TSTP Solution File: NUM563+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM563+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 09:33:50 EDT 2022
% Result : Theorem 0.23s 1.41s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 121 ( 27 unt; 0 def)
% Number of atoms : 414 ( 84 equ)
% Maximal formula atoms : 39 ( 3 avg)
% Number of connectives : 517 ( 224 ~; 219 |; 45 &)
% ( 8 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 156 ( 10 sgn 63 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSubTrans,axiom,
! [X1,X2,X3] :
( ( aSet0(X1)
& aSet0(X2)
& aSet0(X3) )
=> ( ( aSubsetOf0(X1,X2)
& aSubsetOf0(X2,X3) )
=> aSubsetOf0(X1,X3) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSubTrans) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefSub) ).
fof(m__,conjecture,
( xK = sz00
=> ? [X1] :
( aElementOf0(X1,xT)
& ? [X2] :
( aSubsetOf0(X2,xS)
& isCountable0(X2)
& ! [X3] :
( aElementOf0(X3,slbdtsldtrb0(X2,xK))
=> sdtlpdtrp0(xc,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefEmp) ).
fof(mZeroLess,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(sz00,X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mZeroLess) ).
fof(m__3453,hypothesis,
( aFunction0(xc)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__3453) ).
fof(m__3291,hypothesis,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__3291) ).
fof(mSegLess,axiom,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( sdtlseqdt0(X1,X2)
<=> aSubsetOf0(slbdtrb0(X1),slbdtrb0(X2)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSegLess) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSegZero) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mZeroNum) ).
fof(mDefSel,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElementOf0(X2,szNzAzT0) )
=> ! [X3] :
( X3 = slbdtsldtrb0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aSubsetOf0(X4,X1)
& sbrdtbr0(X4) = X2 ) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefSel) ).
fof(m__3435,hypothesis,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__3435) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mNATSet) ).
fof(mSelNSet,axiom,
! [X1] :
( ( aSet0(X1)
& ~ isFinite0(X1) )
=> ! [X2] :
( aElementOf0(X2,szNzAzT0)
=> slbdtsldtrb0(X1,X2) != slcrc0 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSelNSet) ).
fof(mImgRng,axiom,
! [X1] :
( aFunction0(X1)
=> ! [X2] :
( aElementOf0(X2,szDzozmdt0(X1))
=> aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1))) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mImgRng) ).
fof(mDomSet,axiom,
! [X1] :
( aFunction0(X1)
=> aSet0(szDzozmdt0(X1)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDomSet) ).
fof(mCountNFin,axiom,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> ~ isFinite0(X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mCountNFin) ).
fof(mCardEmpty,axiom,
! [X1] :
( aSet0(X1)
=> ( sbrdtbr0(X1) = sz00
<=> X1 = slcrc0 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mCardEmpty) ).
fof(mDefSeg,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( X2 = slbdtrb0(X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefSeg) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSubRefl) ).
fof(mCardSeg,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sbrdtbr0(slbdtrb0(X1)) = X1 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mCardSeg) ).
fof(c_0_21,plain,
! [X4,X5,X6] :
( ~ aSet0(X4)
| ~ aSet0(X5)
| ~ aSet0(X6)
| ~ aSubsetOf0(X4,X5)
| ~ aSubsetOf0(X5,X6)
| aSubsetOf0(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubTrans])]) ).
fof(c_0_22,plain,
! [X4,X5,X6,X5] :
( ( aSet0(X5)
| ~ aSubsetOf0(X5,X4)
| ~ aSet0(X4) )
& ( ~ aElementOf0(X6,X5)
| aElementOf0(X6,X4)
| ~ aSubsetOf0(X5,X4)
| ~ aSet0(X4) )
& ( aElementOf0(esk4_2(X4,X5),X5)
| ~ aSet0(X5)
| aSubsetOf0(X5,X4)
| ~ aSet0(X4) )
& ( ~ aElementOf0(esk4_2(X4,X5),X4)
| ~ aSet0(X5)
| aSubsetOf0(X5,X4)
| ~ aSet0(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSub])])])])])])]) ).
