%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM536+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 : 300s
% DateTime : Tue May 5 04:57:43 PM UTC 2026
% Result : Theorem 146.74s 90.58s
% Output : CNFRefutation 147.84s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_15384)
% Comments :
%------------------------------------------------------------------------------
fof(mCountNFin,axiom,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> ~ isFinite0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& aElementOf0(X4,X1)
& X4 != X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(mDefCons,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtpldt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& ( aElementOf0(X4,X1)
| X4 = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefCons) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
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/benchmark/theBenchmark.p',mSubTrans) ).
fof(mConsDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> sdtpldt0(sdtmndt0(X1,X2),X2) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
fof(mSubASymm,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ( ( aSubsetOf0(X1,X2)
& aSubsetOf0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubASymm) ).
fof(m__,conjecture,
sdtmndt0(sdtpldt0(xS,xx),xx) = xS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mSubFSet,axiom,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aSubsetOf0(X2,X1)
=> isFinite0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubFSet) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(mSubRefl,axiom,
! [X1] :
( aSet0(X1)
=> aSubsetOf0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(m__679_02,hypothesis,
~ aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__679_02) ).
fof(mCountNFin_01,axiom,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> X1 != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(mEmpFin,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEmpFin) ).
fof(m__679,hypothesis,
( aElement0(xx)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__679) ).
fof(i_0_16,plain,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> ~ isFinite0(X1) ),
inference(fof_simplification,[status(thm)],[mCountNFin]) ).
fof(i_0_17,plain,
! [X64,X65,X66,X67,X68,X69] :
( ( aSet0(X66)
| X66 != sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( aElement0(X67)
| ~ aElementOf0(X67,X66)
| X66 != sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( aElementOf0(X67,X64)
| ~ aElementOf0(X67,X66)
| X66 != sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( X67 != X65
| ~ aElementOf0(X67,X66)
| X66 != sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( ~ aElement0(X68)
| ~ aElementOf0(X68,X64)
| X68 = X65
| aElementOf0(X68,X66)
| X66 != sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( ~ aElementOf0(esk4_3(X64,X65,X69),X69)
| ~ aElement0(esk4_3(X64,X65,X69))
| ~ aElementOf0(esk4_3(X64,X65,X69),X64)
| esk4_3(X64,X65,X69) = X65
| ~ aSet0(X69)
| X69 = sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( aElement0(esk4_3(X64,X65,X69))
| aElementOf0(esk4_3(X64,X65,X69),X69)
| ~ aSet0(X69)
| X69 = sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( aElementOf0(esk4_3(X64,X65,X69),X64)
| aElementOf0(esk4_3(X64,X65,X69),X69)
| ~ aSet0(X69)
| X69 = sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) )
& ( esk4_3(X64,X65,X69) != X65
| aElementOf0(esk4_3(X64,X65,X69),X69)
| ~ aSet0(X69)
| X69 = sdtmndt0(X64,X65)
| ~ aSet0(X64)
| ~ aElement0(X65) ) ),
inference(distribute,[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)],[mDefDiff])])])])])]) ).
fof(i_0_18,plain,
! [X57,X58,X59,X60,X61,X62] :
( ( aSet0(X59)
| X59 != sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( aElement0(X60)
| ~ aElementOf0(X60,X59)
| X59 != sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( aElementOf0(X60,X57)
| X60 = X58
| ~ aElementOf0(X60,X59)
| X59 != sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( ~ aElementOf0(X61,X57)
| ~ aElement0(X61)
| aElementOf0(X61,X59)
| X59 != sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( X61 != X58
| ~ aElement0(X61)
| aElementOf0(X61,X59)
| X59 != sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( ~ aElementOf0(esk3_3(X57,X58,X62),X57)
| ~ aElement0(esk3_3(X57,X58,X62))
| ~ aElementOf0(esk3_3(X57,X58,X62),X62)
| ~ aSet0(X62)
| X62 = sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( esk3_3(X57,X58,X62) != X58
| ~ aElement0(esk3_3(X57,X58,X62))
| ~ aElementOf0(esk3_3(X57,X58,X62),X62)
| ~ aSet0(X62)
| X62 = sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( aElement0(esk3_3(X57,X58,X62))
| aElementOf0(esk3_3(X57,X58,X62),X62)
| ~ aSet0(X62)
| X62 = sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) )
& ( aElementOf0(esk3_3(X57,X58,X62),X57)
| esk3_3(X57,X58,X62) = X58
| aElementOf0(esk3_3(X57,X58,X62),X62)
| ~ aSet0(X62)
| X62 = sdtpldt0(X57,X58)
| ~ aSet0(X57)
| ~ aElement0(X58) ) ),
inference(distribute,[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)],[mDefCons])])])])])]) ).
