%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM583+3 : 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 01:49:39 PM UTC 2026
% Result : Theorem 2.91s 1.17s
% Output : CNFRefutation 2.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 11 unt; 0 def)
% Number of atoms : 260 ( 36 equ)
% Maximal formula atoms : 52 ( 6 avg)
% Number of connectives : 319 ( 98 ~; 104 |; 86 &)
% ( 10 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-3 aty)
% Number of variables : 66 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(m__3989_02,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989_02) ).
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__4037,hypothesis,
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,xS) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4037) ).
fof(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__,conjecture,
( ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( X1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X1,xS) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__4007,hypothesis,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( X1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4007) ).
fof(c_0_8,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_9,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(fof_simplification,[status(thm)],[m__3989_02]) ).
fof(c_0_10,plain,
! [X20,X21,X22,X23] :
( ( ~ aSet0(X20)
| aSubsetOf0(X23,X20)
| ~ aSet0(X23)
| ~ aElementOf0(esk2_2(X20,X23),X20) )
& ( ~ aSet0(X20)
| aSubsetOf0(X23,X20)
| ~ aSet0(X23)
| aElementOf0(esk2_2(X20,X23),X23) )
& ( ~ aSet0(X20)
| ~ aSubsetOf0(X21,X20)
| aElementOf0(X22,X20)
| ~ aElementOf0(X22,X21) )
& ( ~ aSet0(X20)
| ~ aSubsetOf0(X21,X20)
| aSet0(X21) ) ),
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_11,hypothesis,
! [X226] :
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
& ( aElementOf0(X226,xS)
| ~ aElementOf0(X226,sdtlpdtrp0(xN,xi)) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4037])])])]) ).
fof(c_0_12,hypothesis,
! [X178] :
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ( aElementOf0(X178,szNzAzT0)
| ~ aElementOf0(X178,xS) )
& aSet0(xS) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3435])])])]) ).
fof(c_0_13,plain,
! [X40,X41,X42,X43,X44,X45] :
( ( ~ aElement0(X41)
| ~ aSet0(X40)
| X45 = sdtmndt0(X40,X41)
| ~ aSet0(X45)
| aElementOf0(esk4_3(X40,X41,X45),X45)
| esk4_3(X40,X41,X45) != X41 )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X45 = sdtmndt0(X40,X41)
| ~ aSet0(X45)
| aElementOf0(esk4_3(X40,X41,X45),X45)
| aElementOf0(esk4_3(X40,X41,X45),X40) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X45 = sdtmndt0(X40,X41)
| ~ aSet0(X45)
| aElementOf0(esk4_3(X40,X41,X45),X45)
| aElement0(esk4_3(X40,X41,X45)) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X45 = sdtmndt0(X40,X41)
| ~ aSet0(X45)
| esk4_3(X40,X41,X45) = X41
| ~ aElementOf0(esk4_3(X40,X41,X45),X40)
| ~ aElement0(esk4_3(X40,X41,X45))
| ~ aElementOf0(esk4_3(X40,X41,X45),X45) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| aElementOf0(X44,X42)
| X44 = X41
| ~ aElementOf0(X44,X40)
| ~ aElement0(X44) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| ~ aElementOf0(X43,X42)
| X43 != X41 )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| ~ aElementOf0(X43,X42)
| aElementOf0(X43,X40) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| ~ aElementOf0(X43,X42)
| aElement0(X43) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| aSet0(X42) ) ),
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_8])])])])])])]) ).
fof(c_0_14,plain,
! [X10,X11] :
( aElement0(X11)
| ~ aElementOf0(X11,X10)
| ~ aSet0(X10) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
fof(c_0_15,hypothesis,
! [X221,X222,X223] :
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElementOf0(X223,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X223,xQ) )
& aSet0(xQ)
& ( aElementOf0(X222,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| X222 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X222,sdtlpdtrp0(xN,xi))
| ~ aElement0(X222) )
& ( ~ aElementOf0(X222,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| X222 != szmzizndt0(sdtlpdtrp0(xN,xi)) )
& ( ~ aElementOf0(X222,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(X222,sdtlpdtrp0(xN,xi)) )
& ( ~ aElementOf0(X222,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElement0(X222) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X221)
| ~ aElementOf0(X221,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])]) ).
