TSTP Solution File: NUM556+3 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM556+3 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n012.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 01:14:40 EDT 2024
% Result : Theorem 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 73 ( 23 unt; 0 def)
% Number of atoms : 410 ( 85 equ)
% Maximal formula atoms : 67 ( 5 avg)
% Number of connectives : 504 ( 167 ~; 167 |; 129 &)
% ( 10 <=>; 31 =>; 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 : 20 ( 20 usr; 11 con; 0-3 aty)
% Number of variables : 95 ( 0 sgn 69 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2202_02,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
fof(m__2357,hypothesis,
( aSet0(sdtmndt0(xQ,xy))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& X1 != xy ) )
& aSet0(xP)
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xQ,xy))
| X1 = xx ) ) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
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(m__2411,hypothesis,
( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
& aSet0(sdtmndt0(xQ,xy))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& X1 != xy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2411) ).
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(mFDiffSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( aSet0(X2)
& isFinite0(X2) )
=> isFinite0(sdtmndt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
fof(m__2270,hypothesis,
( aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,xS) )
& aSubsetOf0(xQ,xS)
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
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(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__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(m__,conjecture,
( ( ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xS) )
| aSubsetOf0(xP,xS) )
& sbrdtbr0(xP) = xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2227,hypothesis,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [X1] :
( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSubsetOf0(X1,xS)
& sbrdtbr0(X1) = xk ) )
& ( ( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) ) )
| aSubsetOf0(X1,xS) )
& sbrdtbr0(X1) = xk )
=> aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X1] :
( ( aElementOf0(X1,slbdtsldtrb0(xT,xk))
=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xT) )
& aSubsetOf0(X1,xT)
& sbrdtbr0(X1) = xk ) )
& ( ( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xT) ) )
| aSubsetOf0(X1,xT) )
& sbrdtbr0(X1) = xk )
=> aElementOf0(X1,slbdtsldtrb0(xT,xk)) ) )
& ! [X1] :
( aElementOf0(X1,slbdtsldtrb0(xS,xk))
=> aElementOf0(X1,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ~ ( ! [X1] :
( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) )
& aSubsetOf0(X1,xS)
& sbrdtbr0(X1) = xk ) )
& ( ( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) ) )
| aSubsetOf0(X1,xS) )
& sbrdtbr0(X1) = xk )
=> aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
=> ( ~ ? [X1] : aElementOf0(X1,slbdtsldtrb0(xS,xk))
| slbdtsldtrb0(xS,xk) = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2227) ).
fof(c_0_15,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
inference(fof_simplification,[status(thm)],[m__2202_02]) ).
fof(c_0_16,hypothesis,
( aSet0(sdtmndt0(xQ,xy))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& X1 != xy ) )
& aSet0(xP)
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xQ,xy))
| X1 = xx ) ) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
inference(fof_simplification,[status(thm)],[m__2357]) ).
fof(c_0_17,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_18,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
inference(fof_nnf,[status(thm)],[c_0_15]) ).
fof(c_0_19,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_20,hypothesis,
( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
& aSet0(sdtmndt0(xQ,xy))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& X1 != xy ) ) ),
inference(fof_simplification,[status(thm)],[m__2411]) ).
fof(c_0_21,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])])])]) ).
fof(c_0_22,hypothesis,
! [X146,X147] :
( aSet0(sdtmndt0(xQ,xy))
& ( aElement0(X146)
| ~ aElementOf0(X146,sdtmndt0(xQ,xy)) )
& ( aElementOf0(X146,xQ)
| ~ aElementOf0(X146,sdtmndt0(xQ,xy)) )
& ( X146 != xy
| ~ aElementOf0(X146,sdtmndt0(xQ,xy)) )
& ( ~ aElement0(X146)
| ~ aElementOf0(X146,xQ)
| X146 = xy
| aElementOf0(X146,sdtmndt0(xQ,xy)) )
& aSet0(xP)
& ( aElement0(X147)
| ~ aElementOf0(X147,xP) )
& ( aElementOf0(X147,sdtmndt0(xQ,xy))
| X147 = xx
| ~ aElementOf0(X147,xP) )
& ( ~ aElementOf0(X147,sdtmndt0(xQ,xy))
| ~ aElement0(X147)
| aElementOf0(X147,xP) )
& ( X147 != xx
| ~ aElement0(X147)
| aElementOf0(X147,xP) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
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,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
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] :
( ~ 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_19])])]) ).