fof(i_0_19,plain,
! [X44,X45,X46,X47] :
( ( aSet0(X45)
| ~ aSubsetOf0(X45,X44)
| ~ aSet0(X44) )
& ( ~ aElementOf0(X46,X45)
| aElementOf0(X46,X44)
| ~ aSubsetOf0(X45,X44)
| ~ aSet0(X44) )
& ( aElementOf0(esk2_2(X44,X47),X47)
| ~ aSet0(X47)
| aSubsetOf0(X47,X44)
| ~ aSet0(X44) )
& ( ~ aElementOf0(esk2_2(X44,X47),X44)
| ~ aSet0(X47)
| aSubsetOf0(X47,X44)
| ~ aSet0(X44) ) ),
inference(distribute,[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(i_0_20,plain,
! [X54,X55,X56] :
( ~ aSet0(X54)
| ~ aSet0(X55)
| ~ aSet0(X56)
| ~ aSubsetOf0(X54,X55)
| ~ aSubsetOf0(X55,X56)
| aSubsetOf0(X54,X56) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubTrans])]) ).
fof(i_0_21,plain,
! [X71,X72] :
( ~ aSet0(X71)
| ~ aElementOf0(X72,X71)
| sdtpldt0(sdtmndt0(X71,X72),X72) = X71 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mConsDiff])])]) ).
fof(i_0_22,plain,
! [X52,X53] :
( ~ aSet0(X52)
| ~ aSet0(X53)
| ~ aSubsetOf0(X52,X53)
| ~ aSubsetOf0(X53,X52)
| X52 = X53 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubASymm])]) ).
fof(i_0_23,negated_conjecture,
sdtmndt0(sdtpldt0(xS,xx),xx) != xS,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(i_0_24,plain,
! [X49,X50] :
( ~ aSet0(X49)
| ~ isFinite0(X49)
| ~ aSubsetOf0(X50,X49)
| isFinite0(X50) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubFSet])])]) ).
fof(i_0_25,plain,
! [X36,X37] :
( ~ aSet0(X36)
| ~ aElementOf0(X37,X36)
| aElement0(X37) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(i_0_26,plain,
! [X38,X39,X40] :
( ( aSet0(X38)
| X38 != slcrc0 )
& ( ~ aElementOf0(X39,X38)
| X38 != slcrc0 )
& ( ~ aSet0(X40)
| aElementOf0(esk1_1(X40),X40)
| X40 = slcrc0 ) ),
inference(distribute,[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])])])])])]) ).
fof(i_0_27,plain,
! [X51] :
( ~ aSet0(X51)
| aSubsetOf0(X51,X51) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])]) ).
fof(i_0_28,plain,
! [X42] :
( ~ aSet0(X42)
| ~ isCountable0(X42)
| ~ isFinite0(X42) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_16])]) ).
fof(i_0_29,hypothesis,
~ aElementOf0(xx,xS),
inference(fof_simplification,[status(thm)],[m__679_02]) ).
fof(i_0_30,plain,
! [X43] :
( ~ aSet0(X43)
| ~ isCountable0(X43)
| X43 != slcrc0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCountNFin_01])]) ).
