%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM556+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 : 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 01:55:29 PM UTC 2026
% Result : Theorem 0.15s 5.51s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 71 ( 23 unt; 0 def)
% Number of atoms : 350 ( 70 equ)
% Maximal formula atoms : 67 ( 4 avg)
% Number of connectives : 406 ( 127 ~; 123 |; 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/sandbox/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/sandbox/benchmark/theBenchmark.p',m__2357) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(mDiffCons,axiom,
! [X1,X2] :
( ( aSet0(X2)
& aElement0(X1) )
=> ( ~ aElementOf0(X1,X2)
=> sdtmndt0(sdtpldt0(X2,X1),X1) = X2 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',m__2411) ).
fof(mFConsSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( isFinite0(X2)
& aSet0(X2) )
=> isFinite0(sdtpldt0(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFConsSet) ).
fof(m__2256,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2256) ).
fof(mFDiffSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( isFinite0(X2)
& aSet0(X2) )
=> isFinite0(sdtmndt0(X2,X1)) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mCardCons) ).
fof(m__2291,hypothesis,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
fof(m__2304,hypothesis,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2304) ).
fof(m__,conjecture,
( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xS) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mCardDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( ( aElementOf0(X2,X1)
& isFinite0(X1) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardDiff) ).
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/sandbox/benchmark/theBenchmark.p',m__2227) ).
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,plain,
! [X7,X8] :
( aElement0(X8)
| ~ aElementOf0(X8,X7)
| ~ aSet0(X7) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
fof(c_0_18,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(fof_nnf,[status(thm)],[c_0_15]) ).
fof(c_0_19,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_20,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_21,plain,
! [X52,X53] :
( isFinite0(sdtpldt0(X53,X52))
| ~ isFinite0(X53)
| ~ aSet0(X53)
| ~ aElement0(X52) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFConsSet])])])]) ).
fof(c_0_22,hypothesis,
! [X146,X147] :
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ( aElementOf0(X147,xP)
| ~ aElement0(X147)
| X147 != xx )
& ( aElementOf0(X147,xP)
| ~ aElement0(X147)
| ~ aElementOf0(X147,sdtmndt0(xQ,xy)) )
& ( ~ aElementOf0(X147,xP)
| X147 = xx
| aElementOf0(X147,sdtmndt0(xQ,xy)) )
& ( ~ aElementOf0(X147,xP)
| aElement0(X147) )
& aSet0(xP)
& ( aElementOf0(X146,sdtmndt0(xQ,xy))
| X146 = xy
| ~ aElementOf0(X146,xQ)
| ~ aElement0(X146) )
& ( ~ aElementOf0(X146,sdtmndt0(xQ,xy))
| X146 != xy )
& ( ~ aElementOf0(X146,sdtmndt0(xQ,xy))
| aElementOf0(X146,xQ) )
& ( ~ aElementOf0(X146,sdtmndt0(xQ,xy))
| aElement0(X146) )
& 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])])])])]) ).
cnf(c_0_23,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__2256]) ).
cnf(c_0_25,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_26,plain,
! [X46,X47] :
( sdtmndt0(sdtpldt0(X47,X46),X46) = X47
| aElementOf0(X46,X47)
| ~ aSet0(X47)
| ~ aElement0(X46) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
fof(c_0_27,hypothesis,
! [X148] :
( ( aElementOf0(X148,sdtmndt0(xQ,xy))
| X148 = xy
| ~ aElementOf0(X148,xQ)
| ~ aElement0(X148) )
& ( ~ aElementOf0(X148,sdtmndt0(xQ,xy))
| X148 != xy )
& ( ~ aElementOf0(X148,sdtmndt0(xQ,xy))
| aElementOf0(X148,xQ) )
& ( ~ aElementOf0(X148,sdtmndt0(xQ,xy))
| aElement0(X148) )
& 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_20])])])])]) ).
cnf(c_0_28,plain,
( ~ isFinite0(X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| isFinite0(sdtpldt0(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_31,hypothesis,
aSet0(sdtmndt0(xQ,xy)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_32,plain,
! [X54,X55] :
( isFinite0(sdtmndt0(X55,X54))
| ~ isFinite0(X55)
| ~ aSet0(X55)
| ~ aElement0(X54) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFDiffSet])])])]) ).
fof(c_0_33,hypothesis,
! [X145] :
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ( aElementOf0(X145,xS)
| ~ aElementOf0(X145,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])])])]) ).