fof(c_0_27,hypothesis,
! [X148] :
( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
& aSet0(sdtmndt0(xQ,xy))
& ( aElement0(X148)
| ~ aElementOf0(X148,sdtmndt0(xQ,xy)) )
& ( aElementOf0(X148,xQ)
| ~ aElementOf0(X148,sdtmndt0(xQ,xy)) )
& ( X148 != xy
| ~ aElementOf0(X148,sdtmndt0(xQ,xy)) )
& ( ~ aElement0(X148)
| ~ aElementOf0(X148,xQ)
| X148 = xy
| aElementOf0(X148,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(sdtpldt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ isFinite0(X2) ),
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] :
( ~ 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])])])]) ).
fof(c_0_33,hypothesis,
! [X145] :
( aSet0(xQ)
& ( ~ aElementOf0(X145,xQ)
| aElementOf0(X145,xS) )
& aSubsetOf0(xQ,xS)
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2270])])])]) ).
cnf(c_0_34,hypothesis,
( aElementOf0(X1,xP)
| X1 != xx
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_35,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_36,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_37,plain,
( aElementOf0(X1,X2)
| sdtmndt0(sdtpldt0(X2,X1),X1) = X2
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_38,hypothesis,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,hypothesis,
( isFinite0(xP)
| ~ isFinite0(sdtmndt0(xQ,xy)) ),
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_40,plain,
( isFinite0(sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,hypothesis,
isFinite0(xQ),
inference(split_conjunct,[status(thm)],[m__2291]) ).
cnf(c_0_42,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__2304]) ).
cnf(c_0_43,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_44,hypothesis,
( aElementOf0(xx,xP)
| ~ aElement0(xx) ),
inference(er,[status(thm)],[c_0_34]) ).
fof(c_0_45,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_35])])])])])])]) ).
fof(c_0_46,negated_conjecture,
~ ( ( ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xS) )
| aSubsetOf0(xP,xS) )
& sbrdtbr0(xP) = xk ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_47,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,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_37,c_0_29]),c_0_30]),c_0_31])]),c_0_38]) ).
cnf(c_0_49,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_39,c_0_40]),c_0_41]),c_0_42]),c_0_43])]) ).
cnf(c_0_50,hypothesis,
aElementOf0(xx,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_30])]) ).
cnf(c_0_51,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_52,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_53,negated_conjecture,
( ( aElementOf0(esk16_0,xP)
| sbrdtbr0(xP) != xk )
& ( ~ aElementOf0(esk16_0,xS)
| sbrdtbr0(xP) != xk )
& ( ~ aSubsetOf0(xP,xS)
| sbrdtbr0(xP) != xk ) ),
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_54,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_47,c_0_48]),c_0_49]),c_0_50]),c_0_51])]) ).
cnf(c_0_55,hypothesis,
sbrdtbr0(xQ) = xk,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_56,hypothesis,
aElementOf0(xy,xQ),
inference(split_conjunct,[status(thm)],[m__2304]) ).
fof(c_0_57,hypothesis,
! [X131,X132,X133,X135,X136,X137,X139,X140,X141,X142] :
( aSet0(slbdtsldtrb0(xS,xk))
& ( aSet0(X131)
| ~ aElementOf0(X131,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X132,X131)
| aElementOf0(X132,xS)
| ~ aElementOf0(X131,slbdtsldtrb0(xS,xk)) )
& ( aSubsetOf0(X131,xS)
| ~ aElementOf0(X131,slbdtsldtrb0(xS,xk)) )
& ( sbrdtbr0(X131) = xk
| ~ aElementOf0(X131,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(esk12_1(X133),X133)
| ~ aSet0(X133)
| sbrdtbr0(X133) != xk
| aElementOf0(X133,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(esk12_1(X133),xS)
| ~ aSet0(X133)
| sbrdtbr0(X133) != xk
| aElementOf0(X133,slbdtsldtrb0(xS,xk)) )
& ( ~ aSubsetOf0(X133,xS)
| sbrdtbr0(X133) != xk
| aElementOf0(X133,slbdtsldtrb0(xS,xk)) )
& aSet0(slbdtsldtrb0(xT,xk))
& ( aSet0(X135)
| ~ aElementOf0(X135,slbdtsldtrb0(xT,xk)) )
& ( ~ aElementOf0(X136,X135)
| aElementOf0(X136,xT)
| ~ aElementOf0(X135,slbdtsldtrb0(xT,xk)) )
& ( aSubsetOf0(X135,xT)
| ~ aElementOf0(X135,slbdtsldtrb0(xT,xk)) )
& ( sbrdtbr0(X135) = xk
| ~ aElementOf0(X135,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(esk13_1(X137),X137)
| ~ aSet0(X137)
| sbrdtbr0(X137) != xk
| aElementOf0(X137,slbdtsldtrb0(xT,xk)) )
& ( ~ aElementOf0(esk13_1(X137),xT)
| ~ aSet0(X137)
| sbrdtbr0(X137) != xk
| aElementOf0(X137,slbdtsldtrb0(xT,xk)) )
& ( ~ aSubsetOf0(X137,xT)
| sbrdtbr0(X137) != xk
| aElementOf0(X137,slbdtsldtrb0(xT,xk)) )
& ( ~ aElementOf0(X139,slbdtsldtrb0(xS,xk))
| aElementOf0(X139,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ( aSet0(X140)
