ))
| ~ aElement0(X2) ),
inference(resolution,[],[f2703,f157]) ).
fof(f6732,definition,
( spl15_62
<=> aSet0(sdtpldt1(xI,xJ)) ),
introduced(definition,[new_symbols(definition,[spl15_62])],[avatar_definition]) ).
fof(f6733,plain,
( aSet0(sdtpldt1(xI,xJ))
| ~ spl15_62 ),
inference(avatar_component_clause,[],[f6732]) ).
fof(f6734,plain,
( ~ aSet0(sdtpldt1(xI,xJ))
| spl15_62 ),
inference(avatar_component_clause,[],[f6732]) ).
fof(f6736,definition,
( spl15_63
<=> ! [X2,X0,X1] :
( ~ aElementOf0(X0,X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| aElement0(sdtpldt0(X0,X2)) ) ),
introduced(definition,[new_symbols(definition,[spl15_63])],[avatar_definition]) ).
fof(f6737,plain,
( ! [X2,X0,X1] :
( ~ aElementOf0(X0,X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| aElement0(sdtpldt0(X0,X2)) )
| ~ spl15_63 ),
inference(avatar_component_clause,[],[f6736]) ).
fof(f6738,plain,
( ~ spl15_62
| spl15_63 ),
inference(avatar_split_clause,[],[f6718,f6736,f6732]) ).
fof(f8391,plain,
( sdtpldt0(smndt0(xa),sz00) = sdtpldt0(sdtpldt0(smndt0(xa),sz10),smndt0(sz10))
| ~ spl15_10 ),
inference(resolution,[],[f612,f5397]) ).
fof(f8454,plain,
( sdtpldt0(xb,smndt0(sz10)) = sdtpldt0(smndt0(xa),sz00)
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f8391,f5525]) ).
fof(f8468,plain,
( smndt0(xa) = sdtpldt0(xb,smndt0(sz10))
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f8454,f5411]) ).
fof(f8559,plain,
( ~ aIdeal0(xI)
| ~ aIdeal0(xJ)
| spl15_5 ),
inference(resolution,[],[f235,f151]) ).
fof(f8560,plain,
( ~ aIdeal0(xJ)
| spl15_5 ),
inference(forward_subsumption_resolution,[],[f8559,f156]) ).
fof(f8561,plain,
( $false
| spl15_5 ),
inference(forward_subsumption_resolution,[],[f8560,f155]) ).
fof(f8562,plain,
spl15_5,
inference(avatar_contradiction_clause,[],[f8561]) ).
fof(f8563,plain,
( aElementOf0(sF13,sdtpldt1(xI,xJ))
| ~ aElement0(xx)
| ~ spl15_5
| ~ spl15_11 ),
inference(forward_subsumption_resolution,[],[f526,f234]) ).
fof(f8569,plain,
( aElementOf0(sF13,sdtpldt1(xI,xJ))
| ~ spl15_5
| ~ spl15_11 ),
inference(forward_subsumption_resolution,[],[f8563,f159]) ).
fof(f9363,plain,
( ~ aIdeal0(xJ)
| ~ aIdeal0(xI)
| spl15_62 ),
inference(resolution,[],[f6734,f1611]) ).
fof(f9367,plain,
( ~ aIdeal0(xI)
| spl15_62 ),
inference(forward_subsumption_resolution,[],[f9363,f155]) ).
fof(f9368,plain,
( $false
| spl15_62 ),
inference(forward_subsumption_resolution,[],[f9367,f156]) ).
fof(f9369,plain,
spl15_62,
inference(avatar_contradiction_clause,[],[f9368]) ).
fof(f10423,plain,
( ! [X0] :
( ~ aElement0(X0)
| ~ aSet0(sdtpldt1(xI,xJ))
| aElement0(sdtpldt0(sF13,X0)) )
| ~ spl15_5
| ~ spl15_11
| ~ spl15_63 ),
inference(resolution,[],[f6737,f8569]) ).
fof(f10428,plain,
( ! [X0] :
( aElement0(sdtpldt0(sF13,X0))
| ~ aElement0(X0) )
| ~ spl15_5
| ~ spl15_11
| ~ spl15_62
| ~ spl15_63 ),
inference(forward_subsumption_resolution,[],[f10423,f6733]) ).
