%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM631+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 : n007.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 3.51s 6.20s
% Output : CNFRefutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 55 ( 25 unt; 0 def)
% Number of atoms : 219 ( 63 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 234 ( 70 ~; 65 |; 77 &)
% ( 5 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 14 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__5585,hypothesis,
( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
& ! [X1] :
( aElementOf0(X1,xD)
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,xn))
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& aElement0(X1) ) )
& aSet0(xD)
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5585) ).
fof(m__5164,hypothesis,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( X1 != szmzizndt0(xQ)
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& ! [X1] :
( aElementOf0(X1,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X1) )
& aSet0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__5147,hypothesis,
( xp = szmzizndt0(xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> sdtlseqdt0(xp,X1) )
& aElementOf0(xp,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(m__5078,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,xO) )
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5078) ).
fof(m__4660,hypothesis,
( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(sdtlpdtrp0(xe,X1),X2) )
& aElementOf0(sdtlpdtrp0(xe,X1),sdtlpdtrp0(xN,X1)) ) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
fof(m__5309,hypothesis,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,szDzozmdt0(xd)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
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__,conjecture,
sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(xd,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__5632,hypothesis,
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( ( X1 = szmzizndt0(sdtlpdtrp0(xN,xn))
| aElementOf0(X1,xP) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5632) ).
fof(m__4730,hypothesis,
( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( ( aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk))
| ( sbrdtbr0(X2) = xk
& ( aSubsetOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtlpdtrp0(xN,szszuzczcdt0(X1))) ) ) ) )
& 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__5334,hypothesis,
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5334) ).
fof(m__5217,hypothesis,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5217) ).
fof(c_0_13,hypothesis,
( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
& ! [X1] :
( aElementOf0(X1,xD)
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,xn))
& aElementOf0(X1,sdtlpdtrp0(xN,xn))
& aElement0(X1) ) )
& aSet0(xD)
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1) ) ),
inference(fof_simplification,[status(thm)],[m__5585]) ).
fof(c_0_14,hypothesis,
! [X98,X99] :
( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
& ( aElementOf0(X99,xD)
| X99 = szmzizndt0(sdtlpdtrp0(xN,xn))
| ~ aElementOf0(X99,sdtlpdtrp0(xN,xn))
| ~ aElement0(X99) )
& ( ~ aElementOf0(X99,xD)
| X99 != szmzizndt0(sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(X99,xD)
| aElementOf0(X99,sdtlpdtrp0(xN,xn)) )
& ( ~ aElementOf0(X99,xD)
| aElement0(X99) )
& aSet0(xD)
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X98)
| ~ aElementOf0(X98,sdtlpdtrp0(xN,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)],[c_0_13])])])])]) ).
fof(c_0_15,hypothesis,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( X1 != szmzizndt0(xQ)
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& ! [X1] :
( aElementOf0(X1,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X1) )
& aSet0(xP) ),
inference(fof_simplification,[status(thm)],[m__5164]) ).
fof(c_0_16,plain,
! [X210,X211] :
( aElement0(X211)
| ~ aElementOf0(X211,X210)
| ~ aSet0(X210) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
fof(c_0_17,hypothesis,
! [X91] :
( xp = szmzizndt0(xQ)
& ( sdtlseqdt0(xp,X91)
| ~ aElementOf0(X91,xQ) )
& aElementOf0(xp,xQ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5147])])])]) ).
fof(c_0_18,hypothesis,
! [X85] :
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ( aElementOf0(X85,xO)
| ~ aElementOf0(X85,xQ) )
& aSet0(xQ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5078])])])]) ).
fof(c_0_19,hypothesis,
! [X65,X66] :
( ( ~ aElementOf0(X65,szNzAzT0)
| sdtlpdtrp0(xe,X65) = szmzizndt0(sdtlpdtrp0(xN,X65)) )
& ( ~ aElementOf0(X65,szNzAzT0)
| sdtlseqdt0(sdtlpdtrp0(xe,X65),X66)
| ~ aElementOf0(X66,sdtlpdtrp0(xN,X65)) )
& ( ~ aElementOf0(X65,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,X65),sdtlpdtrp0(xN,X65)) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
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__4660])])])])]) ).
