%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM543+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 : Thu Sep 24 01:49:30 PM UTC 2026
% Result : Theorem 0.17s 0.54s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 80 ( 14 unt; 0 def)
% Number of atoms : 371 ( 72 equ)
% Maximal formula atoms : 52 ( 4 avg)
% Number of connectives : 480 ( 189 ~; 195 |; 59 &)
% ( 13 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 118 ( 1 sgn 67 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefMax,axiom,
! [X1] :
( ( X1 != slcrc0
& isFinite0(X1)
& aSubsetOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = szmzazxdt0(X1)
<=> ( ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X3,X2) )
& aElementOf0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMax) ).
fof(m__1986,hypothesis,
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1986) ).
fof(m__,conjecture,
? [X1] :
( ( ( ! [X2] :
( aElementOf0(X2,slbdtrb0(X1))
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X1)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(slbdtrb0(X1)) )
=> ( aSubsetOf0(xS,slbdtrb0(X1))
| ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,slbdtrb0(X1)) ) ) )
& aElementOf0(X1,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mSuccNum,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( szszuzczcdt0(X1) != sz00
& aElementOf0(szszuzczcdt0(X1),szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
fof(mSuccLess,axiom,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X1,X2)
<=> sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccLess) ).
fof(mCardDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( ( aElementOf0(X2,X1)
& isFinite0(X1) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( X4 != X2
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(mCardNum,axiom,
! [X1] :
( aSet0(X1)
=> ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
<=> isFinite0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( ~ ? [X2] : aElementOf0(X2,X1)
& aSet0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(mFDiffSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( isFinite0(X2)
& aSet0(X2) )
=> isFinite0(sdtmndt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(mCardEmpty,axiom,
! [X1] :
( aSet0(X1)
=> ( sbrdtbr0(X1) = sz00
<=> X1 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
fof(c_0_15,plain,
! [X1] :
( ( X1 != slcrc0
& isFinite0(X1)
& aSubsetOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = szmzazxdt0(X1)
<=> ( ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X3,X2) )
& aElementOf0(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[mDefMax]) ).
fof(c_0_16,plain,
! [X97,X98,X99,X100] :
( ( X97 = slcrc0
| ~ isFinite0(X97)
| ~ aSubsetOf0(X97,szNzAzT0)
| X100 = szmzazxdt0(X97)
| ~ aElementOf0(X100,X97)
| ~ sdtlseqdt0(esk8_2(X97,X100),X100) )
& ( X97 = slcrc0
| ~ isFinite0(X97)
| ~ aSubsetOf0(X97,szNzAzT0)
| X100 = szmzazxdt0(X97)
| ~ aElementOf0(X100,X97)
| aElementOf0(esk8_2(X97,X100),X97) )
& ( X97 = slcrc0
| ~ isFinite0(X97)
| ~ aSubsetOf0(X97,szNzAzT0)
| X98 != szmzazxdt0(X97)
| sdtlseqdt0(X99,X98)
| ~ aElementOf0(X99,X97) )
& ( X97 = slcrc0
| ~ isFinite0(X97)
| ~ aSubsetOf0(X97,szNzAzT0)
| X98 != szmzazxdt0(X97)
| aElementOf0(X98,X97) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])])])]) ).
cnf(c_0_17,plain,
( ~ isFinite0(X2)
| ~ aSubsetOf0(X2,szNzAzT0)
| X3 != szmzazxdt0(X2)
| ~ aElementOf0(X1,X2)
| X2 = slcrc0
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_18,hypothesis,
! [X115] :
( isFinite0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ( aElementOf0(X115,szNzAzT0)
| ~ aElementOf0(X115,xS) )
& aSet0(xS) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1986])])])]) ).
fof(c_0_19,negated_conjecture,
~ ? [X1] :
( ( ( ! [X2] :
( aElementOf0(X2,slbdtrb0(X1))
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X1)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(slbdtrb0(X1)) )
=> ( aSubsetOf0(xS,slbdtrb0(X1))
| ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,slbdtrb0(X1)) ) ) )
& aElementOf0(X1,szNzAzT0) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_20,plain,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( szszuzczcdt0(X1) != sz00
& aElementOf0(szszuzczcdt0(X1),szNzAzT0) ) ),
inference(fof_simplification,[status(thm)],[mSuccNum]) ).
