%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG092+2 : 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 : n010.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 1.88s 1.73s
% Output : Refutation 6.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 115 ( 19 unt; 10 def)
% Number of atoms : 683 ( 74 equ)
% Maximal formula atoms : 39 ( 5 avg)
% Number of connectives : 800 ( 232 ~; 213 |; 301 &)
% ( 15 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 7 prp; 0-5 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-5 aty)
% Number of variables : 329 ( 0 sgn 221 !; 108 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
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,
( aSet0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElementOf0(X1,xJ)
=> aElementOf0(sdtpldt0(X0,X1),xJ) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) ) ) )
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
fof(f26,conjecture,
( ! [X0,X1,X2] :
( ( ( ? [X3,X4] :
( aElementOf0(X3,xI)
& aElementOf0(X4,xJ)
& sdtpldt0(X3,X4) = X0 )
| aElementOf0(X0,sdtpldt1(xI,xJ)) )
& ( ? [X3,X4] :
( aElementOf0(X3,xI)
& aElementOf0(X4,xJ)
& sdtpldt0(X3,X4) = X1 )
| aElementOf0(X1,sdtpldt1(xI,xJ)) )
& aElement0(X2) )
=> ? [X3,X4] :
( aElementOf0(X3,xI)
& aElementOf0(X4,xJ)
& X0 = sdtpldt0(X3,X4)
& ? [X5,X6] :
( aElementOf0(X5,xI)
& aElementOf0(X6,xJ)
& X1 = sdtpldt0(X5,X6)
& aElementOf0(sdtpldt0(X3,X5),xI)
& aElementOf0(sdtpldt0(X4,X6),xJ)
& aElementOf0(sdtasdt0(X2,X3),xI)
& aElementOf0(sdtasdt0(X2,X4),xJ)
& sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(X3,X5),sdtpldt0(X4,X6))
& ? [X7,X8] :
( aElementOf0(X7,xI)
& aElementOf0(X8,xJ)
& sdtpldt0(X7,X8) = sdtpldt0(X0,X1) )
& aElementOf0(sdtpldt0(X0,X1),sdtpldt1(xI,xJ))
& ? [X7,X8] :
( aElementOf0(X7,xI)
& aElementOf0(X8,xJ)
& sdtpldt0(X7,X8) = sdtasdt0(X2,X0) )
& aElementOf0(sdtasdt0(X2,X0),sdtpldt1(xI,xJ)) ) ) )
=> ( ( aSet0(sdtpldt1(xI,xJ))
& ! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
<=> ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& sdtpldt0(X1,X2) = X0 ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
=> ( ! [X1] :
( aElementOf0(X1,sdtpldt1(xI,xJ))
=> aElementOf0(sdtpldt0(X0,X1),sdtpldt1(xI,xJ)) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),sdtpldt1(xI,xJ)) ) ) )
| aIdeal0(sdtpldt1(xI,xJ)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f27,negated_conjecture,
~ ( ! [X0,X1,X2] :
( ( ( ? [X3,X4] :
( aElementOf0(X3,xI)
& aElementOf0(X4,xJ)
& sdtpldt0(X3,X4) = X0 )
| aElementOf0(X0,sdtpldt1(xI,xJ)) )
& ( ? [X3,X4] :
( aElementOf0(X3,xI)
& aElementOf0(X4,xJ)
& sdtpldt0(X3,X4) = X1 )
| aElementOf0(X1,sdtpldt1(xI,xJ)) )
& aElement0(X2) )
=> ? [X3,X4] :
( aElementOf0(X3,xI)
& aElementOf0(X4,xJ)
& X0 = sdtpldt0(X3,X4)
& ? [X5,X6] :
( aElementOf0(X5,xI)
& aElementOf0(X6,xJ)
& X1 = sdtpldt0(X5,X6)
& aElementOf0(sdtpldt0(X3,X5),xI)
& aElementOf0(sdtpldt0(X4,X6),xJ)
& aElementOf0(sdtasdt0(X2,X3),xI)
& aElementOf0(sdtasdt0(X2,X4),xJ)
& sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(X3,X5),sdtpldt0(X4,X6))
& ? [X7,X8] :
( aElementOf0(X7,xI)
& aElementOf0(X8,xJ)
& sdtpldt0(X7,X8) = sdtpldt0(X0,X1) )
& aElementOf0(sdtpldt0(X0,X1),sdtpldt1(xI,xJ))
& ? [X7,X8] :
( aElementOf0(X7,xI)
& aElementOf0(X8,xJ)
& sdtpldt0(X7,X8) = sdtasdt0(X2,X0) )
& aElementOf0(sdtasdt0(X2,X0),sdtpldt1(xI,xJ)) ) ) )
=> ( ( aSet0(sdtpldt1(xI,xJ))
& ! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
<=> ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& sdtpldt0(X1,X2) = X0 ) ) )
=> ( ! [X0] :
( aElementOf0(X0,sdtpldt1(xI,xJ))
=> ( ! [X1] :
( aElementOf0(X1,sdtpldt1(xI,xJ))
=> aElementOf0(sdtpldt0(X0,X1),sdtpldt1(xI,xJ)) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),sdtpldt1(xI,xJ)) ) ) )
| aIdeal0(sdtpldt1(xI,xJ)) ) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
( aSet0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X3] :
( aElementOf0(X3,xJ)
=> ( ! [X4] :
( aElementOf0(X4,xJ)
=> aElementOf0(sdtpldt0(X3,X4),xJ) )
& ! [X5] :
( aElement0(X5)
=> aElementOf0(sdtasdt0(X5,X3),xJ) ) ) )
& aIdeal0(xJ) ),
inference(rectify,[],[f25]) ).