cnf(c_0_20,hypothesis,
( ~ aElementOf0(X1,xD)
| X1 != szmzizndt0(sdtlpdtrp0(xN,xn)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,hypothesis,
! [X92,X93] :
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ( aElementOf0(X93,xP)
| X93 = szmzizndt0(xQ)
| ~ aElementOf0(X93,xQ)
| ~ aElement0(X93) )
& ( ~ aElementOf0(X93,xP)
| X93 != szmzizndt0(xQ) )
& ( ~ aElementOf0(X93,xP)
| aElementOf0(X93,xQ) )
& ( ~ aElementOf0(X93,xP)
| aElement0(X93) )
& ( sdtlseqdt0(szmzizndt0(xQ),X92)
| ~ aElementOf0(X92,xQ) )
& aSet0(xP) ),
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_15])])])])]) ).
cnf(c_0_22,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,hypothesis,
aElementOf0(xp,xQ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,X1),sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,hypothesis,
sdtlpdtrp0(xe,xn) = xp,
inference(split_conjunct,[status(thm)],[m__5309]) ).
cnf(c_0_27,hypothesis,
aElementOf0(xn,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5309]) ).
cnf(c_0_28,hypothesis,
~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),xD),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_29,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_30,plain,
! [X198,X199] :
( sdtpldt0(sdtmndt0(X198,X199),X199) = X198
| ~ aElementOf0(X199,X198)
| ~ aSet0(X198) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mConsDiff])])])]) ).
cnf(c_0_31,hypothesis,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,hypothesis,
xp = szmzizndt0(xQ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_33,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_34,hypothesis,
! [X101,X102] :
( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)
& ( aElementOf0(X102,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElement0(X102)
| X102 != szmzizndt0(sdtlpdtrp0(xN,xn)) )
& ( aElementOf0(X102,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| ~ aElement0(X102)
| ~ aElementOf0(X102,xP) )
& ( ~ aElementOf0(X102,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| X102 = szmzizndt0(sdtlpdtrp0(xN,xn))
| aElementOf0(X102,xP) )
& ( ~ aElementOf0(X102,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
| aElement0(X102) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X101)
| ~ aElementOf0(X101,sdtlpdtrp0(xN,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__5632])])])])]) ).
cnf(c_0_35,hypothesis,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xn))
| ~ aElement0(X1)
| aElementOf0(X1,xD)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_36,hypothesis,
aElement0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_37,hypothesis,
aElementOf0(xp,sdtlpdtrp0(xN,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_38,hypothesis,
~ aElementOf0(xp,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26]),c_0_27])]) ).
cnf(c_0_39,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| sdtpldt0(sdtmndt0(X1,X2),X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,hypothesis,
sdtmndt0(xQ,xp) = xP,
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_41,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_42,hypothesis,
! [X67,X68] :
( ( ~ aElementOf0(X67,szNzAzT0)
| sdtlpdtrp0(xd,X67) = sdtlpdtrp0(sdtlpdtrp0(xC,X67),X68)
| ~ aSet0(X68)
| ~ aElementOf0(X68,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X67)),xk)) )
& ( ~ aElementOf0(X67,szNzAzT0)
| sdtlpdtrp0(xd,X67) = sdtlpdtrp0(sdtlpdtrp0(xC,X67),X68)
| ~ aSet0(X68)
| sbrdtbr0(X68) != xk
| ~ aSubsetOf0(X68,sdtlpdtrp0(xN,szszuzczcdt0(X67))) )
& ( ~ aElementOf0(X67,szNzAzT0)
| sdtlpdtrp0(xd,X67) = sdtlpdtrp0(sdtlpdtrp0(xC,X67),X68)
| ~ aSet0(X68)
| sbrdtbr0(X68) != xk
| ~ aElementOf0(esk17_2(X67,X68),sdtlpdtrp0(xN,szszuzczcdt0(X67))) )
& ( ~ aElementOf0(X67,szNzAzT0)
| sdtlpdtrp0(xd,X67) = sdtlpdtrp0(sdtlpdtrp0(xC,X67),X68)
| ~ aSet0(X68)
| sbrdtbr0(X68) != xk
| aElementOf0(esk17_2(X67,X68),X68) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
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)],[m__4730])])])])])]) ).