fof(c_0_34,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_35,plain,
( ~ aSet0(X2)
| ~ aElement0(X1)
| sdtmndt0(sdtpldt0(X2,X1),X1) = X2
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,hypothesis,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,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_28,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_38,plain,
( ~ isFinite0(X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| isFinite0(sdtmndt0(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,hypothesis,
isFinite0(xQ),
inference(split_conjunct,[status(thm)],[m__2291]) ).
cnf(c_0_40,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__2304]) ).
cnf(c_0_41,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_42,plain,
! [X83,X84] :
( sbrdtbr0(sdtpldt0(X83,X84)) = szszuzczcdt0(sbrdtbr0(X83))
| aElementOf0(X84,X83)
| ~ aElement0(X84)
| ~ isFinite0(X83)
| ~ aSet0(X83) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).
cnf(c_0_43,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_35,c_0_29]),c_0_30]),c_0_31])]),c_0_36]) ).
cnf(c_0_44,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_37,c_0_38]),c_0_39]),c_0_40]),c_0_41])]) ).
cnf(c_0_45,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_46,negated_conjecture,
~ ( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xS) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_47,plain,
( ~ aElement0(X2)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1))
| aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,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_38,c_0_43]),c_0_44]),c_0_30]),c_0_45])]) ).
fof(c_0_49,plain,
! [X85,X86] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X85,X86))) = sbrdtbr0(X85)
| ~ aElementOf0(X86,X85)
| ~ isFinite0(X85)
| ~ aSet0(X85) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardDiff])])])]) ).
fof(c_0_50,negated_conjecture,
( ( sbrdtbr0(xP) != xk
| ~ aSubsetOf0(xP,xS) )
& ( sbrdtbr0(xP) != xk
| ~ aElementOf0(esk16_0,xS) )
& ( sbrdtbr0(xP) != xk
| aElementOf0(esk16_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_46])])])])]) ).
cnf(c_0_51,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_47,c_0_29]),c_0_48]),c_0_30]),c_0_31])]),c_0_36]) ).
cnf(c_0_52,plain,
( ~ aElementOf0(X2,X1)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,hypothesis,
sbrdtbr0(xQ) = xk,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_54,hypothesis,
aElementOf0(xy,xQ),
inference(split_conjunct,[status(thm)],[m__2304]) ).
fof(c_0_55,hypothesis,
! [X131,X132,X133,X135,X136,X137,X139,X140,X141,X142] :
( slbdtsldtrb0(xS,xk) != slcrc0
& aElementOf0(esk15_0,slbdtsldtrb0(xS,xk))
& ( aElementOf0(X142,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X142) != xk
| ~ aSubsetOf0(X142,xS) )
& ( aElementOf0(X142,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X142) != xk
| ~ aSet0(X142)
| ~ aElementOf0(esk14_1(X142),xS) )
& ( aElementOf0(X142,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X142) != xk
| ~ aSet0(X142)
| aElementOf0(esk14_1(X142),X142) )
& ( ~ aElementOf0(X140,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X140) = xk )
& ( ~ aElementOf0(X140,slbdtsldtrb0(xS,xk))
| aSubsetOf0(X140,xS) )
& ( ~ aElementOf0(X140,slbdtsldtrb0(xS,xk))
| aElementOf0(X141,xS)
| ~ aElementOf0(X141,X140) )
& ( ~ aElementOf0(X140,slbdtsldtrb0(xS,xk))
| aSet0(X140) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ( aElementOf0(X139,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X139,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X137,slbdtsldtrb0(xT,xk))
| sbrdtbr0(X137) != xk
| ~ aSubsetOf0(X137,xT) )
& ( aElementOf0(X137,slbdtsldtrb0(xT,xk))
| sbrdtbr0(X137) != xk
| ~ aSet0(X137)
| ~ aElementOf0(esk13_1(X137),xT) )
& ( aElementOf0(X137,slbdtsldtrb0(xT,xk))
| sbrdtbr0(X137) != xk
| ~ aSet0(X137)
| aElementOf0(esk13_1(X137),X137) )
& ( ~ aElementOf0(X135,slbdtsldtrb0(xT,xk))
| sbrdtbr0(X135) = xk )
& ( ~ aElementOf0(X135,slbdtsldtrb0(xT,xk))
| aSubsetOf0(X135,xT) )
& ( ~ aElementOf0(X135,slbdtsldtrb0(xT,xk))
| aElementOf0(X136,xT)
| ~ aElementOf0(X136,X135) )
& ( ~ aElementOf0(X135,slbdtsldtrb0(xT,xk))
| aSet0(X135) )
& aSet0(slbdtsldtrb0(xT,xk))
& ( aElementOf0(X133,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X133) != xk
| ~ aSubsetOf0(X133,xS) )
& ( aElementOf0(X133,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X133) != xk
| ~ aSet0(X133)
| ~ aElementOf0(esk12_1(X133),xS) )
& ( aElementOf0(X133,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X133) != xk
| ~ aSet0(X133)
| aElementOf0(esk12_1(X133),X133) )
& ( ~ aElementOf0(X131,slbdtsldtrb0(xS,xk))
| sbrdtbr0(X131) = xk )
& ( ~ aElementOf0(X131,slbdtsldtrb0(xS,xk))
| aSubsetOf0(X131,xS) )
& ( ~ aElementOf0(X131,slbdtsldtrb0(xS,xk))
| aElementOf0(X132,xS)
| ~ aElementOf0(X132,X131) )
& ( ~ aElementOf0(X131,slbdtsldtrb0(xS,xk))
| aSet0(X131) )
& 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])])])])])])]) ).