fof(f29,plain,
~ ( ! [X0,X1,X2] :
( ( ( ? [X3,X4] :
( aElementOf0(X3,xI)
& aElementOf0(X4,xJ)
& sdtpldt0(X3,X4) = X0 )
| aElementOf0(X0,sdtpldt1(xI,xJ)) )
& ( ? [X5,X6] :
( aElementOf0(X5,xI)
& aElementOf0(X6,xJ)
& sdtpldt0(X5,X6) = X1 )
| aElementOf0(X1,sdtpldt1(xI,xJ)) )
& aElement0(X2) )
=> ? [X7,X8] :
( aElementOf0(X7,xI)
& aElementOf0(X8,xJ)
& sdtpldt0(X7,X8) = X0
& ? [X9,X10] :
( aElementOf0(X9,xI)
& aElementOf0(X10,xJ)
& sdtpldt0(X9,X10) = X1
& aElementOf0(sdtpldt0(X7,X9),xI)
& aElementOf0(sdtpldt0(X8,X10),xJ)
& aElementOf0(sdtasdt0(X2,X7),xI)
& aElementOf0(sdtasdt0(X2,X8),xJ)
& sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(X7,X9),sdtpldt0(X8,X10))
& ? [X11,X12] :
( aElementOf0(X11,xI)
& aElementOf0(X12,xJ)
& sdtpldt0(X0,X1) = sdtpldt0(X11,X12) )
& aElementOf0(sdtpldt0(X0,X1),sdtpldt1(xI,xJ))
& ? [X13,X14] :
( aElementOf0(X13,xI)
& aElementOf0(X14,xJ)
& sdtasdt0(X2,X0) = sdtpldt0(X13,X14) )
& aElementOf0(sdtasdt0(X2,X0),sdtpldt1(xI,xJ)) ) ) )
=> ( ( aSet0(sdtpldt1(xI,xJ))
& ! [X15] :
( aElementOf0(X15,sdtpldt1(xI,xJ))
<=> ? [X16,X17] :
( aElementOf0(X16,xI)
& aElementOf0(X17,xJ)
& sdtpldt0(X16,X17) = X15 ) ) )
=> ( ! [X18] :
( aElementOf0(X18,sdtpldt1(xI,xJ))
=> ( ! [X19] :
( aElementOf0(X19,sdtpldt1(xI,xJ))
=> aElementOf0(sdtpldt0(X18,X19),sdtpldt1(xI,xJ)) )
& ! [X20] :
( aElement0(X20)
=> aElementOf0(sdtasdt0(X20,X18),sdtpldt1(xI,xJ)) ) ) )
| aIdeal0(sdtpldt1(xI,xJ)) ) ) ),
inference(rectify,[],[f27]) ).
fof(f33,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(f34,plain,
( aSet0(xI)
& ! [X0] :
( ( ! [X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI) )
& ! [X2] :
( aElementOf0(sdtasdt0(X2,X0),xI)
| ~ aElement0(X2) ) )
| ~ aElementOf0(X0,xI) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X3] :
( ( ! [X4] :
( aElementOf0(sdtpldt0(X3,X4),xJ)
| ~ aElementOf0(X4,xJ) )
& ! [X5] :
( aElementOf0(sdtasdt0(X5,X3),xJ)
| ~ aElement0(X5) ) )
| ~ aElementOf0(X3,xJ) )
& aIdeal0(xJ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f35,plain,
( ? [X18] :
( ( ? [X19] :
( ~ aElementOf0(sdtpldt0(X18,X19),sdtpldt1(xI,xJ))
& aElementOf0(X19,sdtpldt1(xI,xJ)) )
| ? [X20] :
( ~ aElementOf0(sdtasdt0(X20,X18),sdtpldt1(xI,xJ))
& aElement0(X20) ) )
& aElementOf0(X18,sdtpldt1(xI,xJ)) )
& ~ aIdeal0(sdtpldt1(xI,xJ))
& aSet0(sdtpldt1(xI,xJ))
& ! [X15] :
( aElementOf0(X15,sdtpldt1(xI,xJ))
<=> ? [X16,X17] :
( aElementOf0(X16,xI)
& aElementOf0(X17,xJ)
& sdtpldt0(X16,X17) = X15 ) )
& ! [X0,X1,X2] :
( ? [X7,X8] :
( aElementOf0(X7,xI)
& aElementOf0(X8,xJ)
& sdtpldt0(X7,X8) = X0
& ? [X9,X10] :
( aElementOf0(X9,xI)
& aElementOf0(X10,xJ)
& sdtpldt0(X9,X10) = X1
& aElementOf0(sdtpldt0(X7,X9),xI)
& aElementOf0(sdtpldt0(X8,X10),xJ)
& aElementOf0(sdtasdt0(X2,X7),xI)
& aElementOf0(sdtasdt0(X2,X8),xJ)
& sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(X7,X9),sdtpldt0(X8,X10))
& ? [X11,X12] :
( aElementOf0(X11,xI)
& aElementOf0(X12,xJ)
& sdtpldt0(X0,X1) = sdtpldt0(X11,X12) )
& aElementOf0(sdtpldt0(X0,X1),sdtpldt1(xI,xJ))
& ? [X13,X14] :
( aElementOf0(X13,xI)
& aElementOf0(X14,xJ)
& sdtasdt0(X2,X0) = sdtpldt0(X13,X14) )
& aElementOf0(sdtasdt0(X2,X0),sdtpldt1(xI,xJ)) ) )
| ( ! [X3,X4] :
( ~ aElementOf0(X3,xI)
| ~ aElementOf0(X4,xJ)
| sdtpldt0(X3,X4) != X0 )
& ~ aElementOf0(X0,sdtpldt1(xI,xJ)) )
| ( ! [X5,X6] :
( ~ aElementOf0(X5,xI)
| ~ aElementOf0(X6,xJ)
| sdtpldt0(X5,X6) != X1 )
& ~ aElementOf0(X1,sdtpldt1(xI,xJ)) )
| ~ aElement0(X2) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f36,plain,
( ? [X18] :
( ( ? [X19] :
( ~ aElementOf0(sdtpldt0(X18,X19),sdtpldt1(xI,xJ))
