%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM556+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 : n011.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 1.07s 0.69s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 78 ( 21 unt; 0 def)
% Number of atoms : 383 ( 79 equ)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 513 ( 208 ~; 223 |; 57 &)
% ( 9 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 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 : 112 ( 0 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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__2202_02,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
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(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(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(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2256,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).
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__2411,hypothesis,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2411) ).
fof(m__2291,hypothesis,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
fof(m__2357,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).
fof(m__2304,hypothesis,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
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__,conjecture,
( sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_16,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])])])])])])]) ).
fof(c_0_17,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(fof_simplification,[status(thm)],[m__2202_02]) ).
cnf(c_0_18,plain,
( ~ aElementOf0(X4,szNzAzT0)
| ~ aSet0(X2)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aElementOf0(X1,X3)
| aSubsetOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(fof_nnf,[status(thm)],[c_0_17]) ).
fof(c_0_20,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_21,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_22,plain,
( ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| aSubsetOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_23,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[m__2270]) ).
cnf(c_0_24,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__2202]) ).
cnf(c_0_25,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_26,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_20])])])])])])]) ).
cnf(c_0_27,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,hypothesis,
aSubsetOf0(xQ,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_29,plain,
( ~ aElement0(X4)
| ~ aSet0(X2)
| X3 != sdtmndt0(X2,X4)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X1 != sdtmndt0(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_31,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_32,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])])])]) ).
cnf(c_0_33,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_34,hypothesis,
( ~ aElementOf0(X1,xQ)
| aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25])]) ).
cnf(c_0_35,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| aElementOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSubsetOf0(X2,X1)
| aElementOf0(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_37,plain,
( ~ aSet0(X1)
| ~ aElement0(X2)
| aSet0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X4 != sdtpldt0(X2,X3)
| ~ aElementOf0(X1,X4)
| X1 = X3
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__2256]) ).
fof(c_0_41,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]) ).
fof(c_0_42,hypothesis,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
inference(fof_simplification,[status(thm)],[m__2411]) ).
cnf(c_0_43,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_33,c_0_34]),c_0_25])]) ).
cnf(c_0_44,plain,
( ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2)
| aElementOf0(esk2_2(X3,sdtmndt0(X1,X2)),X1)
| aSubsetOf0(sdtmndt0(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_45,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[m__2291]) ).
cnf(c_0_46,plain,
( ~ aSet0(X3)
| ~ aElement0(X2)
| ~ aElementOf0(X1,sdtpldt0(X3,X2))
| aElementOf0(X1,X3)
| X1 = X2 ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_47,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(split_conjunct,[status(thm)],[m__2357]) ).
cnf(c_0_48,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_25])]) ).
fof(c_0_49,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_41])])])]) ).
fof(c_0_50,hypothesis,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
inference(fof_nnf,[status(thm)],[c_0_42]) ).
cnf(c_0_51,hypothesis,
( ~ aSet0(sdtmndt0(xQ,X1))
| ~ aElement0(X1)
| aSubsetOf0(sdtmndt0(xQ,X1),xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_25])]) ).
cnf(c_0_52,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_46,c_0_47]),c_0_48])]) ).
cnf(c_0_53,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__2304]) ).
cnf(c_0_54,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X1 != sdtpldt0(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_55,plain,
( ~ aElement0(X2)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1))
| aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,hypothesis,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_57,hypothesis,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_58,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_59,hypothesis,
( ~ aSet0(sdtmndt0(xQ,X2))
| ~ aElement0(X2)
| ~ aElementOf0(X1,sdtmndt0(xQ,X2))
| aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_51]),c_0_25])]) ).
cnf(c_0_60,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_52,c_0_37]),c_0_53]),c_0_45])]) ).
cnf(c_0_61,plain,
( ~ aSet0(X1)
| ~ aElement0(X2)
| aSet0(sdtpldt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_54]) ).
fof(c_0_62,negated_conjecture,
~ ( sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_63,hypothesis,
( ~ aSet0(sdtmndt0(xQ,xy))
| ~ isFinite0(sdtmndt0(xQ,xy))
| 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_55,c_0_47]),c_0_56]),c_0_48])]),c_0_57]) ).
