%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM554+1 : 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 : n013.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 01:49:32 PM UTC 2026
% Result : Theorem 1.20s 0.68s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 94 ( 33 unt; 0 def)
% Number of atoms : 416 ( 80 equ)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 547 ( 225 ~; 241 |; 54 &)
% ( 9 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-3 aty)
% Number of variables : 130 ( 0 sgn 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2202_02,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
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(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(mDefCons,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtpldt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( ( X4 = X2
| aElementOf0(X4,X1) )
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
fof(m__2256,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).
fof(mFConsSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( isFinite0(X2)
& aSet0(X2) )
=> isFinite0(sdtpldt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).
fof(mDefSel,axiom,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aSet0(X1) )
=> ! [X3] :
( X3 = slbdtsldtrb0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( sbrdtbr0(X4) = X2
& aSubsetOf0(X4,X1) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(m__2357,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).
fof(m__2323,hypothesis,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2323) ).
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__2304,hypothesis,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
fof(m__2291,hypothesis,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(m__2270,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
fof(m__2202,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202) ).
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(m__,conjecture,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_18,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(fof_simplification,[status(thm)],[m__2202_02]) ).
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,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_21,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
fof(c_0_22,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_23,plain,
! [X30,X31,X32,X33,X34,X35] :
( ( ~ aElement0(X31)
| ~ aSet0(X30)
| X35 = sdtpldt0(X30,X31)
| ~ aSet0(X35)
| aElementOf0(esk3_3(X30,X31,X35),X35)
| esk3_3(X30,X31,X35) = X31
| aElementOf0(esk3_3(X30,X31,X35),X30) )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X35 = sdtpldt0(X30,X31)
| ~ aSet0(X35)
| aElementOf0(esk3_3(X30,X31,X35),X35)
| aElement0(esk3_3(X30,X31,X35)) )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X35 = sdtpldt0(X30,X31)
| ~ aSet0(X35)
| ~ aElementOf0(esk3_3(X30,X31,X35),X35)
| ~ aElement0(esk3_3(X30,X31,X35))
| esk3_3(X30,X31,X35) != X31 )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X35 = sdtpldt0(X30,X31)
| ~ aSet0(X35)
| ~ aElementOf0(esk3_3(X30,X31,X35),X35)
| ~ aElement0(esk3_3(X30,X31,X35))
| ~ aElementOf0(esk3_3(X30,X31,X35),X30) )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X32 != sdtpldt0(X30,X31)
| aElementOf0(X34,X32)
| ~ aElement0(X34)
| X34 != X31 )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X32 != sdtpldt0(X30,X31)
| aElementOf0(X34,X32)
| ~ aElement0(X34)
| ~ aElementOf0(X34,X30) )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X32 != sdtpldt0(X30,X31)
| ~ aElementOf0(X33,X32)
| X33 = X31
| aElementOf0(X33,X30) )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X32 != sdtpldt0(X30,X31)
| ~ aElementOf0(X33,X32)
| aElement0(X33) )
& ( ~ aElement0(X31)
| ~ aSet0(X30)
| X32 != sdtpldt0(X30,X31)
| aSet0(X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefCons])])])])])])]) ).
fof(c_0_24,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])])]) ).
cnf(c_0_25,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__2256]) ).
cnf(c_0_27,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_28,plain,
! [X37,X38,X39,X40,X41,X42] :
( ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| aElementOf0(esk4_3(X37,X38,X42),X42)
| esk4_3(X37,X38,X42) != X38 )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| aElementOf0(esk4_3(X37,X38,X42),X42)
| aElementOf0(esk4_3(X37,X38,X42),X37) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| aElementOf0(esk4_3(X37,X38,X42),X42)
| aElement0(esk4_3(X37,X38,X42)) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X42)
| esk4_3(X37,X38,X42) = X38
| ~ aElementOf0(esk4_3(X37,X38,X42),X37)
| ~ aElement0(esk4_3(X37,X38,X42))
| ~ aElementOf0(esk4_3(X37,X38,X42),X42) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| aElementOf0(X41,X39)
| X41 = X38
| ~ aElementOf0(X41,X37)
| ~ aElement0(X41) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| ~ aElementOf0(X40,X39)
| X40 != X38 )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| ~ aElementOf0(X40,X39)
| aElementOf0(X40,X37) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| ~ aElementOf0(X40,X39)
| aElement0(X40) )
& ( ~ aElement0(X38)
| ~ aSet0(X37)
| X39 != sdtmndt0(X37,X38)
| aSet0(X39) ) ),
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_22])])])])])])]) ).