& aElementOf0(X19,sdtpldt1(xI,xJ)) )
| ? [X20] :
( ~ aElementOf0(sdtasdt0(X20,X18),sdtpldt1(xI,xJ))
& aElement0(X20) ) )
& aElementOf0(X18,sdtpldt1(xI,xJ)) )
& ~ aIdeal0(sdtpldt1(xI,xJ))
& aSet0(sdtpldt1(xI,xJ))
& ! [X15] :
( aElementOf0(X15,sdtpldt1(xI,xJ))
<=> ? [X16,X17] :
( aElementOf0(X16,xI)
& aElementOf0(X17,xJ)
& sdtpldt0(X16,X17) = X15 ) )
& ! [X0,X1,X2] :
( ? [X7,X8] :
( aElementOf0(X7,xI)
& aElementOf0(X8,xJ)
& sdtpldt0(X7,X8) = X0
& ? [X9,X10] :
( aElementOf0(X9,xI)
& aElementOf0(X10,xJ)
& sdtpldt0(X9,X10) = X1
& aElementOf0(sdtpldt0(X7,X9),xI)
& aElementOf0(sdtpldt0(X8,X10),xJ)
& aElementOf0(sdtasdt0(X2,X7),xI)
& aElementOf0(sdtasdt0(X2,X8),xJ)
& sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(X7,X9),sdtpldt0(X8,X10))
& ? [X11,X12] :
( aElementOf0(X11,xI)
& aElementOf0(X12,xJ)
& sdtpldt0(X0,X1) = sdtpldt0(X11,X12) )
& aElementOf0(sdtpldt0(X0,X1),sdtpldt1(xI,xJ))
& ? [X13,X14] :
( aElementOf0(X13,xI)
& aElementOf0(X14,xJ)
& sdtasdt0(X2,X0) = sdtpldt0(X13,X14) )
& aElementOf0(sdtasdt0(X2,X0),sdtpldt1(xI,xJ)) ) )
| ( ! [X3,X4] :
( ~ aElementOf0(X3,xI)
| ~ aElementOf0(X4,xJ)
| sdtpldt0(X3,X4) != X0 )
& ~ aElementOf0(X0,sdtpldt1(xI,xJ)) )
| ( ! [X5,X6] :
( ~ aElementOf0(X5,xI)
| ~ aElementOf0(X6,xJ)
| sdtpldt0(X5,X6) != X1 )
& ~ aElementOf0(X1,sdtpldt1(xI,xJ)) )
| ~ aElement0(X2) ) ),
inference(flattening,[],[f35]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f44,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f45,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f44]) ).
fof(f48,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,[],[f33]) ).
fof(f57,definition,
! [X0,X2] :
( ? [X13,X14] :
( aElementOf0(X13,xI)
& aElementOf0(X14,xJ)
& sdtasdt0(X2,X0) = sdtpldt0(X13,X14) )
| ~ sP0(X0,X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f58,definition,
! [X1,X0] :
( ? [X11,X12] :
( aElementOf0(X11,xI)
& aElementOf0(X12,xJ)
& sdtpldt0(X0,X1) = sdtpldt0(X11,X12) )
| ~ sP1(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f59,definition,
! [X1,X7,X8,X2,X0] :
( ? [X9,X10] :
( aElementOf0(X9,xI)
& aElementOf0(X10,xJ)
& sdtpldt0(X9,X10) = X1
& aElementOf0(sdtpldt0(X7,X9),xI)
& aElementOf0(sdtpldt0(X8,X10),xJ)
& aElementOf0(sdtasdt0(X2,X7),xI)
& aElementOf0(sdtasdt0(X2,X8),xJ)
& sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(X7,X9),sdtpldt0(X8,X10))
& sP1(X1,X0)
& aElementOf0(sdtpldt0(X0,X1),sdtpldt1(xI,xJ))
& sP0(X0,X2)
& aElementOf0(sdtasdt0(X2,X0),sdtpldt1(xI,xJ)) )
| ~ sP2(X1,X7,X8,X2,X0) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f60,definition,
! [X0,X2,X1] :
( ? [X7,X8] :
( aElementOf0(X7,xI)
& aElementOf0(X8,xJ)
& sdtpldt0(X7,X8) = X0
& sP2(X1,X7,X8,X2,X0) )
| ~ sP3(X0,X2,X1) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f61,plain,
( ? [X18] :
( ( ? [X19] :
( ~ aElementOf0(sdtpldt0(X18,X19),sdtpldt1(xI,xJ))
& aElementOf0(X19,sdtpldt1(xI,xJ)) )
| ? [X20] :
( ~ aElementOf0(sdtasdt0(X20,X18),sdtpldt1(xI,xJ))
& aElement0(X20) ) )
& aElementOf0(X18,sdtpldt1(xI,xJ)) )
& ~ aIdeal0(sdtpldt1(xI,xJ))
& aSet0(sdtpldt1(xI,xJ))
& ! [X15] :
( aElementOf0(X15,sdtpldt1(xI,xJ))
<=> ? [X16,X17] :
( aElementOf0(X16,xI)
& aElementOf0(X17,xJ)
& sdtpldt0(X16,X17) = X15 ) )
& ! [X0,X1,X2] :
( sP3(X0,X2,X1)
| ( ! [X3,X4] :
( ~ aElementOf0(X3,xI)
| ~ aElementOf0(X4,xJ)
| sdtpldt0(X3,X4) != X0 )
& ~ aElementOf0(X0,sdtpldt1(xI,xJ)) )
| ( ! [X5,X6] :
( ~ aElementOf0(X5,xI)
| ~ aElementOf0(X6,xJ)
| sdtpldt0(X5,X6) != X1 )
& ~ aElementOf0(X1,sdtpldt1(xI,xJ)) )
| ~ aElement0(X2) ) ),
inference(definition_folding,[],[f36,f60,f59,f58,f57]) ).