cnf(i_0_31,plain,
( esk4_3(X1,X2,X3) = X2
| X3 = sdtmndt0(X1,X2)
| ~ aElementOf0(esk4_3(X1,X2,X3),X3)
| ~ aElement0(esk4_3(X1,X2,X3))
| ~ aElementOf0(esk4_3(X1,X2,X3),X1)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_32,plain,
( X3 = sdtpldt0(X1,X2)
| ~ aElementOf0(esk3_3(X1,X2,X3),X1)
| ~ aElement0(esk3_3(X1,X2,X3))
| ~ aElementOf0(esk3_3(X1,X2,X3),X3)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_33,plain,
( X3 = sdtpldt0(X1,X2)
| esk3_3(X1,X2,X3) != X2
| ~ aElement0(esk3_3(X1,X2,X3))
| ~ aElementOf0(esk3_3(X1,X2,X3),X3)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_34,plain,
( aElementOf0(esk3_3(X1,X2,X3),X1)
| esk3_3(X1,X2,X3) = X2
| aElementOf0(esk3_3(X1,X2,X3),X3)
| X3 = sdtpldt0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_35,plain,
( aElementOf0(esk4_3(X1,X2,X3),X1)
| aElementOf0(esk4_3(X1,X2,X3),X3)
| X3 = sdtmndt0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_36,plain,
( aElement0(esk4_3(X1,X2,X3))
| aElementOf0(esk4_3(X1,X2,X3),X3)
| X3 = sdtmndt0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_37,plain,
( aElement0(esk3_3(X1,X2,X3))
| aElementOf0(esk3_3(X1,X2,X3),X3)
| X3 = sdtpldt0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_38,plain,
( aElementOf0(esk4_3(X1,X2,X3),X3)
| X3 = sdtmndt0(X1,X2)
| esk4_3(X1,X2,X3) != X2
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_39,plain,
( aSubsetOf0(X2,X1)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_40,plain,
( X1 = X3
| aElementOf0(X1,X4)
| ~ aElement0(X1)
| ~ aElementOf0(X1,X2)
| X4 != sdtmndt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_41,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aElement0(X1)
| X3 != sdtpldt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_42,plain,
( aSubsetOf0(X1,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_43,plain,
( aElementOf0(X1,X2)
| X1 = X3
| ~ aElementOf0(X1,X4)
| X4 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_44,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_45,plain,
( sdtpldt0(sdtmndt0(X1,X2),X2) = X1
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_46,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_47,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_48,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X2)
| X2 != sdtmndt0(X3,X4)
| ~ aSet0(X3)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_49,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X2)
| X2 != sdtpldt0(X3,X4)
| ~ aSet0(X3)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_50,plain,
( X1 != X2
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X4,X2)
| ~ aSet0(X4)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_51,plain,
( aElementOf0(X1,X3)
| X1 != X2
| ~ aElement0(X1)
| X3 != sdtpldt0(X4,X2)
| ~ aSet0(X4)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_52,plain,
( X1 = X2
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_53,negated_conjecture,
sdtmndt0(sdtpldt0(xS,xx),xx) != xS,
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_54,plain,
( aSet0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_55,plain,
( aSet0(X1)
| X1 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_56,plain,
( isFinite0(X2)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_57,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_58,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_59,plain,
( aElementOf0(esk1_1(X1),X1)
| X1 = slcrc0
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_60,plain,
( ~ aElementOf0(X1,X2)
| X2 != slcrc0 ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_61,plain,
( aSubsetOf0(X1,X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_62,plain,
( ~ aSet0(X1)
| ~ isCountable0(X1)
| ~ isFinite0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_63,hypothesis,
~ aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_64,plain,
( ~ aSet0(X1)
| ~ isCountable0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_65,plain,
( aSet0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_66,plain,
isFinite0(slcrc0),
inference(split_conjunct,[status(thm)],[mEmpFin]),
[final] ).
cnf(i_0_67,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__679]),
[final] ).
cnf(i_0_68,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__679]),
[final] ).
cnf(i_0_69,axiom,
X1 = X1 ).
cnf(i_0_70,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_71,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_72,axiom,
( X1 != X2
| esk4_3(X1,X3,X4) = esk4_3(X2,X3,X4) ) ).