cnf(c_0_21,plain,
( ~ aElementOf0(X2,X1)
| ~ isFinite0(X1)
| ~ aSubsetOf0(X1,szNzAzT0)
| sdtlseqdt0(X2,szmzazxdt0(X1))
| X1 = slcrc0 ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_22,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,hypothesis,
isFinite0(xS),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,negated_conjecture,
! [X116,X117,X118] :
( ( ~ aElementOf0(X116,szNzAzT0)
| ~ aSubsetOf0(xS,slbdtrb0(X116)) )
& ( ~ aElementOf0(X116,szNzAzT0)
| ~ aElementOf0(esk10_1(X116),slbdtrb0(X116)) )
& ( ~ aElementOf0(X116,szNzAzT0)
| aElementOf0(esk10_1(X116),xS) )
& ( ~ aElementOf0(X116,szNzAzT0)
| aElementOf0(X118,slbdtrb0(X116))
| ~ sdtlseqdt0(szszuzczcdt0(X118),X116)
| ~ aElementOf0(X118,szNzAzT0) )
& ( ~ aElementOf0(X116,szNzAzT0)
| ~ aElementOf0(X117,slbdtrb0(X116))
| sdtlseqdt0(szszuzczcdt0(X117),X116) )
& ( ~ aElementOf0(X116,szNzAzT0)
| ~ aElementOf0(X117,slbdtrb0(X116))
| aElementOf0(X117,szNzAzT0) )
& ( ~ aElementOf0(X116,szNzAzT0)
| aSet0(slbdtrb0(X116)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])])]) ).
cnf(c_0_25,plain,
( ~ isFinite0(X2)
| ~ aSubsetOf0(X2,szNzAzT0)
| X1 != szmzazxdt0(X2)
| X2 = slcrc0
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_26,plain,
! [X66,X67] :
( ( ~ aElementOf0(X67,szNzAzT0)
| ~ aElementOf0(X66,szNzAzT0)
| sdtlseqdt0(X66,X67)
| ~ sdtlseqdt0(szszuzczcdt0(X66),szszuzczcdt0(X67)) )
& ( ~ aElementOf0(X67,szNzAzT0)
| ~ aElementOf0(X66,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X66),szszuzczcdt0(X67))
| ~ sdtlseqdt0(X66,X67) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccLess])])])]) ).
fof(c_0_27,plain,
! [X56] :
( ( ~ aElementOf0(X56,szNzAzT0)
| szszuzczcdt0(X56) != sz00 )
& ( ~ aElementOf0(X56,szNzAzT0)
| aElementOf0(szszuzczcdt0(X56),szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_28,hypothesis,
( ~ aElementOf0(X1,xS)
| sdtlseqdt0(X1,szmzazxdt0(xS))
| xS = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_29,negated_conjecture,
( ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(esk10_1(X1),xS) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
( ~ isFinite0(X1)
| ~ aSubsetOf0(X1,szNzAzT0)
| aElementOf0(szmzazxdt0(X1),X1)
| X1 = slcrc0 ),
inference(er,[status(thm)],[c_0_25]) ).
fof(c_0_31,plain,
! [X85,X86] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X85,X86))) = sbrdtbr0(X85)
| ~ aElementOf0(X86,X85)
| ~ isFinite0(X85)
| ~ aSet0(X85) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardDiff])])])]) ).
fof(c_0_32,plain,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( X4 != X2
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
inference(fof_simplification,[status(thm)],[mDefDiff]) ).
cnf(c_0_33,negated_conjecture,
( ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),X2)
| ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(X1,slbdtrb0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
( ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(szszuzczcdt0(X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,negated_conjecture,
( ~ aElementOf0(X1,szNzAzT0)
| sdtlseqdt0(esk10_1(X1),szmzazxdt0(xS))
| xS = slcrc0 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,hypothesis,
( ~ aElementOf0(X1,xS)
| aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_38,hypothesis,
( aElementOf0(szmzazxdt0(xS),xS)
| xS = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_22]),c_0_23])]) ).