cnf(c_0_56,hypothesis,
( ~ aElementOf0(X1,sdtmndt0(xQ,xy))
| aElementOf0(X1,xQ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_57,hypothesis,
( ~ aElementOf0(X1,xP)
| X1 = xx
| aElementOf0(X1,sdtmndt0(xQ,xy)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_58,negated_conjecture,
( sbrdtbr0(xP) != xk
| aElementOf0(esk16_0,xP) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_59,hypothesis,
sbrdtbr0(xP) = xk,
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_51,c_0_52]),c_0_53]),c_0_39]),c_0_54]),c_0_41])]) ).
cnf(c_0_60,hypothesis,
( ~ aElementOf0(X2,slbdtsldtrb0(xS,xk))
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,hypothesis,
( sbrdtbr0(X1) != xk
| ~ aSubsetOf0(X1,xS)
| aElementOf0(X1,slbdtsldtrb0(xS,xk)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,hypothesis,
( ~ aElementOf0(X1,xP)
| aElementOf0(X1,xQ)
| X1 = xx ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,negated_conjecture,
aElementOf0(esk16_0,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).
cnf(c_0_64,negated_conjecture,
( sbrdtbr0(xP) != xk
| ~ aElementOf0(esk16_0,xS) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_65,hypothesis,
( ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,xS)
| sbrdtbr0(X2) != xk
| aElementOf0(X1,xS) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,hypothesis,
( aElementOf0(esk16_0,xQ)
| esk16_0 = xx ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,hypothesis,
aSubsetOf0(xQ,xS),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_68,negated_conjecture,
~ aElementOf0(esk16_0,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_59])]) ).
cnf(c_0_69,hypothesis,
esk16_0 = xx,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_53]),c_0_67])]),c_0_68]) ).
cnf(c_0_70,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69]),c_0_24])]),
[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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.39 % Computer : n015.cluster.edu
% 0.13/5.39 % Model : x86_64 x86_64
% 0.13/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.39 % Memory : 8046.5625MB
% 0.13/5.39 % OS : Linux 6.8.0-71-generic
% 0.13/5.39 % CPULimit : 300
% 0.13/5.39 % WCLimit : 300
% 0.13/5.39 % DateTime : Mon Sep 21 02:42:56 UTC 2026
% 0.13/5.40 % CPUTime :
% 0.13/5.40 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.44 Running first-order theorem proving
% 0.15/5.44 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
% 0.15/5.51 % Version: 3.5.1
% 0.15/5.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.51 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.51 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.51 % Starting sh5l with 300s (1) cores
% 0.15/5.51 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 382261 completed with status 0
% 0.15/5.51 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.15/5.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.51 % No SInE strategy applied
% 0.15/5.51 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.15/5.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.51 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.15/5.51 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/5.51 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.15/5.51 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 136s (1) cores
% 0.15/5.51 % SubtermCWHack with pid 382266 completed with status 0
% 0.15/5.51 % Result found by SubtermCWHack
% 0.15/5.51 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.51 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.51 % No SInE strategy applied
% 0.15/5.51 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.15/5.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.51 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.51 % Preprocessing time : 0.002 s
% 0.15/5.51
% 0.15/5.51 % Proof found!