fof(f65,plain,
! [X0,X2,X1] :
( ? [X7,X8] :
( aElementOf0(X7,xI)
& aElementOf0(X8,xJ)
& sdtpldt0(X7,X8) = X0
& sP2(X1,X7,X8,X2,X0) )
| ~ sP3(X0,X2,X1) ),
inference(nnf_transformation,[],[f60]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( aElementOf0(X3,xI)
& aElementOf0(X4,xJ)
& sdtpldt0(X3,X4) = X0
& sP2(X2,X3,X4,X1,X0) )
| ~ sP3(X0,X1,X2) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( aElementOf0(sK6(X0,X1,X2),xI)
& aElementOf0(sK7(X0,X1,X2),xJ)
& sdtpldt0(sK6(X0,X1,X2),sK7(X0,X1,X2)) = X0
& sP2(X2,sK6(X0,X1,X2),sK7(X0,X1,X2),X1,X0) )
| ~ sP3(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X4,sK7(X0,X1,X2))],[f66]) ).
fof(f68,plain,
! [X1,X7,X8,X2,X0] :
( ? [X9,X10] :
( aElementOf0(X9,xI)
& aElementOf0(X10,xJ)
& sdtpldt0(X9,X10) = X1
& aElementOf0(sdtpldt0(X7,X9),xI)
& aElementOf0(sdtpldt0(X8,X10),xJ)
& aElementOf0(sdtasdt0(X2,X7),xI)
& aElementOf0(sdtasdt0(X2,X8),xJ)
& sdtpldt0(X0,X1) = sdtpldt0(sdtpldt0(X7,X9),sdtpldt0(X8,X10))
& sP1(X1,X0)
& aElementOf0(sdtpldt0(X0,X1),sdtpldt1(xI,xJ))
& sP0(X0,X2)
& aElementOf0(sdtasdt0(X2,X0),sdtpldt1(xI,xJ)) )
| ~ sP2(X1,X7,X8,X2,X0) ),
inference(nnf_transformation,[],[f59]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5,X6] :
( aElementOf0(X5,xI)
& aElementOf0(X6,xJ)
& sdtpldt0(X5,X6) = X0
& aElementOf0(sdtpldt0(X1,X5),xI)
& aElementOf0(sdtpldt0(X2,X6),xJ)
& aElementOf0(sdtasdt0(X3,X1),xI)
& aElementOf0(sdtasdt0(X3,X2),xJ)
& sdtpldt0(X4,X0) = sdtpldt0(sdtpldt0(X1,X5),sdtpldt0(X2,X6))
& sP1(X0,X4)
& aElementOf0(sdtpldt0(X4,X0),sdtpldt1(xI,xJ))
& sP0(X4,X3)
& aElementOf0(sdtasdt0(X3,X4),sdtpldt1(xI,xJ)) )
| ~ sP2(X0,X1,X2,X3,X4) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
! [X0,X1,X2,X3,X4] :
( ( aElementOf0(sK8(X0,X1,X2,X3,X4),xI)
& aElementOf0(sK9(X0,X1,X2,X3,X4),xJ)
& sdtpldt0(sK8(X0,X1,X2,X3,X4),sK9(X0,X1,X2,X3,X4)) = X0
& aElementOf0(sdtpldt0(X1,sK8(X0,X1,X2,X3,X4)),xI)
& aElementOf0(sdtpldt0(X2,sK9(X0,X1,X2,X3,X4)),xJ)
& aElementOf0(sdtasdt0(X3,X1),xI)
& aElementOf0(sdtasdt0(X3,X2),xJ)
& sdtpldt0(X4,X0) = sdtpldt0(sdtpldt0(X1,sK8(X0,X1,X2,X3,X4)),sdtpldt0(X2,sK9(X0,X1,X2,X3,X4)))
& sP1(X0,X4)
& aElementOf0(sdtpldt0(X4,X0),sdtpldt1(xI,xJ))
& sP0(X4,X3)
& aElementOf0(sdtasdt0(X3,X4),sdtpldt1(xI,xJ)) )
| ~ sP2(X0,X1,X2,X3,X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X5,sK8(X0,X1,X2,X3,X4)),skolemize(X6,sK9(X0,X1,X2,X3,X4))],[f69]) ).