cnf(c_0_39,plain,
( ~ aElementOf0(X1,szNzAzT0)
| szszuzczcdt0(X1) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_40,plain,
( ~ aElementOf0(X2,X1)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_41,plain,
! [X81] :
( ( ~ aSet0(X81)
| aElementOf0(sbrdtbr0(X81),szNzAzT0)
| ~ isFinite0(X81) )
& ( ~ aSet0(X81)
| isFinite0(X81)
| ~ aElementOf0(sbrdtbr0(X81),szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardNum])])])]) ).
fof(c_0_42,plain,
! [X37,X38,X39,X40,X41,X42] :
( ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| aElementOf0(esk4_3(X37,X38,X42),X42)
| esk4_3(X37,X38,X42) != X38 )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| aElementOf0(esk4_3(X37,X38,X42),X42)
| aElementOf0(esk4_3(X37,X38,X42),X37) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| aElementOf0(esk4_3(X37,X38,X42),X42)
| aElement0(esk4_3(X37,X38,X42)) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| esk4_3(X37,X38,X42) = X38
| ~ aElementOf0(esk4_3(X37,X38,X42),X37)
| ~ aElement0(esk4_3(X37,X38,X42))
| ~ aElementOf0(esk4_3(X37,X38,X42),X42) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| aElementOf0(X41,X39)
| X41 = X38
| ~ aElementOf0(X41,X37)
| ~ aElement0(X41) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| ~ aElementOf0(X40,X39)
| X40 != X38 )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| ~ aElementOf0(X40,X39)
| aElementOf0(X40,X37) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| ~ aElementOf0(X40,X39)
| aElement0(X40) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| aSet0(X39) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])])])])]) ).
fof(c_0_43,plain,
! [X17,X18,X19,X20] :
( ( ~ aSet0(X17)
| aSubsetOf0(X20,X17)
| ~ aSet0(X20)
| ~ aElementOf0(esk2_2(X17,X20),X17) )
& ( ~ aSet0(X17)
| aSubsetOf0(X20,X17)
| ~ aSet0(X20)
| aElementOf0(esk2_2(X17,X20),X20) )
& ( ~ aSet0(X17)
| ~ aSubsetOf0(X18,X17)
| aElementOf0(X19,X17)
| ~ aElementOf0(X19,X18) )
& ( ~ aSet0(X17)
| ~ aSubsetOf0(X18,X17)
| aSet0(X18) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSub])])])])])])]) ).
fof(c_0_44,plain,
! [X10,X11,X12] :
( ( X12 = slcrc0
| aElementOf0(esk1_1(X12),X12)
| ~ aSet0(X12) )
& ( X10 != slcrc0
| ~ aElementOf0(X11,X10) )
& ( X10 != slcrc0
| aSet0(X10) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefEmp])])])])])])]) ).
cnf(c_0_45,negated_conjecture,
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(esk10_1(X1),slbdtrb0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_46,negated_conjecture,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| aElementOf0(X1,slbdtrb0(szszuzczcdt0(X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_47,negated_conjecture,
( ~ aElementOf0(X1,szNzAzT0)
| sdtlseqdt0(esk10_1(szszuzczcdt0(X1)),szmzazxdt0(xS))
| xS = slcrc0 ),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_48,hypothesis,
( aElementOf0(szmzazxdt0(xS),szNzAzT0)
| xS = slcrc0 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_49,plain,
( ~ aSet0(X1)
| ~ aElementOf0(X2,X1)
| ~ aElementOf0(sbrdtbr0(sdtmndt0(X1,X2)),szNzAzT0)
| ~ isFinite0(X1)
| sbrdtbr0(X1) != sz00 ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_50,plain,
( ~ aSet0(X1)
| ~ isFinite0(X1)
| aElementOf0(sbrdtbr0(X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_51,plain,
! [X54,X55] :
( isFinite0(sdtmndt0(X55,X54))
| ~ isFinite0(X55)
| ~ aSet0(X55)
| ~ aElement0(X54) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFDiffSet])])])]) ).
