TSTP Solution File: NUM554+1 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : NUM554+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 01:26:52 EDT 2024
% Result : Theorem 1.67s 0.73s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 97 ( 31 unt; 0 def)
% Number of atoms : 432 ( 81 equ)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 573 ( 238 ~; 254 |; 54 &)
% ( 9 <=>; 18 =>; 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 : 137 ( 0 sgn 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2202_02,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
fof(mDefSel,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElementOf0(X2,szNzAzT0) )
=> ! [X3] :
( X3 = slbdtsldtrb0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aSubsetOf0(X4,X1)
& sbrdtbr0(X4) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
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] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& aElementOf0(X4,X1)
& X4 != X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(mDiffCons,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aSet0(X2) )
=> ( ~ aElementOf0(X1,X2)
=> sdtmndt0(sdtpldt0(X2,X1),X1) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDiffCons) ).
fof(mFConsSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( aSet0(X2)
& isFinite0(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(mDefCons,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtpldt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& ( aElementOf0(X4,X1)
| X4 = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
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(m__2323,hypothesis,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2323) ).
fof(m__2357,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).
fof(mFDiffSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( aSet0(X2)
& isFinite0(X2) )
=> isFinite0(sdtmndt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
fof(m__2291,hypothesis,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
fof(m__2304,hypothesis,
( aElement0(xy)
& aElementOf0(xy,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
fof(mCardDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( ( isFinite0(X1)
& aElementOf0(X2,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,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
inference(fof_simplification,[status(thm)],[m__2202_02]) ).
fof(c_0_19,plain,
! [X118,X119,X120,X121,X122,X123] :
( ( aSet0(X120)
| X120 != slbdtsldtrb0(X118,X119)
| ~ aSet0(X118)
| ~ aElementOf0(X119,szNzAzT0) )
& ( aSubsetOf0(X121,X118)
| ~ aElementOf0(X121,X120)
| X120 != slbdtsldtrb0(X118,X119)
| ~ aSet0(X118)
| ~ aElementOf0(X119,szNzAzT0) )
& ( sbrdtbr0(X121) = X119
| ~ aElementOf0(X121,X120)
| X120 != slbdtsldtrb0(X118,X119)
| ~ aSet0(X118)
| ~ aElementOf0(X119,szNzAzT0) )
& ( ~ aSubsetOf0(X122,X118)
| sbrdtbr0(X122) != X119
| aElementOf0(X122,X120)
| X120 != slbdtsldtrb0(X118,X119)
| ~ aSet0(X118)
| ~ aElementOf0(X119,szNzAzT0) )
& ( ~ aElementOf0(esk11_3(X118,X119,X123),X123)
| ~ aSubsetOf0(esk11_3(X118,X119,X123),X118)
| sbrdtbr0(esk11_3(X118,X119,X123)) != X119
| ~ aSet0(X123)
| X123 = slbdtsldtrb0(X118,X119)
| ~ aSet0(X118)
| ~ aElementOf0(X119,szNzAzT0) )
& ( aSubsetOf0(esk11_3(X118,X119,X123),X118)
| aElementOf0(esk11_3(X118,X119,X123),X123)
| ~ aSet0(X123)
| X123 = slbdtsldtrb0(X118,X119)
| ~ aSet0(X118)
| ~ aElementOf0(X119,szNzAzT0) )
& ( sbrdtbr0(esk11_3(X118,X119,X123)) = X119
| aElementOf0(esk11_3(X118,X119,X123),X123)
| ~ aSet0(X123)
| X123 = slbdtsldtrb0(X118,X119)
| ~ aSet0(X118)
| ~ aElementOf0(X119,szNzAzT0) ) ),
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_20,plain,
! [X7,X8] :
( ~ aSet0(X7)
| ~ aElementOf0(X8,X7)
| aElement0(X8) ),
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,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aSet0(X2)
| ~ aElementOf0(X4,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,plain,
! [X1,X2] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& aElementOf0(X4,X1)
& X4 != X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefDiff]) ).
