%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM556+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:49:33 PM UTC 2026
% Result : Theorem 0.15s 5.49s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 71 ( 20 unt; 0 def)
% Number of atoms : 355 ( 74 equ)
% Maximal formula atoms : 67 ( 5 avg)
% Number of connectives : 415 ( 131 ~; 128 |; 115 &)
% ( 6 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 61 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2202_02,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
fof(m__2357,hypothesis,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( ( X1 = xx
| aElementOf0(X1,sdtmndt0(xQ,xy)) )
& aElement0(X1) ) )
& aSet0(xP)
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
<=> ( X1 != xy
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).
fof(m__,conjecture,
( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xS) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2227,hypothesis,
( ~ ( ! [X1] :
( ( ( sbrdtbr0(X1) = xk
& ( aSubsetOf0(X1,xS)
| ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSet0(X1) ) ) )
=> aElementOf0(X1,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(X1) = xk
& aSubsetOf0(X1,xS)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSet0(X1) ) ) )
=> ( slbdtsldtrb0(xS,xk) = slcrc0
| ~ ? [X1] : aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X1] :
( aElementOf0(X1,slbdtsldtrb0(xS,xk))
=> aElementOf0(X1,slbdtsldtrb0(xT,xk)) )
& ! [X1] :
( ( ( sbrdtbr0(X1) = xk
& ( aSubsetOf0(X1,xT)
| ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xT) )
& aSet0(X1) ) ) )
=> aElementOf0(X1,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X1,slbdtsldtrb0(xT,xk))
=> ( sbrdtbr0(X1) = xk
& aSubsetOf0(X1,xT)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xT) )
& aSet0(X1) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X1] :
( ( ( sbrdtbr0(X1) = xk
& ( aSubsetOf0(X1,xS)
| ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSet0(X1) ) ) )
=> aElementOf0(X1,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(X1) = xk
& aSubsetOf0(X1,xS)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSet0(X1) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2227) ).
fof(mDiffCons,axiom,
! [X1,X2] :
( ( aSet0(X2)
& aElement0(X1) )
=> ( ~ aElementOf0(X1,X2)
=> sdtmndt0(sdtpldt0(X2,X1),X1) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDiffCons) ).
fof(m__2411,hypothesis,
( ! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
<=> ( X1 != xy
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& aSet0(sdtmndt0(xQ,xy))
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2411) ).
fof(mFConsSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( isFinite0(X2)
& aSet0(X2) )
=> isFinite0(sdtpldt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).
fof(m__2256,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).
fof(mFDiffSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( isFinite0(X2)
& aSet0(X2) )
=> isFinite0(sdtmndt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
fof(m__2270,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,xS) )
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
fof(mCardCons,axiom,
! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardCons) ).
fof(m__2291,hypothesis,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
fof(m__2304,hypothesis,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
fof(mCardDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( ( aElementOf0(X2,X1)
& isFinite0(X1) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
fof(c_0_15,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(fof_simplification,[status(thm)],[m__2202_02]) ).
fof(c_0_16,hypothesis,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( ( X1 = xx
| aElementOf0(X1,sdtmndt0(xQ,xy)) )
& aElement0(X1) ) )
& aSet0(xP)
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
<=> ( X1 != xy
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
inference(fof_simplification,[status(thm)],[m__2357]) ).
fof(c_0_17,negated_conjecture,
~ ( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xS) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_18,plain,
! [X71,X72] :
( aElement0(X72)
| ~ aElementOf0(X72,X71)
| ~ aSet0(X71) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
fof(c_0_19,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(fof_nnf,[status(thm)],[c_0_15]) ).