fof(f77,plain,
( ? [X18] :
( ( ? [X19] :
( ~ aElementOf0(sdtpldt0(X18,X19),sdtpldt1(xI,xJ))
& aElementOf0(X19,sdtpldt1(xI,xJ)) )
| ? [X20] :
( ~ aElementOf0(sdtasdt0(X20,X18),sdtpldt1(xI,xJ))
& aElement0(X20) ) )
& aElementOf0(X18,sdtpldt1(xI,xJ)) )
& ~ aIdeal0(sdtpldt1(xI,xJ))
& aSet0(sdtpldt1(xI,xJ))
& ! [X15] :
( ( aElementOf0(X15,sdtpldt1(xI,xJ))
| ! [X16,X17] :
( ~ aElementOf0(X16,xI)
| ~ aElementOf0(X17,xJ)
| sdtpldt0(X16,X17) != X15 ) )
& ( ? [X16,X17] :
( aElementOf0(X16,xI)
& aElementOf0(X17,xJ)
& sdtpldt0(X16,X17) = X15 )
| ~ aElementOf0(X15,sdtpldt1(xI,xJ)) ) )
& ! [X0,X1,X2] :
( sP3(X0,X2,X1)
| ( ! [X3,X4] :
( ~ aElementOf0(X3,xI)
| ~ aElementOf0(X4,xJ)
| sdtpldt0(X3,X4) != X0 )
& ~ aElementOf0(X0,sdtpldt1(xI,xJ)) )
| ( ! [X5,X6] :
( ~ aElementOf0(X5,xI)
| ~ aElementOf0(X6,xJ)
| sdtpldt0(X5,X6) != X1 )
& ~ aElementOf0(X1,sdtpldt1(xI,xJ)) )
| ~ aElement0(X2) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f78,plain,
( ? [X0] :
( ( ? [X1] :
( ~ aElementOf0(sdtpldt0(X0,X1),sdtpldt1(xI,xJ))
& aElementOf0(X1,sdtpldt1(xI,xJ)) )
| ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X0),sdtpldt1(xI,xJ))
& aElement0(X2) ) )
& aElementOf0(X0,sdtpldt1(xI,xJ)) )
& ~ aIdeal0(sdtpldt1(xI,xJ))
& aSet0(sdtpldt1(xI,xJ))
& ! [X3] :
( ( aElementOf0(X3,sdtpldt1(xI,xJ))
| ! [X4,X5] :
( ~ aElementOf0(X4,xI)
| ~ aElementOf0(X5,xJ)
| sdtpldt0(X4,X5) != X3 ) )
& ( ? [X6,X7] :
( aElementOf0(X6,xI)
& aElementOf0(X7,xJ)
& sdtpldt0(X6,X7) = X3 )
| ~ aElementOf0(X3,sdtpldt1(xI,xJ)) ) )
& ! [X8,X9,X10] :
( sP3(X8,X10,X9)
| ( ! [X11,X12] :
( ~ aElementOf0(X11,xI)
| ~ aElementOf0(X12,xJ)
| sdtpldt0(X11,X12) != X8 )
& ~ aElementOf0(X8,sdtpldt1(xI,xJ)) )
| ( ! [X13,X14] :
( ~ aElementOf0(X13,xI)
| ~ aElementOf0(X14,xJ)
| sdtpldt0(X13,X14) != X9 )
& ~ aElementOf0(X9,sdtpldt1(xI,xJ)) )
| ~ aElement0(X10) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
( ( ( ~ aElementOf0(sdtpldt0(sK14,sK15),sdtpldt1(xI,xJ))
& aElementOf0(sK15,sdtpldt1(xI,xJ)) )
| ( ~ aElementOf0(sdtasdt0(sK16,sK14),sdtpldt1(xI,xJ))
& aElement0(sK16) ) )
& aElementOf0(sK14,sdtpldt1(xI,xJ))
& ~ aIdeal0(sdtpldt1(xI,xJ))
& aSet0(sdtpldt1(xI,xJ))
& ! [X3] :
( ( aElementOf0(X3,sdtpldt1(xI,xJ))
| ! [X4,X5] :
( ~ aElementOf0(X4,xI)
| ~ aElementOf0(X5,xJ)
| sdtpldt0(X4,X5) != X3 ) )
& ( ( aElementOf0(sK17(X3),xI)
& aElementOf0(sK18(X3),xJ)
& sdtpldt0(sK17(X3),sK18(X3)) = X3 )
| ~ aElementOf0(X3,sdtpldt1(xI,xJ)) ) )
& ! [X8,X9,X10] :
( sP3(X8,X10,X9)
| ( ! [X11,X12] :
( ~ aElementOf0(X11,xI)
| ~ aElementOf0(X12,xJ)
| sdtpldt0(X11,X12) != X8 )
& ~ aElementOf0(X8,sdtpldt1(xI,xJ)) )
| ( ! [X13,X14] :
( ~ aElementOf0(X13,xI)
| ~ aElementOf0(X14,xJ)
| sdtpldt0(X13,X14) != X9 )
& ~ aElementOf0(X9,sdtpldt1(xI,xJ)) )
| ~ aElement0(X10) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18]),skolemize(X0,sK14),skolemize(X1,sK15),skolemize(X2,sK16),skolemize(X6,sK17(X3)),skolemize(X7,sK18(X3))],[f78]) ).
fof(f81,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,[],[f48]) ).
fof(f82,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,[],[f81]) ).
fof(f83,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,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ( aIdeal0(X0)
| ~ aSet0(X0)
| ( ( ( ~ aElementOf0(sdtpldt0(sK21(X0),sK22(X0)),X0)
& aElementOf0(sK22(X0),X0) )
| ( ~ aElementOf0(sdtasdt0(sK23(X0),sK21(X0)),X0)
& aElement0(sK23(X0)) ) )
& aElementOf0(sK21(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,[sK21,sK22,sK23]),skolemize(X1,sK21(X0)),skolemize(X2,sK22(X0)),skolemize(X3,sK23(X0))],[f83]) ).
fof(f94,plain,
aSet0(xJ),
inference(cnf_transformation,[],[f34]) ).
fof(f99,plain,
! [X2,X0,X1] :
( sP2(X2,sK6(X0,X1,X2),sK7(X0,X1,X2),X1,X0)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f103,plain,
! [X2,X3,X0,X1,X4] :
( aElementOf0(sdtasdt0(X3,X4),sdtpldt1(xI,xJ))
| ~ sP2(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X4] :
( aElementOf0(sdtpldt0(X4,X0),sdtpldt1(xI,xJ))
| ~ sP2(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f121,plain,
! [X10,X8,X9] :
( ~ aElementOf0(X9,sdtpldt1(xI,xJ))
| ~ aElementOf0(X8,sdtpldt1(xI,xJ))
| sP3(X8,X10,X9)
| ~ aElement0(X10) ),
inference(cnf_transformation,[],[f79]) ).