| ~ aElementOf0(X140,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(X141,X140)
| aElementOf0(X141,xS)
| ~ aElementOf0(X140,slbdtsldtrb0(xS,xk)) )
& ( aSubsetOf0(X140,xS)
| ~ aElementOf0(X140,slbdtsldtrb0(xS,xk)) )
& ( sbrdtbr0(X140) = xk
| ~ aElementOf0(X140,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(esk14_1(X142),X142)
| ~ aSet0(X142)
| sbrdtbr0(X142) != xk
| aElementOf0(X142,slbdtsldtrb0(xS,xk)) )
& ( ~ aElementOf0(esk14_1(X142),xS)
| ~ aSet0(X142)
| sbrdtbr0(X142) != xk
| aElementOf0(X142,slbdtsldtrb0(xS,xk)) )
& ( ~ aSubsetOf0(X142,xS)
| sbrdtbr0(X142) != xk
| aElementOf0(X142,slbdtsldtrb0(xS,xk)) )
& aElementOf0(esk15_0,slbdtsldtrb0(xS,xk))
& slbdtsldtrb0(xS,xk) != slcrc0 ),
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_58,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_52]) ).
cnf(c_0_59,hypothesis,
( aElementOf0(X1,sdtmndt0(xQ,xy))
| X1 = xx
| ~ aElementOf0(X1,xP) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_60,negated_conjecture,
( aElementOf0(esk16_0,xP)
| sbrdtbr0(xP) != xk ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,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_47,c_0_54]),c_0_55]),c_0_41]),c_0_56]),c_0_43])]) ).
cnf(c_0_62,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X2,slbdtsldtrb0(xS,xk)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,hypothesis,
( aElementOf0(X1,slbdtsldtrb0(xS,xk))
| ~ aSubsetOf0(X1,xS)
| sbrdtbr0(X1) != xk ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,hypothesis,
( X1 = xx
| aElementOf0(X1,xQ)
| ~ aElementOf0(X1,xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_42]),c_0_43])]) ).
cnf(c_0_65,negated_conjecture,
aElementOf0(esk16_0,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]) ).
cnf(c_0_66,negated_conjecture,
( ~ aElementOf0(esk16_0,xS)
| sbrdtbr0(xP) != xk ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_67,hypothesis,
( aElementOf0(X1,xS)
| sbrdtbr0(X2) != xk
| ~ aSubsetOf0(X2,xS)
| ~ aElementOf0(X1,X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,hypothesis,
( esk16_0 = xx
| aElementOf0(esk16_0,xQ) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,hypothesis,
aSubsetOf0(xQ,xS),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_70,negated_conjecture,
~ aElementOf0(esk16_0,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_61])]) ).
cnf(c_0_71,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_67,c_0_68]),c_0_55]),c_0_69])]),c_0_70]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : NUM556+3 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.10 % Command : run_E %s %d THM
% 0.09/0.30 % Computer : n012.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon May 20 04:36:52 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.46 # Version: 3.1.0
% 0.14/0.46 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.46 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.46 # Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 # Starting new_bool_1 with 300s (1) cores
% 0.14/0.46 # Starting sh5l with 300s (1) cores
% 0.14/0.46 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 17001 completed with status 0
% 0.14/0.46 # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.14/0.46 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.46 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.46 # No SInE strategy applied
% 0.14/0.46 # Search class: FGHSF-FSLM31-MFFFFFNN
% 0.14/0.46 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.46 # Starting G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with 811s (1) cores
% 0.14/0.46 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.14/0.46 # Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.14/0.46 # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 136s (1) cores
% 0.14/0.46 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S2S with 136s (1) cores
% 0.14/0.46 # SAT001_MinMin_p005000_rr_RG with pid 17010 completed with status 0
% 0.14/0.46 # Result found by SAT001_MinMin_p005000_rr_RG
% 0.14/0.46 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.46 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.46 # No SInE strategy applied
% 0.14/0.46 # Search class: FGHSF-FSLM31-MFFFFFNN
% 0.14/0.46 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.46 # Starting G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with 811s (1) cores
% 0.14/0.46 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.14/0.46 # Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.14/0.46 # Preprocessing time : 0.003 s
% 0.14/0.46 # Presaturation interreduction done
% 0.14/0.46
% 0.14/0.46 # Proof found!