fof(f20835,plain,
( sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))) = sdtpldt0(sdtasdt0(xx,xb),sdtasdt0(xx,smndt0(sz10)))
| ~ spl15_9
| ~ spl15_10 ),
inference(resolution,[],[f643,f159]) ).
fof(f20848,plain,
( sdtpldt0(sdtasdt0(xx,xb),sF13) = sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10)))
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f20835,f251]) ).
fof(f20905,plain,
( sdtpldt0(sdtasdt0(xx,xb),sF13) = sdtasdt0(xx,smndt0(xa))
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f20848,f8468]) ).
fof(f20949,plain,
( sdtpldt0(sdtasdt0(xx,xb),sF13) = sdtasdt0(xa,sF13)
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f20905,f5503]) ).
fof(f20991,plain,
( sdtpldt0(sdtasdt0(xb,xx),sF13) = sdtasdt0(xa,sF13)
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f20949,f588]) ).
fof(f20999,plain,
( sdtasdt0(xa,sF13) = sdtpldt0(sF13,sdtasdt0(xb,xx))
| ~ spl15_1
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f20991,f1055]) ).
fof(f21890,plain,
( aElement0(sdtpldt0(xy,sF13))
| ~ aElement0(xy)
| ~ spl15_5
| ~ spl15_11
| ~ spl15_62
| ~ spl15_63 ),
inference(superposition,[],[f10428,f453]) ).
fof(f21894,plain,
( aElement0(sdtpldt0(xy,sF13))
| ~ spl15_5
| ~ spl15_11
| ~ spl15_62
| ~ spl15_63 ),
inference(forward_subsumption_resolution,[],[f21890,f158]) ).
fof(f33280,plain,
sdtpldt0(sdtasdt0(sF13,xa),sdtasdt0(xy,xa)) = sdtasdt0(sdtpldt0(xy,sF13),xa),
inference(resolution,[],[f1205,f268]) ).
fof(f33286,plain,
sdtasdt0(sdtpldt0(xy,sF13),xa) = sdtpldt0(sdtasdt0(sF13,xa),sdtasdt0(xa,xy)),
inference(forward_demodulation,[],[f33280,f570]) ).
fof(f33301,plain,
sdtpldt0(sdtasdt0(xa,sF13),sdtasdt0(xa,xy)) = sdtasdt0(sdtpldt0(xy,sF13),xa),
inference(forward_demodulation,[],[f33286,f1477]) ).
fof(f69809,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sF13),sdtasdt0(xx,xb)) = sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sF13,sdtasdt0(xx,xb)))
| ~ spl15_1
| ~ spl15_2 ),
inference(resolution,[],[f467,f187]) ).
fof(f69850,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sF13),sdtasdt0(xb,xx)) = sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sF13,sdtasdt0(xb,xx)))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_9 ),
inference(forward_demodulation,[],[f69809,f588]) ).
fof(f69956,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sF13),sdtasdt0(xb,xx)) = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xa,sF13))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f69850,f20999]) ).
fof(f70062,plain,
( sdtpldt0(sdtpldt0(sdtasdt0(xa,xy),sF13),sdtasdt0(xb,xx)) = sdtpldt0(sdtasdt0(xa,xy),sdtasdt0(xa,sF13))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f69956,f570]) ).
fof(f70141,plain,
( sdtpldt0(sdtpldt0(sF13,sdtasdt0(xa,xy)),sdtasdt0(xb,xx)) = sdtpldt0(sdtasdt0(xa,xy),sdtasdt0(xa,sF13))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f70062,f1056]) ).
fof(f70178,plain,
( sF14 = sdtpldt0(sdtasdt0(xa,xy),sdtasdt0(xa,sF13))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f70141,f957]) ).
fof(f84775,plain,
( sdtpldt0(sdtasdt0(xa,sF13),sdtasdt0(xy,xa)) = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xa,sF13))
| ~ spl15_2 ),
inference(resolution,[],[f366,f6135]) ).
