TSTP Solution File: NUM583+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM583+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n005.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 : Thu Aug 31 10:38:58 EDT 2023
% Result : Theorem 181.12s 181.13s
% Output : CNFRefutation 181.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 76
% Syntax : Number of formulae : 153 ( 23 unt; 55 typ; 0 def)
% Number of atoms : 472 ( 91 equ)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 627 ( 253 ~; 284 |; 63 &)
% ( 9 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 85 ( 44 >; 41 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 46 ( 46 usr; 11 con; 0-4 aty)
% Number of variables : 145 ( 0 sgn; 70 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aSet0: $i > $o ).
tff(decl_23,type,
aElement0: $i > $o ).
tff(decl_24,type,
aElementOf0: ( $i * $i ) > $o ).
tff(decl_25,type,
isFinite0: $i > $o ).
tff(decl_26,type,
slcrc0: $i ).
tff(decl_27,type,
isCountable0: $i > $o ).
tff(decl_28,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(decl_29,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_30,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(decl_31,type,
szNzAzT0: $i ).
tff(decl_32,type,
sz00: $i ).
tff(decl_33,type,
szszuzczcdt0: $i > $i ).
tff(decl_34,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(decl_35,type,
iLess0: ( $i * $i ) > $o ).
tff(decl_36,type,
sbrdtbr0: $i > $i ).
tff(decl_37,type,
szmzizndt0: $i > $i ).
tff(decl_38,type,
szmzazxdt0: $i > $i ).
tff(decl_39,type,
slbdtrb0: $i > $i ).
tff(decl_40,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(decl_41,type,
aFunction0: $i > $o ).
tff(decl_42,type,
szDzozmdt0: $i > $i ).
tff(decl_43,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(decl_44,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(decl_45,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(decl_46,type,
sdtexdt0: ( $i * $i ) > $i ).
tff(decl_47,type,
szDzizrdt0: $i > $i ).
tff(decl_48,type,
xT: $i ).
tff(decl_49,type,
xK: $i ).
tff(decl_50,type,
xS: $i ).
tff(decl_51,type,
xc: $i ).
tff(decl_52,type,
xk: $i ).
tff(decl_53,type,
xN: $i ).
tff(decl_54,type,
xi: $i ).
tff(decl_55,type,
xQ: $i ).
tff(decl_56,type,
esk1_1: $i > $i ).
tff(decl_57,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_59,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_60,type,
esk5_1: $i > $i ).
tff(decl_61,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_62,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_64,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_65,type,
esk10_1: $i > $i ).
tff(decl_66,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_67,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_69,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_70,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_74,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_75,type,
esk20_3: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
esk21_3: ( $i * $i * $i ) > $i ).
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/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(m__3989_02,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989_02) ).
fof(m__3533,hypothesis,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__3435,hypothesis,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(mSubTrans,axiom,
! [X1,X2,X3] :
( ( aSet0(X1)
& aSet0(X2)
& aSet0(X3) )
=> ( ( aSubsetOf0(X1,X2)
& aSubsetOf0(X2,X3) )
=> aSubsetOf0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).
fof(m__4037,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4037) ).
fof(mDefMin,axiom,
! [X1] :
( ( aSubsetOf0(X1,szNzAzT0)
& X1 != slcrc0 )
=> ! [X2] :
( X2 = szmzizndt0(X1)
<=> ( aElementOf0(X2,X1)
& ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMin) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
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/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
fof(mCountNFin_01,axiom,
! [X1] :
( ( aSet0(X1)
& isCountable0(X1) )
=> X1 != slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(m__3671,hypothesis,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).
fof(m__3754,hypothesis,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( sdtlseqdt0(X2,X1)
=> aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3754) ).