fof(c_0_23,negated_conjecture,
~ ( xK = sz00
=> ? [X1] :
( aElementOf0(X1,xT)
& ? [X2] :
( aSubsetOf0(X2,xS)
& isCountable0(X2)
& ! [X3] :
( aElementOf0(X3,slbdtsldtrb0(X2,xK))
=> sdtlpdtrp0(xc,X3) = X1 ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_24,plain,
( aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X3,X2)
| ~ aSubsetOf0(X1,X3)
| ~ aSet0(X2)
| ~ aSet0(X3)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
( aSet0(X2)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_26,plain,
! [X3,X4,X3] :
( ( aSet0(X3)
| X3 != slcrc0 )
& ( ~ aElementOf0(X4,X3)
| X3 != slcrc0 )
& ( ~ aSet0(X3)
| aElementOf0(esk13_1(X3),X3)
| X3 = slcrc0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefEmp])])])])])])]) ).
fof(c_0_27,plain,
! [X2] :
( ~ aElementOf0(X2,szNzAzT0)
| sdtlseqdt0(sz00,X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])]) ).
fof(c_0_28,negated_conjecture,
! [X4,X5] :
( xK = sz00
& ( aElementOf0(esk3_2(X4,X5),slbdtsldtrb0(X5,xK))
| ~ aSubsetOf0(X5,xS)
| ~ isCountable0(X5)
| ~ aElementOf0(X4,xT) )
& ( sdtlpdtrp0(xc,esk3_2(X4,X5)) != X4
| ~ aSubsetOf0(X5,xS)
| ~ isCountable0(X5)
| ~ aElementOf0(X4,xT) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])])])])]) ).
cnf(c_0_29,plain,
( aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X3,X2)
| ~ aSubsetOf0(X1,X3)
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_24,c_0_25]),c_0_25]) ).
cnf(c_0_30,hypothesis,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_31,hypothesis,
aSet0(xT),
inference(split_conjunct,[status(thm)],[m__3291]) ).
cnf(c_0_32,plain,
( X1 != slcrc0
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( aSubsetOf0(X2,X1)
| aElementOf0(esk4_2(X1,X2),X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_34,plain,
( aSet0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_35,plain,
! [X3,X4] :
( ( ~ sdtlseqdt0(X3,X4)
| aSubsetOf0(slbdtrb0(X3),slbdtrb0(X4))
| ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X4,szNzAzT0) )
& ( ~ aSubsetOf0(slbdtrb0(X3),slbdtrb0(X4))
| sdtlseqdt0(X3,X4)
| ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X4,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSegLess])])]) ).
cnf(c_0_36,plain,
( sdtlseqdt0(sz00,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,negated_conjecture,
xK = sz00,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
slbdtrb0(sz00) = slcrc0,
inference(split_conjunct,[status(thm)],[mSegZero]) ).
cnf(c_0_39,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_40,hypothesis,
( aSubsetOf0(X1,xT)
| ~ aSubsetOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_41,plain,
( aSubsetOf0(X1,X2)
| X1 != slcrc0
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_42,hypothesis,
aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_30]),c_0_31])]) ).
cnf(c_0_43,plain,
( aSubsetOf0(slbdtrb0(X2),slbdtrb0(X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
( sdtlseqdt0(xK,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,plain,
slbdtrb0(xK) = slcrc0,
inference(rw,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_46,plain,
aElementOf0(xK,szNzAzT0),
inference(rw,[status(thm)],[c_0_39,c_0_37]) ).