fof(f84801,plain,
( sdtpldt0(sdtasdt0(xa,sF13),sdtasdt0(xa,xy)) = sdtpldt0(sdtasdt0(xa,xy),sdtasdt0(xa,sF13))
| ~ spl15_2 ),
inference(forward_demodulation,[],[f84775,f570]) ).
fof(f84904,plain,
( sF14 = sdtpldt0(sdtasdt0(xa,sF13),sdtasdt0(xa,xy))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f84801,f70178]) ).
fof(f84966,plain,
( sF14 = sdtasdt0(sdtpldt0(xy,sF13),xa)
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_9
| ~ spl15_10 ),
inference(forward_demodulation,[],[f84904,f33301]) ).
fof(f84986,plain,
( ! [X0] :
( aElementOf0(sF14,X0)
| ~ aElement0(sdtpldt0(xy,sF13))
| ~ aElementOf0(xa,X0)
| ~ aIdeal0(X0) )
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_9
| ~ spl15_10 ),
inference(superposition,[],[f143,f84966]) ).
fof(f84988,plain,
( ! [X0] :
( ~ aElementOf0(xa,X0)
| aElementOf0(sF14,X0)
| ~ aIdeal0(X0) )
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_5
| ~ spl15_9
| ~ spl15_10
| ~ spl15_11
| ~ spl15_62
| ~ spl15_63 ),
inference(forward_subsumption_resolution,[],[f84986,f21894]) ).
fof(f84989,plain,
( aElementOf0(sF14,xI)
| ~ aIdeal0(xI)
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_5
| ~ spl15_9
| ~ spl15_10
| ~ spl15_11
| ~ spl15_62
| ~ spl15_63 ),
inference(resolution,[],[f84988,f162]) ).
fof(f84992,plain,
( ~ aIdeal0(xI)
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_5
| ~ spl15_9
| ~ spl15_10
| ~ spl15_11
| ~ spl15_62
| ~ spl15_63 ),
inference(forward_subsumption_resolution,[],[f84989,f175]) ).
fof(f84993,plain,
( $false
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_5
| ~ spl15_9
| ~ spl15_10
| ~ spl15_11
| ~ spl15_62
| ~ spl15_63 ),
inference(forward_subsumption_resolution,[],[f84992,f156]) ).
fof(f84994,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_5
| ~ spl15_9
| ~ spl15_10
| ~ spl15_11
| ~ spl15_62
| ~ spl15_63 ),
inference(avatar_contradiction_clause,[],[f84993]) ).
cnf(s1,plain,
( ~ spl15_1
| ~ spl15_2
| spl15_3 ),
inference(sat_conversion,[],[f193]) ).
cnf(s4,plain,
spl15_1,
inference(sat_conversion,[],[f278]) ).
cnf(s5,plain,
( ~ spl15_8
| spl15_9 ),
inference(sat_conversion,[],[f287]) ).
cnf(s6,plain,
spl15_8,
inference(sat_conversion,[],[f288]) ).
cnf(s7,plain,
spl15_2,
inference(sat_conversion,[],[f292]) ).
cnf(s8,plain,
( ~ spl15_10
| spl15_11 ),
inference(sat_conversion,[],[f411]) ).
cnf(s9,plain,
spl15_10,
inference(sat_conversion,[],[f414]) ).
cnf(s49,plain,
( ~ spl15_62
| spl15_63 ),
inference(sat_conversion,[],[f6738]) ).
cnf(s54,plain,
spl15_5,
inference(sat_conversion,[],[f8562]) ).
cnf(s60,plain,
spl15_62,
inference(sat_conversion,[],[f9369]) ).
cnf(s295,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_5
| ~ spl15_9
| ~ spl15_10
| ~ spl15_11
| ~ spl15_62
| ~ spl15_63 ),
inference(sat_conversion,[],[f84994]) ).
cnf(s310,plain,
spl15_63,
inference(rat,[],[s49,s60]) ).
cnf(s337,plain,
spl15_11,
inference(rat,[],[s8,s9]) ).
cnf(s343,plain,
spl15_9,
inference(rat,[],[s5,s6]) ).
cnf(s368,plain,
~ spl15_3,
inference(rat,[],[s295,s310,s60,s337,s9,s343,s54,s7,s4]) ).
cnf(s373,plain,
$false,
inference(rat,[],[s1,s368,s7,s4]) ).
fof(f84995,plain,
$false,
inference(avatar_sat_refutation,[],[s373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG096+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 23:14:55 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.59/2.82 % (1717328)Detected formulas, will run a generic FOF schedule.