fof(m__3623,hypothesis,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
fof(mZeroLess,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(sz00,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
fof(m__3989,hypothesis,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(m__,conjecture,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_21,plain,
! [X112,X113,X114,X115,X116,X117] :
( ( aSet0(X114)
| X114 != slbdtsldtrb0(X112,X113)
| ~ aSet0(X112)
| ~ aElementOf0(X113,szNzAzT0) )
& ( aSubsetOf0(X115,X112)
| ~ aElementOf0(X115,X114)
| X114 != slbdtsldtrb0(X112,X113)
| ~ aSet0(X112)
| ~ aElementOf0(X113,szNzAzT0) )
& ( sbrdtbr0(X115) = X113
| ~ aElementOf0(X115,X114)
| X114 != slbdtsldtrb0(X112,X113)
| ~ aSet0(X112)
| ~ aElementOf0(X113,szNzAzT0) )
& ( ~ aSubsetOf0(X116,X112)
| sbrdtbr0(X116) != X113
| aElementOf0(X116,X114)
| X114 != slbdtsldtrb0(X112,X113)
| ~ aSet0(X112)
| ~ aElementOf0(X113,szNzAzT0) )
& ( ~ aElementOf0(esk11_3(X112,X113,X117),X117)
| ~ aSubsetOf0(esk11_3(X112,X113,X117),X112)
| sbrdtbr0(esk11_3(X112,X113,X117)) != X113
| ~ aSet0(X117)
| X117 = slbdtsldtrb0(X112,X113)
| ~ aSet0(X112)
| ~ aElementOf0(X113,szNzAzT0) )
& ( aSubsetOf0(esk11_3(X112,X113,X117),X112)
| aElementOf0(esk11_3(X112,X113,X117),X117)
| ~ aSet0(X117)
| X117 = slbdtsldtrb0(X112,X113)
| ~ aSet0(X112)
| ~ aElementOf0(X113,szNzAzT0) )
& ( sbrdtbr0(esk11_3(X112,X113,X117)) = X113
| aElementOf0(esk11_3(X112,X113,X117),X117)
| ~ aSet0(X117)
| X117 = slbdtsldtrb0(X112,X113)
| ~ aSet0(X112)
| ~ aElementOf0(X113,szNzAzT0) ) ),
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)],[mDefSel])])])])])]) ).
cnf(c_0_22,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aSet0(X2)
| ~ aElementOf0(X4,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_23,plain,
! [X15,X16,X17,X18] :
( ( aSet0(X16)
| ~ aSubsetOf0(X16,X15)
| ~ aSet0(X15) )
& ( ~ aElementOf0(X17,X16)
| aElementOf0(X17,X15)
| ~ aSubsetOf0(X16,X15)
| ~ aSet0(X15) )
& ( aElementOf0(esk2_2(X15,X18),X18)
| ~ aSet0(X18)
| aSubsetOf0(X18,X15)
| ~ aSet0(X15) )
& ( ~ aElementOf0(esk2_2(X15,X18),X15)
| ~ aSet0(X18)
| aSubsetOf0(X18,X15)
| ~ aSet0(X15) ) ),
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])])])])])]) ).
cnf(c_0_24,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| ~ aElementOf0(X3,szNzAzT0)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_25,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),
inference(split_conjunct,[status(thm)],[m__3989_02]) ).
cnf(c_0_26,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3533]) ).
fof(c_0_27,plain,
! [X35,X36,X37,X38,X39,X40] :
( ( aSet0(X37)
| X37 != sdtmndt0(X35,X36)
| ~ aSet0(X35)
| ~ aElement0(X36) )
& ( aElement0(X38)
| ~ aElementOf0(X38,X37)
| X37 != sdtmndt0(X35,X36)
| ~ aSet0(X35)
| ~ aElement0(X36) )
& ( aElementOf0(X38,X35)
| ~ aElementOf0(X38,X37)
| X37 != sdtmndt0(X35,X36)
| ~ aSet0(X35)
| ~ aElement0(X36) )
& ( X38 != X36
| ~ aElementOf0(X38,X37)
| X37 != sdtmndt0(X35,X36)
| ~ aSet0(X35)
| ~ aElement0(X36) )
& ( ~ aElement0(X39)
| ~ aElementOf0(X39,X35)
| X39 = X36
| aElementOf0(X39,X37)
| X37 != sdtmndt0(X35,X36)
| ~ aSet0(X35)
| ~ aElement0(X36) )
& ( ~ aElementOf0(esk4_3(X35,X36,X40),X40)
| ~ aElement0(esk4_3(X35,X36,X40))
| ~ aElementOf0(esk4_3(X35,X36,X40),X35)
| esk4_3(X35,X36,X40) = X36
| ~ aSet0(X40)
| X40 = sdtmndt0(X35,X36)
| ~ aSet0(X35)
| ~ aElement0(X36) )
& ( aElement0(esk4_3(X35,X36,X40))
| aElementOf0(esk4_3(X35,X36,X40),X40)
| ~ aSet0(X40)
| X40 = sdtmndt0(X35,X36)
| ~ aSet0(X35)
| ~ aElement0(X36) )
& ( aElementOf0(esk4_3(X35,X36,X40),X35)
| aElementOf0(esk4_3(X35,X36,X40),X40)
| ~ aSet0(X40)
| X40 = sdtmndt0(X35,X36)
| ~ aSet0(X35)
| ~ aElement0(X36) )
& ( esk4_3(X35,X36,X40) != X36
| aElementOf0(esk4_3(X35,X36,X40),X40)
| ~ aSet0(X40)
| X40 = sdtmndt0(X35,X36)
| ~ aSet0(X35)
| ~ aElement0(X36) ) ),
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])])])])])]) ).