fof(c_0_29,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_30,plain,
! [X118,X119,X120,X121,X122,X123] :
( ( ~ aElementOf0(X119,szNzAzT0)
| ~ aSet0(X118)
| X123 = slbdtsldtrb0(X118,X119)
| ~ aSet0(X123)
| aElementOf0(esk11_3(X118,X119,X123),X123)
| sbrdtbr0(esk11_3(X118,X119,X123)) = X119 )
& ( ~ aElementOf0(X119,szNzAzT0)
| ~ aSet0(X118)
| X123 = slbdtsldtrb0(X118,X119)
| ~ aSet0(X123)
| aElementOf0(esk11_3(X118,X119,X123),X123)
| aSubsetOf0(esk11_3(X118,X119,X123),X118) )
& ( ~ aElementOf0(X119,szNzAzT0)
| ~ aSet0(X118)
| X123 = slbdtsldtrb0(X118,X119)
| ~ aSet0(X123)
| sbrdtbr0(esk11_3(X118,X119,X123)) != X119
| ~ aSubsetOf0(esk11_3(X118,X119,X123),X118)
| ~ aElementOf0(esk11_3(X118,X119,X123),X123) )
& ( ~ aElementOf0(X119,szNzAzT0)
| ~ aSet0(X118)
| X120 != slbdtsldtrb0(X118,X119)
| aElementOf0(X122,X120)
| sbrdtbr0(X122) != X119
| ~ aSubsetOf0(X122,X118) )
& ( ~ aElementOf0(X119,szNzAzT0)
| ~ aSet0(X118)
| X120 != slbdtsldtrb0(X118,X119)
| ~ aElementOf0(X121,X120)
| sbrdtbr0(X121) = X119 )
& ( ~ aElementOf0(X119,szNzAzT0)
| ~ aSet0(X118)
| X120 != slbdtsldtrb0(X118,X119)
| ~ aElementOf0(X121,X120)
| aSubsetOf0(X121,X118) )
& ( ~ aElementOf0(X119,szNzAzT0)
| ~ aSet0(X118)
| X120 != slbdtsldtrb0(X118,X119)
| aSet0(X120) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSel])])])])])])]) ).
cnf(c_0_31,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X4 != sdtpldt0(X2,X3)
| ~ aElementOf0(X1,X4)
| X1 = X3
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( ~ aSet0(X2)
| ~ aElement0(X1)
| sdtmndt0(sdtpldt0(X2,X1),X1) = X2
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(split_conjunct,[status(thm)],[m__2357]) ).
cnf(c_0_34,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_35,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X1 != sdtmndt0(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_36,hypothesis,
~ aElementOf0(xx,xQ),
inference(fof_simplification,[status(thm)],[m__2323]) ).
cnf(c_0_37,plain,
( ~ isFinite0(X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| isFinite0(sdtpldt0(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_38,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])])])]) ).
cnf(c_0_39,plain,
( ~ aElement0(X2)
| ~ aSet0(X4)
| X3 != sdtpldt0(X4,X2)
| ~ aElement0(X1)
| X1 != X2
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_40,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X1 != sdtpldt0(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_41,plain,
( ~ aElementOf0(X4,szNzAzT0)
| ~ aSet0(X2)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aElementOf0(X1,X3)
| aSubsetOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,plain,
( ~ aSet0(X3)
| ~ aElement0(X2)
| ~ aElementOf0(X1,sdtpldt0(X3,X2))
| aElementOf0(X1,X3)
| X1 = X2 ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_43,plain,
( ~ aElement0(X4)
| ~ aSet0(X2)
| X3 != sdtmndt0(X2,X4)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_44,hypothesis,
( ~ aSet0(sdtmndt0(xQ,xy))
| aElementOf0(xx,sdtmndt0(xQ,xy))
| sdtmndt0(xP,xx) = sdtmndt0(xQ,xy) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_45,plain,
( ~ aSet0(X1)
| ~ aElement0(X2)
| aSet0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_46,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__2304]) ).