cnf(c_0_16,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( ~ aElement0(X4)
| ~ aSet0(X2)
| X3 != sdtmndt0(X2,X4)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,hypothesis,
aSet0(sdtlpdtrp0(xN,xi)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
fof(c_0_23,negated_conjecture,
~ ( ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( X1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X1,xS) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_24,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| aElementOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_25,hypothesis,
( ~ aElementOf0(X1,xQ)
| aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,hypothesis,
aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
fof(c_0_27,negated_conjecture,
! [X227,X228] :
( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ~ aElementOf0(esk33_0,xS)
& aElementOf0(esk33_0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElementOf0(X228,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X228)
| X228 != szmzizndt0(sdtlpdtrp0(xN,xi)) )
& ( aElementOf0(X228,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X228)
| ~ aElementOf0(X228,xQ) )
& ( ~ aElementOf0(X228,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| X228 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X228,xQ) )
& ( ~ aElementOf0(X228,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElement0(X228) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X227)
| ~ aElementOf0(X227,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])])])]) ).
cnf(c_0_28,hypothesis,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,hypothesis,
( ~ aElementOf0(X1,xQ)
| aElementOf0(X1,sdtlpdtrp0(xN,xi)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_22])]) ).
fof(c_0_30,hypothesis,
! [X224,X225] :
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ( aElementOf0(X225,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X225)
| X225 != szmzizndt0(sdtlpdtrp0(xN,xi)) )
& ( aElementOf0(X225,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X225)
| ~ aElementOf0(X225,xQ) )
& ( ~ aElementOf0(X225,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| X225 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X225,xQ) )
& ( ~ aElementOf0(X225,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElement0(X225) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X224)
| ~ aElementOf0(X224,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
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__4007])])])])]) ).
cnf(c_0_31,negated_conjecture,
~ aElementOf0(esk33_0,xS),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,hypothesis,
( ~ aElementOf0(X1,xQ)
| aElementOf0(X1,xS) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,hypothesis,
( ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X1,xQ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,negated_conjecture,
aElementOf0(esk33_0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
~ aElementOf0(esk33_0,xQ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS),
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_37,negated_conjecture,
szmzizndt0(sdtlpdtrp0(xN,xi)) = esk33_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_38,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM583+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n018.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 02:43:58 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.51 Running first-order theorem proving
% 0.24/0.51 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
% 2.91/1.17 % Version: 3.5.1
% 2.91/1.17 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.91/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.91/1.17 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.91/1.17 % Starting new_bool_3 with 300s (1) cores
% 2.91/1.17 % Starting new_bool_1 with 300s (1) cores
% 2.91/1.17 % Starting sh5l with 300s (1) cores
% 2.91/1.17 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 794506 completed with status 0
% 2.91/1.17 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 2.91/1.17 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.91/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.91/1.17 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.91/1.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.91/1.17 % No SInE strategy applied
% 2.91/1.17 % Search class: FGHSF-SMLM32-MFFFFFNN
% 2.91/1.17 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.91/1.17 % Starting SubtermCWHack with 136s (1) cores
% 2.91/1.17 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 2.91/1.17 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 2.91/1.17 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 2.91/1.17 % Starting new_bool_3 with 136s (1) cores
% 2.91/1.17 % SubtermCWHack with pid 794510 completed with status 0
% 2.91/1.17 % Result found by SubtermCWHack
% 2.91/1.17 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.91/1.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.91/1.17 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.91/1.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.91/1.17 % No SInE strategy applied
% 2.91/1.17 % Search class: FGHSF-SMLM32-MFFFFFNN
% 2.91/1.17 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.91/1.17 % Starting SubtermCWHack with 136s (1) cores
% 2.91/1.17 % Preprocessing time : 0.083 s
% 2.91/1.17
% 2.91/1.17 % Proof found!