% 0.15/5.51 % SZS status Theorem
% 0.15/5.51 % SZS output start CNFRefutation
% See solution above
% 0.15/5.51 % Parsed axioms : 72
% 0.15/5.51 % Removed by relevancy pruning/SinE : 0
% 0.15/5.51 % Initial clauses : 174
% 0.15/5.51 % Removed in clause preprocessing : 6
% 0.15/5.51 % Initial clauses in saturation : 168
% 0.15/5.51 % Processed clauses : 683
% 0.15/5.51 % ...of these trivial : 10
% 0.15/5.51 % ...subsumed : 199
% 0.15/5.51 % ...remaining for further processing : 474
% 0.15/5.51 % Other redundant clauses eliminated : 47
% 0.15/5.51 % Clauses deleted for lack of memory : 0
% 0.15/5.51 % Backward-subsumed : 41
% 0.15/5.51 % Backward-rewritten : 42
% 0.15/5.51 % Generated clauses : 1484
% 0.15/5.51 % ...of the previous two non-redundant : 1275
% 0.15/5.51 % ...aggressively subsumed : 0
% 0.15/5.51 % Contextual simplify-reflections : 18
% 0.15/5.51 % Paramodulations : 1439
% 0.15/5.51 % Factorizations : 0
% 0.15/5.51 % NegExts : 0
% 0.15/5.51 % Equation resolutions : 48
% 0.15/5.51 % Disequality decompositions : 0
% 0.15/5.51 % Total rewrite steps : 1018
% 0.15/5.51 % ...of those cached : 960
% 0.15/5.51 % Propositional unsat checks : 0
% 0.15/5.51 % Propositional check models : 0
% 0.15/5.51 % Propositional check unsatisfiable : 0
% 0.15/5.51 % Propositional clauses : 0
% 0.15/5.51 % Propositional clauses after purity: 0
% 0.15/5.51 % Propositional unsat core size : 0
% 0.15/5.51 % Propositional preprocessing time : 0.000
% 0.15/5.51 % Propositional encoding time : 0.000
% 0.15/5.51 % Propositional solver time : 0.000
% 0.15/5.51 % Success case prop preproc time : 0.000
% 0.15/5.51 % Success case prop encoding time : 0.000
% 0.15/5.51 % Success case prop solver time : 0.000
% 0.15/5.51 % Current number of processed clauses : 361
% 0.15/5.51 % Positive orientable unit clauses : 60
% 0.15/5.51 % Positive unorientable unit clauses: 0
% 0.15/5.51 % Negative unit clauses : 22
% 0.15/5.51 % Non-unit-clauses : 279
% 0.15/5.51 % Current number of unprocessed clauses: 747
% 0.15/5.51 % ...number of literals in the above : 3428
% 0.15/5.51 % Current number of archived formulas : 0
% 0.15/5.51 % Current number of archived clauses : 83
% 0.15/5.51 % Clause-clause subsumption calls (NU) : 7815
% 0.15/5.51 % Rec. Clause-clause subsumption calls : 5408
% 0.15/5.51 % Non-unit clause-clause subsumptions : 172
% 0.15/5.51 % Unit Clause-clause subsumption calls : 2471
% 0.15/5.51 % Rewrite failures with RHS unbound : 0
% 0.15/5.51 % BW rewrite match attempts : 10
% 0.15/5.51 % BW rewrite match successes : 10
% 0.15/5.51 % Condensation attempts : 0
% 0.15/5.51 % Condensation successes : 0
% 0.15/5.51 % Termbank termtop insertions : 33020
% 0.15/5.51 % Search garbage collected termcells : 2906
% 0.15/5.51
% 0.15/5.51 % -------------------------------------------------
% 0.15/5.51 % User time : 0.036 s
% 0.15/5.51 % System time : 0.011 s
% 0.15/5.51 % Total time : 0.047 s
% 0.15/5.51 % Maximum resident set size: 3976 pages
% 0.15/5.51
% 0.15/5.51 % -------------------------------------------------
% 0.15/5.51 % User time : 0.164 s
% 0.15/5.51 % System time : 0.027 s
% 0.15/5.51 % Total time : 0.191 s
% 0.15/5.51 % Maximum resident set size: 4864 pages
% 0.15/5.51 % E exiting
%------------------------------------------------------------------------------