cnf(c_0_64,plain,
( ~ isFinite0(X2)
| ~ aSet0(X2)
| ~ aElement0(X1)
| isFinite0(sdtmndt0(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,hypothesis,
isFinite0(xQ),
inference(split_conjunct,[status(thm)],[m__2291]) ).
cnf(c_0_66,hypothesis,
( ~ aSet0(sdtmndt0(xQ,xy))
| ~ aElementOf0(X1,xP)
| aElementOf0(X1,xS)
| X1 = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_53])]) ).
cnf(c_0_67,hypothesis,
( ~ aSet0(sdtmndt0(xQ,xy))
| aSet0(xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_47]),c_0_48])]) ).
fof(c_0_68,negated_conjecture,
( sbrdtbr0(xP) != xk
| ~ aSubsetOf0(xP,xS) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])]) ).
cnf(c_0_69,hypothesis,
( ~ aSet0(sdtmndt0(xQ,xy))
| sbrdtbr0(xP) = xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_53]),c_0_45])]) ).
cnf(c_0_70,hypothesis,
( ~ aElementOf0(X1,xP)
| aElementOf0(X1,xS)
| X1 = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_37]),c_0_53]),c_0_45])]) ).
cnf(c_0_71,hypothesis,
aSet0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_37]),c_0_53]),c_0_45])]) ).
cnf(c_0_72,negated_conjecture,
( sbrdtbr0(xP) != xk
| ~ aSubsetOf0(xP,xS) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_73,hypothesis,
sbrdtbr0(xP) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_37]),c_0_53]),c_0_45])]) ).
cnf(c_0_74,hypothesis,
( ~ aSet0(X1)
| aElementOf0(esk2_2(X1,xP),xS)
| aSubsetOf0(xP,X1)
| esk2_2(X1,xP) = xx ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_36]),c_0_71])]) ).
cnf(c_0_75,negated_conjecture,
~ aSubsetOf0(xP,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73])]) ).
cnf(c_0_76,hypothesis,
esk2_2(xS,xP) = xx,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_74]),c_0_71]),c_0_25])]),c_0_75]) ).
cnf(c_0_77,hypothesis,
$false,
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_33,c_0_76]),c_0_40]),c_0_71]),c_0_25])]),c_0_75]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM556+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n011.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 02:39:25 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 1.07/0.69 % Version: 3.5.1
% 1.07/0.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.07/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.07/0.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.07/0.69 % Starting new_bool_3 with 300s (1) cores
% 1.07/0.69 % Starting new_bool_1 with 300s (1) cores
% 1.07/0.69 % Starting sh5l with 300s (1) cores
% 1.07/0.69 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 788643 completed with status 0
% 1.07/0.69 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.07/0.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.07/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.07/0.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.07/0.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.07/0.69 % No SInE strategy applied
% 1.07/0.69 % Search class: FGHSF-FSMM31-MFFFFFNN
% 1.07/0.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.07/0.69 % Starting SubtermCWHack with 136s (1) cores
% 1.07/0.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.07/0.69 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 1.07/0.69 % Starting new_bool_3 with 136s (1) cores
% 1.07/0.69 % Starting new_bool_1 with 136s (1) cores
% 1.07/0.69 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 788650 completed with status 0
% 1.07/0.69 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.07/0.69 % Preprocessing class: FSLSSMSMSSSNFFN.
% 1.07/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.07/0.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.07/0.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.07/0.69 % No SInE strategy applied
% 1.07/0.69 % Search class: FGHSF-FSMM31-MFFFFFNN
% 1.07/0.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.07/0.69 % Starting SubtermCWHack with 136s (1) cores
% 1.07/0.69 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.07/0.69 % Preprocessing time : 0.003 s
% 1.07/0.69 % Presaturation interreduction done
% 1.07/0.69
% 1.07/0.69 % Proof found!