cnf(c_0_52,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X1 != sdtmndt0(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_53,plain,
! [X7,X8] :
( aElement0(X8)
| ~ aElementOf0(X8,X7)
| ~ aSet0(X7) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_54,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSubsetOf0(X2,X1)
| aElementOf0(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_56,plain,
( X1 != slcrc0
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,negated_conjecture,
( ~ aElementOf0(X1,szNzAzT0)
| ~ aSubsetOf0(xS,slbdtrb0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_58,plain,
slbdtrb0(sz00) = slcrc0,
inference(split_conjunct,[status(thm)],[mSegZero]) ).
cnf(c_0_59,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_60,negated_conjecture,
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(esk10_1(szszuzczcdt0(X1)),szNzAzT0)
| ~ sdtlseqdt0(esk10_1(szszuzczcdt0(X1)),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_35]) ).
cnf(c_0_61,hypothesis,
( sdtlseqdt0(esk10_1(szszuzczcdt0(szmzazxdt0(xS))),szmzazxdt0(xS))
| xS = slcrc0 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_62,plain,
( ~ aSet0(X1)
| ~ aSet0(sdtmndt0(X1,X2))
| ~ aElementOf0(X2,X1)
| ~ isFinite0(X1)
| ~ isFinite0(sdtmndt0(X1,X2))
| sbrdtbr0(X1) != sz00 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_63,plain,
( ~ isFinite0(X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| isFinite0(sdtmndt0(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_64,plain,
( ~ aSet0(X1)
| ~ aElement0(X2)
| aSet0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_52]) ).
cnf(c_0_65,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_66,hypothesis,
( ~ aSet0(X1)
| aElementOf0(esk2_2(X1,xS),xS)
| aSubsetOf0(xS,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_67,plain,
aSet0(slcrc0),
inference(er,[status(thm)],[c_0_56]) ).
cnf(c_0_68,negated_conjecture,
~ aSubsetOf0(xS,slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).
cnf(c_0_69,hypothesis,
( ~ aElementOf0(esk10_1(szszuzczcdt0(szmzazxdt0(xS))),szNzAzT0)
| xS = slcrc0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_48]) ).
cnf(c_0_70,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(esk10_1(X1),szNzAzT0) ),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
fof(c_0_71,plain,
! [X82] :
( ( ~ aSet0(X82)
| sbrdtbr0(X82) = sz00
| X82 != slcrc0 )
& ( ~ aSet0(X82)
| X82 = slcrc0
| sbrdtbr0(X82) != sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardEmpty])])])]) ).
cnf(c_0_72,plain,
( ~ aSet0(X1)
| ~ aElementOf0(X2,X1)
| ~ isFinite0(X1)
| sbrdtbr0(X1) != sz00 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_65]) ).
cnf(c_0_73,hypothesis,
aElementOf0(esk2_2(slcrc0,xS),xS),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_74,hypothesis,
( ~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)
| xS = slcrc0 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,plain,
( ~ aSet0(X1)
| X1 != slcrc0
| sbrdtbr0(X1) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_76,hypothesis,
sbrdtbr0(xS) != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_23]),c_0_55])]) ).
cnf(c_0_77,hypothesis,
xS = slcrc0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_35]),c_0_48]) ).
cnf(c_0_78,plain,
sbrdtbr0(slcrc0) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_75]),c_0_67])]) ).
cnf(c_0_79,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77]),c_0_78])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM543+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 02:39:49 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.54 % Version: 3.5.1
% 0.17/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.54 % Starting sh5l with 300s (1) cores
% 0.17/0.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1816570 completed with status 0
% 0.17/0.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.17/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.54 % No SInE strategy applied
% 0.17/0.54 % Search class: FGHSF-FFMM31-MFFFFFNN
% 0.17/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.17/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.17/0.54 % Starting new_bool_3 with 136s (1) cores
% 0.17/0.54 % Starting new_bool_1 with 136s (1) cores
% 0.17/0.54 % G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with pid 1816579 completed with status 0
% 0.17/0.54 % Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN
% 0.17/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.54 % No SInE strategy applied
% 0.17/0.54 % Search class: FGHSF-FFMM31-MFFFFFNN
% 0.17/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.17/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.17/0.54 % Preprocessing time : 0.003 s
% 0.17/0.54 % Presaturation interreduction done
% 0.17/0.54
% 0.17/0.54 % Proof found!