fof(f122,plain,
! [X10,X8,X9,X14,X13] :
( sP3(X8,X10,X9)
| ~ aElementOf0(X8,sdtpldt1(xI,xJ))
| ~ aElementOf0(X13,xI)
| ~ aElementOf0(X14,xJ)
| sdtpldt0(X13,X14) != X9
| ~ aElement0(X10) ),
inference(cnf_transformation,[],[f79]) ).
fof(f126,plain,
! [X3] :
( ~ aElementOf0(X3,sdtpldt1(xI,xJ))
| aElementOf0(sK18(X3),xJ) ),
inference(cnf_transformation,[],[f79]) ).
fof(f127,plain,
! [X3] :
( ~ aElementOf0(X3,sdtpldt1(xI,xJ))
| aElementOf0(sK17(X3),xI) ),
inference(cnf_transformation,[],[f79]) ).
fof(f129,plain,
aSet0(sdtpldt1(xI,xJ)),
inference(cnf_transformation,[],[f79]) ).
fof(f130,plain,
~ aIdeal0(sdtpldt1(xI,xJ)),
inference(cnf_transformation,[],[f79]) ).
fof(f131,plain,
aElementOf0(sK14,sdtpldt1(xI,xJ)),
inference(cnf_transformation,[],[f79]) ).
fof(f132,plain,
( aElementOf0(sK15,sdtpldt1(xI,xJ))
| aElement0(sK16) ),
inference(cnf_transformation,[],[f79]) ).
fof(f133,plain,
( aElementOf0(sK15,sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtasdt0(sK16,sK14),sdtpldt1(xI,xJ)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f134,plain,
( ~ aElementOf0(sdtpldt0(sK14,sK15),sdtpldt1(xI,xJ))
| aElement0(sK16) ),
inference(cnf_transformation,[],[f79]) ).
fof(f135,plain,
( ~ aElementOf0(sdtpldt0(sK14,sK15),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtasdt0(sK16,sK14),sdtpldt1(xI,xJ)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f140,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f144,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f149,plain,
! [X0] :
( aElementOf0(sK21(X0),X0)
| ~ aSet0(X0)
| aIdeal0(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f173,plain,
! [X10,X8,X14,X13] :
( sP3(X8,X10,sdtpldt0(X13,X14))
| ~ aElementOf0(X8,sdtpldt1(xI,xJ))
| ~ aElementOf0(X13,xI)
| ~ aElementOf0(X14,xJ)
| ~ aElement0(X10) ),
inference(equality_resolution,[],[f122]) ).
fof(f179,definition,
( spl30_1
<=> aElement0(sK16) ),
introduced(definition,[new_symbols(definition,[spl30_1])],[avatar_definition]) ).
fof(f181,plain,
( aElement0(sK16)
| ~ spl30_1 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f183,definition,
( spl30_2
<=> aElementOf0(sK15,sdtpldt1(xI,xJ)) ),
introduced(definition,[new_symbols(definition,[spl30_2])],[avatar_definition]) ).
fof(f185,plain,
( aElementOf0(sK15,sdtpldt1(xI,xJ))
| ~ spl30_2 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f186,plain,
( spl30_1
| spl30_2 ),
inference(avatar_split_clause,[],[f132,f183,f179]) ).
fof(f188,definition,
( spl30_3
<=> aElementOf0(sdtasdt0(sK16,sK14),sdtpldt1(xI,xJ)) ),
introduced(definition,[new_symbols(definition,[spl30_3])],[avatar_definition]) ).
fof(f190,plain,
( ~ aElementOf0(sdtasdt0(sK16,sK14),sdtpldt1(xI,xJ))
| spl30_3 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f191,plain,
( ~ spl30_3
| spl30_2 ),
inference(avatar_split_clause,[],[f133,f183,f188]) ).
fof(f193,definition,
( spl30_4
<=> aElementOf0(sdtpldt0(sK14,sK15),sdtpldt1(xI,xJ)) ),
introduced(definition,[new_symbols(definition,[spl30_4])],[avatar_definition]) ).
fof(f195,plain,
( ~ aElementOf0(sdtpldt0(sK14,sK15),sdtpldt1(xI,xJ))
| spl30_4 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f196,plain,
( spl30_1
| ~ spl30_4 ),
inference(avatar_split_clause,[],[f134,f193,f179]) ).
fof(f197,plain,
( ~ spl30_3
| ~ spl30_4 ),
inference(avatar_split_clause,[],[f135,f193,f188]) ).
fof(f212,plain,
( aElement0(sK14)
| ~ aSet0(sdtpldt1(xI,xJ)) ),
inference(resolution,[],[f131,f140]) ).
fof(f215,plain,
aElement0(sK14),
inference(forward_subsumption_resolution,[],[f212,f129]) ).
fof(f216,plain,
( aElement0(sK15)
| ~ aSet0(sdtpldt1(xI,xJ))
| ~ spl30_2 ),
inference(resolution,[],[f185,f140]) ).
fof(f219,plain,
( aElement0(sK15)
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f216,f129]) ).
fof(f224,plain,
( ~ aElementOf0(sdtpldt0(sK15,sK14),sdtpldt1(xI,xJ))
| ~ aElement0(sK14)
| ~ aElement0(sK15)
| spl30_4 ),
inference(superposition,[],[f195,f144]) ).