fof(c_0_20,hypothesis,
! [X20,X21] :
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ( aElementOf0(X21,xP)
| ~ aElement0(X21)
| X21 != xx )
& ( aElementOf0(X21,xP)
| ~ aElement0(X21)
| ~ aElementOf0(X21,sdtmndt0(xQ,xy)) )
& ( ~ aElementOf0(X21,xP)
| X21 = xx
| aElementOf0(X21,sdtmndt0(xQ,xy)) )
& ( ~ aElementOf0(X21,xP)
| aElement0(X21) )
& aSet0(xP)
& ( aElementOf0(X20,sdtmndt0(xQ,xy))
| X20 = xy
| ~ aElementOf0(X20,xQ)
| ~ aElement0(X20) )
& ( ~ aElementOf0(X20,sdtmndt0(xQ,xy))
| X20 != xy )
& ( ~ aElementOf0(X20,sdtmndt0(xQ,xy))
| aElementOf0(X20,xQ) )
& ( ~ aElementOf0(X20,sdtmndt0(xQ,xy))
| aElement0(X20) )
& aSet0(sdtmndt0(xQ,xy)) ),
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_16])])])])]) ).
fof(c_0_21,negated_conjecture,
( ( sbrdtbr0(xP) != xk
| ~ aSubsetOf0(xP,xS) )
& ( sbrdtbr0(xP) != xk
| ~ aElementOf0(esk5_0,xS) )
& ( sbrdtbr0(xP) != xk
| aElementOf0(esk5_0,xP) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])]) ).
fof(c_0_22,hypothesis,
! [X5,X6,X7,X9,X10,X11,X13,X14,X15,X16] :
( slbdtsldtrb0(xS,xk) != slcrc0
& aElementOf0(esk4_0,slbdtsldtrb0(xS,xk))
& ( aElementOf0(X16,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X16) != xk
| ~ aSubsetOf0(X16,xS) )
& ( aElementOf0(X16,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X16) != xk
| ~ aSet0(X16)
| ~ aElementOf0(esk3_1(X16),xS) )
& ( aElementOf0(X16,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X16) != xk
| ~ aSet0(X16)
| aElementOf0(esk3_1(X16),X16) )
& ( ~ aElementOf0(X14,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X14) = xk )
& ( ~ aElementOf0(X14,slbdtsldtrb0(xS,xk))
| aSubsetOf0(X14,xS) )
& ( ~ aElementOf0(X14,slbdtsldtrb0(xS,xk))
| aElementOf0(X15,xS)
| ~ aElementOf0(X15,X14) )
& ( ~ aElementOf0(X14,slbdtsldtrb0(xS,xk))
| aSet0(X14) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ( aElementOf0(X13,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X13,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X11,slbdtsldtrb0(xT,xk))
| sbrdtbr0(X11) != xk
| ~ aSubsetOf0(X11,xT) )
& ( aElementOf0(X11,slbdtsldtrb0(xT,xk))
| sbrdtbr0(X11) != xk
| ~ aSet0(X11)
| ~ aElementOf0(esk2_1(X11),xT) )
& ( aElementOf0(X11,slbdtsldtrb0(xT,xk))
| sbrdtbr0(X11) != xk
| ~ aSet0(X11)
| aElementOf0(esk2_1(X11),X11) )
& ( ~ aElementOf0(X9,slbdtsldtrb0(xT,xk))
| sbrdtbr0(X9) = xk )
& ( ~ aElementOf0(X9,slbdtsldtrb0(xT,xk))
| aSubsetOf0(X9,xT) )
& ( ~ aElementOf0(X9,slbdtsldtrb0(xT,xk))
| aElementOf0(X10,xT)
| ~ aElementOf0(X10,X9) )
& ( ~ aElementOf0(X9,slbdtsldtrb0(xT,xk))
| aSet0(X9) )
& aSet0(slbdtsldtrb0(xT,xk))
& ( aElementOf0(X7,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X7) != xk
| ~ aSubsetOf0(X7,xS) )
& ( aElementOf0(X7,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X7) != xk
| ~ aSet0(X7)
| ~ aElementOf0(esk1_1(X7),xS) )
& ( aElementOf0(X7,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X7) != xk
| ~ aSet0(X7)
| aElementOf0(esk1_1(X7),X7) )
& ( ~ aElementOf0(X5,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X5) = xk )
& ( ~ aElementOf0(X5,slbdtsldtrb0(xS,xk))
| aSubsetOf0(X5,xS) )
& ( ~ aElementOf0(X5,slbdtsldtrb0(xS,xk))
| aElementOf0(X6,xS)
| ~ aElementOf0(X6,X5) )
& ( ~ aElementOf0(X5,slbdtsldtrb0(xS,xk))
| aSet0(X5) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
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)],[m__2227])])])])])])]) ).