cnf(c_0_28,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_30,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
fof(c_0_31,plain,
! [X25,X26,X27] :
( ~ aSet0(X25)
| ~ aSet0(X26)
| ~ aSet0(X27)
| ~ aSubsetOf0(X25,X26)
| ~ aSubsetOf0(X26,X27)
| aSubsetOf0(X25,X27) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubTrans])]) ).
cnf(c_0_32,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,hypothesis,
( aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_34,plain,
( aSet0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(split_conjunct,[status(thm)],[m__4037]) ).
cnf(c_0_36,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
fof(c_0_37,plain,
! [X86,X87,X88,X89] :
( ( aElementOf0(X87,X86)
| X87 != szmzizndt0(X86)
| ~ aSubsetOf0(X86,szNzAzT0)
| X86 = slcrc0 )
& ( ~ aElementOf0(X88,X86)
| sdtlseqdt0(X87,X88)
| X87 != szmzizndt0(X86)
| ~ aSubsetOf0(X86,szNzAzT0)
| X86 = slcrc0 )
& ( aElementOf0(esk7_2(X86,X89),X86)
| ~ aElementOf0(X89,X86)
| X89 = szmzizndt0(X86)
| ~ aSubsetOf0(X86,szNzAzT0)
| X86 = slcrc0 )
& ( ~ sdtlseqdt0(X89,esk7_2(X86,X89))
| ~ aElementOf0(X89,X86)
| X89 = szmzizndt0(X86)
| ~ aSubsetOf0(X86,szNzAzT0)
| X86 = 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)],[mDefMin])])])])])]) ).
cnf(c_0_38,plain,
( aSubsetOf0(X1,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_40,hypothesis,
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X1,xQ)
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
( aSet0(sdtmndt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_42,hypothesis,
aSet0(sdtlpdtrp0(xN,xi)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_35]),c_0_36])]) ).
fof(c_0_43,plain,
! [X7,X8] :
( ~ aSet0(X7)
| ~ aElementOf0(X8,X7)
| aElement0(X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_44,plain,
( aElementOf0(X1,X2)
| X2 = slcrc0
| X1 != szmzizndt0(X2)
| ~ aSubsetOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
( aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X3,X2)
| ~ aSubsetOf0(X1,X3)
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_38,c_0_28]),c_0_28]) ).
fof(c_0_46,plain,
! [X9,X10,X11] :
( ( aSet0(X9)
| X9 != slcrc0 )
& ( ~ aElementOf0(X10,X9)
| X9 != slcrc0 )
& ( ~ aSet0(X11)
| aElementOf0(esk1_1(X11),X11)
| X11 = 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])])])])])]) ).
cnf(c_0_47,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_48,hypothesis,
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X1,xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_49,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,plain,
( X1 = slcrc0
| aElementOf0(szmzizndt0(X1),X1)
| ~ aSubsetOf0(X1,szNzAzT0) ),
inference(er,[status(thm)],[c_0_44]) ).
cnf(c_0_51,hypothesis,
( aSubsetOf0(X1,szNzAzT0)
| ~ aSubsetOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_29]),c_0_30])]) ).