fof(c_0_24,plain,
! [X1,X2] :
( ( aElement0(X1)
& aSet0(X2) )
=> ( ~ aElementOf0(X1,X2)
=> sdtmndt0(sdtpldt0(X2,X1),X1) = X2 ) ),
inference(fof_simplification,[status(thm)],[mDiffCons]) ).
fof(c_0_25,plain,
! [X52,X53] :
( ~ aElement0(X52)
| ~ aSet0(X53)
| ~ isFinite0(X53)
| isFinite0(sdtpldt0(X53,X52)) ),
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,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
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_21]) ).
fof(c_0_29,plain,
! [X30,X31,X32,X33,X34,X35] :
( ( aSet0(X32)
| X32 != sdtpldt0(X30,X31)
| ~ aSet0(X30)
| ~ aElement0(X31) )
& ( aElement0(X33)
| ~ aElementOf0(X33,X32)
| X32 != sdtpldt0(X30,X31)
| ~ aSet0(X30)
| ~ aElement0(X31) )
& ( aElementOf0(X33,X30)
| X33 = X31
| ~ aElementOf0(X33,X32)
| X32 != sdtpldt0(X30,X31)
| ~ aSet0(X30)
| ~ aElement0(X31) )
& ( ~ aElementOf0(X34,X30)
| ~ aElement0(X34)
| aElementOf0(X34,X32)
| X32 != sdtpldt0(X30,X31)
| ~ aSet0(X30)
| ~ aElement0(X31) )
& ( X34 != X31
| ~ aElement0(X34)
| aElementOf0(X34,X32)
| X32 != sdtpldt0(X30,X31)
| ~ aSet0(X30)
| ~ aElement0(X31) )
& ( ~ aElementOf0(esk3_3(X30,X31,X35),X30)
| ~ aElement0(esk3_3(X30,X31,X35))
| ~ aElementOf0(esk3_3(X30,X31,X35),X35)
| ~ aSet0(X35)
| X35 = sdtpldt0(X30,X31)
| ~ aSet0(X30)
| ~ aElement0(X31) )
& ( esk3_3(X30,X31,X35) != X31
| ~ aElement0(esk3_3(X30,X31,X35))
| ~ aElementOf0(esk3_3(X30,X31,X35),X35)
| ~ aSet0(X35)
| X35 = sdtpldt0(X30,X31)
| ~ aSet0(X30)
| ~ aElement0(X31) )
& ( aElement0(esk3_3(X30,X31,X35))
| aElementOf0(esk3_3(X30,X31,X35),X35)
| ~ aSet0(X35)
| X35 = sdtpldt0(X30,X31)
| ~ aSet0(X30)
| ~ aElement0(X31) )
& ( aElementOf0(esk3_3(X30,X31,X35),X30)
| esk3_3(X30,X31,X35) = X31
| aElementOf0(esk3_3(X30,X31,X35),X35)
| ~ aSet0(X35)
| X35 = sdtpldt0(X30,X31)
| ~ aSet0(X30)
| ~ aElement0(X31) ) ),
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_30,plain,
! [X17,X18,X19,X20] :
( ( aSet0(X18)
| ~ aSubsetOf0(X18,X17)
| ~ aSet0(X17) )
& ( ~ aElementOf0(X19,X18)
| aElementOf0(X19,X17)
| ~ aSubsetOf0(X18,X17)
| ~ aSet0(X17) )
& ( aElementOf0(esk2_2(X17,X20),X20)
| ~ aSet0(X20)
| aSubsetOf0(X20,X17)
| ~ aSet0(X17) )
& ( ~ aElementOf0(esk2_2(X17,X20),X17)
| ~ aSet0(X20)
| aSubsetOf0(X20,X17)
| ~ aSet0(X17) ) ),
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_31,plain,
( aSubsetOf0(X1,X2)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| ~ aElementOf0(X3,szNzAzT0)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_32,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[m__2270]) ).
cnf(c_0_33,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__2202]) ).