cnf(c_0_47,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[m__2291]) ).
fof(c_0_48,hypothesis,
~ aElementOf0(xx,xQ),
inference(fof_nnf,[status(thm)],[c_0_36]) ).
cnf(c_0_49,hypothesis,
( ~ aSet0(sdtmndt0(xQ,xy))
| ~ isFinite0(sdtmndt0(xQ,xy))
| isFinite0(xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_33]),c_0_34])]) ).
cnf(c_0_50,plain,
( ~ isFinite0(X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| isFinite0(sdtmndt0(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_51,hypothesis,
isFinite0(xQ),
inference(split_conjunct,[status(thm)],[m__2291]) ).
cnf(c_0_52,plain,
( ~ aSet0(X2)
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(X2,X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_39])]) ).
cnf(c_0_53,plain,
( ~ aSet0(X1)
| ~ aElement0(X2)
| aSet0(sdtpldt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_40]) ).
fof(c_0_54,plain,
! [X17,X18,X19,X20] :
( ( ~ aSet0(X17)
| aSubsetOf0(X20,X17)
| ~ aSet0(X20)
| ~ aElementOf0(esk2_2(X17,X20),X17) )
& ( ~ aSet0(X17)
| aSubsetOf0(X20,X17)
| ~ aSet0(X20)
| aElementOf0(esk2_2(X17,X20),X20) )
& ( ~ aSet0(X17)
| ~ aSubsetOf0(X18,X17)
| aElementOf0(X19,X17)
| ~ aElementOf0(X19,X18) )
& ( ~ aSet0(X17)
| ~ aSubsetOf0(X18,X17)
| aSet0(X18) ) ),
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])])])])])])]) ).
cnf(c_0_55,plain,
( ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| aSubsetOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_56,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[m__2270]) ).
cnf(c_0_57,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__2202]) ).
cnf(c_0_58,hypothesis,
( ~ aSet0(sdtmndt0(xQ,xy))
| ~ aElementOf0(X1,xP)
| aElementOf0(X1,sdtmndt0(xQ,xy))
| X1 = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_33]),c_0_34])]) ).
fof(c_0_59,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])])])]) ).
cnf(c_0_60,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| aElementOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_61,hypothesis,
( aElementOf0(xx,sdtmndt0(xQ,xy))
| sdtmndt0(xP,xx) = sdtmndt0(xQ,xy) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_62,hypothesis,
~ aElementOf0(xx,xQ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_63,hypothesis,
( ~ aSet0(sdtmndt0(xQ,xy))
| 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_46]),c_0_47])]) ).
cnf(c_0_64,hypothesis,
( ~ aSet0(sdtmndt0(xQ,xy))
| aElementOf0(xx,xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_33]),c_0_34])]) ).
cnf(c_0_65,hypothesis,
( ~ aSet0(sdtmndt0(xQ,xy))
| aSet0(xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_33]),c_0_34])]) ).
cnf(c_0_66,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_67,hypothesis,
aSubsetOf0(xQ,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_27])]) ).
cnf(c_0_68,hypothesis,
( ~ aElementOf0(X1,xP)
| aElementOf0(X1,sdtmndt0(xQ,xy))
| X1 = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_45]),c_0_46]),c_0_47])]) ).
fof(c_0_69,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_70,plain,
( ~ aElementOf0(X2,X1)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_71,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_60,c_0_61]),c_0_46]),c_0_47])]),c_0_62]) ).
cnf(c_0_72,hypothesis,
isFinite0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_73,hypothesis,
aElementOf0(xx,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_74,hypothesis,
aSet0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_75,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_76,hypothesis,
( ~ aElementOf0(X1,xQ)
| aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_27])]) ).