cnf(i_0_73,axiom,
( X1 != X2
| esk4_3(X3,X1,X4) = esk4_3(X3,X2,X4) ) ).
cnf(i_0_74,axiom,
( X1 != X2
| esk4_3(X3,X4,X1) = esk4_3(X3,X4,X2) ) ).
cnf(i_0_75,axiom,
( X1 != X2
| sdtmndt0(X1,X3) = sdtmndt0(X2,X3) ) ).
cnf(i_0_76,axiom,
( X1 != X2
| sdtmndt0(X3,X1) = sdtmndt0(X3,X2) ) ).
cnf(i_0_77,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_78,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_79,axiom,
( X1 != X2
| esk3_3(X1,X3,X4) = esk3_3(X2,X3,X4) ) ).
cnf(i_0_80,axiom,
( X1 != X2
| esk3_3(X3,X1,X4) = esk3_3(X3,X2,X4) ) ).
cnf(i_0_81,axiom,
( X1 != X2
| esk3_3(X3,X4,X1) = esk3_3(X3,X4,X2) ) ).
cnf(i_0_82,axiom,
( X1 != X2
| ~ aElementOf0(X1,X3)
| aElementOf0(X2,X3) ) ).
cnf(i_0_83,axiom,
( X1 != X2
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X2) ) ).
cnf(i_0_84,axiom,
( X1 != X2
| ~ aElement0(X1)
| aElement0(X2) ) ).
cnf(i_0_85,axiom,
( X1 != X2
| ~ aSet0(X1)
| aSet0(X2) ) ).
cnf(i_0_86,axiom,
( X1 != X2
| ~ aSubsetOf0(X1,X3)
| aSubsetOf0(X2,X3) ) ).
cnf(i_0_87,axiom,
( X1 != X2
| ~ aSubsetOf0(X3,X1)
| aSubsetOf0(X3,X2) ) ).
cnf(i_0_88,axiom,
( X1 != X2
| ~ isFinite0(X1)
| isFinite0(X2) ) ).
cnf(i_0_89,axiom,
( X1 != X2
| ~ isCountable0(X1)
| isCountable0(X2) ) ).
cnf(i_0_15393,plain,
aSubsetOf0(sdtpldt0(slcrc0,xx),sdtpldt0(slcrc0,xx)),
inference(scs_inference,[],[i_0_15384,i_0_15183,i_0_87]) ).
cnf(i_0_15403,plain,
esk4_3(sdtmndt0(slcrc0,xx),slcrc0,sdtmndt0(slcrc0,xx)) = esk4_3(slcrc0,slcrc0,slcrc0),
inference(scs_inference,[],[i_0_15285,i_0_15144,i_0_71]) ).
cnf(i_0_15475,plain,
aSubsetOf0(sdtpldt0(xS,xx),sdtpldt0(xS,xx)),
inference(scs_inference,[],[i_0_15466,i_0_15462,i_0_15206,i_0_15148,i_0_15294,i_0_86,i_0_87,i_0_61]) ).
cnf(i_0_15478,plain,
aSubsetOf0(slcrc0,sdtpldt0(sdtmndt0(slcrc0,xx),xx)),
inference(scs_inference,[],[i_0_15466,i_0_15462,i_0_15147,i_0_15169,i_0_15206,i_0_15148,i_0_15294,i_0_98,i_0_100,i_0_86,i_0_87,i_0_61,i_0_88,i_0_46]) ).
cnf(i_0_15535,plain,
esk4_3(sdtmndt0(slcrc0,xx),slcrc0,sdtmndt0(slcrc0,xx)) = esk4_3(slcrc0,sdtmndt0(slcrc0,xx),slcrc0),
inference(scs_inference,[],[i_0_15508,i_0_15144,i_0_15288,i_0_82,i_0_71]) ).
cnf(i_0_15576,plain,
aSubsetOf0(sdtmndt0(sdtmndt0(slcrc0,xx),xx),sdtmndt0(xS,xx)),
inference(scs_inference,[],[i_0_15173,i_0_15157,i_0_15292,i_0_46]) ).