fof(c_0_34,plain,
! [X37,X38,X39,X40,X41,X42] :
( ( aSet0(X39)
| X39 != sdtmndt0(X37,X38)
| ~ aSet0(X37)
| ~ aElement0(X38) )
& ( aElement0(X40)
| ~ aElementOf0(X40,X39)
| X39 != sdtmndt0(X37,X38)
| ~ aSet0(X37)
| ~ aElement0(X38) )
& ( aElementOf0(X40,X37)
| ~ aElementOf0(X40,X39)
| X39 != sdtmndt0(X37,X38)
| ~ aSet0(X37)
| ~ aElement0(X38) )
& ( X40 != X38
| ~ aElementOf0(X40,X39)
| X39 != sdtmndt0(X37,X38)
| ~ aSet0(X37)
| ~ aElement0(X38) )
& ( ~ aElement0(X41)
| ~ aElementOf0(X41,X37)
| X41 = X38
| aElementOf0(X41,X39)
| X39 != sdtmndt0(X37,X38)
| ~ aSet0(X37)
| ~ aElement0(X38) )
& ( ~ aElementOf0(esk4_3(X37,X38,X42),X42)
| ~ aElement0(esk4_3(X37,X38,X42))
| ~ aElementOf0(esk4_3(X37,X38,X42),X37)
| esk4_3(X37,X38,X42) = X38
| ~ aSet0(X42)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X37)
| ~ aElement0(X38) )
& ( aElement0(esk4_3(X37,X38,X42))
| aElementOf0(esk4_3(X37,X38,X42),X42)
| ~ aSet0(X42)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X37)
| ~ aElement0(X38) )
& ( aElementOf0(esk4_3(X37,X38,X42),X37)
| aElementOf0(esk4_3(X37,X38,X42),X42)
| ~ aSet0(X42)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X37)
| ~ aElement0(X38) )
& ( esk4_3(X37,X38,X42) != X38
| aElementOf0(esk4_3(X37,X38,X42),X42)
| ~ aSet0(X42)
| X42 = sdtmndt0(X37,X38)
| ~ aSet0(X37)
| ~ aElement0(X38) ) ),
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_23])])])])])])]) ).
fof(c_0_35,plain,
! [X46,X47] :
( ~ aElement0(X46)
| ~ aSet0(X47)
| aElementOf0(X46,X47)
| sdtmndt0(sdtpldt0(X47,X46),X46) = X47 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
fof(c_0_36,hypothesis,
~ aElementOf0(xx,xQ),
inference(fof_simplification,[status(thm)],[m__2323]) ).
cnf(c_0_37,plain,
( isFinite0(sdtpldt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(split_conjunct,[status(thm)],[m__2357]) ).
cnf(c_0_39,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
fof(c_0_40,plain,
! [X54,X55] :
( ~ aElement0(X54)
| ~ aSet0(X55)
| ~ isFinite0(X55)
| isFinite0(sdtmndt0(X55,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_41,plain,
( aElementOf0(X1,X3)
| X1 != X2
| ~ aElement0(X1)
| X3 != sdtpldt0(X4,X2)
| ~ aSet0(X4)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_42,plain,
( aSet0(X1)
| X1 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_43,plain,
( aElementOf0(X1,X3)
| ~ aElementOf0(X1,X2)
| ~ aSubsetOf0(X2,X3)
| ~ aSet0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_44,hypothesis,
aSubsetOf0(xQ,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_28])]) ).
cnf(c_0_45,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,plain,
( aSet0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_47,plain,
( aElementOf0(X1,X2)
| sdtmndt0(sdtpldt0(X2,X1),X1) = X2
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_48,hypothesis,
~ aElementOf0(xx,xQ),
inference(fof_nnf,[status(thm)],[c_0_36]) ).
cnf(c_0_49,hypothesis,
( isFinite0(xP)
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_50,plain,
( isFinite0(sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ isFinite0(X2) ),
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)],[m__2291]) ).
cnf(c_0_54,plain,
( aElementOf0(X1,sdtpldt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_41])]) ).
cnf(c_0_55,plain,
( aSet0(sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_56,plain,
( aSubsetOf0(X2,X1)
| ~ aElementOf0(esk2_2(X1,X2),X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_57,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,xQ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_28])]) ).
