%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM631+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 01:49:50 PM UTC 2026
% Result : Theorem 81.23s 17.43s
% Output : CNFRefutation 81.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 25
% Syntax : Number of formulae : 102 ( 39 unt; 0 def)
% Number of atoms : 432 ( 100 equ)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 548 ( 218 ~; 231 |; 72 &)
% ( 9 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 17 con; 0-3 aty)
% Number of variables : 123 ( 0 sgn 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__5093,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
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/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(m__4660,hypothesis,
( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1)) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__4891,hypothesis,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
fof(mDefCons,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtpldt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( ( X4 = X2
| aElementOf0(X4,X1) )
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefCons) ).
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(m__5164,hypothesis,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& aSet0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(m__5147,hypothesis,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(m__3623,hypothesis,
( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(m__3671,hypothesis,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(m__5585,hypothesis,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5585) ).
fof(m__5309,hypothesis,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
fof(m__5173,hypothesis,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).
fof(mDefSel,axiom,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aSet0(X1) )
=> ! [X3] :
( X3 = slbdtsldtrb0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( sbrdtbr0(X4) = X2
& aSubsetOf0(X4,X1) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(m__5195,hypothesis,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5195) ).
fof(mSubTrans,axiom,
! [X1,X2,X3] :
( ( aSet0(X3)
& aSet0(X2)
& aSet0(X1) )
=> ( ( aSubsetOf0(X2,X3)
& aSubsetOf0(X1,X2) )
=> aSubsetOf0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
fof(m__,conjecture,
sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(xd,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__4730,hypothesis,
( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk))
& aSet0(X2) )
=> sdtlpdtrp0(xd,X1) = sdtlpdtrp0(sdtlpdtrp0(xC,X1),X2) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4730) ).
fof(m__5217,hypothesis,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5217) ).
fof(m__3533,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
fof(m__5334,hypothesis,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5334) ).
fof(m__5632,hypothesis,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5632) ).
fof(c_0_25,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
inference(fof_simplification,[status(thm)],[m__5093]) ).
fof(c_0_26,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]) ).
fof(c_0_27,plain,
! [X52,X53,X54,X55] :
( ( ~ aSet0(X52)
| aSubsetOf0(X55,X52)
| ~ aSet0(X55)
| ~ aElementOf0(esk8_2(X52,X55),X52) )
& ( ~ aSet0(X52)
| aSubsetOf0(X55,X52)
| ~ aSet0(X55)
| aElementOf0(esk8_2(X52,X55),X55) )
& ( ~ aSet0(X52)
| ~ aSubsetOf0(X53,X52)
| aElementOf0(X54,X52)
| ~ aElementOf0(X54,X53) )
& ( ~ aSet0(X52)
| ~ aSubsetOf0(X53,X52)
| aSet0(X53) ) ),
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_28,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
inference(fof_nnf,[status(thm)],[c_0_25]) ).
fof(c_0_29,plain,
! [X110,X111,X112,X113,X114,X115] :
( ( ~ aElement0(X111)
| ~ aSet0(X110)
| X115 = sdtmndt0(X110,X111)
| ~ aSet0(X115)
| aElementOf0(esk15_3(X110,X111,X115),X115)
| esk15_3(X110,X111,X115) != X111 )
& ( ~ aElement0(X111)
| ~ aSet0(X110)
| X115 = sdtmndt0(X110,X111)
| ~ aSet0(X115)
| aElementOf0(esk15_3(X110,X111,X115),X115)
| aElementOf0(esk15_3(X110,X111,X115),X110) )
& ( ~ aElement0(X111)
| ~ aSet0(X110)
| X115 = sdtmndt0(X110,X111)
| ~ aSet0(X115)
| aElementOf0(esk15_3(X110,X111,X115),X115)
| aElement0(esk15_3(X110,X111,X115)) )
& ( ~ aElement0(X111)
| ~ aSet0(X110)
| X115 = sdtmndt0(X110,X111)
| ~ aSet0(X115)
| esk15_3(X110,X111,X115) = X111
| ~ aElementOf0(esk15_3(X110,X111,X115),X110)
| ~ aElement0(esk15_3(X110,X111,X115))
| ~ aElementOf0(esk15_3(X110,X111,X115),X115) )
& ( ~ aElement0(X111)
| ~ aSet0(X110)
| X112 != sdtmndt0(X110,X111)
| aElementOf0(X114,X112)
| X114 = X111
| ~ aElementOf0(X114,X110)
| ~ aElement0(X114) )
& ( ~ aElement0(X111)
| ~ aSet0(X110)
| X112 != sdtmndt0(X110,X111)
| ~ aElementOf0(X113,X112)
| X113 != X111 )
& ( ~ aElement0(X111)
| ~ aSet0(X110)
| X112 != sdtmndt0(X110,X111)
| ~ aElementOf0(X113,X112)
| aElementOf0(X113,X110) )
& ( ~ aElement0(X111)
| ~ aSet0(X110)
| X112 != sdtmndt0(X110,X111)
| ~ aElementOf0(X113,X112)
| aElement0(X113) )
& ( ~ aElement0(X111)
| ~ aSet0(X110)
| X112 != sdtmndt0(X110,X111)
| aSet0(X112) ) ),
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_26])])])])])])]) ).