fof(c_0_43,hypothesis,
! [X97] :
( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& ( aElementOf0(X97,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(X97,xP) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5334])])])]) ).
cnf(c_0_44,hypothesis,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,hypothesis,
szmzizndt0(sdtlpdtrp0(xN,xn)) = xp,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_46,hypothesis,
sdtpldt0(xP,xp) = xQ,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_23]),c_0_24])]) ).
fof(c_0_47,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(fof_nnf,[status(thm)],[c_0_41]) ).
cnf(c_0_48,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X1)
| sbrdtbr0(X1) != xk
| ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X2)))
| sdtlpdtrp0(xd,X2) = sdtlpdtrp0(sdtlpdtrp0(xC,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,hypothesis,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,hypothesis,
sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xc,xQ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_51,hypothesis,
sbrdtbr0(xP) = xk,
inference(split_conjunct,[status(thm)],[m__5217]) ).
cnf(c_0_52,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_53,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,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_48,c_0_49]),c_0_50]),c_0_51]),c_0_27]),c_0_52])]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM631+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/5.44 % Computer : n007.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.45 % CPULimit : 300
% 0.17/5.45 % WCLimit : 300
% 0.17/5.45 % DateTime : Mon Sep 21 02:43:25 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/5.52 Running first-order theorem proving
% 0.22/5.52 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
% 3.51/6.20 % Version: 3.5.1
% 3.51/6.20 % Preprocessing class: FSLSSMSMSSSNFFN.
% 3.51/6.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.51/6.20 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.51/6.20 % Starting new_bool_3 with 300s (1) cores
% 3.51/6.20 % Starting new_bool_1 with 300s (1) cores
% 3.51/6.20 % Starting sh5l with 300s (1) cores
% 3.51/6.20 % new_bool_3 with pid 913 completed with status 0
% 3.51/6.20 % Result found by new_bool_3
% 3.51/6.20 % Preprocessing class: FSLSSMSMSSSNFFN.
% 3.51/6.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.51/6.20 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.51/6.20 % Starting new_bool_3 with 300s (1) cores
% 3.51/6.20 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 3.51/6.20 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.51/6.20 % Search class: FGHSF-SMLM32-MFFFFFNN
% 3.51/6.20 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 3.51/6.20 % Starting SubtermCWHack with 31s (1) cores
% 3.51/6.20 % SubtermCWHack with pid 916 completed with status 0
% 3.51/6.20 % Result found by SubtermCWHack
% 3.51/6.20 % Preprocessing class: FSLSSMSMSSSNFFN.
% 3.51/6.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.51/6.20 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 3.51/6.20 % Starting new_bool_3 with 300s (1) cores
% 3.51/6.20 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 3.51/6.20 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.51/6.20 % Search class: FGHSF-SMLM32-MFFFFFNN
% 3.51/6.20 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 3.51/6.20 % Starting SubtermCWHack with 31s (1) cores
% 3.51/6.20 % Preprocessing time : 0.174 s
% 3.51/6.20
% 3.51/6.20 % Proof found!