cnf(c_0_77,hypothesis,
( ~ aElementOf0(X1,xP)
| aElementOf0(X1,xQ)
| X1 = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_68]),c_0_46]),c_0_47])]) ).
cnf(c_0_78,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSubsetOf0(X2,X1)
| aElementOf0(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_79,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
cnf(c_0_80,plain,
( ~ aElementOf0(X3,szNzAzT0)
| ~ aSet0(X2)
| X4 != slbdtsldtrb0(X2,X3)
| sbrdtbr0(X1) != X3
| ~ aSubsetOf0(X1,X2)
| aElementOf0(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_81,hypothesis,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),c_0_73]),c_0_74])]) ).
cnf(c_0_82,hypothesis,
sbrdtbr0(xQ) = xk,
inference(split_conjunct,[status(thm)],[m__2291]) ).
cnf(c_0_83,hypothesis,
aElementOf0(xy,xQ),
inference(split_conjunct,[status(thm)],[m__2304]) ).
cnf(c_0_84,hypothesis,
( ~ aSet0(X1)
| ~ aElementOf0(esk2_2(xS,X1),xQ)
| aSubsetOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_27])]) ).
cnf(c_0_85,hypothesis,
( ~ aSet0(X1)
| aElementOf0(esk2_2(X1,xP),xQ)
| aSubsetOf0(xP,X1)
| esk2_2(X1,xP) = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_74])]) ).
fof(c_0_86,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(fof_nnf,[status(thm)],[c_0_79]) ).
cnf(c_0_87,plain,
( ~ aSet0(X2)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSubsetOf0(X1,X2)
| aElementOf0(X1,slbdtsldtrb0(X2,sbrdtbr0(X1))) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_80])]) ).
cnf(c_0_88,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_70,c_0_81]),c_0_82]),c_0_51]),c_0_83]),c_0_47])]) ).
cnf(c_0_89,hypothesis,
( aSubsetOf0(xP,xS)
| esk2_2(xS,xP) = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_74]),c_0_27])]) ).
cnf(c_0_90,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_91,hypothesis,
( ~ aSet0(X1)
| ~ aSubsetOf0(xP,X1)
| aElementOf0(xP,slbdtsldtrb0(X1,xk)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_57])]) ).
cnf(c_0_92,hypothesis,
aSubsetOf0(xP,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_89]),c_0_26]),c_0_74]),c_0_27])]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM554+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n013.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 02:39:06 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.50 Running first-order theorem proving
% 0.16/0.50 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
% 1.20/0.68 % Version: 3.5.1
% 1.20/0.68 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.20/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/0.68 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.20/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.20/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.20/0.68 % Starting sh5l with 300s (1) cores
% 1.20/0.68 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 3967438 completed with status 0
% 1.20/0.68 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.20/0.68 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.20/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/0.68 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.20/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.20/0.68 % No SInE strategy applied
% 1.20/0.68 % Search class: FGHSF-FSMM31-MFFFFFNN
% 1.20/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.20/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.20/0.68 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.20/0.68 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 1.20/0.68 % Starting new_bool_3 with 136s (1) cores
% 1.20/0.68 % Starting new_bool_1 with 136s (1) cores
% 1.20/0.68 % SubtermCWHack with pid 3967444 completed with status 0
% 1.20/0.68 % Result found by SubtermCWHack
% 1.20/0.68 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.20/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/0.68 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.20/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.20/0.68 % No SInE strategy applied
% 1.20/0.68 % Search class: FGHSF-FSMM31-MFFFFFNN
% 1.20/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.20/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.20/0.68 % Preprocessing time : 0.004 s
% 1.20/0.68
% 1.20/0.68 % Proof found!