cnf(i_0_15620,plain,
aSet0(sdtmndt0(sdtpldt0(slcrc0,xx),xx)),
inference(equality_inference,[],[15616]) ).
cnf(i_0_15664,plain,
aSubsetOf0(sdtmndt0(sdtmndt0(slcrc0,xx),xx),sdtpldt0(xS,xx)),
inference(scs_inference,[],[i_0_15173,i_0_15157,i_0_15294,i_0_46]) ).
cnf(i_0_15784,plain,
aSet0(sdtpldt0(sdtpldt0(slcrc0,xx),xx)),
inference(equality_inference,[],[15777]) ).
cnf(i_0_15895,plain,
aSubsetOf0(slcrc0,sdtmndt0(sdtpldt0(slcrc0,xx),xx)),
inference(scs_inference,[],[i_0_15881,i_0_15164,i_0_86]) ).
cnf(i_0_15261,plain,
aSubsetOf0(slcrc0,sdtpldt0(sdtpldt0(slcrc0,xx),xx)),
inference(scs_inference,[],[i_0_15178,i_0_15179,i_0_15248,i_0_15164,i_0_71,i_0_86]) ).
cnf(i_0_15263,plain,
aSubsetOf0(sdtmndt0(sdtmndt0(slcrc0,xx),xx),sdtpldt0(sdtpldt0(slcrc0,xx),xx)),
inference(scs_inference,[],[i_0_15178,i_0_15259,i_0_15179,i_0_15248,i_0_15214,i_0_15157,i_0_15164,i_0_15209,i_0_15133,i_0_71,i_0_86,i_0_89,i_0_42]) ).
cnf(i_0_15325,plain,
aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(scs_inference,[],[i_0_15311,i_0_61]) ).
cnf(i_0_15329,plain,
sdtpldt0(sdtmndt0(slcrc0,xx),sdtmndt0(slcrc0,xx)) = sdtpldt0(slcrc0,slcrc0),
inference(scs_inference,[],[i_0_15311,i_0_15183,i_0_15184,i_0_61,i_0_57,i_0_71]) ).
cnf(i_0_15345,plain,
aSubsetOf0(sdtmndt0(slcrc0,xx),sdtmndt0(sdtmndt0(xS,xx),xx)),
inference(scs_inference,[],[i_0_15300,i_0_15152,i_0_15151,i_0_15137,i_0_15133,i_0_71,i_0_46]) ).
cnf(i_0_15349,plain,
aSubsetOf0(slcrc0,sdtmndt0(sdtmndt0(xS,xx),xx)),
inference(scs_inference,[],[i_0_15300,i_0_15182,i_0_15152,i_0_15151,i_0_15137,i_0_15164,i_0_15133,i_0_71,i_0_46,i_0_87,i_0_86]) ).
cnf(i_0_15412,plain,
aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(scs_inference,[],[i_0_15298,i_0_61]) ).
cnf(i_0_15449,plain,
aSubsetOf0(sdtmndt0(sdtmndt0(xS,xx),xx),sdtmndt0(sdtmndt0(xS,xx),xx)),
inference(scs_inference,[],[i_0_15441,i_0_15300,i_0_83,i_0_61]) ).
cnf(i_0_15457,plain,
~ aElementOf0(xx,sdtmndt0(xS,xx)),
inference(equality_inference,[],[15453]) ).
cnf(i_0_15483,plain,
esk4_3(slcrc0,sdtmndt0(slcrc0,xx),sdtmndt0(slcrc0,xx)) = esk4_3(slcrc0,slcrc0,slcrc0),
inference(scs_inference,[],[i_0_15441,i_0_15403,i_0_71]) ).
cnf(i_0_15551,plain,
~ aElementOf0(xx,sdtmndt0(xS,xx)),
inference(equality_inference,[],[15534]) ).
cnf(i_0_15556,plain,
aSubsetOf0(sdtmndt0(sdtpldt0(slcrc0,xx),xx),sdtmndt0(sdtpldt0(slcrc0,xx),xx)),
inference(equality_inference,[],[15552]) ).