fof(c_0_30,hypothesis,
! [X34] :
( ( sdtlpdtrp0(xe,X34) = szmzizndt0(sdtlpdtrp0(xN,X34))
| ~ aElementOf0(X34,szNzAzT0) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4660])])])]) ).
fof(c_0_31,plain,
! [X183,X184] :
( aElement0(X184)
| ~ aElementOf0(X184,X183)
| ~ aSet0(X183) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_32,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,hypothesis,
aSubsetOf0(xQ,xO),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,hypothesis,
aSet0(xO),
inference(split_conjunct,[status(thm)],[m__4891]) ).
fof(c_0_35,plain,
! [X138,X139,X140,X141,X142,X143] :
( ( ~ aElement0(X139)
| ~ aSet0(X138)
| X143 = sdtpldt0(X138,X139)
| ~ aSet0(X143)
| aElementOf0(esk17_3(X138,X139,X143),X143)
| esk17_3(X138,X139,X143) = X139
| aElementOf0(esk17_3(X138,X139,X143),X138) )
& ( ~ aElement0(X139)
| ~ aSet0(X138)
| X143 = sdtpldt0(X138,X139)
| ~ aSet0(X143)
| aElementOf0(esk17_3(X138,X139,X143),X143)
| aElement0(esk17_3(X138,X139,X143)) )
& ( ~ aElement0(X139)
| ~ aSet0(X138)
| X143 = sdtpldt0(X138,X139)
| ~ aSet0(X143)
| ~ aElementOf0(esk17_3(X138,X139,X143),X143)
| ~ aElement0(esk17_3(X138,X139,X143))
| esk17_3(X138,X139,X143) != X139 )
& ( ~ aElement0(X139)
| ~ aSet0(X138)
| X143 = sdtpldt0(X138,X139)
| ~ aSet0(X143)
| ~ aElementOf0(esk17_3(X138,X139,X143),X143)
| ~ aElement0(esk17_3(X138,X139,X143))
| ~ aElementOf0(esk17_3(X138,X139,X143),X138) )
& ( ~ aElement0(X139)
| ~ aSet0(X138)
| X140 != sdtpldt0(X138,X139)
| aElementOf0(X142,X140)
| ~ aElement0(X142)
| X142 != X139 )
& ( ~ aElement0(X139)
| ~ aSet0(X138)
| X140 != sdtpldt0(X138,X139)
| aElementOf0(X142,X140)
| ~ aElement0(X142)
| ~ aElementOf0(X142,X138) )
& ( ~ aElement0(X139)
| ~ aSet0(X138)
| X140 != sdtpldt0(X138,X139)
| ~ aElementOf0(X141,X140)
| X141 = X139
| aElementOf0(X141,X138) )
& ( ~ aElement0(X139)
| ~ aSet0(X138)
| X140 != sdtpldt0(X138,X139)
| ~ aElementOf0(X141,X140)
| aElement0(X141) )
& ( ~ aElement0(X139)
| ~ aSet0(X138)
| X140 != sdtpldt0(X138,X139)
| aSet0(X140) ) ),
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)],[mDefCons])])])])])])]) ).