% 13.59/2.82 % (1717333)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1190366925:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 13.59/2.82 % (1717338)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=576055332:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 13.59/2.82 % (1717337)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=546020692:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 13.59/2.82 % (1717336)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=855055446:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 13.59/2.82 % (1717339)dis-21_1_sil=8000:lcm=predicate:random_seed=2651491014:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 13.59/2.82 % (1717335)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2327071009:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 13.59/2.82 % (1717334)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1723234581:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 13.59/2.82 % (1717336)Refutation not found, incomplete strategy
% 13.59/2.82 % (1717336)------------------------------
% 13.59/2.82 % (1717336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.59/2.82 % (1717336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.59/2.82 % (1717336)CaDiCaL version: 2.1.3
% 13.59/2.82 % (1717336)Termination reason: Refutation not found, incomplete strategy
% 13.59/2.82 % (1717336)Time elapsed: 0.009 s
% 13.59/2.82 % (1717336)Peak memory usage: 88 MB
% 13.59/2.82 % (1717336)Instructions burned: 13 (million)
% 13.59/2.82 % (1717337)Instruction limit reached!
% 13.59/2.82 % (1717337)------------------------------
% 13.59/2.82 % (1717337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.59/2.82 % (1717337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.59/2.82 % (1717337)CaDiCaL version: 2.1.3
% 13.59/2.82 % (1717337)Termination reason: Instruction limit
% 13.59/2.82 % (1717337)Termination phase: Saturation
% 13.59/2.82 % (1717337)Time elapsed: 0.071 s
% 13.59/2.82 % (1717337)Peak memory usage: 88 MB
% 13.59/2.82 % (1717337)Instructions burned: 120 (million)
% 13.59/2.82 % (1717339)Instruction limit reached!
% 13.59/2.82 % (1717339)------------------------------
% 13.59/2.82 % (1717339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.59/2.82 % (1717339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.59/2.82 % (1717339)CaDiCaL version: 2.1.3
% 13.59/2.82 % (1717339)Termination reason: Instruction limit
% 13.59/2.82 % (1717339)Termination phase: Saturation
% 13.59/2.82 % (1717339)Time elapsed: 0.076 s
% 13.59/2.82 % (1717339)Peak memory usage: 90 MB
% 13.59/2.82 % (1717339)Instructions burned: 131 (million)
% 13.59/2.82 % (1717338)Instruction limit reached!
% 13.59/2.82 % (1717338)------------------------------
% 13.59/2.82 % (1717338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.59/2.82 % (1717338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.59/2.82 % (1717338)CaDiCaL version: 2.1.3
% 13.59/2.82 % (1717338)Termination reason: Instruction limit
% 13.59/2.82 % (1717338)Termination phase: Saturation
% 13.59/2.82 % (1717338)Time elapsed: 0.097 s
% 13.59/2.82 % (1717338)Peak memory usage: 90 MB
% 13.59/2.82 % (1717338)Instructions burned: 139 (million)
% 13.59/2.82 % (1717347)lrs+10_1_sil=8000:sp=occurrence:random_seed=1092145820:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 13.59/2.82 % (1717348)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1969953964:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 13.59/2.82 % (1717349)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1462421670:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 13.59/2.82 % (1717336)------------------------------
% 13.59/2.82 % (1717336)------------------------------
% 13.59/2.82 % (1717348)Instruction limit reached!
% 13.59/2.82 % (1717348)------------------------------
% 13.59/2.82 % (1717348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.78/3.71 % (1717348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.78/3.71 % (1717348)CaDiCaL version: 2.1.3
% 19.78/3.71 % (1717348)Termination reason: Instruction limit
% 19.78/3.71 % (1717348)Termination phase: Saturation
% 19.78/3.71 % (1717348)Time elapsed: 0.073 s
% 19.78/3.71 % (1717348)Peak memory usage: 91 MB
% 19.78/3.71 % (1717348)Instructions burned: 157 (million)
% 19.78/3.71 % (1717347)Instruction limit reached!