cnf(c_0_58,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_59,plain,
( aElementOf0(esk2_2(X1,X2),X2)
| aSubsetOf0(X2,X1)
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_60,plain,
( aSet0(sdtmndt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_46]) ).
cnf(c_0_61,plain,
( aElementOf0(X1,X2)
| X1 = X3
| ~ aElementOf0(X1,X4)
| X4 != sdtpldt0(X2,X3)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_62,plain,
! [X85,X86] :
( ~ aSet0(X85)
| ~ isFinite0(X85)
| ~ aElementOf0(X86,X85)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X85,X86))) = sbrdtbr0(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_63,hypothesis,
( sdtmndt0(xP,xx) = sdtmndt0(xQ,xy)
| aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_38]),c_0_39])]) ).
cnf(c_0_64,hypothesis,
~ aElementOf0(xx,xQ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_65,hypothesis,
( isFinite0(xP)
| ~ aSet0(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_49,c_0_50]),c_0_51]),c_0_52]),c_0_53])]) ).
cnf(c_0_66,hypothesis,
( aElementOf0(xx,xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_38]),c_0_39])]) ).
cnf(c_0_67,hypothesis,
( aSet0(xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_38]),c_0_39])]) ).
cnf(c_0_68,hypothesis,
( aSubsetOf0(X1,xS)
| ~ aElementOf0(esk2_2(xS,X1),xQ)
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_28])]) ).
cnf(c_0_69,plain,
( aSubsetOf0(sdtmndt0(X1,X2),X3)
| aElementOf0(esk2_2(X3,sdtmndt0(X1,X2)),X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| ~ aSet0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
cnf(c_0_70,plain,
( X1 = X2
| aElementOf0(X1,X3)
| ~ aElementOf0(X1,sdtpldt0(X3,X2))
| ~ aElement0(X2)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_61]) ).
cnf(c_0_71,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_72,hypothesis,
( sdtmndt0(xP,xx) = sdtmndt0(xQ,xy)
| ~ aSet0(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_58,c_0_63]),c_0_52]),c_0_53])]),c_0_64]) ).
cnf(c_0_73,hypothesis,
isFinite0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_60]),c_0_52]),c_0_53])]) ).
cnf(c_0_74,hypothesis,
aElementOf0(xx,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_60]),c_0_52]),c_0_53])]) ).
cnf(c_0_75,hypothesis,
aSet0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_60]),c_0_52]),c_0_53])]) ).
cnf(c_0_76,hypothesis,
( aSubsetOf0(sdtmndt0(xQ,X1),xS)
| ~ aElement0(X1)
| ~ aSet0(sdtmndt0(xQ,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_53]),c_0_28])]) ).
cnf(c_0_77,hypothesis,
( X1 = xx
| aElementOf0(X1,sdtmndt0(xQ,xy))
| ~ aElementOf0(X1,xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_38]),c_0_39])]) ).
cnf(c_0_78,hypothesis,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xP)
| ~ aSet0(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_71,c_0_72]),c_0_73]),c_0_74]),c_0_75])]) ).
cnf(c_0_79,hypothesis,
sbrdtbr0(xQ) = xk,
inference(split_conjunct,[status(thm)],[m__2291]) ).
cnf(c_0_80,hypothesis,
aElementOf0(xy,xQ),
inference(split_conjunct,[status(thm)],[m__2304]) ).
cnf(c_0_81,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,sdtmndt0(xQ,X2))
| ~ aElement0(X2)
| ~ aSet0(sdtmndt0(xQ,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_76]),c_0_28])]) ).
cnf(c_0_82,hypothesis,
( X1 = xx
| aElementOf0(X1,sdtmndt0(xQ,xy))
| ~ aElementOf0(X1,xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_60]),c_0_52]),c_0_53])]) ).