fof(c_0_36,plain,
! [X117,X118] :
( sdtpldt0(sdtmndt0(X117,X118),X118) = X117
| ~ aElementOf0(X118,X117)
| ~ aSet0(X117) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mConsDiff])])])]) ).
cnf(c_0_37,hypothesis,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(split_conjunct,[status(thm)],[m__5164]) ).
cnf(c_0_38,hypothesis,
xp = szmzizndt0(xQ),
inference(split_conjunct,[status(thm)],[m__5147]) ).
fof(c_0_39,hypothesis,
! [X13] :
( ( ~ aElementOf0(X13,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X13))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X13),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X13))) )
& ( ~ aElementOf0(X13,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X13))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X13),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X13)),sdtmndt0(sdtlpdtrp0(xN,X13),szmzizndt0(sdtlpdtrp0(xN,X13)))) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3623])])])])]) ).
fof(c_0_40,hypothesis,
! [X14] :
( ( ~ aElementOf0(X14,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X14)) )
& ( ~ aElementOf0(X14,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X14),szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3671])])])]) ).
cnf(c_0_41,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X1 != sdtmndt0(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_42,hypothesis,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(split_conjunct,[status(thm)],[m__5585]) ).
cnf(c_0_43,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_44,hypothesis,
sdtlpdtrp0(xe,xn) = xp,
inference(split_conjunct,[status(thm)],[m__5309]) ).
cnf(c_0_45,hypothesis,
aElementOf0(xn,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5309]) ).
cnf(c_0_46,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_47,hypothesis,
aElementOf0(xp,xQ),
inference(split_conjunct,[status(thm)],[m__5173]) ).
cnf(c_0_48,hypothesis,
aSet0(xQ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_49,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X4 != sdtpldt0(X2,X3)
| ~ aElementOf0(X1,X4)
| X1 = X3
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_50,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| sdtpldt0(sdtmndt0(X1,X2),X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_51,hypothesis,
sdtmndt0(xQ,xp) = xP,
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_52,plain,
! [X175,X176,X177,X178,X179,X180] :
( ( ~ aElementOf0(X176,szNzAzT0)
| ~ aSet0(X175)
| X180 = slbdtsldtrb0(X175,X176)
| ~ aSet0(X180)
| aElementOf0(esk21_3(X175,X176,X180),X180)
| sbrdtbr0(esk21_3(X175,X176,X180)) = X176 )
& ( ~ aElementOf0(X176,szNzAzT0)
| ~ aSet0(X175)
| X180 = slbdtsldtrb0(X175,X176)
| ~ aSet0(X180)
| aElementOf0(esk21_3(X175,X176,X180),X180)
| aSubsetOf0(esk21_3(X175,X176,X180),X175) )
& ( ~ aElementOf0(X176,szNzAzT0)
| ~ aSet0(X175)
| X180 = slbdtsldtrb0(X175,X176)
| ~ aSet0(X180)
| sbrdtbr0(esk21_3(X175,X176,X180)) != X176
| ~ aSubsetOf0(esk21_3(X175,X176,X180),X175)
| ~ aElementOf0(esk21_3(X175,X176,X180),X180) )
& ( ~ aElementOf0(X176,szNzAzT0)
| ~ aSet0(X175)
| X177 != slbdtsldtrb0(X175,X176)
| aElementOf0(X179,X177)
| sbrdtbr0(X179) != X176
| ~ aSubsetOf0(X179,X175) )
& ( ~ aElementOf0(X176,szNzAzT0)
| ~ aSet0(X175)
| X177 != slbdtsldtrb0(X175,X176)
| ~ aElementOf0(X178,X177)
| sbrdtbr0(X178) = X176 )
& ( ~ aElementOf0(X176,szNzAzT0)
| ~ aSet0(X175)
| X177 != slbdtsldtrb0(X175,X176)
| ~ aElementOf0(X178,X177)
| aSubsetOf0(X178,X175) )
& ( ~ aElementOf0(X176,szNzAzT0)
| ~ aSet0(X175)
| X177 != slbdtsldtrb0(X175,X176)
| aSet0(X177) ) ),
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)],[mDefSel])])])])])])]) ).