fof(c_0_47,plain,
! [X5,X6,X7,X8,X8,X7] :
( ( aSet0(X7)
| X7 != slbdtsldtrb0(X5,X6)
| ~ aSet0(X5)
| ~ aElementOf0(X6,szNzAzT0) )
& ( aSubsetOf0(X8,X5)
| ~ aElementOf0(X8,X7)
| X7 != slbdtsldtrb0(X5,X6)
| ~ aSet0(X5)
| ~ aElementOf0(X6,szNzAzT0) )
& ( sbrdtbr0(X8) = X6
| ~ aElementOf0(X8,X7)
| X7 != slbdtsldtrb0(X5,X6)
| ~ aSet0(X5)
| ~ aElementOf0(X6,szNzAzT0) )
& ( ~ aSubsetOf0(X8,X5)
| sbrdtbr0(X8) != X6
| aElementOf0(X8,X7)
| X7 != slbdtsldtrb0(X5,X6)
| ~ aSet0(X5)
| ~ aElementOf0(X6,szNzAzT0) )
& ( ~ aElementOf0(esk10_3(X5,X6,X7),X7)
| ~ aSubsetOf0(esk10_3(X5,X6,X7),X5)
| sbrdtbr0(esk10_3(X5,X6,X7)) != X6
| ~ aSet0(X7)
| X7 = slbdtsldtrb0(X5,X6)
| ~ aSet0(X5)
| ~ aElementOf0(X6,szNzAzT0) )
& ( aSubsetOf0(esk10_3(X5,X6,X7),X5)
| aElementOf0(esk10_3(X5,X6,X7),X7)
| ~ aSet0(X7)
| X7 = slbdtsldtrb0(X5,X6)
| ~ aSet0(X5)
| ~ aElementOf0(X6,szNzAzT0) )
& ( sbrdtbr0(esk10_3(X5,X6,X7)) = X6
| aElementOf0(esk10_3(X5,X6,X7),X7)
| ~ aSet0(X7)
| X7 = slbdtsldtrb0(X5,X6)
| ~ aSet0(X5)
| ~ aElementOf0(X6,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSel])])])])])])]) ).
cnf(c_0_48,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_49,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_50,hypothesis,
( aSubsetOf0(X1,xT)
| X1 != slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_51,plain,
( aSubsetOf0(slcrc0,slbdtrb0(X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46])]) ).
cnf(c_0_52,plain,
( aSubsetOf0(X4,X2)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X2)
| X3 != slbdtsldtrb0(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_53,hypothesis,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_54,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_48]),c_0_49])]) ).
cnf(c_0_55,plain,
( aElementOf0(X3,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X1)
| ~ aElementOf0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_56,hypothesis,
( aSubsetOf0(X1,xT)
| X2 != slcrc0
| ~ aSubsetOf0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_50]),c_0_31])]) ).
cnf(c_0_57,plain,
aSubsetOf0(slcrc0,slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_45]),c_0_46])]) ).
cnf(c_0_58,hypothesis,
( aSubsetOf0(X1,xS)
| X2 != szDzozmdt0(xc)
| ~ aElementOf0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_46])]),c_0_54])]) ).
cnf(c_0_59,negated_conjecture,
( aElementOf0(esk3_2(X1,X2),slbdtsldtrb0(X2,xK))
| ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_60,hypothesis,
isCountable0(xS),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_61,hypothesis,
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_30]),c_0_31])]) ).
cnf(c_0_62,plain,
( X1 = slcrc0
| aElementOf0(esk13_1(X1),X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_63,hypothesis,
aSubsetOf0(slcrc0,xT),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
fof(c_0_64,plain,
! [X3,X4] :
( ~ aSet0(X3)
| isFinite0(X3)
| ~ aElementOf0(X4,szNzAzT0)
| slbdtsldtrb0(X3,X4) != slcrc0 ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mSelNSet])])])])])]) ).
cnf(c_0_65,hypothesis,
( aSubsetOf0(X1,xS)
| ~ aElementOf0(X1,szDzozmdt0(xc)) ),
inference(er,[status(thm)],[c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( aElementOf0(esk3_2(X1,xS),szDzozmdt0(xc))
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X1,xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_53]),c_0_60])]) ).
fof(c_0_67,plain,
! [X3,X4] :
( ~ aFunction0(X3)
| ~ aElementOf0(X4,szDzozmdt0(X3))
| aElementOf0(sdtlpdtrp0(X3,X4),sdtlcdtrc0(X3,szDzozmdt0(X3))) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mImgRng])])])])]) ).
cnf(c_0_68,hypothesis,
( sdtlcdtrc0(xc,szDzozmdt0(xc)) = slcrc0
| aElementOf0(esk13_1(sdtlcdtrc0(xc,szDzozmdt0(xc))),xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_42])]) ).
cnf(c_0_69,hypothesis,
( aElementOf0(X1,xT)
| ~ aElementOf0(X1,slcrc0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_63]),c_0_31])]) ).
fof(c_0_70,plain,
! [X2] :
( ~ aFunction0(X2)
| aSet0(szDzozmdt0(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDomSet])]) ).