fof(f227,plain,
( ~ aElementOf0(sdtpldt0(sK15,sK14),sdtpldt1(xI,xJ))
| ~ aElement0(sK15)
| spl30_4 ),
inference(forward_subsumption_resolution,[],[f224,f215]) ).
fof(f229,plain,
( ~ aElementOf0(sdtpldt0(sK15,sK14),sdtpldt1(xI,xJ))
| ~ spl30_2
| spl30_4 ),
inference(forward_subsumption_resolution,[],[f227,f219]) ).
fof(f236,plain,
aElementOf0(sK18(sK14),xJ),
inference(resolution,[],[f126,f131]) ).
fof(f239,plain,
( aElementOf0(sK18(sK21(sdtpldt1(xI,xJ))),xJ)
| ~ aSet0(sdtpldt1(xI,xJ))
| aIdeal0(sdtpldt1(xI,xJ)) ),
inference(resolution,[],[f126,f149]) ).
fof(f248,plain,
( aElementOf0(sK18(sK21(sdtpldt1(xI,xJ))),xJ)
| aIdeal0(sdtpldt1(xI,xJ)) ),
inference(forward_subsumption_resolution,[],[f239,f129]) ).
fof(f251,plain,
aElementOf0(sK18(sK21(sdtpldt1(xI,xJ))),xJ),
inference(forward_subsumption_resolution,[],[f248,f130]) ).
fof(f268,plain,
aElementOf0(sK17(sK14),xI),
inference(resolution,[],[f127,f131]) ).
fof(f331,plain,
! [X0,X1] :
( ~ aElementOf0(X0,sdtpldt1(xI,xJ))
| sP3(X0,X1,sK14)
| ~ aElement0(X1) ),
inference(resolution,[],[f121,f131]) ).
fof(f498,plain,
( ! [X2,X0,X1] : ~ sP2(sK14,X0,X1,X2,sK15)
| ~ spl30_2
| spl30_4 ),
inference(resolution,[],[f229,f105]) ).
fof(f512,plain,
( aElement0(sK18(sK21(sdtpldt1(xI,xJ))))
| ~ aSet0(xJ) ),
inference(resolution,[],[f251,f140]) ).
fof(f515,plain,
aElement0(sK18(sK21(sdtpldt1(xI,xJ)))),
inference(forward_subsumption_resolution,[],[f512,f94]) ).
fof(f520,plain,
( ! [X0] : ~ sP3(sK15,X0,sK14)
| ~ spl30_2
| spl30_4 ),
inference(resolution,[],[f498,f99]) ).
fof(f644,plain,
( ! [X0] :
( sP3(sK15,X0,sK14)
| ~ aElement0(X0) )
| ~ spl30_2 ),
inference(resolution,[],[f331,f185]) ).
fof(f656,plain,
( ! [X0] : ~ aElement0(X0)
| ~ spl30_2
| spl30_4 ),
inference(forward_subsumption_resolution,[],[f644,f520]) ).
fof(f668,plain,
( $false
| ~ spl30_2
| spl30_4 ),
inference(resolution,[],[f656,f515]) ).
fof(f671,plain,
( ~ spl30_2
| spl30_4 ),
inference(avatar_contradiction_clause,[],[f668]) ).
fof(f680,definition,
( spl30_19
<=> ! [X1] : ~ aElementOf0(X1,xI) ),
introduced(definition,[new_symbols(definition,[spl30_19])],[avatar_definition]) ).
fof(f681,plain,
( ! [X1] : ~ aElementOf0(X1,xI)
| ~ spl30_19 ),
inference(avatar_component_clause,[],[f680]) ).
fof(f683,definition,
( spl30_20
<=> ! [X0] : ~ aElementOf0(X0,xJ) ),
introduced(definition,[new_symbols(definition,[spl30_20])],[avatar_definition]) ).
fof(f684,plain,
( ! [X0] : ~ aElementOf0(X0,xJ)
| ~ spl30_20 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f714,plain,
( ! [X2,X0,X1] : ~ sP2(X0,X1,X2,sK16,sK14)
| spl30_3 ),
inference(resolution,[],[f190,f103]) ).
fof(f729,plain,
( ! [X0] : ~ sP3(sK14,sK16,X0)
| spl30_3 ),
inference(resolution,[],[f714,f99]) ).
fof(f732,plain,
( ! [X0,X1] :
( ~ aElementOf0(sK14,sdtpldt1(xI,xJ))
| ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| ~ aElement0(sK16) )
| spl30_3 ),
inference(resolution,[],[f729,f173]) ).
fof(f733,plain,
( ! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| ~ aElement0(sK16) )
| spl30_3 ),
inference(forward_subsumption_resolution,[],[f732,f131]) ).
fof(f734,plain,
( ! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ) )
| ~ spl30_1
| spl30_3 ),
inference(forward_subsumption_resolution,[],[f733,f181]) ).
fof(f735,plain,
( spl30_20
| spl30_19
| ~ spl30_1
| spl30_3 ),
inference(avatar_split_clause,[],[f734,f188,f179,f680,f683]) ).
fof(f757,plain,
( $false
| ~ spl30_20 ),
inference(resolution,[],[f684,f236]) ).
fof(f767,plain,
~ spl30_20,
inference(avatar_contradiction_clause,[],[f757]) ).
fof(f780,plain,
( $false
| ~ spl30_19 ),
inference(resolution,[],[f681,f268]) ).
fof(f790,plain,
~ spl30_19,
inference(avatar_contradiction_clause,[],[f780]) ).
cnf(s1,plain,
( spl30_1
| spl30_2 ),
inference(sat_conversion,[],[f186]) ).
cnf(s2,plain,
( spl30_2
| ~ spl30_3 ),
inference(sat_conversion,[],[f191]) ).