% 1.07/0.69 % SZS status Theorem
% 1.07/0.69 % SZS output start CNFRefutation
% See solution above
% 1.07/0.69 % Parsed axioms : 72
% 1.07/0.69 % Removed by relevancy pruning/SinE : 0
% 1.07/0.69 % Initial clauses : 129
% 1.07/0.69 % Removed in clause preprocessing : 6
% 1.07/0.69 % Initial clauses in saturation : 123
% 1.07/0.69 % Processed clauses : 1377
% 1.07/0.69 % ...of these trivial : 4
% 1.07/0.69 % ...subsumed : 591
% 1.07/0.69 % ...remaining for further processing : 782
% 1.07/0.69 % Other redundant clauses eliminated : 50
% 1.07/0.69 % Clauses deleted for lack of memory : 0
% 1.07/0.69 % Backward-subsumed : 49
% 1.07/0.69 % Backward-rewritten : 18
% 1.07/0.69 % Generated clauses : 3595
% 1.07/0.69 % ...of the previous two non-redundant : 3225
% 1.07/0.69 % ...aggressively subsumed : 0
% 1.07/0.69 % Contextual simplify-reflections : 131
% 1.07/0.69 % Paramodulations : 3547
% 1.07/0.69 % Factorizations : 0
% 1.07/0.69 % NegExts : 0
% 1.07/0.69 % Equation resolutions : 51
% 1.07/0.69 % Disequality decompositions : 0
% 1.07/0.69 % Total rewrite steps : 2225
% 1.07/0.69 % ...of those cached : 2182
% 1.07/0.69 % Propositional unsat checks : 0
% 1.07/0.69 % Propositional check models : 0
% 1.07/0.69 % Propositional check unsatisfiable : 0
% 1.07/0.69 % Propositional clauses : 0
% 1.07/0.69 % Propositional clauses after purity: 0
% 1.07/0.69 % Propositional unsat core size : 0
% 1.07/0.69 % Propositional preprocessing time : 0.000
% 1.07/0.69 % Propositional encoding time : 0.000
% 1.07/0.69 % Propositional solver time : 0.000
% 1.07/0.69 % Success case prop preproc time : 0.000
% 1.07/0.69 % Success case prop encoding time : 0.000
% 1.07/0.69 % Success case prop solver time : 0.000
% 1.07/0.69 % Current number of processed clauses : 566
% 1.07/0.69 % Positive orientable unit clauses : 48
% 1.07/0.69 % Positive unorientable unit clauses: 0
% 1.07/0.69 % Negative unit clauses : 17
% 1.07/0.69 % Non-unit-clauses : 501
% 1.07/0.69 % Current number of unprocessed clauses: 2038
% 1.07/0.69 % ...number of literals in the above : 12724
% 1.07/0.69 % Current number of archived formulas : 0
% 1.07/0.69 % Current number of archived clauses : 189
% 1.07/0.69 % Clause-clause subsumption calls (NU) : 30628
% 1.07/0.69 % Rec. Clause-clause subsumption calls : 10110
% 1.07/0.69 % Non-unit clause-clause subsumptions : 536
% 1.07/0.69 % Unit Clause-clause subsumption calls : 1323
% 1.07/0.69 % Rewrite failures with RHS unbound : 0
% 1.07/0.69 % BW rewrite match attempts : 15
% 1.07/0.69 % BW rewrite match successes : 15
% 1.07/0.69 % Condensation attempts : 0
% 1.07/0.69 % Condensation successes : 0
% 1.07/0.69 % Termbank termtop insertions : 78730
% 1.07/0.69 % Search garbage collected termcells : 2317
% 1.07/0.69
% 1.07/0.69 % -------------------------------------------------
% 1.07/0.69 % User time : 0.136 s
% 1.07/0.69 % System time : 0.009 s
% 1.07/0.69 % Total time : 0.146 s
% 1.07/0.69 % Maximum resident set size: 3916 pages
% 1.07/0.69
% 1.07/0.69 % -------------------------------------------------
% 1.07/0.69 % User time : 0.580 s
% 1.07/0.69 % System time : 0.037 s
% 1.07/0.69 % Total time : 0.617 s
% 1.07/0.69 % Maximum resident set size: 4608 pages
% 1.07/0.69 % E exiting
%------------------------------------------------------------------------------