fof(c_0_23,plain,
! [X1,X2] :
( ( aSet0(X2)
& aElement0(X1) )
=> ( ~ aElementOf0(X1,X2)
=> sdtmndt0(sdtpldt0(X2,X1),X1) = X2 ) ),
inference(fof_simplification,[status(thm)],[mDiffCons]) ).
fof(c_0_24,hypothesis,
( ! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
<=> ( X1 != xy
& aElementOf0(X1,xQ)
& aElement0(X1) ) )
& aSet0(sdtmndt0(xQ,xy))
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
inference(fof_simplification,[status(thm)],[m__2411]) ).
fof(c_0_25,plain,
! [X86,X87] :
( isFinite0(sdtpldt0(X87,X86))
| ~ isFinite0(X87)
| ~ aSet0(X87)
| ~ aElement0(X86) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFConsSet])])])]) ).
cnf(c_0_26,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__2256]) ).
cnf(c_0_28,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,hypothesis,
( ~ aElementOf0(X1,sdtmndt0(xQ,xy))
| aElementOf0(X1,xQ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,hypothesis,
( ~ aElementOf0(X1,xP)
| X1 = xx
| aElementOf0(X1,sdtmndt0(xQ,xy)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,negated_conjecture,
( sbrdtbr0(xP) != xk
| ~ aSubsetOf0(xP,xS) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,hypothesis,
( ~ aElementOf0(X1,slbdtsldtrb0(xS,xk))
| aSubsetOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,hypothesis,
( ~ aElementOf0(X1,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X1) = xk ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_34,plain,
! [X82,X83] :
( sdtmndt0(sdtpldt0(X83,X82),X82) = X83
| aElementOf0(X82,X83)
| ~ aSet0(X83)
| ~ aElement0(X82) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
fof(c_0_35,hypothesis,
! [X22] :
( ( aElementOf0(X22,sdtmndt0(xQ,xy))
| X22 = xy
| ~ aElementOf0(X22,xQ)
| ~ aElement0(X22) )
& ( ~ aElementOf0(X22,sdtmndt0(xQ,xy))
| X22 != xy )
& ( ~ aElementOf0(X22,sdtmndt0(xQ,xy))
| aElementOf0(X22,xQ) )
& ( ~ aElementOf0(X22,sdtmndt0(xQ,xy))
| aElement0(X22) )
& aSet0(sdtmndt0(xQ,xy))
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
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_24])])])])]) ).
cnf(c_0_36,plain,
( ~ isFinite0(X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| isFinite0(sdtpldt0(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_38,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_39,hypothesis,
aSet0(sdtmndt0(xQ,xy)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_40,plain,
! [X99,X100] :
( isFinite0(sdtmndt0(X100,X99))
| ~ isFinite0(X100)
| ~ aSet0(X100)
| ~ aElement0(X99) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFDiffSet])])])]) ).
fof(c_0_41,hypothesis,
! [X19] :
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ( aElementOf0(X19,xS)
| ~ aElementOf0(X19,xQ) )
& aSet0(xQ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2270])])])]) ).
cnf(c_0_42,hypothesis,
( ~ aElementOf0(X1,xP)
| aElementOf0(X1,xQ)
| X1 = xx ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_43,hypothesis,
( sbrdtbr0(X1) != xk
| ~ aSet0(X1)
| aElementOf0(X1,slbdtsldtrb0(xS,xk))
| aElementOf0(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_44,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_45,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
fof(c_0_46,plain,
! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[mCardCons]) ).
cnf(c_0_47,plain,
( ~ aSet0(X2)
| ~ aElement0(X1)
| sdtmndt0(sdtpldt0(X2,X1),X1) = X2
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_48,hypothesis,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_49,hypothesis,
( ~ isFinite0(sdtmndt0(xQ,xy))
| isFinite0(xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39])]) ).