fof(c_0_52,plain,
! [X28,X29,X30,X31,X32,X33] :
( ( aSet0(X30)
| X30 != sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( aElement0(X31)
| ~ aElementOf0(X31,X30)
| X30 != sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( aElementOf0(X31,X28)
| X31 = X29
| ~ aElementOf0(X31,X30)
| X30 != sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( ~ aElementOf0(X32,X28)
| ~ aElement0(X32)
| aElementOf0(X32,X30)
| X30 != sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( X32 != X29
| ~ aElement0(X32)
| aElementOf0(X32,X30)
| X30 != sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( ~ aElementOf0(esk3_3(X28,X29,X33),X28)
| ~ aElement0(esk3_3(X28,X29,X33))
| ~ aElementOf0(esk3_3(X28,X29,X33),X33)
| ~ aSet0(X33)
| X33 = sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( esk3_3(X28,X29,X33) != X29
| ~ aElement0(esk3_3(X28,X29,X33))
| ~ aElementOf0(esk3_3(X28,X29,X33),X33)
| ~ aSet0(X33)
| X33 = sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( aElement0(esk3_3(X28,X29,X33))
| aElementOf0(esk3_3(X28,X29,X33),X33)
| ~ aSet0(X33)
| X33 = sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) )
& ( aElementOf0(esk3_3(X28,X29,X33),X28)
| esk3_3(X28,X29,X33) = X29
| aElementOf0(esk3_3(X28,X29,X33),X33)
| ~ aSet0(X33)
| X33 = sdtpldt0(X28,X29)
| ~ aSet0(X28)
| ~ aElement0(X29) ) ),
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])])])])])]) ).
cnf(c_0_53,hypothesis,
( aSet0(xQ)
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(spm,[status(thm)],[c_0_28,c_0_33]) ).
fof(c_0_54,plain,
! [X14] :
( ~ aSet0(X14)
| ~ isCountable0(X14)
| X14 != slcrc0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCountNFin_01])]) ).
cnf(c_0_55,plain,
( aSet0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,hypothesis,
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X1,xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_42])]) ).
cnf(c_0_57,plain,
( X1 = slcrc0
| aElement0(szmzizndt0(X1))
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aSet0(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0),
inference(spm,[status(thm)],[c_0_51,c_0_35]) ).
cnf(c_0_59,plain,
( aElementOf0(X1,X2)
| X1 = X3
| ~ aElementOf0(X1,X4)
| X4 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_60,plain,
( aSet0(X1)
| X1 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_61,hypothesis,
! [X175] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X175),szNzAzT0)
| ~ aElementOf0(X175,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,X175))
| ~ aElementOf0(X175,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3671])])]) ).
cnf(c_0_62,hypothesis,
( aSet0(xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_41]),c_0_42])]) ).
cnf(c_0_63,plain,
( ~ aSet0(X1)
| ~ isCountable0(X1)
| X1 != slcrc0 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_64,plain,
aSet0(slcrc0),
inference(er,[status(thm)],[c_0_55]) ).
fof(c_0_65,hypothesis,
! [X176,X177] :
( ~ aElementOf0(X176,szNzAzT0)
| ~ aElementOf0(X177,szNzAzT0)
| ~ sdtlseqdt0(X177,X176)
| aSubsetOf0(sdtlpdtrp0(xN,X176),sdtlpdtrp0(xN,X177)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3754])]) ).
fof(c_0_66,hypothesis,
! [X174] :
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X174)),sdtmndt0(sdtlpdtrp0(xN,X174),szmzizndt0(sdtlpdtrp0(xN,X174))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X174),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X174))
| ~ aElementOf0(X174,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X174)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X174),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X174))
| ~ aElementOf0(X174,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3623])])])]) ).
fof(c_0_67,plain,
! [X60] :
( ~ aElementOf0(X60,szNzAzT0)
| sdtlseqdt0(sz00,X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])]) ).
cnf(c_0_68,plain,
( aSubsetOf0(X2,X1)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_69,hypothesis,
( sdtlpdtrp0(xN,xi) = slcrc0
| aElementOf0(X1,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X1,xQ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_42])]) ).