% 19.78/3.71 % (1717347)------------------------------
% 19.78/3.71 % (1717347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.78/3.71 % (1717347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.78/3.71 % (1717347)CaDiCaL version: 2.1.3
% 19.78/3.71 % (1717347)Termination reason: Instruction limit
% 19.78/3.71 % (1717347)Termination phase: Saturation
% 19.78/3.71 % (1717347)Time elapsed: 0.174 s
% 19.78/3.71 % (1717347)Peak memory usage: 93 MB
% 19.78/3.71 % (1717347)Instructions burned: 302 (million)
% 19.78/3.71 % (1717353)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1862359706:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 19.78/3.71 % (1717354)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=672954793:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 19.78/3.71 % (1717349)Instruction limit reached!
% 19.78/3.71 % (1717349)------------------------------
% 19.78/3.71 % (1717349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.78/3.71 % (1717349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.78/3.71 % (1717349)CaDiCaL version: 2.1.3
% 19.78/3.71 % (1717349)Termination reason: Instruction limit
% 19.78/3.71 % (1717349)Termination phase: Saturation
% 19.78/3.71 % (1717349)Time elapsed: 0.197 s
% 19.78/3.71 % (1717349)Peak memory usage: 94 MB
% 19.78/3.71 % (1717349)Instructions burned: 325 (million)
% 19.78/3.71 % (1717355)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2749641253:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 19.78/3.71 % (1717353)Instruction limit reached!
% 19.78/3.71 % (1717353)------------------------------
% 19.78/3.71 % (1717353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.78/3.71 % (1717353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.78/3.71 % (1717353)CaDiCaL version: 2.1.3
% 19.78/3.71 % (1717353)Termination reason: Instruction limit
% 19.78/3.71 % (1717353)Termination phase: Saturation
% 19.78/3.71 % (1717353)Time elapsed: 0.118 s
% 19.78/3.71 % (1717353)Peak memory usage: 94 MB
% 19.78/3.71 % (1717353)Instructions burned: 249 (million)
% 19.78/3.71 % (1717358)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=373540243:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 19.78/3.71 % (1717354)Instruction limit reached!
% 19.78/3.71 % (1717354)------------------------------
% 19.78/3.71 % (1717354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.78/3.71 % (1717354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.78/3.71 % (1717354)CaDiCaL version: 2.1.3
% 19.78/3.71 % (1717354)Termination reason: Instruction limit
% 19.78/3.71 % (1717354)Termination phase: Saturation
% 19.78/3.71 % (1717354)Time elapsed: 0.176 s
% 19.78/3.71 % (1717354)Peak memory usage: 90 MB
% 19.78/3.71 % (1717354)Instructions burned: 294 (million)
% 19.78/3.71 % (1717358)Instruction limit reached!
% 19.78/3.71 % (1717358)------------------------------
% 19.78/3.71 % (1717358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.78/3.71 % (1717358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.78/3.71 % (1717358)CaDiCaL version: 2.1.3
% 19.78/3.71 % (1717358)Termination reason: Instruction limit
% 19.78/3.71 % (1717358)Termination phase: Saturation
% 19.78/3.71 % (1717358)Time elapsed: 0.078 s
% 19.78/3.71 % (1717358)Peak memory usage: 91 MB
% 19.78/3.71 % (1717358)Instructions burned: 114 (million)
% 19.78/3.71 % (1717360)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1091792492:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 19.78/3.71 % (1717362)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3453799978:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 19.78/3.71 % (1717362)Refutation not found, incomplete strategy
% 19.78/3.71 % (1717362)------------------------------
% 19.78/3.71 % (1717362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717362)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717362)Termination reason: Refutation not found, incomplete strategy
% 44.75/7.18 % (1717362)Time elapsed: 0.002 s
% 44.75/7.18 % (1717362)Peak memory usage: 88 MB
% 44.75/7.18 % (1717362)Instructions burned: 1 (million)
% 44.75/7.18 % (1717360)Instruction limit reached!