cnf(c_0_50,plain,
( ~ isFinite0(X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| isFinite0(sdtmndt0(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,hypothesis,
isFinite0(xQ),
inference(split_conjunct,[status(thm)],[m__2291]) ).
cnf(c_0_52,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__2304]) ).
cnf(c_0_53,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,hypothesis,
( ~ aElementOf0(X1,xQ)
| aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_55,hypothesis,
( sbrdtbr0(xP) != xk
| aElementOf0(esk1_1(xP),xQ)
| esk1_1(xP) = xx ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]),c_0_45]) ).
fof(c_0_56,plain,
! [X88,X89] :
( sbrdtbr0(sdtpldt0(X88,X89)) = szszuzczcdt0(sbrdtbr0(X88))
| aElementOf0(X89,X88)
| ~ aElement0(X89)
| ~ isFinite0(X88)
| ~ aSet0(X88) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])]) ).
cnf(c_0_57,hypothesis,
sdtmndt0(xP,xx) = sdtmndt0(xQ,xy),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_37]),c_0_38]),c_0_39])]),c_0_48]) ).
cnf(c_0_58,hypothesis,
isFinite0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52]),c_0_53])]) ).
cnf(c_0_59,hypothesis,
( sbrdtbr0(X1) != xk
| ~ aSet0(X1)
| ~ aElementOf0(esk1_1(X1),xS)
| aElementOf0(X1,slbdtsldtrb0(xS,xk)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_60,hypothesis,
( sbrdtbr0(xP) != xk
| aElementOf0(esk1_1(xP),xS)
| esk1_1(xP) = xx ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
( ~ aElement0(X2)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1))
| aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_62,hypothesis,
isFinite0(sdtmndt0(xQ,xy)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_57]),c_0_58]),c_0_38]),c_0_44])]) ).
fof(c_0_63,plain,
! [X101,X102] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X101,X102))) = sbrdtbr0(X101)
| ~ aElementOf0(X102,X101)
| ~ isFinite0(X101)
| ~ aSet0(X101) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardDiff])])])]) ).
cnf(c_0_64,hypothesis,
( sbrdtbr0(xP) != xk
| esk1_1(xP) = xx ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_44])]),c_0_45]) ).
cnf(c_0_65,hypothesis,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xP),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_37]),c_0_62]),c_0_38]),c_0_39])]),c_0_48]) ).
cnf(c_0_66,plain,
( ~ aElementOf0(X2,X1)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_67,hypothesis,
sbrdtbr0(xQ) = xk,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_68,hypothesis,
aElementOf0(xy,xQ),
inference(split_conjunct,[status(thm)],[m__2304]) ).
cnf(c_0_69,hypothesis,
sbrdtbr0(xP) != xk,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_64]),c_0_27]),c_0_44])]),c_0_45]) ).
cnf(c_0_70,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_65,c_0_66]),c_0_67]),c_0_51]),c_0_68]),c_0_53])]),c_0_69]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM556+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/5.38 % Computer : n015.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Mon Sep 21 02:42:56 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.15/5.49 % Version: 3.5.1
% 0.15/5.49 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.49 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.49 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.49 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.49 % Starting sh5l with 300s (1) cores
% 0.15/5.49 % new_bool_3 with pid 382290 completed with status 0
% 0.15/5.49 % Result found by new_bool_3
% 0.15/5.49 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.49 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.49 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.49 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.15/5.49 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.49 % Starting SubtermCWHack with 28s (1) cores
% 0.15/5.49 % SubtermCWHack with pid 382293 completed with status 0
% 0.15/5.49 % Result found by SubtermCWHack
% 0.15/5.49 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.49 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.49 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.49 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.15/5.49 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.49 % Starting SubtermCWHack with 28s (1) cores
% 0.15/5.49 % Preprocessing time : 0.002 s
% 0.15/5.49
% 0.15/5.49 % Proof found!