cnf(c_0_53,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X1))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_54,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_55,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_56,plain,
( ~ aSet0(X1)
| ~ aElement0(X2)
| aSet0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_57,hypothesis,
sdtmndt0(sdtlpdtrp0(xN,xn),xp) = xD,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]) ).
cnf(c_0_58,hypothesis,
aElement0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
cnf(c_0_59,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_60,plain,
( ~ aSet0(X3)
| ~ aElement0(X2)
| ~ aElementOf0(X1,sdtpldt0(X3,X2))
| aElementOf0(X1,X3)
| X1 = X2 ),
inference(er,[status(thm)],[c_0_49]) ).
cnf(c_0_61,hypothesis,
sdtpldt0(xP,xp) = xQ,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_47]),c_0_48])]) ).
cnf(c_0_62,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[m__5164]) ).
cnf(c_0_63,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_64,hypothesis,
aSubsetOf0(xP,xQ),
inference(split_conjunct,[status(thm)],[m__5195]) ).
cnf(c_0_65,plain,
( ~ aElementOf0(X3,szNzAzT0)
| ~ aSet0(X2)
| X4 != slbdtsldtrb0(X2,X3)
| sbrdtbr0(X1) != X3
| ~ aSubsetOf0(X1,X2)
| aElementOf0(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_66,plain,
! [X60,X61,X62] :
( aSubsetOf0(X60,X62)
| ~ aSubsetOf0(X61,X62)
| ~ aSubsetOf0(X60,X61)
| ~ aSet0(X62)
| ~ aSet0(X61)
| ~ aSet0(X60) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubTrans])])]) ).
cnf(c_0_67,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_68,hypothesis,
( ~ aSet0(sdtlpdtrp0(xN,xn))
| aSet0(xD) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58])]) ).
cnf(c_0_69,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_55]),c_0_59])]) ).
cnf(c_0_70,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(esk8_2(X1,X2),X1)
| aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_71,hypothesis,
( ~ aElementOf0(X1,xQ)
| aElementOf0(X1,xP)
| X1 = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_58]),c_0_62])]) ).
cnf(c_0_72,hypothesis,
( ~ aElementOf0(X1,xP)
| aElementOf0(X1,xQ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_48])]) ).
cnf(c_0_73,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSubsetOf0(X2,X1)
| aElementOf0(esk8_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_74,plain,
( ~ aElement0(X2)
| ~ aSet0(X4)
| X3 != sdtmndt0(X4,X2)
| ~ aElementOf0(X1,X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_75,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_76,hypothesis,
! [X35,X36] :
( ( sdtlpdtrp0(xd,X35) = sdtlpdtrp0(sdtlpdtrp0(xC,X35),X36)
| ~ aElementOf0(X36,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X35)),xk))
| ~ aSet0(X36)
| ~ aElementOf0(X35,szNzAzT0) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4730])])])]) ).
cnf(c_0_77,plain,
( ~ aSet0(X2)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSubsetOf0(X1,X2)
| aElementOf0(X1,slbdtsldtrb0(X2,sbrdtbr0(X1))) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_65])]) ).
cnf(c_0_78,hypothesis,
sbrdtbr0(xP) = xk,
inference(split_conjunct,[status(thm)],[m__5217]) ).
cnf(c_0_79,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3533]) ).
cnf(c_0_80,plain,
( ~ aSubsetOf0(X2,X3)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aSubsetOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_81,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_42]),c_0_45])]) ).
cnf(c_0_82,hypothesis,
aSet0(xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_45])]) ).
cnf(c_0_83,hypothesis,
( ~ aSet0(X1)
| ~ aElementOf0(esk8_2(xP,X1),xQ)
| aSubsetOf0(X1,xP)
| esk8_2(xP,X1) = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_62])]) ).
cnf(c_0_84,hypothesis,
( ~ aSet0(X1)
| aElementOf0(esk8_2(X1,xP),xQ)
| aSubsetOf0(xP,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_62])]) ).
cnf(c_0_85,plain,
( ~ aSet0(X2)
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtmndt0(X2,X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_74])]) ).