% 44.75/7.18 % (1717360)------------------------------
% 44.75/7.18 % (1717360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717360)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717360)Termination reason: Instruction limit
% 44.75/7.18 % (1717360)Termination phase: Saturation
% 44.75/7.18 % (1717360)Time elapsed: 0.062 s
% 44.75/7.18 % (1717360)Peak memory usage: 89 MB
% 44.75/7.18 % (1717360)Instructions burned: 128 (million)
% 44.75/7.18 % (1717363)lrs+10_1_sil=8000:sp=occurrence:random_seed=2043802187:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 44.75/7.18 % (1717386)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=42723445:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 44.75/7.18 % (1717362)------------------------------
% 44.75/7.18 % (1717362)------------------------------
% 44.75/7.18 % (1717473)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3327207640:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 44.75/7.18 % (1717386)Instruction limit reached!
% 44.75/7.18 % (1717386)------------------------------
% 44.75/7.18 % (1717386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717386)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717386)Termination reason: Instruction limit
% 44.75/7.18 % (1717386)Termination phase: Saturation
% 44.75/7.18 % (1717386)Time elapsed: 0.266 s
% 44.75/7.18 % (1717386)Peak memory usage: 94 MB
% 44.75/7.18 % (1717386)Instructions burned: 438 (million)
% 44.75/7.18 % (1717523)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1972839926:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 44.75/7.18 % (1717363)Instruction limit reached!
% 44.75/7.18 % (1717363)------------------------------
% 44.75/7.18 % (1717363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717363)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717363)Termination reason: Instruction limit
% 44.75/7.18 % (1717363)Termination phase: Saturation
% 44.75/7.18 % (1717363)Time elapsed: 0.508 s
% 44.75/7.18 % (1717363)Peak memory usage: 103 MB
% 44.75/7.18 % (1717363)Instructions burned: 908 (million)
% 44.75/7.18 % (1717523)Instruction limit reached!
% 44.75/7.18 % (1717523)------------------------------
% 44.75/7.18 % (1717523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717523)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717523)Termination reason: Instruction limit
% 44.75/7.18 % (1717523)Termination phase: Saturation
% 44.75/7.18 % (1717523)Time elapsed: 0.060 s
% 44.75/7.18 % (1717523)Peak memory usage: 91 MB
% 44.75/7.18 % (1717523)Instructions burned: 135 (million)
% 44.75/7.18 % (1717525)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=535936912:st=8:i=592:sd=3:ep=RST:ss=axioms_2985 on theBenchmark for (2985ds/592Mi)
% 44.75/7.18 % (1717526)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1108947431:st=3:i=13193:sd=3:ss=axioms_2985 on theBenchmark for (2985ds/13193Mi)
% 44.75/7.18 % (1717525)Instruction limit reached!
% 44.75/7.18 % (1717525)------------------------------
% 44.75/7.18 % (1717525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717525)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717525)Termination reason: Instruction limit
% 44.75/7.18 % (1717525)Termination phase: Saturation
% 44.75/7.18 % (1717525)Time elapsed: 0.313 s
% 44.75/7.18 % (1717525)Peak memory usage: 96 MB
% 44.75/7.18 % (1717525)Instructions burned: 593 (million)
% 44.75/7.18 % (1717529)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=908617682:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2981 on theBenchmark for (2981ds/125Mi)
% 44.75/7.18 % (1717529)Instruction limit reached!
% 44.75/7.18 % (1717529)------------------------------
% 44.75/7.18 % (1717529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717529)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717529)Termination reason: Instruction limit
% 44.75/7.18 % (1717529)Termination phase: Saturation
% 44.75/7.18 % (1717529)Time elapsed: 0.068 s
% 44.75/7.18 % (1717529)Peak memory usage: 91 MB
% 44.75/7.18 % (1717529)Instructions burned: 127 (million)
% 44.75/7.18 % (1717355)Instruction limit reached!