% 1.20/0.68 % SZS status Theorem
% 1.20/0.68 % SZS output start CNFRefutation
% See solution above
% 1.20/0.68 % Parsed axioms : 71
% 1.20/0.68 % Removed by relevancy pruning/SinE : 0
% 1.20/0.68 % Initial clauses : 127
% 1.20/0.68 % Removed in clause preprocessing : 6
% 1.20/0.68 % Initial clauses in saturation : 121
% 1.20/0.68 % Processed clauses : 1043
% 1.20/0.68 % ...of these trivial : 5
% 1.20/0.68 % ...subsumed : 470
% 1.20/0.68 % ...remaining for further processing : 568
% 1.20/0.68 % Other redundant clauses eliminated : 34
% 1.20/0.68 % Clauses deleted for lack of memory : 0
% 1.20/0.68 % Backward-subsumed : 49
% 1.20/0.68 % Backward-rewritten : 25
% 1.20/0.68 % Generated clauses : 2168
% 1.20/0.68 % ...of the previous two non-redundant : 1914
% 1.20/0.68 % ...aggressively subsumed : 0
% 1.20/0.68 % Contextual simplify-reflections : 83
% 1.20/0.68 % Paramodulations : 2136
% 1.20/0.68 % Factorizations : 0
% 1.20/0.68 % NegExts : 0
% 1.20/0.68 % Equation resolutions : 35
% 1.20/0.68 % Disequality decompositions : 0
% 1.20/0.68 % Total rewrite steps : 1310
% 1.20/0.68 % ...of those cached : 1267
% 1.20/0.68 % Propositional unsat checks : 0
% 1.20/0.68 % Propositional check models : 0
% 1.20/0.68 % Propositional check unsatisfiable : 0
% 1.20/0.68 % Propositional clauses : 0
% 1.20/0.68 % Propositional clauses after purity: 0
% 1.20/0.68 % Propositional unsat core size : 0
% 1.20/0.68 % Propositional preprocessing time : 0.000
% 1.20/0.68 % Propositional encoding time : 0.000
% 1.20/0.68 % Propositional solver time : 0.000
% 1.20/0.68 % Success case prop preproc time : 0.000
% 1.20/0.68 % Success case prop encoding time : 0.000
% 1.20/0.68 % Success case prop solver time : 0.000
% 1.20/0.68 % Current number of processed clauses : 467
% 1.20/0.68 % Positive orientable unit clauses : 48
% 1.20/0.68 % Positive unorientable unit clauses: 0
% 1.20/0.68 % Negative unit clauses : 16
% 1.20/0.68 % Non-unit-clauses : 403
% 1.20/0.68 % Current number of unprocessed clauses: 913
% 1.20/0.68 % ...number of literals in the above : 5319
% 1.20/0.68 % Current number of archived formulas : 0
% 1.20/0.68 % Current number of archived clauses : 74
% 1.20/0.68 % Clause-clause subsumption calls (NU) : 21472
% 1.20/0.68 % Rec. Clause-clause subsumption calls : 9322
% 1.20/0.68 % Non-unit clause-clause subsumptions : 473
% 1.20/0.68 % Unit Clause-clause subsumption calls : 1908
% 1.20/0.68 % Rewrite failures with RHS unbound : 0
% 1.20/0.68 % BW rewrite match attempts : 18
% 1.20/0.68 % BW rewrite match successes : 16
% 1.20/0.68 % Condensation attempts : 0
% 1.20/0.68 % Condensation successes : 0
% 1.20/0.68 % Termbank termtop insertions : 46548
% 1.20/0.68 % Search garbage collected termcells : 2305
% 1.20/0.68
% 1.20/0.68 % -------------------------------------------------
% 1.20/0.68 % User time : 0.152 s
% 1.20/0.68 % System time : 0.005 s
% 1.20/0.68 % Total time : 0.157 s
% 1.20/0.68 % Maximum resident set size: 3708 pages
% 1.20/0.68
% 1.20/0.68 % -------------------------------------------------
% 1.20/0.68 % User time : 0.683 s
% 1.20/0.68 % System time : 0.047 s
% 1.20/0.68 % Total time : 0.730 s
% 1.20/0.68 % Maximum resident set size: 4864 pages
% 1.20/0.68 % E exiting
%------------------------------------------------------------------------------