cnf(c_0_70,plain,
( X1 = X2
| aElementOf0(X1,X3)
| ~ aElementOf0(X1,sdtpldt0(X3,X2))
| ~ aElement0(X2)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_59]) ).
cnf(c_0_71,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_72,plain,
( aSet0(sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_60]) ).
cnf(c_0_73,hypothesis,
( isCountable0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_74,hypothesis,
( sdtlpdtrp0(xN,xi) = slcrc0
| aSet0(xQ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_57]),c_0_58]),c_0_42])]) ).
cnf(c_0_75,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3989]) ).
cnf(c_0_76,plain,
~ isCountable0(slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_63]),c_0_64])]) ).
cnf(c_0_77,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_78,hypothesis,
sdtlpdtrp0(xN,sz00) = xS,
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_79,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_80,plain,
( sdtlseqdt0(sz00,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_81,hypothesis,
( sdtlpdtrp0(xN,xi) = slcrc0
| aSubsetOf0(X1,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(esk2_2(sdtlpdtrp0(xN,xi),X1),xQ)
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_42])]) ).
cnf(c_0_82,plain,
( esk2_2(X1,sdtpldt0(X2,X3)) = X3
| aSubsetOf0(sdtpldt0(X2,X3),X1)
| aElementOf0(esk2_2(X1,sdtpldt0(X2,X3)),X2)
| ~ aElement0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_83,hypothesis,
aSet0(xQ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]),c_0_76]) ).
cnf(c_0_84,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,X1),xS)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79])]),c_0_80]) ).
cnf(c_0_85,hypothesis,
( esk2_2(sdtlpdtrp0(xN,xi),sdtpldt0(xQ,X1)) = X1
| sdtlpdtrp0(xN,xi) = slcrc0
| aSubsetOf0(sdtpldt0(xQ,X1),sdtlpdtrp0(xN,xi))
| ~ aElement0(X1)
| ~ aSet0(sdtpldt0(xQ,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]),c_0_42])]) ).
cnf(c_0_86,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_35]),c_0_36])]) ).
fof(c_0_87,negated_conjecture,
~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_88,hypothesis,
( aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X1,sdtlpdtrp0(xN,X2))
| ~ aElementOf0(X2,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_84]),c_0_36])]) ).
cnf(c_0_89,hypothesis,
( sdtlpdtrp0(xN,xi) = slcrc0
| aSubsetOf0(sdtpldt0(xQ,X1),sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| ~ aElement0(X1)
| ~ aSet0(sdtpldt0(xQ,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_85]),c_0_42])]) ).
cnf(c_0_90,hypothesis,
( sdtlpdtrp0(xN,xi) = slcrc0
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_50]),c_0_58])]) ).
cnf(c_0_91,negated_conjecture,
~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_92,hypothesis,
( sdtlpdtrp0(xN,xi) = slcrc0
| aSubsetOf0(sdtpldt0(xQ,X1),xS)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| ~ aElement0(X1)
| ~ aSet0(sdtpldt0(xQ,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_75])]) ).
cnf(c_0_93,hypothesis,
( sdtlpdtrp0(xN,xi) = slcrc0
| aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_90]),c_0_36])]) ).
cnf(c_0_94,negated_conjecture,
( sdtlpdtrp0(xN,xi) = slcrc0
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]) ).
cnf(c_0_95,negated_conjecture,
( sdtlpdtrp0(xN,xi) = slcrc0
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_72]),c_0_83])]),c_0_93]) ).
cnf(c_0_96,negated_conjecture,
sdtlpdtrp0(xN,xi) = slcrc0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_50]),c_0_58])]) ).
cnf(c_0_97,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_96]),c_0_75])]),c_0_76]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM583+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 15:10:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 181.12/181.13 % Version : CSE_E---1.5
% 181.12/181.13 % Problem : theBenchmark.p
% 181.12/181.13 % Proof found
% 181.12/181.13 % SZS status Theorem for theBenchmark.p
% 181.12/181.13 % SZS output start Proof
% See solution above
% 181.12/181.14 % Total time : 180.561000 s
% 181.12/181.14 % SZS output end Proof
% 181.12/181.14 % Total time : 180.574000 s
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