fof(c_0_83,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_84,plain,
( aElementOf0(X1,X4)
| ~ aSubsetOf0(X1,X2)
| sbrdtbr0(X1) != X3
| X4 != slbdtsldtrb0(X2,X3)
| ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_85,hypothesis,
( sbrdtbr0(xP) = xk
| ~ aSet0(sdtmndt0(xQ,xy)) ),
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_71,c_0_78]),c_0_79]),c_0_51]),c_0_80]),c_0_53])]) ).
cnf(c_0_86,hypothesis,
( X1 = xx
| aElementOf0(X1,xS)
| ~ aElementOf0(X1,xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_52])]) ).
fof(c_0_87,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(fof_nnf,[status(thm)],[c_0_83]) ).
cnf(c_0_88,plain,
( aElementOf0(X1,slbdtsldtrb0(X2,sbrdtbr0(X1)))
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_84])]) ).
cnf(c_0_89,hypothesis,
sbrdtbr0(xP) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_60]),c_0_52]),c_0_53])]) ).
cnf(c_0_90,hypothesis,
( X1 = xx
| aElementOf0(X1,xS)
| ~ aElementOf0(X1,xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_60]),c_0_52]),c_0_53])]) ).
cnf(c_0_91,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_92,hypothesis,
( aElementOf0(xP,slbdtsldtrb0(X1,xk))
| ~ aSubsetOf0(xP,X1)
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_33])]) ).
cnf(c_0_93,hypothesis,
( esk2_2(X1,xP) = xx
| aSubsetOf0(xP,X1)
| aElementOf0(esk2_2(X1,xP),xS)
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_59]),c_0_75])]) ).
cnf(c_0_94,negated_conjecture,
~ aSubsetOf0(xP,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_28])]) ).
cnf(c_0_95,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_56,c_0_93]),c_0_75]),c_0_28])]),c_0_94]) ).
cnf(c_0_96,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_56,c_0_95]),c_0_27]),c_0_75]),c_0_28])]),c_0_94]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.15 % Problem : NUM554+1 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.16 % Command : run_E %s %d THM
% 0.13/0.37 % Computer : n003.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon May 20 04:59:53 EDT 2024
% 0.13/0.38 % CPUTime :
% 0.21/0.52 Running first-order model finding
% 0.21/0.52 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.67/0.73 # Version: 3.1.0
% 1.67/0.73 # Preprocessing class: FSLSSMSMSSSNFFN.
% 1.67/0.73 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.67/0.73 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.67/0.73 # Starting new_bool_3 with 300s (1) cores
% 1.67/0.73 # Starting new_bool_1 with 300s (1) cores
% 1.67/0.73 # Starting sh5l with 300s (1) cores
% 1.67/0.73 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 3101 completed with status 0
% 1.67/0.73 # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.67/0.73 # Preprocessing class: FSLSSMSMSSSNFFN.
% 1.67/0.73 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.67/0.73 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.67/0.73 # No SInE strategy applied
% 1.67/0.73 # Search class: FGHSF-FSMM31-MFFFFFNN
% 1.67/0.73 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.67/0.73 # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 1.67/0.73 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.67/0.73 # Starting new_bool_3 with 136s (1) cores
% 1.67/0.73 # Starting new_bool_1 with 136s (1) cores
% 1.67/0.73 # Starting sh5l with 136s (1) cores
% 1.67/0.73 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 3109 completed with status 0
% 1.67/0.73 # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 1.67/0.73 # Preprocessing class: FSLSSMSMSSSNFFN.
% 1.67/0.73 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.67/0.73 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 1.67/0.73 # No SInE strategy applied
% 1.67/0.73 # Search class: FGHSF-FSMM31-MFFFFFNN
% 1.67/0.73 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.67/0.73 # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 1.67/0.73 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 1.67/0.73 # Preprocessing time : 0.003 s
% 1.67/0.73 # Presaturation interreduction done
% 1.67/0.73
% 1.67/0.73 # Proof found!