cnf(i_0_15581,plain,
aSubsetOf0(sdtmndt0(slcrc0,xx),sdtmndt0(xS,xx)),
inference(scs_inference,[],[i_0_15173,i_0_15181,i_0_15157,i_0_15300,i_0_15292,i_0_46,i_0_64,i_0_86]) ).
cnf(i_0_15646,plain,
esk3_3(slcrc0,sdtmndt0(slcrc0,xx),sdtmndt0(slcrc0,xx)) = esk3_3(sdtmndt0(slcrc0,xx),slcrc0,slcrc0),
inference(scs_inference,[],[i_0_15313,i_0_15150,i_0_71]) ).
cnf(i_0_15648,plain,
esk3_3(X1,sdtmndt0(slcrc0,xx),sdtmndt0(slcrc0,xx)) = esk3_3(X1,slcrc0,slcrc0),
inference(rename_variables,[],[i_0_15313]) ).
cnf(i_0_15668,plain,
aSubsetOf0(sdtmndt0(slcrc0,xx),sdtpldt0(xS,xx)),
inference(scs_inference,[],[i_0_15173,i_0_15181,i_0_15298,i_0_15157,i_0_15294,i_0_46,i_0_85,i_0_86]) ).
cnf(i_0_15708,plain,
aSubsetOf0(slcrc0,sdtpldt0(sdtpldt0(xS,xx),xx)),
inference(scs_inference,[],[i_0_98,i_0_15309,i_0_100,i_0_46]) ).
cnf(i_0_15900,plain,
aSubsetOf0(sdtmndt0(slcrc0,xx),sdtmndt0(sdtpldt0(slcrc0,xx),xx)),
inference(equality_inference,[],[15896]) ).
cnf(i_0_15901,plain,
aSubsetOf0(sdtmndt0(sdtmndt0(slcrc0,xx),xx),sdtmndt0(sdtpldt0(slcrc0,xx),xx)),
inference(scs_inference,[],[i_0_15895,i_0_15153,i_0_86]) ).
cnf(i_0_15353,plain,
aSubsetOf0(sdtmndt0(sdtmndt0(slcrc0,xx),xx),sdtmndt0(sdtmndt0(xS,xx),xx)),
inference(scs_inference,[],[i_0_15349,i_0_15153,i_0_86]) ).
cnf(i_0_15355,plain,
aSubsetOf0(sdtpldt0(sdtpldt0(xS,xx),xx),sdtpldt0(sdtpldt0(xS,xx),xx)),
inference(scs_inference,[],[i_0_15342,i_0_15309,i_0_15349,i_0_15153,i_0_86,i_0_88,i_0_61]) ).
cnf(i_0_15408,plain,
aSubsetOf0(sdtmndt0(xS,xx),sdtmndt0(xS,xx)),
inference(equality_inference,[],[15405]) ).
cnf(i_0_15418,plain,
~ aElementOf0(xx,sdtmndt0(sdtmndt0(xS,xx),xx)),
inference(equality_inference,[],[15414]) ).
cnf(i_0_15461,plain,
~ aElementOf0(xx,sdtmndt0(sdtmndt0(xS,xx),xx)),
inference(equality_inference,[],[15458]) ).
cnf(c_0_80,plain,
( aSet0(X1)
| X1 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
i_0_55 ).
cnf(c_0_81,negated_conjecture,
sdtmndt0(sdtpldt0(xS,xx),xx) != xS,
i_0_53 ).
cnf(c_0_82,plain,
( aElementOf0(esk4_3(X1,X2,X3),X1)
| aElementOf0(esk4_3(X1,X2,X3),X3)
| X3 = sdtmndt0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
i_0_35 ).
cnf(c_0_83,hypothesis,
aElement0(xx),
i_0_67 ).
cnf(c_0_84,hypothesis,
aSet0(xS),
i_0_68 ).
cnf(c_0_85,plain,
( aSet0(sdtpldt0(X1,X2))
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(er,[status(thm)],[c_0_80]) ).