fof(c_0_86,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
cnf(c_0_87,hypothesis,
( ~ aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk))
| ~ aSet0(X2)
| ~ aElementOf0(X1,szNzAzT0)
| sdtlpdtrp0(xd,X1) = sdtlpdtrp0(sdtlpdtrp0(xC,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_88,hypothesis,
( ~ aSet0(X1)
| ~ aSubsetOf0(xP,X1)
| aElementOf0(xP,slbdtsldtrb0(X1,xk)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79])]) ).
cnf(c_0_89,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X3)
| ~ aSubsetOf0(X3,X2)
| aSubsetOf0(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_80,c_0_32]),c_0_32]) ).
cnf(c_0_90,hypothesis,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(split_conjunct,[status(thm)],[m__5334]) ).
cnf(c_0_91,hypothesis,
aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_81]),c_0_82])]) ).
cnf(c_0_92,hypothesis,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(split_conjunct,[status(thm)],[m__5632]) ).
cnf(c_0_93,hypothesis,
( aSubsetOf0(xP,xP)
| esk8_2(xP,xP) = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_62])]) ).
cnf(c_0_94,hypothesis,
~ aElementOf0(xp,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_51]),c_0_58]),c_0_48])]) ).
fof(c_0_95,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(fof_nnf,[status(thm)],[c_0_86]) ).
cnf(c_0_96,hypothesis,
( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| sdtlpdtrp0(sdtlpdtrp0(xC,X1),xP) = sdtlpdtrp0(xd,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_62])]) ).
cnf(c_0_97,hypothesis,
( ~ aSubsetOf0(X1,xP)
| aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91])]) ).
cnf(c_0_98,hypothesis,
sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xc,xQ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_43]),c_0_44]),c_0_61]),c_0_45])]) ).
cnf(c_0_99,hypothesis,
aSubsetOf0(xP,xP),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_93]),c_0_62])]),c_0_94]) ).
cnf(c_0_100,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_101,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98]),c_0_45]),c_0_91]),c_0_99])]),c_0_100]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM631+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.42 % Computer : n018.cluster.edu
% 0.13/5.42 % Model : x86_64 x86_64
% 0.13/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.42 % Memory : 8046.5625MB
% 0.13/5.42 % OS : Linux 6.8.0-71-generic
% 0.13/5.42 % CPULimit : 300
% 0.13/5.42 % WCLimit : 300
% 0.13/5.42 % DateTime : Mon Sep 21 02:47:34 UTC 2026
% 0.13/5.43 % CPUTime :
% 0.13/5.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.50 Running first-order theorem proving
% 0.20/5.50 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 81.23/17.43 % Version: 3.5.1
% 81.23/17.43 % Preprocessing class: FSLSSMSMSSSNFFN.
% 81.23/17.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 81.23/17.43 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 81.23/17.43 % Starting new_bool_3 with 300s (1) cores
% 81.23/17.43 % Starting new_bool_1 with 300s (1) cores
% 81.23/17.43 % Starting sh5l with 300s (1) cores
% 81.23/17.43 % new_bool_3 with pid 800552 completed with status 0
% 81.23/17.43 % Result found by new_bool_3
% 81.23/17.43 % Preprocessing class: FSLSSMSMSSSNFFN.
% 81.23/17.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 81.23/17.43 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 81.23/17.43 % Starting new_bool_3 with 300s (1) cores
% 81.23/17.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 81.23/17.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 81.23/17.43 % Search class: FGHSF-FSLM31-MFFFFFNN
% 81.23/17.43 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 81.23/17.43 % Starting SubtermCWHack with 28s (1) cores
% 81.23/17.43 % SubtermCWHack with pid 800556 completed with status 0
% 81.23/17.43 % Result found by SubtermCWHack
% 81.23/17.43 % Preprocessing class: FSLSSMSMSSSNFFN.
% 81.23/17.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 81.23/17.43 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 81.23/17.43 % Starting new_bool_3 with 300s (1) cores
% 81.23/17.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 81.23/17.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 81.23/17.43 % Search class: FGHSF-FSLM31-MFFFFFNN
% 81.23/17.43 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 81.23/17.43 % Starting SubtermCWHack with 28s (1) cores
% 81.23/17.43 % Preprocessing time : 0.006 s
% 81.23/17.43
% 81.23/17.43 % Proof found!