% 3.51/6.20 % SZS status Theorem
% 3.51/6.20 % SZS output start CNFRefutation
% See solution above
% 3.51/6.20 % Parsed axioms : 117
% 3.51/6.20 % Removed by relevancy pruning/SinE : 9
% 3.51/6.20 % Initial clauses : 4910
% 3.51/6.20 % Removed in clause preprocessing : 7
% 3.51/6.20 % Initial clauses in saturation : 4903
% 3.51/6.20 % Processed clauses : 1287
% 3.51/6.20 % ...of these trivial : 39
% 3.51/6.20 % ...subsumed : 344
% 3.51/6.20 % ...remaining for further processing : 904
% 3.51/6.20 % Other redundant clauses eliminated : 44
% 3.51/6.20 % Clauses deleted for lack of memory : 0
% 3.51/6.20 % Backward-subsumed : 32
% 3.51/6.20 % Backward-rewritten : 39
% 3.51/6.20 % Generated clauses : 3518
% 3.51/6.20 % ...of the previous two non-redundant : 2873
% 3.51/6.20 % ...aggressively subsumed : 0
% 3.51/6.20 % Contextual simplify-reflections : 23
% 3.51/6.20 % Paramodulations : 3475
% 3.51/6.20 % Factorizations : 0
% 3.51/6.20 % NegExts : 0
% 3.51/6.20 % Equation resolutions : 46
% 3.51/6.20 % Disequality decompositions : 0
% 3.51/6.20 % Total rewrite steps : 2961
% 3.51/6.20 % ...of those cached : 2794
% 3.51/6.20 % Propositional unsat checks : 0
% 3.51/6.20 % Propositional check models : 0
% 3.51/6.20 % Propositional check unsatisfiable : 0
% 3.51/6.20 % Propositional clauses : 0
% 3.51/6.20 % Propositional clauses after purity: 0
% 3.51/6.20 % Propositional unsat core size : 0
% 3.51/6.20 % Propositional preprocessing time : 0.000
% 3.51/6.20 % Propositional encoding time : 0.000
% 3.51/6.20 % Propositional solver time : 0.000
% 3.51/6.20 % Success case prop preproc time : 0.000
% 3.51/6.20 % Success case prop encoding time : 0.000
% 3.51/6.20 % Success case prop solver time : 0.000
% 3.51/6.20 % Current number of processed clauses : 796
% 3.51/6.20 % Positive orientable unit clauses : 188
% 3.51/6.20 % Positive unorientable unit clauses: 0
% 3.51/6.20 % Negative unit clauses : 38
% 3.51/6.20 % Non-unit-clauses : 570
% 3.51/6.20 % Current number of unprocessed clauses: 6098
% 3.51/6.20 % ...number of literals in the above : 61281
% 3.51/6.20 % Current number of archived formulas : 0
% 3.51/6.20 % Current number of archived clauses : 73
% 3.51/6.20 % Clause-clause subsumption calls (NU) : 40450
% 3.51/6.20 % Rec. Clause-clause subsumption calls : 26335
% 3.51/6.20 % Non-unit clause-clause subsumptions : 248
% 3.51/6.20 % Unit Clause-clause subsumption calls : 4685
% 3.51/6.20 % Rewrite failures with RHS unbound : 0
% 3.51/6.20 % BW rewrite match attempts : 64
% 3.51/6.20 % BW rewrite match successes : 25
% 3.51/6.20 % Condensation attempts : 0
% 3.51/6.20 % Condensation successes : 0
% 3.51/6.20 % Termbank termtop insertions : 431276
% 3.51/6.20 % Search garbage collected termcells : 31654
% 3.51/6.20
% 3.51/6.20 % -------------------------------------------------
% 3.51/6.20 % User time : 0.585 s
% 3.51/6.20 % System time : 0.040 s
% 3.51/6.20 % Total time : 0.625 s
% 3.51/6.20 % Maximum resident set size: 16120 pages
% 3.51/6.20
% 3.51/6.20 % -------------------------------------------------
% 3.51/6.20 % User time : 0.596 s
% 3.51/6.20 % System time : 0.050 s
% 3.51/6.20 % Total time : 0.646 s
% 3.51/6.20 % Maximum resident set size: 5120 pages
% 3.51/6.20 % E exiting
%------------------------------------------------------------------------------