cnf(c_0_86,plain,
( aElementOf0(X1,X2)
| X1 = X3
| ~ aElementOf0(X1,X4)
| X4 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
i_0_43 ).
cnf(c_0_87,negated_conjecture,
( aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx))
| aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),xS)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])])]),c_0_84])]) ).
cnf(c_0_88,hypothesis,
( aSet0(sdtpldt0(X1,xx))
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_83]) ).
cnf(c_0_89,plain,
( X1 = X2
| aElementOf0(X1,X3)
| ~ aSet0(X3)
| ~ aElement0(X2)
| ~ aElementOf0(X1,sdtpldt0(X3,X2)) ),
inference(er,[status(thm)],[c_0_86]) ).
cnf(c_0_90,hypothesis,
( aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx))
| aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_84])]) ).
cnf(c_0_91,plain,
( aElementOf0(esk4_3(X1,X2,X3),X3)
| X3 = sdtmndt0(X1,X2)
| esk4_3(X1,X2,X3) != X2
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
i_0_38 ).
cnf(c_0_92,plain,
( esk4_3(sdtpldt0(xS,xx),xx,xS) = xx
| aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_84]),c_0_83])]) ).
cnf(c_0_93,hypothesis,
~ aElementOf0(xx,xS),
i_0_63 ).
cnf(c_0_94,plain,
( esk4_3(X1,X2,X3) = X2
| X3 = sdtmndt0(X1,X2)
| ~ aElementOf0(esk4_3(X1,X2,X3),X3)
| ~ aElement0(esk4_3(X1,X2,X3))
| ~ aElementOf0(esk4_3(X1,X2,X3),X1)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
i_0_31 ).
cnf(c_0_95,plain,
( aElement0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(X1,X2) ),
i_0_57 ).
cnf(c_0_96,plain,
( aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),xS)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_84]),c_0_83])]),c_0_81]),c_0_93]) ).
cnf(c_0_97,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| ~ aElement0(X1)
| X2 != sdtpldt0(X3,X4)
| ~ aSet0(X3)
| ~ aElement0(X4) ),
i_0_41 ).
cnf(c_0_98,plain,
( esk4_3(X1,X2,X3) = X2
| X3 = sdtmndt0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(esk4_3(X1,X2,X3),X3)
| ~ aElementOf0(esk4_3(X1,X2,X3),X1) ),
inference(csr,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_99,hypothesis,
aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_88]),c_0_84])]) ).
cnf(c_0_100,plain,
( aElementOf0(X1,sdtpldt0(X2,X3))
| ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,X2) ),
inference(er,[status(thm)],[inference(csr,[status(thm)],[c_0_97,c_0_95])]) ).
cnf(c_0_101,plain,
( esk4_3(sdtpldt0(xS,xx),xx,xS) = xx
| ~ aSet0(sdtpldt0(xS,xx))
| ~ aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_84]),c_0_83])]),c_0_81]) ).
cnf(c_0_102,plain,
( aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,X1))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_99]),c_0_84])]) ).
cnf(c_0_103,hypothesis,
( esk4_3(sdtpldt0(xS,xx),xx,xS) = xx
| ~ aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_88]),c_0_84])]) ).
cnf(c_0_104,hypothesis,
aElementOf0(esk4_3(sdtpldt0(xS,xx),xx,xS),sdtpldt0(xS,xx)),
inference(spm,[status(thm)],[c_0_102,c_0_83]) ).
cnf(c_0_105,hypothesis,
esk4_3(sdtpldt0(xS,xx),xx,xS) = xx,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104])]) ).
cnf(c_0_106,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_105]),c_0_93]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM536+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:43:35 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 146.74/90.58 % Version : CSE_E---1.7
% 146.74/90.58 % Problem : theBenchmark.p
% 146.74/90.58 % SZS status Theorem for theBenchmark.p
% 146.74/90.58 % SZS output start CNFRefutation
% See solution above
% 147.84/91.63 % Total time : 89.467s
%------------------------------------------------------------------------------