fof(c_0_71,plain,
! [X2] :
( ~ aSet0(X2)
| ~ isCountable0(X2)
| ~ isFinite0(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mCountNFin])])]) ).
cnf(c_0_72,plain,
( isFinite0(X1)
| slbdtsldtrb0(X1,X2) != slcrc0
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_73,negated_conjecture,
( aSubsetOf0(esk3_2(X1,xS),xS)
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X1,xT) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_74,plain,
( aSubsetOf0(X1,X2)
| X3 != slcrc0
| ~ aSubsetOf0(X1,X3)
| ~ aSet0(X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_41]) ).
cnf(c_0_75,plain,
( aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1)))
| ~ aElementOf0(X2,szDzozmdt0(X1))
| ~ aFunction0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_76,hypothesis,
( sdtlcdtrc0(xc,szDzozmdt0(xc)) = slcrc0
| xT != slcrc0 ),
inference(spm,[status(thm)],[c_0_32,c_0_68]) ).
cnf(c_0_77,hypothesis,
aFunction0(xc),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_78,hypothesis,
( xT != slcrc0
| ~ aElementOf0(X1,slcrc0) ),
inference(spm,[status(thm)],[c_0_32,c_0_69]) ).
cnf(c_0_79,plain,
( aSet0(szDzozmdt0(X1))
| ~ aFunction0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_80,plain,
( ~ isFinite0(X1)
| ~ isCountable0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_81,hypothesis,
( isFinite0(xS)
| szDzozmdt0(xc) != slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_53]),c_0_46])]),c_0_54])]) ).
cnf(c_0_82,negated_conjecture,
( aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X1,esk3_2(X2,xS))
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X2,xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_73]),c_0_54])]) ).
cnf(c_0_83,plain,
( aSubsetOf0(slcrc0,X1)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_57]) ).
cnf(c_0_84,negated_conjecture,
( aSet0(esk3_2(X1,xS))
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X1,xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_73]),c_0_54])]) ).
cnf(c_0_85,hypothesis,
( xT != slcrc0
| ~ aElementOf0(X1,szDzozmdt0(xc)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77])]),c_0_78]) ).
cnf(c_0_86,hypothesis,
aSet0(szDzozmdt0(xc)),
inference(spm,[status(thm)],[c_0_79,c_0_77]) ).
cnf(c_0_87,hypothesis,
szDzozmdt0(xc) != slcrc0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_60]),c_0_54])]) ).
fof(c_0_88,plain,
! [X2] :
( ( sbrdtbr0(X2) != sz00
| X2 = slcrc0
| ~ aSet0(X2) )
& ( X2 != slcrc0
| sbrdtbr0(X2) = sz00
| ~ aSet0(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardEmpty])])]) ).
cnf(c_0_89,plain,
( sbrdtbr0(X4) = X1
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X2)
| X3 != slbdtsldtrb0(X2,X1)
| ~ aElementOf0(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_90,negated_conjecture,
( aSubsetOf0(slcrc0,xS)
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X1,xT) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]) ).
cnf(c_0_91,hypothesis,
xT != slcrc0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_62]),c_0_86])]),c_0_87]) ).
fof(c_0_92,plain,
! [X4,X5,X6,X6,X5] :
( ( aSet0(X5)
| X5 != slbdtrb0(X4)
| ~ aElementOf0(X4,szNzAzT0) )
& ( aElementOf0(X6,szNzAzT0)
| ~ aElementOf0(X6,X5)
| X5 != slbdtrb0(X4)
| ~ aElementOf0(X4,szNzAzT0) )
& ( sdtlseqdt0(szszuzczcdt0(X6),X4)
| ~ aElementOf0(X6,X5)
| X5 != slbdtrb0(X4)
| ~ aElementOf0(X4,szNzAzT0) )
& ( ~ aElementOf0(X6,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X6),X4)
| aElementOf0(X6,X5)
| X5 != slbdtrb0(X4)
| ~ aElementOf0(X4,szNzAzT0) )
& ( ~ aElementOf0(esk15_2(X4,X5),X5)
| ~ aElementOf0(esk15_2(X4,X5),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(esk15_2(X4,X5)),X4)
| ~ aSet0(X5)
| X5 = slbdtrb0(X4)
| ~ aElementOf0(X4,szNzAzT0) )
& ( aElementOf0(esk15_2(X4,X5),szNzAzT0)
| aElementOf0(esk15_2(X4,X5),X5)
| ~ aSet0(X5)
| X5 = slbdtrb0(X4)
| ~ aElementOf0(X4,szNzAzT0) )
& ( sdtlseqdt0(szszuzczcdt0(esk15_2(X4,X5)),X4)
| aElementOf0(esk15_2(X4,X5),X5)
| ~ aSet0(X5)
| X5 = slbdtrb0(X4)
| ~ aElementOf0(X4,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSeg])])])])])])]) ).