% 44.75/7.18 % (1717355)------------------------------
% 44.75/7.18 % (1717355)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717355)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717355)Termination reason: Instruction limit
% 44.75/7.18 % (1717355)Termination phase: Saturation
% 44.75/7.18 % (1717355)Time elapsed: 1.436 s
% 44.75/7.18 % (1717355)Peak memory usage: 144 MB
% 44.75/7.18 % (1717355)Instructions burned: 2351 (million)
% 44.75/7.18 % (1717531)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=1782411412:i=134:gtgl=5:slsql=off:gtg=exists_sym_2979 on theBenchmark for (2979ds/134Mi)
% 44.75/7.18 % (1717532)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=2363211212:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2979 on theBenchmark for (2979ds/141Mi)
% 44.75/7.18 % (1717531)Instruction limit reached!
% 44.75/7.18 % (1717531)------------------------------
% 44.75/7.18 % (1717531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717531)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717531)Termination reason: Instruction limit
% 44.75/7.18 % (1717531)Termination phase: Saturation
% 44.75/7.18 % (1717531)Time elapsed: 0.072 s
% 44.75/7.18 % (1717531)Peak memory usage: 90 MB
% 44.75/7.18 % (1717531)Instructions burned: 136 (million)
% 44.75/7.18 % (1717532)Instruction limit reached!
% 44.75/7.18 % (1717532)------------------------------
% 44.75/7.18 % (1717532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717532)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717532)Termination reason: Instruction limit
% 44.75/7.18 % (1717532)Termination phase: Saturation
% 44.75/7.18 % (1717532)Time elapsed: 0.082 s
% 44.75/7.18 % (1717532)Peak memory usage: 91 MB
% 44.75/7.18 % (1717532)Instructions burned: 141 (million)
% 44.75/7.18 % (1717535)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=894947769:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2977 on theBenchmark for (2977ds/431Mi)
% 44.75/7.18 % (1717536)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=108726867:i=6060:aac=none:ins=25_2977 on theBenchmark for (2977ds/6060Mi)
% 44.75/7.18 % (1717535)Instruction limit reached!
% 44.75/7.18 % (1717535)------------------------------
% 44.75/7.18 % (1717535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717535)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717535)Termination reason: Instruction limit
% 44.75/7.18 % (1717535)Termination phase: Saturation
% 44.75/7.18 % (1717535)Time elapsed: 0.251 s
% 44.75/7.18 % (1717535)Peak memory usage: 91 MB
% 44.75/7.18 % (1717535)Instructions burned: 431 (million)
% 44.75/7.18 % (1717539)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=4072480767:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2973 on theBenchmark for (2973ds/150Mi)
% 44.75/7.18 % (1717539)Instruction limit reached!
% 44.75/7.18 % (1717539)------------------------------
% 44.75/7.18 % (1717539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717539)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717539)Termination reason: Instruction limit
% 44.75/7.18 % (1717539)Termination phase: Saturation
% 44.75/7.18 % (1717539)Time elapsed: 0.081 s
% 44.75/7.18 % (1717539)Peak memory usage: 92 MB
% 44.75/7.18 % (1717539)Instructions burned: 152 (million)
% 44.75/7.18 % (1717541)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=21037291:i=14155:bd=all_2971 on theBenchmark for (2971ds/14155Mi)
% 44.75/7.18 % (1717473)Instruction limit reached!
% 44.75/7.18 % (1717473)------------------------------
% 44.75/7.18 % (1717473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717473)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717473)Termination reason: Instruction limit
% 44.75/7.18 % (1717473)Termination phase: Saturation
% 44.75/7.18 % (1717473)Time elapsed: 3.081 s
% 44.75/7.18 % (1717473)Peak memory usage: 167 MB
% 44.75/7.18 % (1717473)Instructions burned: 5203 (million)
% 44.75/7.18 % (1717543)lrs+10_1024_sil=16000:plsq=on:plsqr=32,1:sos=all:fs=off:gs=on:newcnf=on:random_seed=3386952557:i=667:av=off:fsr=off_2956 on theBenchmark for (2956ds/667Mi)
% 44.75/7.18 % (1717543)Instruction limit reached!