% 0.14/0.46 # SZS status Theorem
% 0.14/0.46 # SZS output start CNFRefutation
% See solution above
% 0.14/0.46 # Parsed axioms : 72
% 0.14/0.46 # Removed by relevancy pruning/SinE : 0
% 0.14/0.46 # Initial clauses : 174
% 0.14/0.46 # Removed in clause preprocessing : 6
% 0.14/0.46 # Initial clauses in saturation : 168
% 0.14/0.46 # Processed clauses : 591
% 0.14/0.46 # ...of these trivial : 6
% 0.14/0.46 # ...subsumed : 104
% 0.14/0.46 # ...remaining for further processing : 481
% 0.14/0.46 # Other redundant clauses eliminated : 47
% 0.14/0.46 # Clauses deleted for lack of memory : 0
% 0.14/0.46 # Backward-subsumed : 5
% 0.14/0.46 # Backward-rewritten : 18
% 0.14/0.46 # Generated clauses : 842
% 0.14/0.46 # ...of the previous two non-redundant : 705
% 0.14/0.46 # ...aggressively subsumed : 0
% 0.14/0.46 # Contextual simplify-reflections : 25
% 0.14/0.46 # Paramodulations : 797
% 0.14/0.46 # Factorizations : 0
% 0.14/0.46 # NegExts : 0
% 0.14/0.46 # Equation resolutions : 48
% 0.14/0.46 # Disequality decompositions : 0
% 0.14/0.46 # Total rewrite steps : 636
% 0.14/0.46 # ...of those cached : 585
% 0.14/0.46 # Propositional unsat checks : 0
% 0.14/0.46 # Propositional check models : 0
% 0.14/0.46 # Propositional check unsatisfiable : 0
% 0.14/0.46 # Propositional clauses : 0
% 0.14/0.46 # Propositional clauses after purity: 0
% 0.14/0.46 # Propositional unsat core size : 0
% 0.14/0.46 # Propositional preprocessing time : 0.000
% 0.14/0.46 # Propositional encoding time : 0.000
% 0.14/0.46 # Propositional solver time : 0.000
% 0.14/0.46 # Success case prop preproc time : 0.000
% 0.14/0.46 # Success case prop encoding time : 0.000
% 0.14/0.46 # Success case prop solver time : 0.000
% 0.14/0.46 # Current number of processed clauses : 273
% 0.14/0.46 # Positive orientable unit clauses : 50
% 0.14/0.46 # Positive unorientable unit clauses: 0
% 0.14/0.46 # Negative unit clauses : 13
% 0.14/0.46 # Non-unit-clauses : 210
% 0.14/0.46 # Current number of unprocessed clauses: 434
% 0.14/0.46 # ...number of literals in the above : 1870
% 0.14/0.46 # Current number of archived formulas : 0
% 0.14/0.46 # Current number of archived clauses : 178
% 0.14/0.46 # Clause-clause subsumption calls (NU) : 7271
% 0.14/0.46 # Rec. Clause-clause subsumption calls : 3283
% 0.14/0.46 # Non-unit clause-clause subsumptions : 85
% 0.14/0.46 # Unit Clause-clause subsumption calls : 1163
% 0.14/0.46 # Rewrite failures with RHS unbound : 0
% 0.14/0.46 # BW rewrite match attempts : 6
% 0.14/0.46 # BW rewrite match successes : 5
% 0.14/0.46 # Condensation attempts : 0
% 0.14/0.46 # Condensation successes : 0
% 0.14/0.46 # Termbank termtop insertions : 25620
% 0.14/0.46 # Search garbage collected termcells : 2906
% 0.14/0.46
% 0.14/0.46 # -------------------------------------------------
% 0.14/0.46 # User time : 0.045 s
% 0.14/0.46 # System time : 0.005 s
% 0.14/0.46 # Total time : 0.050 s
% 0.14/0.46 # Maximum resident set size: 2328 pages
% 0.14/0.46
% 0.14/0.46 # -------------------------------------------------
% 0.14/0.46 # User time : 0.201 s
% 0.14/0.46 # System time : 0.015 s
% 0.14/0.46 # Total time : 0.215 s
% 0.14/0.46 # Maximum resident set size: 1780 pages
% 0.14/0.46 % E---3.1 exiting
% 0.14/0.46 % E exiting
%------------------------------------------------------------------------------