cnf(c_0_93,plain,
( X1 = slcrc0
| ~ aSet0(X1)
| sbrdtbr0(X1) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_94,plain,
( sbrdtbr0(X1) = X2
| ~ aElementOf0(X1,slbdtsldtrb0(X3,X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_89]) ).
cnf(c_0_95,negated_conjecture,
( aSubsetOf0(slcrc0,xS)
| ~ aSubsetOf0(xS,xS) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_62]),c_0_31])]),c_0_91]) ).
fof(c_0_96,plain,
! [X2] :
( ~ aSet0(X2)
| aSubsetOf0(X2,X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])]) ).
cnf(c_0_97,plain,
( aSet0(X2)
| ~ aElementOf0(X1,szNzAzT0)
| X2 != slbdtrb0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_98,plain,
( X1 = slcrc0
| sbrdtbr0(X1) != xK
| ~ aSet0(X1) ),
inference(rw,[status(thm)],[c_0_93,c_0_37]) ).
cnf(c_0_99,hypothesis,
( sbrdtbr0(X1) = xK
| ~ aElementOf0(X1,szDzozmdt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_53]),c_0_46]),c_0_54])]) ).
cnf(c_0_100,negated_conjecture,
( aSubsetOf0(X1,xS)
| ~ aSubsetOf0(xS,xS)
| ~ aSubsetOf0(X1,slcrc0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_95]),c_0_54])]) ).
cnf(c_0_101,plain,
( aSubsetOf0(X1,X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_102,plain,
( aSet0(slbdtrb0(X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(er,[status(thm)],[c_0_97]) ).
fof(c_0_103,plain,
! [X2] :
( ~ aElementOf0(X2,szNzAzT0)
| sbrdtbr0(slbdtrb0(X2)) = X2 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardSeg])]) ).
cnf(c_0_104,hypothesis,
( X1 = slcrc0
| ~ aElementOf0(X1,szDzozmdt0(xc))
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_105,plain,
( aElementOf0(X4,X3)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X2)
| X3 != slbdtsldtrb0(X2,X1)
| sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_106,negated_conjecture,
( aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X1,slcrc0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_54])]) ).
cnf(c_0_107,plain,
aSet0(slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_45]),c_0_46])]) ).
cnf(c_0_108,plain,
( sbrdtbr0(slbdtrb0(X1)) = X1
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_109,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ isCountable0(X2)
| ~ aSubsetOf0(X2,xS)
| sdtlpdtrp0(xc,esk3_2(X1,X2)) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_110,negated_conjecture,
( esk3_2(X1,xS) = slcrc0
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X1,xT) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_66]),c_0_84]) ).
cnf(c_0_111,plain,
( aElementOf0(X1,slbdtsldtrb0(X2,X3))
| sbrdtbr0(X1) != X3
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X3,szNzAzT0)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_105]) ).
cnf(c_0_112,negated_conjecture,
aSubsetOf0(slcrc0,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_83]),c_0_107])]) ).
cnf(c_0_113,plain,
sbrdtbr0(slcrc0) = xK,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_45]),c_0_46])]) ).
cnf(c_0_114,negated_conjecture,
( sdtlpdtrp0(xc,slcrc0) != X1
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X1,xT) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_60])]) ).
cnf(c_0_115,negated_conjecture,
( aElementOf0(slcrc0,slbdtsldtrb0(xS,X1))
| xK != X1
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]),c_0_54])]) ).