% 44.75/7.18 % (1717543)------------------------------
% 44.75/7.18 % (1717543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717543)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717543)Termination reason: Instruction limit
% 44.75/7.18 % (1717543)Termination phase: Saturation
% 44.75/7.18 % (1717543)Time elapsed: 0.271 s
% 44.75/7.18 % (1717543)Peak memory usage: 93 MB
% 44.75/7.18 % (1717543)Instructions burned: 670 (million)
% 44.75/7.18 % (1717545)ott-1011_3:1_anc=all_dependent:to=lpo:sil=8000:drc=ordering:sas=cadical:fdtod=off:sp=reverse_frequency:spb=goal_then_units:urr=full:lftc=20:newcnf=on:random_seed=2808907459:s2a=on:i=185:s2at=1.8:fdi=4_2952 on theBenchmark for (2952ds/185Mi)
% 44.75/7.18 % (1717545)Instruction limit reached!
% 44.75/7.18 % (1717545)------------------------------
% 44.75/7.18 % (1717545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717545)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717545)Termination reason: Instruction limit
% 44.75/7.18 % (1717545)Termination phase: Saturation
% 44.75/7.18 % (1717545)Time elapsed: 0.099 s
% 44.75/7.18 % (1717545)Peak memory usage: 94 MB
% 44.75/7.18 % (1717545)Instructions burned: 187 (million)
% 44.75/7.18 % (1717547)dis+1010_14_anc=all:to=lpo:sil=8000:sp=arity:slsq=on:random_seed=3261427558:i=193:ins=10:fsr=off:ss=axioms:fsd=on_2950 on theBenchmark for (2950ds/193Mi)
% 44.75/7.18 % (1717547)Instruction limit reached!
% 44.75/7.18 % (1717547)------------------------------
% 44.75/7.18 % (1717547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717547)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717547)Termination reason: Instruction limit
% 44.75/7.18 % (1717547)Termination phase: Saturation
% 44.75/7.18 % (1717547)Time elapsed: 0.105 s
% 44.75/7.18 % (1717547)Peak memory usage: 90 MB
% 44.75/7.18 % (1717547)Instructions burned: 194 (million)
% 44.75/7.18 % (1717549)dis+1011_7_sil=8000:sp=occurrence:sos=all:fd=off:random_seed=2222599177:st=5.3:i=4850:sd=4:av=off:sup=off:ss=included:sgt=16_2948 on theBenchmark for (2948ds/4850Mi)
% 44.75/7.18 % (1717333)First to succeed.
% 44.75/7.18 % (1717333)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1717328"
% 44.75/7.18 % (1717536)Instruction limit reached!
% 44.75/7.18 % (1717536)------------------------------
% 44.75/7.18 % (1717536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 44.75/7.18 % (1717536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.75/7.18 % (1717536)CaDiCaL version: 2.1.3
% 44.75/7.18 % (1717536)Termination reason: Instruction limit
% 44.75/7.18 % (1717536)Termination phase: Saturation
% 44.75/7.18 % (1717536)Time elapsed: 3.737 s
% 44.75/7.18 % (1717536)Peak memory usage: 169 MB
% 44.75/7.18 % (1717536)Instructions burned: 6061 (million)
% 44.75/7.18 % (1717551)lrs+1011_1_ncem=casc2026/models/loop8.pt:sil=32000:tgt=ground:npcc=on:sp=const_frequency:acc=on:urr=on:random_seed=1770058869:i=12111:sd=1:ss=included_2938 on theBenchmark for (2938ds/12111Mi)
% 44.75/7.18 % (1717333)Refutation found. Thanks to Tanya!
% 44.75/7.18 % SZS status Theorem for theBenchmark
% 44.75/7.18 % SZS output start Proof for theBenchmark
% See solution above
% 45.29/7.38 % (1717333)------------------------------
% 45.29/7.38 % (1717333)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 45.29/7.38 % (1717333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 45.29/7.38 % (1717333)CaDiCaL version: 2.1.3
% 45.29/7.38 % (1717333)Termination reason: Refutation
% 45.29/7.38 % (1717333)Time elapsed: 5.998 s
% 45.29/7.38 % (1717333)Peak memory usage: 328 MB
% 45.29/7.38 % (1717333)Instructions burned: 19366 (million)
% 45.29/7.38 % (1717333)------------------------------
% 45.29/7.38 % (1717333)------------------------------
% 45.29/7.38 % (1717328)Success in time 6.328 s
% 45.29/7.38 % Vampire exiting
%------------------------------------------------------------------------------