cnf(s3,plain,
( spl30_1
| ~ spl30_4 ),
inference(sat_conversion,[],[f196]) ).
cnf(s4,plain,
( ~ spl30_3
| ~ spl30_4 ),
inference(sat_conversion,[],[f197]) ).
cnf(s17,plain,
( ~ spl30_2
| spl30_4 ),
inference(sat_conversion,[],[f671]) ).
cnf(s32,plain,
( ~ spl30_1
| spl30_3
| spl30_19
| spl30_20 ),
inference(sat_conversion,[],[f735]) ).
cnf(s35,plain,
~ spl30_20,
inference(sat_conversion,[],[f767]) ).
cnf(s37,plain,
~ spl30_19,
inference(sat_conversion,[],[f790]) ).
cnf(s38,plain,
( ~ spl30_1
| spl30_3 ),
inference(rat,[],[s32,s35,s37]) ).
cnf(s41,plain,
spl30_1,
inference(rat,[],[s17,s1,s3]) ).
cnf(s42,plain,
spl30_3,
inference(rat,[],[s38,s41]) ).
cnf(s43,plain,
~ spl30_4,
inference(rat,[],[s4,s42]) ).
cnf(s44,plain,
spl30_2,
inference(rat,[],[s2,s42]) ).
cnf(s45,plain,
$false,
inference(rat,[],[s17,s43,s44]) ).
fof(f792,plain,
$false,
inference(avatar_sat_refutation,[],[s45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG092+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n010.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 27 23:13:47 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 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
% 1.88/1.73 % (1413233)Detected formulas, will run a generic FOF schedule.
% 1.88/1.73 % (1413244)dis-21_1_sil=8000:lcm=predicate:random_seed=687218142: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)
% 1.88/1.73 % (1413240)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=1703001719:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.88/1.73 % (1413239)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=1231515359:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.88/1.73 % (1413241)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4294207509:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.88/1.73 % (1413243)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3064042397:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.88/1.73 % (1413238)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=1326593619:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.88/1.73 % (1413242)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2465734715:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.88/1.73 % (1413244)Instruction limit reached!
% 1.88/1.73 % (1413244)------------------------------
% 1.88/1.73 % (1413244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.88/1.73 % (1413244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/1.73 % (1413244)CaDiCaL version: 2.1.3
% 1.88/1.73 % (1413244)Termination reason: Instruction limit
% 1.88/1.73 % (1413244)Termination phase: Saturation
% 1.88/1.73 % (1413244)Time elapsed: 0.074 s
% 1.88/1.73 % (1413244)Peak memory usage: 90 MB
% 1.88/1.73 % (1413244)Instructions burned: 130 (million)
% 1.88/1.73 % (1413241)First to succeed.
% 1.88/1.73 % (1413241)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1413233"
% 1.88/1.73 % (1413242)Instruction limit reached!
% 1.88/1.73 % (1413242)------------------------------
% 1.88/1.73 % (1413242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.88/1.73 % (1413242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/1.73 % (1413242)CaDiCaL version: 2.1.3
% 1.88/1.73 % (1413242)Termination reason: Instruction limit
% 1.88/1.73 % (1413242)Termination phase: Saturation
% 1.88/1.73 % (1413242)Time elapsed: 0.118 s
% 1.88/1.73 % (1413242)Peak memory usage: 88 MB
% 1.88/1.73 % (1413242)Instructions burned: 120 (million)
% 1.88/1.73 % (1413243)Instruction limit reached!
% 1.88/1.73 % (1413243)------------------------------
% 1.88/1.73 % (1413243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.88/1.73 % (1413243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/1.73 % (1413243)CaDiCaL version: 2.1.3
% 1.88/1.73 % (1413243)Termination reason: Instruction limit
% 1.88/1.73 % (1413243)Termination phase: Saturation
% 1.88/1.73 % (1413243)Time elapsed: 0.143 s
% 1.88/1.73 % (1413243)Peak memory usage: 90 MB
% 1.88/1.73 % (1413243)Instructions burned: 139 (million)
% 1.88/1.73 % (1413252)lrs+10_1_sil=8000:sp=occurrence:random_seed=1378915786:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 1.88/1.73 % (1413253)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1665000319:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 1.88/1.73 % (1413253)Instruction limit reached!
% 1.88/1.73 % (1413253)------------------------------
% 1.88/1.73 % (1413253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.88/1.73 % (1413253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/1.73 % (1413253)CaDiCaL version: 2.1.3
% 1.88/1.73 % (1413253)Termination reason: Instruction limit
% 1.88/1.73 % (1413253)Termination phase: Saturation
% 1.88/1.73 % (1413253)Time elapsed: 0.070 s
% 1.88/1.73 % (1413253)Peak memory usage: 91 MB
% 1.88/1.73 % (1413253)Instructions burned: 158 (million)
% 1.88/1.73 % (1413241)Refutation found. Thanks to Tanya!
% 1.88/1.73 % SZS status Theorem for theBenchmark
% 1.88/1.73 % SZS output start Proof for theBenchmark
% See solution above
% 6.10/2.06 % (1413241)------------------------------
% 6.10/2.06 % (1413241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.06 % (1413241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.06 % (1413241)CaDiCaL version: 2.1.3
% 6.10/2.06 % (1413241)Termination reason: Refutation
% 6.10/2.06 % (1413241)Time elapsed: 0.036 s
% 6.10/2.06 % (1413241)Peak memory usage: 90 MB
% 6.10/2.06 % (1413241)Instructions burned: 32 (million)
% 6.10/2.06 % (1413241)------------------------------
% 6.10/2.06 % (1413241)------------------------------
% 6.10/2.06 % (1413233)Success in time 0.731 s
% 6.10/2.06 % Vampire exiting
%------------------------------------------------------------------------------