cnf(c_0_116,negated_conjecture,
( ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
inference(er,[status(thm)],[c_0_114]) ).
cnf(c_0_117,hypothesis,
( aElementOf0(sdtlpdtrp0(xc,X1),xT)
| ~ aElementOf0(X1,szDzozmdt0(xc)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_75]),c_0_77])]) ).
cnf(c_0_118,hypothesis,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_53]),c_0_46])]) ).
cnf(c_0_119,hypothesis,
~ aSubsetOf0(xS,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118])]) ).
cnf(c_0_120,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_101]),c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM563+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jul 6 09:53:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.23/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.41 # Preprocessing time : 0.022 s
% 0.23/1.41
% 0.23/1.41 # Proof found!
% 0.23/1.41 # SZS status Theorem
% 0.23/1.41 # SZS output start CNFRefutation
% See solution above
% 0.23/1.42 # Proof object total steps : 121
% 0.23/1.42 # Proof object clause steps : 84
% 0.23/1.42 # Proof object formula steps : 37
% 0.23/1.42 # Proof object conjectures : 19
% 0.23/1.42 # Proof object clause conjectures : 16
% 0.23/1.42 # Proof object formula conjectures : 3
% 0.23/1.42 # Proof object initial clauses used : 32
% 0.23/1.42 # Proof object initial formulas used : 21
% 0.23/1.42 # Proof object generating inferences : 47
% 0.23/1.42 # Proof object simplifying inferences : 82
% 0.23/1.42 # Training examples: 0 positive, 0 negative
% 0.23/1.42 # Parsed axioms : 78
% 0.23/1.42 # Removed by relevancy pruning/SinE : 17
% 0.23/1.42 # Initial clauses : 109
% 0.23/1.42 # Removed in clause preprocessing : 7
% 0.23/1.42 # Initial clauses in saturation : 102
% 0.23/1.42 # Processed clauses : 751
% 0.23/1.42 # ...of these trivial : 17
% 0.23/1.42 # ...subsumed : 342
% 0.23/1.42 # ...remaining for further processing : 392
% 0.23/1.42 # Other redundant clauses eliminated : 2
% 0.23/1.42 # Clauses deleted for lack of memory : 0
% 0.23/1.42 # Backward-subsumed : 17
% 0.23/1.42 # Backward-rewritten : 15
% 0.23/1.42 # Generated clauses : 1764
% 0.23/1.42 # ...of the previous two non-trivial : 1541
% 0.23/1.42 # Contextual simplify-reflections : 267
% 0.23/1.42 # Paramodulations : 1739
% 0.23/1.42 # Factorizations : 0
% 0.23/1.42 # Equation resolutions : 25
% 0.23/1.42 # Current number of processed clauses : 359
% 0.23/1.42 # Positive orientable unit clauses : 30
% 0.23/1.42 # Positive unorientable unit clauses: 0
% 0.23/1.42 # Negative unit clauses : 13
% 0.23/1.42 # Non-unit-clauses : 316
% 0.23/1.42 # Current number of unprocessed clauses: 834
% 0.23/1.42 # ...number of literals in the above : 4798
% 0.23/1.42 # Current number of archived formulas : 0
% 0.23/1.42 # Current number of archived clauses : 32
% 0.23/1.42 # Clause-clause subsumption calls (NU) : 21335
% 0.23/1.42 # Rec. Clause-clause subsumption calls : 8559
% 0.23/1.42 # Non-unit clause-clause subsumptions : 508
% 0.23/1.42 # Unit Clause-clause subsumption calls : 687
% 0.23/1.42 # Rewrite failures with RHS unbound : 0
% 0.23/1.42 # BW rewrite match attempts : 5
% 0.23/1.42 # BW rewrite match successes : 4
% 0.23/1.42 # Condensation attempts : 0
% 0.23/1.42 # Condensation successes : 0
% 0.23/1.42 # Termbank termtop insertions : 36135
% 0.23/1.42
% 0.23/1.42 # -------------------------------------------------
% 0.23/1.42 # User time : 0.103 s
% 0.23/1.42 # System time : 0.006 s
% 0.23/1.42 # Total time : 0.109 s
% 0.23/1.42 # Maximum resident set size: 4884 pages
%------------------------------------------------------------------------------