% 0.15/5.49 % SZS status Theorem
% 0.15/5.49 % SZS output start CNFRefutation
% See solution above
% 0.15/5.49 % Parsed axioms : 72
% 0.15/5.49 % Removed by relevancy pruning/SinE : 5
% 0.15/5.49 % Initial clauses : 163
% 0.15/5.49 % Removed in clause preprocessing : 5
% 0.15/5.49 % Initial clauses in saturation : 158
% 0.15/5.49 % Processed clauses : 517
% 0.15/5.49 % ...of these trivial : 5
% 0.15/5.49 % ...subsumed : 151
% 0.15/5.49 % ...remaining for further processing : 361
% 0.15/5.49 % Other redundant clauses eliminated : 33
% 0.15/5.49 % Clauses deleted for lack of memory : 0
% 0.15/5.49 % Backward-subsumed : 28
% 0.15/5.49 % Backward-rewritten : 9
% 0.15/5.49 % Generated clauses : 870
% 0.15/5.49 % ...of the previous two non-redundant : 693
% 0.15/5.49 % ...aggressively subsumed : 0
% 0.15/5.49 % Contextual simplify-reflections : 19
% 0.15/5.49 % Paramodulations : 839
% 0.15/5.49 % Factorizations : 0
% 0.15/5.49 % NegExts : 0
% 0.15/5.49 % Equation resolutions : 34
% 0.15/5.49 % Disequality decompositions : 0
% 0.15/5.49 % Total rewrite steps : 700
% 0.15/5.49 % ...of those cached : 650
% 0.15/5.49 % Propositional unsat checks : 0
% 0.15/5.49 % Propositional check models : 0
% 0.15/5.49 % Propositional check unsatisfiable : 0
% 0.15/5.49 % Propositional clauses : 0
% 0.15/5.49 % Propositional clauses after purity: 0
% 0.15/5.49 % Propositional unsat core size : 0
% 0.15/5.49 % Propositional preprocessing time : 0.000
% 0.15/5.49 % Propositional encoding time : 0.000
% 0.15/5.49 % Propositional solver time : 0.000
% 0.15/5.49 % Success case prop preproc time : 0.000
% 0.15/5.49 % Success case prop encoding time : 0.000
% 0.15/5.49 % Success case prop solver time : 0.000
% 0.15/5.49 % Current number of processed clauses : 298
% 0.15/5.49 % Positive orientable unit clauses : 59
% 0.15/5.49 % Positive unorientable unit clauses: 0
% 0.15/5.49 % Negative unit clauses : 23
% 0.15/5.49 % Non-unit-clauses : 216
% 0.15/5.49 % Current number of unprocessed clauses: 315
% 0.15/5.49 % ...number of literals in the above : 1443
% 0.15/5.49 % Current number of archived formulas : 0
% 0.15/5.49 % Current number of archived clauses : 37
% 0.15/5.49 % Clause-clause subsumption calls (NU) : 5001
% 0.15/5.49 % Rec. Clause-clause subsumption calls : 3113
% 0.15/5.49 % Non-unit clause-clause subsumptions : 149
% 0.15/5.49 % Unit Clause-clause subsumption calls : 1182
% 0.15/5.49 % Rewrite failures with RHS unbound : 0
% 0.15/5.49 % BW rewrite match attempts : 5
% 0.15/5.49 % BW rewrite match successes : 5
% 0.15/5.49 % Condensation attempts : 0
% 0.15/5.49 % Condensation successes : 0
% 0.15/5.49 % Termbank termtop insertions : 23971
% 0.15/5.49 % Search garbage collected termcells : 2646
% 0.15/5.49
% 0.15/5.49 % -------------------------------------------------
% 0.15/5.49 % User time : 0.033 s
% 0.15/5.49 % System time : 0.002 s
% 0.15/5.49 % Total time : 0.034 s
% 0.15/5.49 % Maximum resident set size: 3976 pages
% 0.15/5.49
% 0.15/5.49 % -------------------------------------------------
% 0.15/5.49 % User time : 0.037 s
% 0.15/5.49 % System time : 0.005 s
% 0.15/5.49 % Total time : 0.042 s
% 0.15/5.49 % Maximum resident set size: 4864 pages
% 0.15/5.49 % E exiting
%------------------------------------------------------------------------------