% 81.23/17.43 % SZS status Theorem
% 81.23/17.43 % SZS output start CNFRefutation
% See solution above
% 81.23/17.43 % Parsed axioms : 117
% 81.23/17.43 % Removed by relevancy pruning/SinE : 2
% 81.23/17.43 % Initial clauses : 214
% 81.23/17.43 % Removed in clause preprocessing : 7
% 81.23/17.43 % Initial clauses in saturation : 207
% 81.23/17.43 % Processed clauses : 33319
% 81.23/17.43 % ...of these trivial : 126
% 81.23/17.43 % ...subsumed : 25025
% 81.23/17.43 % ...remaining for further processing : 8168
% 81.23/17.43 % Other redundant clauses eliminated : 69
% 81.23/17.43 % Clauses deleted for lack of memory : 0
% 81.23/17.43 % Backward-subsumed : 848
% 81.23/17.43 % Backward-rewritten : 69
% 81.23/17.43 % Generated clauses : 307765
% 81.23/17.43 % ...of the previous two non-redundant : 288097
% 81.23/17.43 % ...aggressively subsumed : 0
% 81.23/17.43 % Contextual simplify-reflections : 940
% 81.23/17.43 % Paramodulations : 307696
% 81.23/17.43 % Factorizations : 0
% 81.23/17.43 % NegExts : 0
% 81.23/17.43 % Equation resolutions : 73
% 81.23/17.43 % Disequality decompositions : 0
% 81.23/17.43 % Total rewrite steps : 172079
% 81.23/17.43 % ...of those cached : 171856
% 81.23/17.43 % Propositional unsat checks : 0
% 81.23/17.43 % Propositional check models : 0
% 81.23/17.43 % Propositional check unsatisfiable : 0
% 81.23/17.43 % Propositional clauses : 0
% 81.23/17.43 % Propositional clauses after purity: 0
% 81.23/17.43 % Propositional unsat core size : 0
% 81.23/17.43 % Propositional preprocessing time : 0.000
% 81.23/17.43 % Propositional encoding time : 0.000
% 81.23/17.43 % Propositional solver time : 0.000
% 81.23/17.43 % Success case prop preproc time : 0.000
% 81.23/17.43 % Success case prop encoding time : 0.000
% 81.23/17.43 % Success case prop solver time : 0.000
% 81.23/17.43 % Current number of processed clauses : 7217
% 81.23/17.43 % Positive orientable unit clauses : 251
% 81.23/17.43 % Positive unorientable unit clauses: 0
% 81.23/17.43 % Negative unit clauses : 86
% 81.23/17.43 % Non-unit-clauses : 6880
% 81.23/17.43 % Current number of unprocessed clauses: 252878
% 81.23/17.43 % ...number of literals in the above : 1624554
% 81.23/17.43 % Current number of archived formulas : 0
% 81.23/17.43 % Current number of archived clauses : 918
% 81.23/17.43 % Clause-clause subsumption calls (NU) : 4930330
% 81.23/17.43 % Rec. Clause-clause subsumption calls : 1781559
% 81.23/17.43 % Non-unit clause-clause subsumptions : 22022
% 81.23/17.43 % Unit Clause-clause subsumption calls : 67923
% 81.23/17.43 % Rewrite failures with RHS unbound : 0
% 81.23/17.43 % BW rewrite match attempts : 74
% 81.23/17.43 % BW rewrite match successes : 41
% 81.23/17.43 % Condensation attempts : 0
% 81.23/17.43 % Condensation successes : 0
% 81.23/17.43 % Termbank termtop insertions : 8080036
% 81.23/17.43 % Search garbage collected termcells : 3556
% 81.23/17.43
% 81.23/17.43 % -------------------------------------------------
% 81.23/17.43 % User time : 10.999 s
% 81.23/17.43 % System time : 0.341 s
% 81.23/17.43 % Total time : 11.340 s
% 81.23/17.43 % Maximum resident set size: 4236 pages
% 81.23/17.43
% 81.23/17.43 % -------------------------------------------------
% 81.23/17.43 % User time : 11.009 s
% 81.23/17.43 % System time : 0.346 s
% 81.23/17.43 % Total time : 11.355 s
% 81.23/17.43 % Maximum resident set size: 4864 pages
% 81.23/17.43 % E exiting
%------------------------------------------------------------------------------