% 2.91/1.17 % SZS status Theorem
% 2.91/1.17 % SZS output start CNFRefutation
% See solution above
% 2.91/1.17 % Parsed axioms : 89
% 2.91/1.17 % Removed by relevancy pruning/SinE : 0
% 2.91/1.17 % Initial clauses : 4219
% 2.91/1.17 % Removed in clause preprocessing : 7
% 2.91/1.17 % Initial clauses in saturation : 4212
% 2.91/1.17 % Processed clauses : 1035
% 2.91/1.17 % ...of these trivial : 7
% 2.91/1.17 % ...subsumed : 402
% 2.91/1.17 % ...remaining for further processing : 626
% 2.91/1.17 % Other redundant clauses eliminated : 50
% 2.91/1.17 % Clauses deleted for lack of memory : 0
% 2.91/1.17 % Backward-subsumed : 33
% 2.91/1.17 % Backward-rewritten : 21
% 2.91/1.17 % Generated clauses : 2560
% 2.91/1.17 % ...of the previous two non-redundant : 2100
% 2.91/1.17 % ...aggressively subsumed : 0
% 2.91/1.17 % Contextual simplify-reflections : 33
% 2.91/1.17 % Paramodulations : 2510
% 2.91/1.17 % Factorizations : 0
% 2.91/1.17 % NegExts : 0
% 2.91/1.17 % Equation resolutions : 52
% 2.91/1.17 % Disequality decompositions : 0
% 2.91/1.17 % Total rewrite steps : 1847
% 2.91/1.17 % ...of those cached : 1774
% 2.91/1.17 % Propositional unsat checks : 0
% 2.91/1.17 % Propositional check models : 0
% 2.91/1.17 % Propositional check unsatisfiable : 0
% 2.91/1.17 % Propositional clauses : 0
% 2.91/1.17 % Propositional clauses after purity: 0
% 2.91/1.17 % Propositional unsat core size : 0
% 2.91/1.17 % Propositional preprocessing time : 0.000
% 2.91/1.17 % Propositional encoding time : 0.000
% 2.91/1.17 % Propositional solver time : 0.000
% 2.91/1.17 % Success case prop preproc time : 0.000
% 2.91/1.17 % Success case prop encoding time : 0.000
% 2.91/1.17 % Success case prop solver time : 0.000
% 2.91/1.17 % Current number of processed clauses : 529
% 2.91/1.17 % Positive orientable unit clauses : 80
% 2.91/1.17 % Positive unorientable unit clauses: 0
% 2.91/1.17 % Negative unit clauses : 23
% 2.91/1.17 % Non-unit-clauses : 426
% 2.91/1.17 % Current number of unprocessed clauses: 5252
% 2.91/1.17 % ...number of literals in the above : 56476
% 2.91/1.17 % Current number of archived formulas : 0
% 2.91/1.17 % Current number of archived clauses : 57
% 2.91/1.17 % Clause-clause subsumption calls (NU) : 26703
% 2.91/1.17 % Rec. Clause-clause subsumption calls : 15058
% 2.91/1.17 % Non-unit clause-clause subsumptions : 356
% 2.91/1.17 % Unit Clause-clause subsumption calls : 1491
% 2.91/1.17 % Rewrite failures with RHS unbound : 0
% 2.91/1.17 % BW rewrite match attempts : 13
% 2.91/1.17 % BW rewrite match successes : 13
% 2.91/1.17 % Condensation attempts : 0
% 2.91/1.17 % Condensation successes : 0
% 2.91/1.17 % Termbank termtop insertions : 374221
% 2.91/1.17 % Search garbage collected termcells : 27211
% 2.91/1.17
% 2.91/1.17 % -------------------------------------------------
% 2.91/1.17 % User time : 0.567 s
% 2.91/1.17 % System time : 0.043 s
% 2.91/1.17 % Total time : 0.610 s
% 2.91/1.17 % Maximum resident set size: 14988 pages
% 2.91/1.17
% 2.91/1.17 % -------------------------------------------------
% 2.91/1.17 % User time : 1.187 s
% 2.91/1.17 % System time : 0.100 s
% 2.91/1.17 % Total time : 1.287 s
% 2.91/1.17 % Maximum resident set size: 4608 pages
% 2.91/1.17 % E exiting
%------------------------------------------------------------------------------