% 1.67/0.73 # SZS status Theorem
% 1.67/0.73 # SZS output start CNFRefutation
% See solution above
% 1.67/0.73 # Parsed axioms : 71
% 1.67/0.73 # Removed by relevancy pruning/SinE : 0
% 1.67/0.73 # Initial clauses : 127
% 1.67/0.73 # Removed in clause preprocessing : 6
% 1.67/0.73 # Initial clauses in saturation : 121
% 1.67/0.73 # Processed clauses : 1388
% 1.67/0.73 # ...of these trivial : 7
% 1.67/0.73 # ...subsumed : 539
% 1.67/0.73 # ...remaining for further processing : 842
% 1.67/0.73 # Other redundant clauses eliminated : 44
% 1.67/0.73 # Clauses deleted for lack of memory : 0
% 1.67/0.73 # Backward-subsumed : 57
% 1.67/0.73 # Backward-rewritten : 21
% 1.67/0.73 # Generated clauses : 3855
% 1.67/0.73 # ...of the previous two non-redundant : 3512
% 1.67/0.73 # ...aggressively subsumed : 0
% 1.67/0.73 # Contextual simplify-reflections : 141
% 1.67/0.73 # Paramodulations : 3813
% 1.67/0.73 # Factorizations : 0
% 1.67/0.73 # NegExts : 0
% 1.67/0.73 # Equation resolutions : 45
% 1.67/0.73 # Disequality decompositions : 0
% 1.67/0.73 # Total rewrite steps : 2057
% 1.67/0.73 # ...of those cached : 2014
% 1.67/0.73 # Propositional unsat checks : 0
% 1.67/0.73 # Propositional check models : 0
% 1.67/0.73 # Propositional check unsatisfiable : 0
% 1.67/0.73 # Propositional clauses : 0
% 1.67/0.73 # Propositional clauses after purity: 0
% 1.67/0.73 # Propositional unsat core size : 0
% 1.67/0.73 # Propositional preprocessing time : 0.000
% 1.67/0.73 # Propositional encoding time : 0.000
% 1.67/0.73 # Propositional solver time : 0.000
% 1.67/0.73 # Success case prop preproc time : 0.000
% 1.67/0.73 # Success case prop encoding time : 0.000
% 1.67/0.73 # Success case prop solver time : 0.000
% 1.67/0.73 # Current number of processed clauses : 617
% 1.67/0.73 # Positive orientable unit clauses : 47
% 1.67/0.73 # Positive unorientable unit clauses: 0
% 1.67/0.73 # Negative unit clauses : 15
% 1.67/0.73 # Non-unit-clauses : 555
% 1.67/0.73 # Current number of unprocessed clauses: 2303
% 1.67/0.73 # ...number of literals in the above : 14439
% 1.67/0.73 # Current number of archived formulas : 0
% 1.67/0.73 # Current number of archived clauses : 198
% 1.67/0.73 # Clause-clause subsumption calls (NU) : 50808
% 1.67/0.73 # Rec. Clause-clause subsumption calls : 20317
% 1.67/0.73 # Non-unit clause-clause subsumptions : 534
% 1.67/0.73 # Unit Clause-clause subsumption calls : 3094
% 1.67/0.73 # Rewrite failures with RHS unbound : 0
% 1.67/0.73 # BW rewrite match attempts : 15
% 1.67/0.73 # BW rewrite match successes : 15
% 1.67/0.73 # Condensation attempts : 0
% 1.67/0.73 # Condensation successes : 0
% 1.67/0.73 # Termbank termtop insertions : 83859
% 1.67/0.73 # Search garbage collected termcells : 2307
% 1.67/0.73
% 1.67/0.73 # -------------------------------------------------
% 1.67/0.73 # User time : 0.191 s
% 1.67/0.73 # System time : 0.005 s
% 1.67/0.73 # Total time : 0.196 s
% 1.67/0.73 # Maximum resident set size: 2116 pages
% 1.67/0.73
% 1.67/0.73 # -------------------------------------------------
% 1.67/0.73 # User time : 0.927 s
% 1.67/0.73 # System time : 0.014 s
% 1.67/0.73 # Total time : 0.941 s
% 1.67/0.73 # Maximum resident set size: 1768 pages
% 1.67/0.73 % E---3.1 exiting
%------------------------------------------------------------------------------