% 0.17/0.54 % SZS status Theorem
% 0.17/0.54 % SZS output start CNFRefutation
% See solution above
% 0.17/0.54 % Parsed axioms : 56
% 0.17/0.54 % Removed by relevancy pruning/SinE : 0
% 0.17/0.54 % Initial clauses : 108
% 0.17/0.54 % Removed in clause preprocessing : 6
% 0.17/0.54 % Initial clauses in saturation : 102
% 0.17/0.54 % Processed clauses : 851
% 0.17/0.54 % ...of these trivial : 4
% 0.17/0.54 % ...subsumed : 278
% 0.17/0.54 % ...remaining for further processing : 569
% 0.17/0.54 % Other redundant clauses eliminated : 26
% 0.17/0.54 % Clauses deleted for lack of memory : 0
% 0.17/0.54 % Backward-subsumed : 22
% 0.17/0.54 % Backward-rewritten : 152
% 0.17/0.54 % Generated clauses : 2251
% 0.17/0.54 % ...of the previous two non-redundant : 2111
% 0.17/0.54 % ...aggressively subsumed : 0
% 0.17/0.54 % Contextual simplify-reflections : 64
% 0.17/0.54 % Paramodulations : 2223
% 0.17/0.54 % Factorizations : 0
% 0.17/0.54 % NegExts : 0
% 0.17/0.54 % Equation resolutions : 27
% 0.17/0.54 % Disequality decompositions : 0
% 0.17/0.54 % Total rewrite steps : 878
% 0.17/0.54 % ...of those cached : 852
% 0.17/0.54 % Propositional unsat checks : 0
% 0.17/0.54 % Propositional check models : 0
% 0.17/0.54 % Propositional check unsatisfiable : 0
% 0.17/0.54 % Propositional clauses : 0
% 0.17/0.54 % Propositional clauses after purity: 0
% 0.17/0.54 % Propositional unsat core size : 0
% 0.17/0.54 % Propositional preprocessing time : 0.000
% 0.17/0.54 % Propositional encoding time : 0.000
% 0.17/0.54 % Propositional solver time : 0.000
% 0.17/0.54 % Success case prop preproc time : 0.000
% 0.17/0.54 % Success case prop encoding time : 0.000
% 0.17/0.54 % Success case prop solver time : 0.000
% 0.17/0.54 % Current number of processed clauses : 271
% 0.17/0.54 % Positive orientable unit clauses : 26
% 0.17/0.54 % Positive unorientable unit clauses: 0
% 0.17/0.54 % Negative unit clauses : 11
% 0.17/0.54 % Non-unit-clauses : 234
% 0.17/0.54 % Current number of unprocessed clauses: 1397
% 0.17/0.54 % ...number of literals in the above : 5432
% 0.17/0.54 % Current number of archived formulas : 0
% 0.17/0.54 % Current number of archived clauses : 275
% 0.17/0.54 % Clause-clause subsumption calls (NU) : 20160
% 0.17/0.54 % Rec. Clause-clause subsumption calls : 11711
% 0.17/0.54 % Non-unit clause-clause subsumptions : 198
% 0.17/0.54 % Unit Clause-clause subsumption calls : 2206
% 0.17/0.54 % Rewrite failures with RHS unbound : 0
% 0.17/0.54 % BW rewrite match attempts : 10
% 0.17/0.54 % BW rewrite match successes : 8
% 0.17/0.54 % Condensation attempts : 0
% 0.17/0.54 % Condensation successes : 0
% 0.17/0.54 % Termbank termtop insertions : 45740
% 0.17/0.54 % Search garbage collected termcells : 2152
% 0.17/0.54
% 0.17/0.54 % -------------------------------------------------
% 0.17/0.54 % User time : 0.086 s
% 0.17/0.54 % System time : 0.009 s
% 0.17/0.54 % Total time : 0.095 s
% 0.17/0.54 % Maximum resident set size: 3952 pages
% 0.17/0.54
% 0.17/0.54 % -------------------------------------------------
% 0.17/0.54 % User time : 0.382 s
% 0.17/0.54 % System time : 0.047 s
% 0.17/0.54 % Total time : 0.429 s
% 0.17/0.54 % Maximum resident set size: 4608 pages
% 0.17/0.54 % E exiting
%------------------------------------------------------------------------------